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 &what_glasgow_exts_does;
60 Enabling these options is the <emphasis>only</emphasis>
61 effect of <option>-fglasgow-exts</option>.
62 We are trying to move away from this portmanteau flag,
63 and towards enabling features individually.</para>
67 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
68 <sect1 id="primitives">
69 <title>Unboxed types and primitive operations</title>
71 <para>GHC is built on a raft of primitive data types and operations;
72 "primitive" in the sense that they cannot be defined in Haskell itself.
73 While you really can use this stuff to write fast code,
74 we generally find it a lot less painful, and more satisfying in the
75 long run, to use higher-level language features and libraries. With
76 any luck, the code you write will be optimised to the efficient
77 unboxed version in any case. And if it isn't, we'd like to know
80 <para>All these primitive data types and operations are exported by the
81 library <literal>GHC.Prim</literal>, for which there is
82 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
83 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
86 If you want to mention any of the primitive data types or operations in your
87 program, you must first import <literal>GHC.Prim</literal> to bring them
88 into scope. Many of them have names ending in "#", and to mention such
89 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
92 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
93 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
94 we briefly summarise here. </para>
96 <sect2 id="glasgow-unboxed">
101 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
104 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
105 that values of that type are represented by a pointer to a heap
106 object. The representation of a Haskell <literal>Int</literal>, for
107 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
108 type, however, is represented by the value itself, no pointers or heap
109 allocation are involved.
113 Unboxed types correspond to the “raw machine” types you
114 would use in C: <literal>Int#</literal> (long int),
115 <literal>Double#</literal> (double), <literal>Addr#</literal>
116 (void *), etc. The <emphasis>primitive operations</emphasis>
117 (PrimOps) on these types are what you might expect; e.g.,
118 <literal>(+#)</literal> is addition on
119 <literal>Int#</literal>s, and is the machine-addition that we all
120 know and love—usually one instruction.
124 Primitive (unboxed) types cannot be defined in Haskell, and are
125 therefore built into the language and compiler. Primitive types are
126 always unlifted; that is, a value of a primitive type cannot be
127 bottom. We use the convention (but it is only a convention)
128 that primitive types, values, and
129 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
130 For some primitive types we have special syntax for literals, also
131 described in the <link linkend="magic-hash">same section</link>.
135 Primitive values are often represented by a simple bit-pattern, such
136 as <literal>Int#</literal>, <literal>Float#</literal>,
137 <literal>Double#</literal>. But this is not necessarily the case:
138 a primitive value might be represented by a pointer to a
139 heap-allocated object. Examples include
140 <literal>Array#</literal>, the type of primitive arrays. A
141 primitive array is heap-allocated because it is too big a value to fit
142 in a register, and would be too expensive to copy around; in a sense,
143 it is accidental that it is represented by a pointer. If a pointer
144 represents a primitive value, then it really does point to that value:
145 no unevaluated thunks, no indirections…nothing can be at the
146 other end of the pointer than the primitive value.
147 A numerically-intensive program using unboxed types can
148 go a <emphasis>lot</emphasis> faster than its “standard”
149 counterpart—we saw a threefold speedup on one example.
153 There are some restrictions on the use of primitive types:
155 <listitem><para>The main restriction
156 is that you can't pass a primitive value to a polymorphic
157 function or store one in a polymorphic data type. This rules out
158 things like <literal>[Int#]</literal> (i.e. lists of primitive
159 integers). The reason for this restriction is that polymorphic
160 arguments and constructor fields are assumed to be pointers: if an
161 unboxed integer is stored in one of these, the garbage collector would
162 attempt to follow it, leading to unpredictable space leaks. Or a
163 <function>seq</function> operation on the polymorphic component may
164 attempt to dereference the pointer, with disastrous results. Even
165 worse, the unboxed value might be larger than a pointer
166 (<literal>Double#</literal> for instance).
169 <listitem><para> You cannot define a newtype whose representation type
170 (the argument type of the data constructor) is an unboxed type. Thus,
176 <listitem><para> You cannot bind a variable with an unboxed type
177 in a <emphasis>top-level</emphasis> binding.
179 <listitem><para> You cannot bind a variable with an unboxed type
180 in a <emphasis>recursive</emphasis> binding.
182 <listitem><para> You may bind unboxed variables in a (non-recursive,
183 non-top-level) pattern binding, but you must make any such pattern-match
184 strict. For example, rather than:
186 data Foo = Foo Int Int#
188 f x = let (Foo a b, w) = ..rhs.. in ..body..
192 data Foo = Foo Int Int#
194 f x = let !(Foo a b, w) = ..rhs.. in ..body..
196 since <literal>b</literal> has type <literal>Int#</literal>.
204 <sect2 id="unboxed-tuples">
205 <title>Unboxed Tuples
209 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
210 they're available by default with <option>-fglasgow-exts</option>. An
211 unboxed tuple looks like this:
223 where <literal>e_1..e_n</literal> are expressions of any
224 type (primitive or non-primitive). The type of an unboxed tuple looks
229 Unboxed tuples are used for functions that need to return multiple
230 values, but they avoid the heap allocation normally associated with
231 using fully-fledged tuples. When an unboxed tuple is returned, the
232 components are put directly into registers or on the stack; the
233 unboxed tuple itself does not have a composite representation. Many
234 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
236 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
237 tuples to avoid unnecessary allocation during sequences of operations.
241 There are some pretty stringent restrictions on the use of unboxed tuples:
246 Values of unboxed tuple types are subject to the same restrictions as
247 other unboxed types; i.e. they may not be stored in polymorphic data
248 structures or passed to polymorphic functions.
255 No variable can have an unboxed tuple type, nor may a constructor or function
256 argument have an unboxed tuple type. The following are all illegal:
260 data Foo = Foo (# Int, Int #)
262 f :: (# Int, Int #) -> (# Int, Int #)
265 g :: (# Int, Int #) -> Int
268 h x = let y = (# x,x #) in ...
275 The typical use of unboxed tuples is simply to return multiple values,
276 binding those multiple results with a <literal>case</literal> expression, thus:
278 f x y = (# x+1, y-1 #)
279 g x = case f x x of { (# a, b #) -> a + b }
281 You can have an unboxed tuple in a pattern binding, thus
283 f x = let (# p,q #) = h x in ..body..
285 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
286 the resulting binding is lazy like any other Haskell pattern binding. The
287 above example desugars like this:
289 f x = let t = case h x o f{ (# p,q #) -> (p,q)
294 Indeed, the bindings can even be recursive.
301 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
303 <sect1 id="syntax-extns">
304 <title>Syntactic extensions</title>
306 <sect2 id="unicode-syntax">
307 <title>Unicode syntax</title>
309 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
310 enables Unicode characters to be used to stand for certain ASCII
311 character sequences. The following alternatives are provided:</para>
314 <tgroup cols="2" align="left" colsep="1" rowsep="1">
318 <entry>Unicode alternative</entry>
319 <entry>Code point</entry>
325 to find the DocBook entities for these characters, find
326 the Unicode code point (e.g. 0x2237), and grep for it in
327 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
328 your system. Some of these Unicode code points don't have
329 equivalent DocBook entities.
334 <entry><literal>::</literal></entry>
335 <entry>::</entry> <!-- no special char, apparently -->
336 <entry>0x2237</entry>
337 <entry>PROPORTION</entry>
342 <entry><literal>=></literal></entry>
343 <entry>⇒</entry>
344 <entry>0x21D2</entry>
345 <entry>RIGHTWARDS DOUBLE ARROW</entry>
350 <entry><literal>forall</literal></entry>
351 <entry>∀</entry>
352 <entry>0x2200</entry>
353 <entry>FOR ALL</entry>
358 <entry><literal>-></literal></entry>
359 <entry>→</entry>
360 <entry>0x2192</entry>
361 <entry>RIGHTWARDS ARROW</entry>
366 <entry><literal><-</literal></entry>
367 <entry>←</entry>
368 <entry>0x2190</entry>
369 <entry>LEFTWARDS ARROW</entry>
376 <entry>↢</entry>
377 <entry>0x2919</entry>
378 <entry>LEFTWARDS ARROW-TAIL</entry>
385 <entry>↣</entry>
386 <entry>0x291A</entry>
387 <entry>RIGHTWARDS ARROW-TAIL</entry>
393 <entry>-<<</entry>
395 <entry>0x291B</entry>
396 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
402 <entry>>>-</entry>
404 <entry>0x291C</entry>
405 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
412 <entry>★</entry>
413 <entry>0x2605</entry>
414 <entry>BLACK STAR</entry>
422 <sect2 id="magic-hash">
423 <title>The magic hash</title>
424 <para>The language extension <option>-XMagicHash</option> allows "#" as a
425 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
426 a valid type constructor or data constructor.</para>
428 <para>The hash sign does not change sematics at all. We tend to use variable
429 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
430 but there is no requirement to do so; they are just plain ordinary variables.
431 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
432 For example, to bring <literal>Int#</literal> into scope you must
433 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
434 the <option>-XMagicHash</option> extension
435 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
436 that is now in scope.</para>
437 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
439 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
440 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
441 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
442 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
443 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
444 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
445 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
446 is a <literal>Word#</literal>. </para> </listitem>
447 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
448 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
453 <sect2 id="new-qualified-operators">
454 <title>New qualified operator syntax</title>
456 <para>A new syntax for referencing qualified operators is
457 planned to be introduced by Haskell', and is enabled in GHC
459 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
460 option. In the new syntax, the prefix form of a qualified
462 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
463 (in Haskell 98 this would
464 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
465 and the infix form is
466 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
467 (in Haskell 98 this would
468 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
471 add x y = Prelude.(+) x y
472 subtract y = (`Prelude.(-)` y)
474 The new form of qualified operators is intended to regularise
475 the syntax by eliminating odd cases
476 like <literal>Prelude..</literal>. For example,
477 when <literal>NewQualifiedOperators</literal> is on, it is possible to
478 write the enumerated sequence <literal>[Monday..]</literal>
479 without spaces, whereas in Haskell 98 this would be a
480 reference to the operator ‘<literal>.</literal>‘
481 from module <literal>Monday</literal>.</para>
483 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
484 98 syntax for qualified operators is not accepted, so this
485 option may cause existing Haskell 98 code to break.</para>
490 <!-- ====================== HIERARCHICAL MODULES ======================= -->
493 <sect2 id="hierarchical-modules">
494 <title>Hierarchical Modules</title>
496 <para>GHC supports a small extension to the syntax of module
497 names: a module name is allowed to contain a dot
498 <literal>‘.’</literal>. This is also known as the
499 “hierarchical module namespace” extension, because
500 it extends the normally flat Haskell module namespace into a
501 more flexible hierarchy of modules.</para>
503 <para>This extension has very little impact on the language
504 itself; modules names are <emphasis>always</emphasis> fully
505 qualified, so you can just think of the fully qualified module
506 name as <quote>the module name</quote>. In particular, this
507 means that the full module name must be given after the
508 <literal>module</literal> keyword at the beginning of the
509 module; for example, the module <literal>A.B.C</literal> must
512 <programlisting>module A.B.C</programlisting>
515 <para>It is a common strategy to use the <literal>as</literal>
516 keyword to save some typing when using qualified names with
517 hierarchical modules. For example:</para>
520 import qualified Control.Monad.ST.Strict as ST
523 <para>For details on how GHC searches for source and interface
524 files in the presence of hierarchical modules, see <xref
525 linkend="search-path"/>.</para>
527 <para>GHC comes with a large collection of libraries arranged
528 hierarchically; see the accompanying <ulink
529 url="../libraries/index.html">library
530 documentation</ulink>. More libraries to install are available
532 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
535 <!-- ====================== PATTERN GUARDS ======================= -->
537 <sect2 id="pattern-guards">
538 <title>Pattern guards</title>
541 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
542 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.)
546 Suppose we have an abstract data type of finite maps, with a
550 lookup :: FiniteMap -> Int -> Maybe Int
553 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
554 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
558 clunky env var1 var2 | ok1 && ok2 = val1 + val2
559 | otherwise = var1 + var2
570 The auxiliary functions are
574 maybeToBool :: Maybe a -> Bool
575 maybeToBool (Just x) = True
576 maybeToBool Nothing = False
578 expectJust :: Maybe a -> a
579 expectJust (Just x) = x
580 expectJust Nothing = error "Unexpected Nothing"
584 What is <function>clunky</function> doing? The guard <literal>ok1 &&
585 ok2</literal> checks that both lookups succeed, using
586 <function>maybeToBool</function> to convert the <function>Maybe</function>
587 types to booleans. The (lazily evaluated) <function>expectJust</function>
588 calls extract the values from the results of the lookups, and binds the
589 returned values to <varname>val1</varname> and <varname>val2</varname>
590 respectively. If either lookup fails, then clunky takes the
591 <literal>otherwise</literal> case and returns the sum of its arguments.
595 This is certainly legal Haskell, but it is a tremendously verbose and
596 un-obvious way to achieve the desired effect. Arguably, a more direct way
597 to write clunky would be to use case expressions:
601 clunky env var1 var2 = case lookup env var1 of
603 Just val1 -> case lookup env var2 of
605 Just val2 -> val1 + val2
611 This is a bit shorter, but hardly better. Of course, we can rewrite any set
612 of pattern-matching, guarded equations as case expressions; that is
613 precisely what the compiler does when compiling equations! The reason that
614 Haskell provides guarded equations is because they allow us to write down
615 the cases we want to consider, one at a time, independently of each other.
616 This structure is hidden in the case version. Two of the right-hand sides
617 are really the same (<function>fail</function>), and the whole expression
618 tends to become more and more indented.
622 Here is how I would write clunky:
627 | Just val1 <- lookup env var1
628 , Just val2 <- lookup env var2
630 ...other equations for clunky...
634 The semantics should be clear enough. The qualifiers are matched in order.
635 For a <literal><-</literal> qualifier, which I call a pattern guard, the
636 right hand side is evaluated and matched against the pattern on the left.
637 If the match fails then the whole guard fails and the next equation is
638 tried. If it succeeds, then the appropriate binding takes place, and the
639 next qualifier is matched, in the augmented environment. Unlike list
640 comprehensions, however, the type of the expression to the right of the
641 <literal><-</literal> is the same as the type of the pattern to its
642 left. The bindings introduced by pattern guards scope over all the
643 remaining guard qualifiers, and over the right hand side of the equation.
647 Just as with list comprehensions, boolean expressions can be freely mixed
648 with among the pattern guards. For example:
659 Haskell's current guards therefore emerge as a special case, in which the
660 qualifier list has just one element, a boolean expression.
664 <!-- ===================== View patterns =================== -->
666 <sect2 id="view-patterns">
671 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
672 More information and examples of view patterns can be found on the
673 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
678 View patterns are somewhat like pattern guards that can be nested inside
679 of other patterns. They are a convenient way of pattern-matching
680 against values of abstract types. For example, in a programming language
681 implementation, we might represent the syntax of the types of the
690 view :: Type -> TypeView
692 -- additional operations for constructing Typ's ...
695 The representation of Typ is held abstract, permitting implementations
696 to use a fancy representation (e.g., hash-consing to manage sharing).
698 Without view patterns, using this signature a little inconvenient:
700 size :: Typ -> Integer
701 size t = case view t of
703 Arrow t1 t2 -> size t1 + size t2
706 It is necessary to iterate the case, rather than using an equational
707 function definition. And the situation is even worse when the matching
708 against <literal>t</literal> is buried deep inside another pattern.
712 View patterns permit calling the view function inside the pattern and
713 matching against the result:
715 size (view -> Unit) = 1
716 size (view -> Arrow t1 t2) = size t1 + size t2
719 That is, we add a new form of pattern, written
720 <replaceable>expression</replaceable> <literal>-></literal>
721 <replaceable>pattern</replaceable> that means "apply the expression to
722 whatever we're trying to match against, and then match the result of
723 that application against the pattern". The expression can be any Haskell
724 expression of function type, and view patterns can be used wherever
729 The semantics of a pattern <literal>(</literal>
730 <replaceable>exp</replaceable> <literal>-></literal>
731 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
737 <para>The variables bound by the view pattern are the variables bound by
738 <replaceable>pat</replaceable>.
742 Any variables in <replaceable>exp</replaceable> are bound occurrences,
743 but variables bound "to the left" in a pattern are in scope. This
744 feature permits, for example, one argument to a function to be used in
745 the view of another argument. For example, the function
746 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
747 written using view patterns as follows:
750 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
751 ...other equations for clunky...
756 More precisely, the scoping rules are:
760 In a single pattern, variables bound by patterns to the left of a view
761 pattern expression are in scope. For example:
763 example :: Maybe ((String -> Integer,Integer), String) -> Bool
764 example Just ((f,_), f -> 4) = True
767 Additionally, in function definitions, variables bound by matching earlier curried
768 arguments may be used in view pattern expressions in later arguments:
770 example :: (String -> Integer) -> String -> Bool
771 example f (f -> 4) = True
773 That is, the scoping is the same as it would be if the curried arguments
774 were collected into a tuple.
780 In mutually recursive bindings, such as <literal>let</literal>,
781 <literal>where</literal>, or the top level, view patterns in one
782 declaration may not mention variables bound by other declarations. That
783 is, each declaration must be self-contained. For example, the following
784 program is not allowed:
790 (For some amplification on this design choice see
791 <ulink url="http://hackage.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
800 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
801 <replaceable>T1</replaceable> <literal>-></literal>
802 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
803 a <replaceable>T2</replaceable>, then the whole view pattern matches a
804 <replaceable>T1</replaceable>.
807 <listitem><para> Matching: To the equations in Section 3.17.3 of the
808 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
809 Report</ulink>, add the following:
811 case v of { (e -> p) -> e1 ; _ -> e2 }
813 case (e v) of { p -> e1 ; _ -> e2 }
815 That is, to match a variable <replaceable>v</replaceable> against a pattern
816 <literal>(</literal> <replaceable>exp</replaceable>
817 <literal>-></literal> <replaceable>pat</replaceable>
818 <literal>)</literal>, evaluate <literal>(</literal>
819 <replaceable>exp</replaceable> <replaceable> v</replaceable>
820 <literal>)</literal> and match the result against
821 <replaceable>pat</replaceable>.
824 <listitem><para> Efficiency: When the same view function is applied in
825 multiple branches of a function definition or a case expression (e.g.,
826 in <literal>size</literal> above), GHC makes an attempt to collect these
827 applications into a single nested case expression, so that the view
828 function is only applied once. Pattern compilation in GHC follows the
829 matrix algorithm described in Chapter 4 of <ulink
830 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
831 Implementation of Functional Programming Languages</ulink>. When the
832 top rows of the first column of a matrix are all view patterns with the
833 "same" expression, these patterns are transformed into a single nested
834 case. This includes, for example, adjacent view patterns that line up
837 f ((view -> A, p1), p2) = e1
838 f ((view -> B, p3), p4) = e2
842 <para> The current notion of when two view pattern expressions are "the
843 same" is very restricted: it is not even full syntactic equality.
844 However, it does include variables, literals, applications, and tuples;
845 e.g., two instances of <literal>view ("hi", "there")</literal> will be
846 collected. However, the current implementation does not compare up to
847 alpha-equivalence, so two instances of <literal>(x, view x ->
848 y)</literal> will not be coalesced.
858 <!-- ===================== n+k patterns =================== -->
860 <sect2 id="n-k-patterns">
861 <title>n+k patterns</title>
862 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
865 <literal>n+k</literal> pattern support is enabled by default. To disable
866 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
871 <!-- ===================== Recursive do-notation =================== -->
873 <sect2 id="recursive-do-notation">
874 <title>The recursive do-notation
878 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
879 that is, the variables bound in a do-expression are visible only in the textually following
880 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
881 group. It turns out that several applications can benefit from recursive bindings in
882 the do-notation. The <option>-XDoRec</option> flag provides the necessary syntactic support.
885 Here is a simple (albeit contrived) example:
887 {-# LANGUAGE DoRec #-}
888 justOnes = do { rec { xs <- Just (1:xs) }
889 ; return (map negate xs) }
891 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
894 The background and motivation for recursive do-notation is described in
895 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
896 by Levent Erkok, John Launchbury,
897 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
898 The theory behind monadic value recursion is explained further in Erkok's thesis
899 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.
900 However, note that GHC uses a different syntax than the one described in these documents.
904 <title>Details of recursive do-notation</title>
906 The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
907 the LANGUAGE pragma <option>DoRec</option>. It introduces the single new keyword "<literal>rec</literal>",
908 which wraps a mutually-recursive group of monadic statements,
909 producing a single statement.
911 <para>Similar to a <literal>let</literal>
912 statement, the variables bound in the <literal>rec</literal> are
913 visible throughout the <literal>rec</literal> group, and below it.
916 do { a <- getChar do { a <- getChar
917 ; let { r1 = f a r2 ; rec { r1 <- f a r2
918 ; r2 = g r1 } ; r2 <- g r1 }
919 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
921 In both cases, <literal>r1</literal> and <literal>r2</literal> are
922 available both throughout the <literal>let</literal> or <literal>rec</literal> block, and
923 in the statements that follow it. The difference is that <literal>let</literal> is non-monadic,
924 while <literal>rec</literal> is monadic. (In Haskell <literal>let</literal> is
925 really <literal>letrec</literal>, of course.)
928 The static and dynamic semantics of <literal>rec</literal> can be described as follows:
932 similar to let-bindings, the <literal>rec</literal> is broken into
933 minimal recursive groups, a process known as <emphasis>segmentation</emphasis>.
936 rec { a <- getChar ===> a <- getChar
937 ; b <- f a c rec { b <- f a c
938 ; c <- f b a ; c <- f b a }
939 ; putChar c } putChar c
941 The details of segmentation are described in Section 3.2 of
942 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>.
943 Segmentation improves polymorphism, reduces the size of the recursive "knot", and, as the paper
944 describes, also has a semantic effect (unless the monad satisfies the right-shrinking law).
947 Then each resulting <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal>.
948 For example, the <literal>rec</literal> group in the preceding example is desugared like this:
950 rec { b <- f a c ===> (b,c) <- mfix (\~(b,c) -> do { b <- f a c
951 ; c <- f b a } ; c <- f b a
954 In general, the statment <literal>rec <replaceable>ss</replaceable></literal>
955 is desugared to the statement
957 <replaceable>vs</replaceable> <- mfix (\~<replaceable>vs</replaceable> -> do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
959 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
961 The original <literal>rec</literal> typechecks exactly
962 when the above desugared version would do so. For example, this means that
963 the variables <replaceable>vs</replaceable> are all monomorphic in the statements
964 following the <literal>rec</literal>, because they are bound by a lambda.
967 The <literal>mfix</literal> function is defined in the <literal>MonadFix</literal>
968 class, in <literal>Control.Monad.Fix</literal>, thus:
970 class Monad m => MonadFix m where
971 mfix :: (a -> m a) -> m a
978 Here are some other important points in using the recursive-do notation:
981 It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
982 <literal>-fglasgow-exts</literal>.
986 If recursive bindings are required for a monad,
987 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
991 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
992 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
993 for Haskell's internal state monad (strict and lazy, respectively).
997 Like <literal>let</literal> and <literal>where</literal> bindings,
998 name shadowing is not allowed within a <literal>rec</literal>;
999 that is, all the names bound in a single <literal>rec</literal> must
1000 be distinct (Section 3.3 of the paper).
1003 It supports rebindable syntax (see <xref linkend="rebindable-syntax"/>).
1009 <sect3 id="mdo-notation"> <title> Mdo-notation (deprecated) </title>
1011 <para> GHC used to support the flag <option>-XRecursiveDo</option>,
1012 which enabled the keyword <literal>mdo</literal>, precisely as described in
1013 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
1014 but this is now deprecated. Instead of <literal>mdo { Q; e }</literal>, write
1015 <literal>do { rec Q; e }</literal>.
1018 Historical note: The old implementation of the mdo-notation (and most
1019 of the existing documents) used the name
1020 <literal>MonadRec</literal> for the class and the corresponding library.
1021 This name is not supported by GHC.
1028 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1030 <sect2 id="parallel-list-comprehensions">
1031 <title>Parallel List Comprehensions</title>
1032 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1034 <indexterm><primary>parallel list comprehensions</primary>
1037 <para>Parallel list comprehensions are a natural extension to list
1038 comprehensions. List comprehensions can be thought of as a nice
1039 syntax for writing maps and filters. Parallel comprehensions
1040 extend this to include the zipWith family.</para>
1042 <para>A parallel list comprehension has multiple independent
1043 branches of qualifier lists, each separated by a `|' symbol. For
1044 example, the following zips together two lists:</para>
1047 [ (x, y) | x <- xs | y <- ys ]
1050 <para>The behavior of parallel list comprehensions follows that of
1051 zip, in that the resulting list will have the same length as the
1052 shortest branch.</para>
1054 <para>We can define parallel list comprehensions by translation to
1055 regular comprehensions. Here's the basic idea:</para>
1057 <para>Given a parallel comprehension of the form: </para>
1060 [ e | p1 <- e11, p2 <- e12, ...
1061 | q1 <- e21, q2 <- e22, ...
1066 <para>This will be translated to: </para>
1069 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1070 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1075 <para>where `zipN' is the appropriate zip for the given number of
1080 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1082 <sect2 id="generalised-list-comprehensions">
1083 <title>Generalised (SQL-Like) List Comprehensions</title>
1084 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1086 <indexterm><primary>extended list comprehensions</primary>
1088 <indexterm><primary>group</primary></indexterm>
1089 <indexterm><primary>sql</primary></indexterm>
1092 <para>Generalised list comprehensions are a further enhancement to the
1093 list comprehension syntactic sugar to allow operations such as sorting
1094 and grouping which are familiar from SQL. They are fully described in the
1095 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1096 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1097 except that the syntax we use differs slightly from the paper.</para>
1098 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1099 <para>Here is an example:
1101 employees = [ ("Simon", "MS", 80)
1102 , ("Erik", "MS", 100)
1103 , ("Phil", "Ed", 40)
1104 , ("Gordon", "Ed", 45)
1105 , ("Paul", "Yale", 60)]
1107 output = [ (the dept, sum salary)
1108 | (name, dept, salary) <- employees
1109 , then group by dept
1110 , then sortWith by (sum salary)
1113 In this example, the list <literal>output</literal> would take on
1117 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1120 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1121 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1122 function that is exported by <literal>GHC.Exts</literal>.)</para>
1124 <para>There are five new forms of comprehension qualifier,
1125 all introduced by the (existing) keyword <literal>then</literal>:
1133 This statement requires that <literal>f</literal> have the type <literal>
1134 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1135 motivating example, as this form is used to apply <literal>take 5</literal>.
1146 This form is similar to the previous one, but allows you to create a function
1147 which will be passed as the first argument to f. As a consequence f must have
1148 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1149 from the type, this function lets f "project out" some information
1150 from the elements of the list it is transforming.</para>
1152 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1153 is supplied with a function that lets it find out the <literal>sum salary</literal>
1154 for any item in the list comprehension it transforms.</para>
1162 then group by e using f
1165 <para>This is the most general of the grouping-type statements. In this form,
1166 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1167 As with the <literal>then f by e</literal> case above, the first argument
1168 is a function supplied to f by the compiler which lets it compute e on every
1169 element of the list being transformed. However, unlike the non-grouping case,
1170 f additionally partitions the list into a number of sublists: this means that
1171 at every point after this statement, binders occurring before it in the comprehension
1172 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1173 this, let's look at an example:</para>
1176 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1177 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1178 groupRuns f = groupBy (\x y -> f x == f y)
1180 output = [ (the x, y)
1181 | x <- ([1..3] ++ [1..2])
1183 , then group by x using groupRuns ]
1186 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1189 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1192 <para>Note that we have used the <literal>the</literal> function to change the type
1193 of x from a list to its original numeric type. The variable y, in contrast, is left
1194 unchanged from the list form introduced by the grouping.</para>
1204 <para>This form of grouping is essentially the same as the one described above. However,
1205 since no function to use for the grouping has been supplied it will fall back on the
1206 <literal>groupWith</literal> function defined in
1207 <ulink url="&libraryBaseLocation;/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1208 is the form of the group statement that we made use of in the opening example.</para>
1219 <para>With this form of the group statement, f is required to simply have the type
1220 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1221 comprehension so far directly. An example of this form is as follows:</para>
1227 , then group using inits]
1230 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1233 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1241 <!-- ===================== REBINDABLE SYNTAX =================== -->
1243 <sect2 id="rebindable-syntax">
1244 <title>Rebindable syntax and the implicit Prelude import</title>
1246 <para><indexterm><primary>-XNoImplicitPrelude
1247 option</primary></indexterm> GHC normally imports
1248 <filename>Prelude.hi</filename> files for you. If you'd
1249 rather it didn't, then give it a
1250 <option>-XNoImplicitPrelude</option> option. The idea is
1251 that you can then import a Prelude of your own. (But don't
1252 call it <literal>Prelude</literal>; the Haskell module
1253 namespace is flat, and you must not conflict with any
1254 Prelude module.)</para>
1256 <para>Suppose you are importing a Prelude of your own
1257 in order to define your own numeric class
1258 hierarchy. It completely defeats that purpose if the
1259 literal "1" means "<literal>Prelude.fromInteger
1260 1</literal>", which is what the Haskell Report specifies.
1261 So the <option>-XNoImplicitPrelude</option>
1262 flag <emphasis>also</emphasis> causes
1263 the following pieces of built-in syntax to refer to
1264 <emphasis>whatever is in scope</emphasis>, not the Prelude
1268 <para>An integer literal <literal>368</literal> means
1269 "<literal>fromInteger (368::Integer)</literal>", rather than
1270 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1273 <listitem><para>Fractional literals are handed in just the same way,
1274 except that the translation is
1275 <literal>fromRational (3.68::Rational)</literal>.
1278 <listitem><para>The equality test in an overloaded numeric pattern
1279 uses whatever <literal>(==)</literal> is in scope.
1282 <listitem><para>The subtraction operation, and the
1283 greater-than-or-equal test, in <literal>n+k</literal> patterns
1284 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1288 <para>Negation (e.g. "<literal>- (f x)</literal>")
1289 means "<literal>negate (f x)</literal>", both in numeric
1290 patterns, and expressions.
1294 <para>"Do" notation is translated using whatever
1295 functions <literal>(>>=)</literal>,
1296 <literal>(>>)</literal>, and <literal>fail</literal>,
1297 are in scope (not the Prelude
1298 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1299 comprehensions, are unaffected. </para></listitem>
1303 notation (see <xref linkend="arrow-notation"/>)
1304 uses whatever <literal>arr</literal>,
1305 <literal>(>>>)</literal>, <literal>first</literal>,
1306 <literal>app</literal>, <literal>(|||)</literal> and
1307 <literal>loop</literal> functions are in scope. But unlike the
1308 other constructs, the types of these functions must match the
1309 Prelude types very closely. Details are in flux; if you want
1313 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1314 even if that is a little unexpected. For example, the
1315 static semantics of the literal <literal>368</literal>
1316 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1317 <literal>fromInteger</literal> to have any of the types:
1319 fromInteger :: Integer -> Integer
1320 fromInteger :: forall a. Foo a => Integer -> a
1321 fromInteger :: Num a => a -> Integer
1322 fromInteger :: Integer -> Bool -> Bool
1326 <para>Be warned: this is an experimental facility, with
1327 fewer checks than usual. Use <literal>-dcore-lint</literal>
1328 to typecheck the desugared program. If Core Lint is happy
1329 you should be all right.</para>
1333 <sect2 id="postfix-operators">
1334 <title>Postfix operators</title>
1337 The <option>-XPostfixOperators</option> flag enables a small
1338 extension to the syntax of left operator sections, which allows you to
1339 define postfix operators. The extension is this: the left section
1343 is equivalent (from the point of view of both type checking and execution) to the expression
1347 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1348 The strict Haskell 98 interpretation is that the section is equivalent to
1352 That is, the operator must be a function of two arguments. GHC allows it to
1353 take only one argument, and that in turn allows you to write the function
1356 <para>The extension does not extend to the left-hand side of function
1357 definitions; you must define such a function in prefix form.</para>
1361 <sect2 id="tuple-sections">
1362 <title>Tuple sections</title>
1365 The <option>-XTupleSections</option> flag enables Python-style partially applied
1366 tuple constructors. For example, the following program
1370 is considered to be an alternative notation for the more unwieldy alternative
1374 You can omit any combination of arguments to the tuple, as in the following
1376 (, "I", , , "Love", , 1337)
1380 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1385 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1386 will also be available for them, like so
1390 Because there is no unboxed unit tuple, the following expression
1394 continues to stand for the unboxed singleton tuple data constructor.
1399 <sect2 id="disambiguate-fields">
1400 <title>Record field disambiguation</title>
1402 In record construction and record pattern matching
1403 it is entirely unambiguous which field is referred to, even if there are two different
1404 data types in scope with a common field name. For example:
1407 data S = MkS { x :: Int, y :: Bool }
1412 data T = MkT { x :: Int }
1414 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1415 ok2 n = MkT { x = n+1 } -- Unambiguous
1417 bad1 k = k { x = 3 } -- Ambiguous
1418 bad2 k = x k -- Ambiguous
1420 Even though there are two <literal>x</literal>'s in scope,
1421 it is clear that the <literal>x</literal> in the pattern in the
1422 definition of <literal>ok1</literal> can only mean the field
1423 <literal>x</literal> from type <literal>S</literal>. Similarly for
1424 the function <literal>ok2</literal>. However, in the record update
1425 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1426 it is not clear which of the two types is intended.
1429 Haskell 98 regards all four as ambiguous, but with the
1430 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1431 the former two. The rules are precisely the same as those for instance
1432 declarations in Haskell 98, where the method names on the left-hand side
1433 of the method bindings in an instance declaration refer unambiguously
1434 to the method of that class (provided they are in scope at all), even
1435 if there are other variables in scope with the same name.
1436 This reduces the clutter of qualified names when you import two
1437 records from different modules that use the same field name.
1443 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1448 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1453 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1454 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1455 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1458 import qualified M -- Note qualified
1460 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1462 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1463 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1464 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1465 is not. (In effect, it is qualified by the constructor.)
1472 <!-- ===================== Record puns =================== -->
1474 <sect2 id="record-puns">
1479 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1483 When using records, it is common to write a pattern that binds a
1484 variable with the same name as a record field, such as:
1487 data C = C {a :: Int}
1493 Record punning permits the variable name to be elided, so one can simply
1500 to mean the same pattern as above. That is, in a record pattern, the
1501 pattern <literal>a</literal> expands into the pattern <literal>a =
1502 a</literal> for the same name <literal>a</literal>.
1509 Record punning can also be used in an expression, writing, for example,
1515 let a = 1 in C {a = a}
1517 The expansion is purely syntactic, so the expanded right-hand side
1518 expression refers to the nearest enclosing variable that is spelled the
1519 same as the field name.
1523 Puns and other patterns can be mixed in the same record:
1525 data C = C {a :: Int, b :: Int}
1526 f (C {a, b = 4}) = a
1531 Puns can be used wherever record patterns occur (e.g. in
1532 <literal>let</literal> bindings or at the top-level).
1536 A pun on a qualified field name is expanded by stripping off the module qualifier.
1543 f (M.C {M.a = a}) = a
1545 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1546 is only in scope in qualified form.)
1554 <!-- ===================== Record wildcards =================== -->
1556 <sect2 id="record-wildcards">
1557 <title>Record wildcards
1561 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1562 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1566 For records with many fields, it can be tiresome to write out each field
1567 individually in a record pattern, as in
1569 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1570 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1575 Record wildcard syntax permits a "<literal>..</literal>" in a record
1576 pattern, where each elided field <literal>f</literal> is replaced by the
1577 pattern <literal>f = f</literal>. For example, the above pattern can be
1580 f (C {a = 1, ..}) = b + c + d
1588 Wildcards can be mixed with other patterns, including puns
1589 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1590 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1591 wherever record patterns occur, including in <literal>let</literal>
1592 bindings and at the top-level. For example, the top-level binding
1596 defines <literal>b</literal>, <literal>c</literal>, and
1597 <literal>d</literal>.
1601 Record wildcards can also be used in expressions, writing, for example,
1603 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1607 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1609 The expansion is purely syntactic, so the record wildcard
1610 expression refers to the nearest enclosing variables that are spelled
1611 the same as the omitted field names.
1615 The "<literal>..</literal>" expands to the missing
1616 <emphasis>in-scope</emphasis> record fields, where "in scope"
1617 includes both unqualified and qualified-only.
1618 Any fields that are not in scope are not filled in. For example
1621 data R = R { a,b,c :: Int }
1623 import qualified M( R(a,b) )
1626 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1627 omitting <literal>c</literal> since it is not in scope at all.
1634 <!-- ===================== Local fixity declarations =================== -->
1636 <sect2 id="local-fixity-declarations">
1637 <title>Local Fixity Declarations
1640 <para>A careful reading of the Haskell 98 Report reveals that fixity
1641 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1642 <literal>infixr</literal>) are permitted to appear inside local bindings
1643 such those introduced by <literal>let</literal> and
1644 <literal>where</literal>. However, the Haskell Report does not specify
1645 the semantics of such bindings very precisely.
1648 <para>In GHC, a fixity declaration may accompany a local binding:
1655 and the fixity declaration applies wherever the binding is in scope.
1656 For example, in a <literal>let</literal>, it applies in the right-hand
1657 sides of other <literal>let</literal>-bindings and the body of the
1658 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1659 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
1660 declarations of a <literal>let</literal> statement scope over other
1661 statements in the group, just as the bound name does.
1665 Moreover, a local fixity declaration *must* accompany a local binding of
1666 that name: it is not possible to revise the fixity of name bound
1669 let infixr 9 $ in ...
1672 Because local fixity declarations are technically Haskell 98, no flag is
1673 necessary to enable them.
1677 <sect2 id="package-imports">
1678 <title>Package-qualified imports</title>
1680 <para>With the <option>-XPackageImports</option> flag, GHC allows
1681 import declarations to be qualified by the package name that the
1682 module is intended to be imported from. For example:</para>
1685 import "network" Network.Socket
1688 <para>would import the module <literal>Network.Socket</literal> from
1689 the package <literal>network</literal> (any version). This may
1690 be used to disambiguate an import when the same module is
1691 available from multiple packages, or is present in both the
1692 current package being built and an external package.</para>
1694 <para>Note: you probably don't need to use this feature, it was
1695 added mainly so that we can build backwards-compatible versions of
1696 packages when APIs change. It can lead to fragile dependencies in
1697 the common case: modules occasionally move from one package to
1698 another, rendering any package-qualified imports broken.</para>
1701 <sect2 id="syntax-stolen">
1702 <title>Summary of stolen syntax</title>
1704 <para>Turning on an option that enables special syntax
1705 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1706 to compile, perhaps because it uses a variable name which has
1707 become a reserved word. This section lists the syntax that is
1708 "stolen" by language extensions.
1710 notation and nonterminal names from the Haskell 98 lexical syntax
1711 (see the Haskell 98 Report).
1712 We only list syntax changes here that might affect
1713 existing working programs (i.e. "stolen" syntax). Many of these
1714 extensions will also enable new context-free syntax, but in all
1715 cases programs written to use the new syntax would not be
1716 compilable without the option enabled.</para>
1718 <para>There are two classes of special
1723 <para>New reserved words and symbols: character sequences
1724 which are no longer available for use as identifiers in the
1728 <para>Other special syntax: sequences of characters that have
1729 a different meaning when this particular option is turned
1734 The following syntax is stolen:
1739 <literal>forall</literal>
1740 <indexterm><primary><literal>forall</literal></primary></indexterm>
1743 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1744 <option>-XScopedTypeVariables</option>,
1745 <option>-XLiberalTypeSynonyms</option>,
1746 <option>-XRank2Types</option>,
1747 <option>-XRankNTypes</option>,
1748 <option>-XPolymorphicComponents</option>,
1749 <option>-XExistentialQuantification</option>
1755 <literal>mdo</literal>
1756 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1759 Stolen by: <option>-XRecursiveDo</option>,
1765 <literal>foreign</literal>
1766 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1769 Stolen by: <option>-XForeignFunctionInterface</option>,
1775 <literal>rec</literal>,
1776 <literal>proc</literal>, <literal>-<</literal>,
1777 <literal>>-</literal>, <literal>-<<</literal>,
1778 <literal>>>-</literal>, and <literal>(|</literal>,
1779 <literal>|)</literal> brackets
1780 <indexterm><primary><literal>proc</literal></primary></indexterm>
1783 Stolen by: <option>-XArrows</option>,
1789 <literal>?<replaceable>varid</replaceable></literal>,
1790 <literal>%<replaceable>varid</replaceable></literal>
1791 <indexterm><primary>implicit parameters</primary></indexterm>
1794 Stolen by: <option>-XImplicitParams</option>,
1800 <literal>[|</literal>,
1801 <literal>[e|</literal>, <literal>[p|</literal>,
1802 <literal>[d|</literal>, <literal>[t|</literal>,
1803 <literal>$(</literal>,
1804 <literal>$<replaceable>varid</replaceable></literal>
1805 <indexterm><primary>Template Haskell</primary></indexterm>
1808 Stolen by: <option>-XTemplateHaskell</option>,
1814 <literal>[:<replaceable>varid</replaceable>|</literal>
1815 <indexterm><primary>quasi-quotation</primary></indexterm>
1818 Stolen by: <option>-XQuasiQuotes</option>,
1824 <replaceable>varid</replaceable>{<literal>#</literal>},
1825 <replaceable>char</replaceable><literal>#</literal>,
1826 <replaceable>string</replaceable><literal>#</literal>,
1827 <replaceable>integer</replaceable><literal>#</literal>,
1828 <replaceable>float</replaceable><literal>#</literal>,
1829 <replaceable>float</replaceable><literal>##</literal>,
1830 <literal>(#</literal>, <literal>#)</literal>,
1833 Stolen by: <option>-XMagicHash</option>,
1842 <!-- TYPE SYSTEM EXTENSIONS -->
1843 <sect1 id="data-type-extensions">
1844 <title>Extensions to data types and type synonyms</title>
1846 <sect2 id="nullary-types">
1847 <title>Data types with no constructors</title>
1849 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1850 a data type with no constructors. For example:</para>
1854 data T a -- T :: * -> *
1857 <para>Syntactically, the declaration lacks the "= constrs" part. The
1858 type can be parameterised over types of any kind, but if the kind is
1859 not <literal>*</literal> then an explicit kind annotation must be used
1860 (see <xref linkend="kinding"/>).</para>
1862 <para>Such data types have only one value, namely bottom.
1863 Nevertheless, they can be useful when defining "phantom types".</para>
1866 <sect2 id="datatype-contexts">
1867 <title>Data type contexts</title>
1869 <para>Haskell allows datatypes to be given contexts, e.g.</para>
1872 data Eq a => Set a = NilSet | ConsSet a (Set a)
1875 <para>give constructors with types:</para>
1879 ConsSet :: Eq a => a -> Set a -> Set a
1882 <para>In GHC this feature is an extension called
1883 <literal>DatatypeContexts</literal>, and on by default.</para>
1886 <sect2 id="infix-tycons">
1887 <title>Infix type constructors, classes, and type variables</title>
1890 GHC allows type constructors, classes, and type variables to be operators, and
1891 to be written infix, very much like expressions. More specifically:
1894 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1895 The lexical syntax is the same as that for data constructors.
1898 Data type and type-synonym declarations can be written infix, parenthesised
1899 if you want further arguments. E.g.
1901 data a :*: b = Foo a b
1902 type a :+: b = Either a b
1903 class a :=: b where ...
1905 data (a :**: b) x = Baz a b x
1906 type (a :++: b) y = Either (a,b) y
1910 Types, and class constraints, can be written infix. For example
1913 f :: (a :=: b) => a -> b
1917 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1918 The lexical syntax is the same as that for variable operators, excluding "(.)",
1919 "(!)", and "(*)". In a binding position, the operator must be
1920 parenthesised. For example:
1922 type T (+) = Int + Int
1926 liftA2 :: Arrow (~>)
1927 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1933 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1934 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1937 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1938 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1939 sets the fixity for a data constructor and the corresponding type constructor. For example:
1943 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1944 and similarly for <literal>:*:</literal>.
1945 <literal>Int `a` Bool</literal>.
1948 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1955 <sect2 id="type-synonyms">
1956 <title>Liberalised type synonyms</title>
1959 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1960 on individual synonym declarations.
1961 With the <option>-XLiberalTypeSynonyms</option> extension,
1962 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1963 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1966 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1967 in a type synonym, thus:
1969 type Discard a = forall b. Show b => a -> b -> (a, String)
1974 g :: Discard Int -> (Int,String) -- A rank-2 type
1981 If you also use <option>-XUnboxedTuples</option>,
1982 you can write an unboxed tuple in a type synonym:
1984 type Pr = (# Int, Int #)
1992 You can apply a type synonym to a forall type:
1994 type Foo a = a -> a -> Bool
1996 f :: Foo (forall b. b->b)
1998 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2000 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2005 You can apply a type synonym to a partially applied type synonym:
2007 type Generic i o = forall x. i x -> o x
2010 foo :: Generic Id []
2012 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2014 foo :: forall x. x -> [x]
2022 GHC currently does kind checking before expanding synonyms (though even that
2026 After expanding type synonyms, GHC does validity checking on types, looking for
2027 the following mal-formedness which isn't detected simply by kind checking:
2030 Type constructor applied to a type involving for-alls.
2033 Unboxed tuple on left of an arrow.
2036 Partially-applied type synonym.
2040 this will be rejected:
2042 type Pr = (# Int, Int #)
2047 because GHC does not allow unboxed tuples on the left of a function arrow.
2052 <sect2 id="existential-quantification">
2053 <title>Existentially quantified data constructors
2057 The idea of using existential quantification in data type declarations
2058 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2059 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2060 London, 1991). It was later formalised by Laufer and Odersky
2061 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2062 TOPLAS, 16(5), pp1411-1430, 1994).
2063 It's been in Lennart
2064 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2065 proved very useful. Here's the idea. Consider the declaration:
2071 data Foo = forall a. MkFoo a (a -> Bool)
2078 The data type <literal>Foo</literal> has two constructors with types:
2084 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2091 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2092 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2093 For example, the following expression is fine:
2099 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2105 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2106 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2107 isUpper</function> packages a character with a compatible function. These
2108 two things are each of type <literal>Foo</literal> and can be put in a list.
2112 What can we do with a value of type <literal>Foo</literal>?. In particular,
2113 what happens when we pattern-match on <function>MkFoo</function>?
2119 f (MkFoo val fn) = ???
2125 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2126 are compatible, the only (useful) thing we can do with them is to
2127 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2134 f (MkFoo val fn) = fn val
2140 What this allows us to do is to package heterogeneous values
2141 together with a bunch of functions that manipulate them, and then treat
2142 that collection of packages in a uniform manner. You can express
2143 quite a bit of object-oriented-like programming this way.
2146 <sect3 id="existential">
2147 <title>Why existential?
2151 What has this to do with <emphasis>existential</emphasis> quantification?
2152 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2158 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2164 But Haskell programmers can safely think of the ordinary
2165 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2166 adding a new existential quantification construct.
2171 <sect3 id="existential-with-context">
2172 <title>Existentials and type classes</title>
2175 An easy extension is to allow
2176 arbitrary contexts before the constructor. For example:
2182 data Baz = forall a. Eq a => Baz1 a a
2183 | forall b. Show b => Baz2 b (b -> b)
2189 The two constructors have the types you'd expect:
2195 Baz1 :: forall a. Eq a => a -> a -> Baz
2196 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2202 But when pattern matching on <function>Baz1</function> the matched values can be compared
2203 for equality, and when pattern matching on <function>Baz2</function> the first matched
2204 value can be converted to a string (as well as applying the function to it).
2205 So this program is legal:
2212 f (Baz1 p q) | p == q = "Yes"
2214 f (Baz2 v fn) = show (fn v)
2220 Operationally, in a dictionary-passing implementation, the
2221 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2222 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2223 extract it on pattern matching.
2228 <sect3 id="existential-records">
2229 <title>Record Constructors</title>
2232 GHC allows existentials to be used with records syntax as well. For example:
2235 data Counter a = forall self. NewCounter
2237 , _inc :: self -> self
2238 , _display :: self -> IO ()
2242 Here <literal>tag</literal> is a public field, with a well-typed selector
2243 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2244 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2245 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2246 compile-time error. In other words, <emphasis>GHC defines a record selector function
2247 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2248 (This example used an underscore in the fields for which record selectors
2249 will not be defined, but that is only programming style; GHC ignores them.)
2253 To make use of these hidden fields, we need to create some helper functions:
2256 inc :: Counter a -> Counter a
2257 inc (NewCounter x i d t) = NewCounter
2258 { _this = i x, _inc = i, _display = d, tag = t }
2260 display :: Counter a -> IO ()
2261 display NewCounter{ _this = x, _display = d } = d x
2264 Now we can define counters with different underlying implementations:
2267 counterA :: Counter String
2268 counterA = NewCounter
2269 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2271 counterB :: Counter String
2272 counterB = NewCounter
2273 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2276 display (inc counterA) -- prints "1"
2277 display (inc (inc counterB)) -- prints "##"
2280 Record update syntax is supported for existentials (and GADTs):
2282 setTag :: Counter a -> a -> Counter a
2283 setTag obj t = obj{ tag = t }
2285 The rule for record update is this: <emphasis>
2286 the types of the updated fields may
2287 mention only the universally-quantified type variables
2288 of the data constructor. For GADTs, the field may mention only types
2289 that appear as a simple type-variable argument in the constructor's result
2290 type</emphasis>. For example:
2292 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2293 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2294 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2295 -- existentially quantified)
2297 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2298 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2299 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2300 -- type-variable argument in G1's result type)
2308 <title>Restrictions</title>
2311 There are several restrictions on the ways in which existentially-quantified
2312 constructors can be use.
2321 When pattern matching, each pattern match introduces a new,
2322 distinct, type for each existential type variable. These types cannot
2323 be unified with any other type, nor can they escape from the scope of
2324 the pattern match. For example, these fragments are incorrect:
2332 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2333 is the result of <function>f1</function>. One way to see why this is wrong is to
2334 ask what type <function>f1</function> has:
2338 f1 :: Foo -> a -- Weird!
2342 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2347 f1 :: forall a. Foo -> a -- Wrong!
2351 The original program is just plain wrong. Here's another sort of error
2355 f2 (Baz1 a b) (Baz1 p q) = a==q
2359 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2360 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2361 from the two <function>Baz1</function> constructors.
2369 You can't pattern-match on an existentially quantified
2370 constructor in a <literal>let</literal> or <literal>where</literal> group of
2371 bindings. So this is illegal:
2375 f3 x = a==b where { Baz1 a b = x }
2378 Instead, use a <literal>case</literal> expression:
2381 f3 x = case x of Baz1 a b -> a==b
2384 In general, you can only pattern-match
2385 on an existentially-quantified constructor in a <literal>case</literal> expression or
2386 in the patterns of a function definition.
2388 The reason for this restriction is really an implementation one.
2389 Type-checking binding groups is already a nightmare without
2390 existentials complicating the picture. Also an existential pattern
2391 binding at the top level of a module doesn't make sense, because it's
2392 not clear how to prevent the existentially-quantified type "escaping".
2393 So for now, there's a simple-to-state restriction. We'll see how
2401 You can't use existential quantification for <literal>newtype</literal>
2402 declarations. So this is illegal:
2406 newtype T = forall a. Ord a => MkT a
2410 Reason: a value of type <literal>T</literal> must be represented as a
2411 pair of a dictionary for <literal>Ord t</literal> and a value of type
2412 <literal>t</literal>. That contradicts the idea that
2413 <literal>newtype</literal> should have no concrete representation.
2414 You can get just the same efficiency and effect by using
2415 <literal>data</literal> instead of <literal>newtype</literal>. If
2416 there is no overloading involved, then there is more of a case for
2417 allowing an existentially-quantified <literal>newtype</literal>,
2418 because the <literal>data</literal> version does carry an
2419 implementation cost, but single-field existentially quantified
2420 constructors aren't much use. So the simple restriction (no
2421 existential stuff on <literal>newtype</literal>) stands, unless there
2422 are convincing reasons to change it.
2430 You can't use <literal>deriving</literal> to define instances of a
2431 data type with existentially quantified data constructors.
2433 Reason: in most cases it would not make sense. For example:;
2436 data T = forall a. MkT [a] deriving( Eq )
2439 To derive <literal>Eq</literal> in the standard way we would need to have equality
2440 between the single component of two <function>MkT</function> constructors:
2444 (MkT a) == (MkT b) = ???
2447 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2448 It's just about possible to imagine examples in which the derived instance
2449 would make sense, but it seems altogether simpler simply to prohibit such
2450 declarations. Define your own instances!
2461 <!-- ====================== Generalised algebraic data types ======================= -->
2463 <sect2 id="gadt-style">
2464 <title>Declaring data types with explicit constructor signatures</title>
2466 <para>GHC allows you to declare an algebraic data type by
2467 giving the type signatures of constructors explicitly. For example:
2471 Just :: a -> Maybe a
2473 The form is called a "GADT-style declaration"
2474 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2475 can only be declared using this form.</para>
2476 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2477 For example, these two declarations are equivalent:
2479 data Foo = forall a. MkFoo a (a -> Bool)
2480 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2483 <para>Any data type that can be declared in standard Haskell-98 syntax
2484 can also be declared using GADT-style syntax.
2485 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2486 they treat class constraints on the data constructors differently.
2487 Specifically, if the constructor is given a type-class context, that
2488 context is made available by pattern matching. For example:
2491 MkSet :: Eq a => [a] -> Set a
2493 makeSet :: Eq a => [a] -> Set a
2494 makeSet xs = MkSet (nub xs)
2496 insert :: a -> Set a -> Set a
2497 insert a (MkSet as) | a `elem` as = MkSet as
2498 | otherwise = MkSet (a:as)
2500 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2501 gives rise to a <literal>(Eq a)</literal>
2502 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2503 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2504 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2505 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2506 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2507 In the example, the equality dictionary is used to satisfy the equality constraint
2508 generated by the call to <literal>elem</literal>, so that the type of
2509 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2512 For example, one possible application is to reify dictionaries:
2514 data NumInst a where
2515 MkNumInst :: Num a => NumInst a
2517 intInst :: NumInst Int
2520 plus :: NumInst a -> a -> a -> a
2521 plus MkNumInst p q = p + q
2523 Here, a value of type <literal>NumInst a</literal> is equivalent
2524 to an explicit <literal>(Num a)</literal> dictionary.
2527 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2528 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2532 = Num a => MkNumInst (NumInst a)
2534 Notice that, unlike the situation when declaring an existential, there is
2535 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2536 data type's universally quantified type variable <literal>a</literal>.
2537 A constructor may have both universal and existential type variables: for example,
2538 the following two declarations are equivalent:
2541 = forall b. (Num a, Eq b) => MkT1 a b
2543 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2546 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2547 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2548 In Haskell 98 the definition
2550 data Eq a => Set' a = MkSet' [a]
2552 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2553 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2554 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2555 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2556 GHC's behaviour is much more useful, as well as much more intuitive.
2560 The rest of this section gives further details about GADT-style data
2565 The result type of each data constructor must begin with the type constructor being defined.
2566 If the result type of all constructors
2567 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2568 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2569 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2573 As with other type signatures, you can give a single signature for several data constructors.
2574 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2583 The type signature of
2584 each constructor is independent, and is implicitly universally quantified as usual.
2585 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2586 have no scope, and different constructors may have different universally-quantified type variables:
2588 data T a where -- The 'a' has no scope
2589 T1,T2 :: b -> T b -- Means forall b. b -> T b
2590 T3 :: T a -- Means forall a. T a
2595 A constructor signature may mention type class constraints, which can differ for
2596 different constructors. For example, this is fine:
2599 T1 :: Eq b => b -> b -> T b
2600 T2 :: (Show c, Ix c) => c -> [c] -> T c
2602 When patten matching, these constraints are made available to discharge constraints
2603 in the body of the match. For example:
2606 f (T1 x y) | x==y = "yes"
2610 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2611 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2612 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2616 Unlike a Haskell-98-style
2617 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2618 have no scope. Indeed, one can write a kind signature instead:
2620 data Set :: * -> * where ...
2622 or even a mixture of the two:
2624 data Bar a :: (* -> *) -> * where ...
2626 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2629 data Bar a (b :: * -> *) where ...
2635 You can use strictness annotations, in the obvious places
2636 in the constructor type:
2639 Lit :: !Int -> Term Int
2640 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2641 Pair :: Term a -> Term b -> Term (a,b)
2646 You can use a <literal>deriving</literal> clause on a GADT-style data type
2647 declaration. For example, these two declarations are equivalent
2649 data Maybe1 a where {
2650 Nothing1 :: Maybe1 a ;
2651 Just1 :: a -> Maybe1 a
2652 } deriving( Eq, Ord )
2654 data Maybe2 a = Nothing2 | Just2 a
2660 The type signature may have quantified type variables that do not appear
2664 MkFoo :: a -> (a->Bool) -> Foo
2667 Here the type variable <literal>a</literal> does not appear in the result type
2668 of either constructor.
2669 Although it is universally quantified in the type of the constructor, such
2670 a type variable is often called "existential".
2671 Indeed, the above declaration declares precisely the same type as
2672 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2674 The type may contain a class context too, of course:
2677 MkShowable :: Show a => a -> Showable
2682 You can use record syntax on a GADT-style data type declaration:
2686 Adult :: { name :: String, children :: [Person] } -> Person
2687 Child :: Show a => { name :: !String, funny :: a } -> Person
2689 As usual, for every constructor that has a field <literal>f</literal>, the type of
2690 field <literal>f</literal> must be the same (modulo alpha conversion).
2691 The <literal>Child</literal> constructor above shows that the signature
2692 may have a context, existentially-quantified variables, and strictness annotations,
2693 just as in the non-record case. (NB: the "type" that follows the double-colon
2694 is not really a type, because of the record syntax and strictness annotations.
2695 A "type" of this form can appear only in a constructor signature.)
2699 Record updates are allowed with GADT-style declarations,
2700 only fields that have the following property: the type of the field
2701 mentions no existential type variables.
2705 As in the case of existentials declared using the Haskell-98-like record syntax
2706 (<xref linkend="existential-records"/>),
2707 record-selector functions are generated only for those fields that have well-typed
2709 Here is the example of that section, in GADT-style syntax:
2711 data Counter a where
2712 NewCounter { _this :: self
2713 , _inc :: self -> self
2714 , _display :: self -> IO ()
2719 As before, only one selector function is generated here, that for <literal>tag</literal>.
2720 Nevertheless, you can still use all the field names in pattern matching and record construction.
2722 </itemizedlist></para>
2726 <title>Generalised Algebraic Data Types (GADTs)</title>
2728 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2729 by allowing constructors to have richer return types. Here is an example:
2732 Lit :: Int -> Term Int
2733 Succ :: Term Int -> Term Int
2734 IsZero :: Term Int -> Term Bool
2735 If :: Term Bool -> Term a -> Term a -> Term a
2736 Pair :: Term a -> Term b -> Term (a,b)
2738 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2739 case with ordinary data types. This generality allows us to
2740 write a well-typed <literal>eval</literal> function
2741 for these <literal>Terms</literal>:
2745 eval (Succ t) = 1 + eval t
2746 eval (IsZero t) = eval t == 0
2747 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2748 eval (Pair e1 e2) = (eval e1, eval e2)
2750 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2751 For example, in the right hand side of the equation
2756 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2757 A precise specification of the type rules is beyond what this user manual aspires to,
2758 but the design closely follows that described in
2760 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2761 unification-based type inference for GADTs</ulink>,
2763 The general principle is this: <emphasis>type refinement is only carried out
2764 based on user-supplied type annotations</emphasis>.
2765 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2766 and lots of obscure error messages will
2767 occur. However, the refinement is quite general. For example, if we had:
2769 eval :: Term a -> a -> a
2770 eval (Lit i) j = i+j
2772 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2773 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2774 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2777 These and many other examples are given in papers by Hongwei Xi, and
2778 Tim Sheard. There is a longer introduction
2779 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2781 <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
2782 may use different notation to that implemented in GHC.
2785 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2786 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2789 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2790 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2791 The result type of each constructor must begin with the type constructor being defined,
2792 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2793 For example, in the <literal>Term</literal> data
2794 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2795 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2800 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2801 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2802 whose result type is not just <literal>T a b</literal>.
2806 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2807 an ordinary data type.
2811 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2815 Lit { val :: Int } :: Term Int
2816 Succ { num :: Term Int } :: Term Int
2817 Pred { num :: Term Int } :: Term Int
2818 IsZero { arg :: Term Int } :: Term Bool
2819 Pair { arg1 :: Term a
2822 If { cnd :: Term Bool
2827 However, for GADTs there is the following additional constraint:
2828 every constructor that has a field <literal>f</literal> must have
2829 the same result type (modulo alpha conversion)
2830 Hence, in the above example, we cannot merge the <literal>num</literal>
2831 and <literal>arg</literal> fields above into a
2832 single name. Although their field types are both <literal>Term Int</literal>,
2833 their selector functions actually have different types:
2836 num :: Term Int -> Term Int
2837 arg :: Term Bool -> Term Int
2842 When pattern-matching against data constructors drawn from a GADT,
2843 for example in a <literal>case</literal> expression, the following rules apply:
2845 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2846 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2847 <listitem><para>The type of any free variable mentioned in any of
2848 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2850 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2851 way to ensure that a variable a rigid type is to give it a type signature.
2852 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2853 Simple unification-based type inference for GADTs
2854 </ulink>. The criteria implemented by GHC are given in the Appendix.
2864 <!-- ====================== End of Generalised algebraic data types ======================= -->
2866 <sect1 id="deriving">
2867 <title>Extensions to the "deriving" mechanism</title>
2869 <sect2 id="deriving-inferred">
2870 <title>Inferred context for deriving clauses</title>
2873 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2876 data T0 f a = MkT0 a deriving( Eq )
2877 data T1 f a = MkT1 (f a) deriving( Eq )
2878 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2880 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2882 instance Eq a => Eq (T0 f a) where ...
2883 instance Eq (f a) => Eq (T1 f a) where ...
2884 instance Eq (f (f a)) => Eq (T2 f a) where ...
2886 The first of these is obviously fine. The second is still fine, although less obviously.
2887 The third is not Haskell 98, and risks losing termination of instances.
2890 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2891 each constraint in the inferred instance context must consist only of type variables,
2892 with no repetitions.
2895 This rule is applied regardless of flags. If you want a more exotic context, you can write
2896 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2900 <sect2 id="stand-alone-deriving">
2901 <title>Stand-alone deriving declarations</title>
2904 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2906 data Foo a = Bar a | Baz String
2908 deriving instance Eq a => Eq (Foo a)
2910 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2911 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2912 Note the following points:
2915 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2916 exactly as you would in an ordinary instance declaration.
2917 (In contrast, in a <literal>deriving</literal> clause
2918 attached to a data type declaration, the context is inferred.)
2922 A <literal>deriving instance</literal> declaration
2923 must obey the same rules concerning form and termination as ordinary instance declarations,
2924 controlled by the same flags; see <xref linkend="instance-decls"/>.
2928 Unlike a <literal>deriving</literal>
2929 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2930 than the data type (assuming you also use
2931 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2934 data Foo a = Bar a | Baz String
2936 deriving instance Eq a => Eq (Foo [a])
2937 deriving instance Eq a => Eq (Foo (Maybe a))
2939 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2940 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2944 Unlike a <literal>deriving</literal>
2945 declaration attached to a <literal>data</literal> declaration,
2946 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2947 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2948 your problem. (GHC will show you the offending code if it has a type error.)
2949 The merit of this is that you can derive instances for GADTs and other exotic
2950 data types, providing only that the boilerplate code does indeed typecheck. For example:
2956 deriving instance Show (T a)
2958 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2959 data type declaration for <literal>T</literal>,
2960 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2961 the instance declaration using stand-alone deriving.
2966 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2967 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2970 newtype Foo a = MkFoo (State Int a)
2972 deriving instance MonadState Int Foo
2974 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2975 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2977 </itemizedlist></para>
2982 <sect2 id="deriving-typeable">
2983 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2986 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2987 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2988 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2989 classes <literal>Eq</literal>, <literal>Ord</literal>,
2990 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2993 GHC extends this list with several more classes that may be automatically derived:
2995 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2996 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2997 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2999 <para>An instance of <literal>Typeable</literal> can only be derived if the
3000 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3001 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3003 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3004 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3006 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3007 are used, and only <literal>Typeable1</literal> up to
3008 <literal>Typeable7</literal> are provided in the library.)
3009 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3010 class, whose kind suits that of the data type constructor, and
3011 then writing the data type instance by hand.
3015 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3016 the class <literal>Functor</literal>,
3017 defined in <literal>GHC.Base</literal>.
3020 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3021 the class <literal>Foldable</literal>,
3022 defined in <literal>Data.Foldable</literal>.
3025 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3026 the class <literal>Traversable</literal>,
3027 defined in <literal>Data.Traversable</literal>.
3030 In each case the appropriate class must be in scope before it
3031 can be mentioned in the <literal>deriving</literal> clause.
3035 <sect2 id="newtype-deriving">
3036 <title>Generalised derived instances for newtypes</title>
3039 When you define an abstract type using <literal>newtype</literal>, you may want
3040 the new type to inherit some instances from its representation. In
3041 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3042 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3043 other classes you have to write an explicit instance declaration. For
3044 example, if you define
3047 newtype Dollars = Dollars Int
3050 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3051 explicitly define an instance of <literal>Num</literal>:
3054 instance Num Dollars where
3055 Dollars a + Dollars b = Dollars (a+b)
3058 All the instance does is apply and remove the <literal>newtype</literal>
3059 constructor. It is particularly galling that, since the constructor
3060 doesn't appear at run-time, this instance declaration defines a
3061 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3062 dictionary, only slower!
3066 <sect3> <title> Generalising the deriving clause </title>
3068 GHC now permits such instances to be derived instead,
3069 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3072 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3075 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3076 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3077 derives an instance declaration of the form
3080 instance Num Int => Num Dollars
3083 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3087 We can also derive instances of constructor classes in a similar
3088 way. For example, suppose we have implemented state and failure monad
3089 transformers, such that
3092 instance Monad m => Monad (State s m)
3093 instance Monad m => Monad (Failure m)
3095 In Haskell 98, we can define a parsing monad by
3097 type Parser tok m a = State [tok] (Failure m) a
3100 which is automatically a monad thanks to the instance declarations
3101 above. With the extension, we can make the parser type abstract,
3102 without needing to write an instance of class <literal>Monad</literal>, via
3105 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3108 In this case the derived instance declaration is of the form
3110 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3113 Notice that, since <literal>Monad</literal> is a constructor class, the
3114 instance is a <emphasis>partial application</emphasis> of the new type, not the
3115 entire left hand side. We can imagine that the type declaration is
3116 "eta-converted" to generate the context of the instance
3121 We can even derive instances of multi-parameter classes, provided the
3122 newtype is the last class parameter. In this case, a ``partial
3123 application'' of the class appears in the <literal>deriving</literal>
3124 clause. For example, given the class
3127 class StateMonad s m | m -> s where ...
3128 instance Monad m => StateMonad s (State s m) where ...
3130 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3132 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3133 deriving (Monad, StateMonad [tok])
3136 The derived instance is obtained by completing the application of the
3137 class to the new type:
3140 instance StateMonad [tok] (State [tok] (Failure m)) =>
3141 StateMonad [tok] (Parser tok m)
3146 As a result of this extension, all derived instances in newtype
3147 declarations are treated uniformly (and implemented just by reusing
3148 the dictionary for the representation type), <emphasis>except</emphasis>
3149 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3150 the newtype and its representation.
3154 <sect3> <title> A more precise specification </title>
3156 Derived instance declarations are constructed as follows. Consider the
3157 declaration (after expansion of any type synonyms)
3160 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3166 The <literal>ci</literal> are partial applications of
3167 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3168 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3171 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3174 The type <literal>t</literal> is an arbitrary type.
3177 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3178 nor in the <literal>ci</literal>, and
3181 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3182 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3183 should not "look through" the type or its constructor. You can still
3184 derive these classes for a newtype, but it happens in the usual way, not
3185 via this new mechanism.
3188 Then, for each <literal>ci</literal>, the derived instance
3191 instance ci t => ci (T v1...vk)
3193 As an example which does <emphasis>not</emphasis> work, consider
3195 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3197 Here we cannot derive the instance
3199 instance Monad (State s m) => Monad (NonMonad m)
3202 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3203 and so cannot be "eta-converted" away. It is a good thing that this
3204 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3205 not, in fact, a monad --- for the same reason. Try defining
3206 <literal>>>=</literal> with the correct type: you won't be able to.
3210 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3211 important, since we can only derive instances for the last one. If the
3212 <literal>StateMonad</literal> class above were instead defined as
3215 class StateMonad m s | m -> s where ...
3218 then we would not have been able to derive an instance for the
3219 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3220 classes usually have one "main" parameter for which deriving new
3221 instances is most interesting.
3223 <para>Lastly, all of this applies only for classes other than
3224 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3225 and <literal>Data</literal>, for which the built-in derivation applies (section
3226 4.3.3. of the Haskell Report).
3227 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3228 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3229 the standard method is used or the one described here.)
3236 <!-- TYPE SYSTEM EXTENSIONS -->
3237 <sect1 id="type-class-extensions">
3238 <title>Class and instances declarations</title>
3240 <sect2 id="multi-param-type-classes">
3241 <title>Class declarations</title>
3244 This section, and the next one, documents GHC's type-class extensions.
3245 There's lots of background in the paper <ulink
3246 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3247 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3248 Jones, Erik Meijer).
3251 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3255 <title>Multi-parameter type classes</title>
3257 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3262 class Collection c a where
3263 union :: c a -> c a -> c a
3270 <sect3 id="superclass-rules">
3271 <title>The superclasses of a class declaration</title>
3274 In Haskell 98 the context of a class declaration (which introduces superclasses)
3275 must be simple; that is, each predicate must consist of a class applied to
3276 type variables. The flag <option>-XFlexibleContexts</option>
3277 (<xref linkend="flexible-contexts"/>)
3278 lifts this restriction,
3279 so that the only restriction on the context in a class declaration is
3280 that the class hierarchy must be acyclic. So these class declarations are OK:
3284 class Functor (m k) => FiniteMap m k where
3287 class (Monad m, Monad (t m)) => Transform t m where
3288 lift :: m a -> (t m) a
3294 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3295 of "acyclic" involves only the superclass relationships. For example,
3301 op :: D b => a -> b -> b
3304 class C a => D a where { ... }
3308 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3309 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3310 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3317 <sect3 id="class-method-types">
3318 <title>Class method types</title>
3321 Haskell 98 prohibits class method types to mention constraints on the
3322 class type variable, thus:
3325 fromList :: [a] -> s a
3326 elem :: Eq a => a -> s a -> Bool
3328 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3329 contains the constraint <literal>Eq a</literal>, constrains only the
3330 class type variable (in this case <literal>a</literal>).
3331 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3338 <sect2 id="functional-dependencies">
3339 <title>Functional dependencies
3342 <para> Functional dependencies are implemented as described by Mark Jones
3343 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3344 In Proceedings of the 9th European Symposium on Programming,
3345 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3349 Functional dependencies are introduced by a vertical bar in the syntax of a
3350 class declaration; e.g.
3352 class (Monad m) => MonadState s m | m -> s where ...
3354 class Foo a b c | a b -> c where ...
3356 There should be more documentation, but there isn't (yet). Yell if you need it.
3359 <sect3><title>Rules for functional dependencies </title>
3361 In a class declaration, all of the class type variables must be reachable (in the sense
3362 mentioned in <xref linkend="flexible-contexts"/>)
3363 from the free variables of each method type.
3367 class Coll s a where
3369 insert :: s -> a -> s
3372 is not OK, because the type of <literal>empty</literal> doesn't mention
3373 <literal>a</literal>. Functional dependencies can make the type variable
3376 class Coll s a | s -> a where
3378 insert :: s -> a -> s
3381 Alternatively <literal>Coll</literal> might be rewritten
3384 class Coll s a where
3386 insert :: s a -> a -> s a
3390 which makes the connection between the type of a collection of
3391 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3392 Occasionally this really doesn't work, in which case you can split the
3400 class CollE s => Coll s a where
3401 insert :: s -> a -> s
3408 <title>Background on functional dependencies</title>
3410 <para>The following description of the motivation and use of functional dependencies is taken
3411 from the Hugs user manual, reproduced here (with minor changes) by kind
3412 permission of Mark Jones.
3415 Consider the following class, intended as part of a
3416 library for collection types:
3418 class Collects e ce where
3420 insert :: e -> ce -> ce
3421 member :: e -> ce -> Bool
3423 The type variable e used here represents the element type, while ce is the type
3424 of the container itself. Within this framework, we might want to define
3425 instances of this class for lists or characteristic functions (both of which
3426 can be used to represent collections of any equality type), bit sets (which can
3427 be used to represent collections of characters), or hash tables (which can be
3428 used to represent any collection whose elements have a hash function). Omitting
3429 standard implementation details, this would lead to the following declarations:
3431 instance Eq e => Collects e [e] where ...
3432 instance Eq e => Collects e (e -> Bool) where ...
3433 instance Collects Char BitSet where ...
3434 instance (Hashable e, Collects a ce)
3435 => Collects e (Array Int ce) where ...
3437 All this looks quite promising; we have a class and a range of interesting
3438 implementations. Unfortunately, there are some serious problems with the class
3439 declaration. First, the empty function has an ambiguous type:
3441 empty :: Collects e ce => ce
3443 By "ambiguous" we mean that there is a type variable e that appears on the left
3444 of the <literal>=></literal> symbol, but not on the right. The problem with
3445 this is that, according to the theoretical foundations of Haskell overloading,
3446 we cannot guarantee a well-defined semantics for any term with an ambiguous
3450 We can sidestep this specific problem by removing the empty member from the
3451 class declaration. However, although the remaining members, insert and member,
3452 do not have ambiguous types, we still run into problems when we try to use
3453 them. For example, consider the following two functions:
3455 f x y = insert x . insert y
3458 for which GHC infers the following types:
3460 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3461 g :: (Collects Bool c, Collects Char c) => c -> c
3463 Notice that the type for f allows the two parameters x and y to be assigned
3464 different types, even though it attempts to insert each of the two values, one
3465 after the other, into the same collection. If we're trying to model collections
3466 that contain only one type of value, then this is clearly an inaccurate
3467 type. Worse still, the definition for g is accepted, without causing a type
3468 error. As a result, the error in this code will not be flagged at the point
3469 where it appears. Instead, it will show up only when we try to use g, which
3470 might even be in a different module.
3473 <sect4><title>An attempt to use constructor classes</title>
3476 Faced with the problems described above, some Haskell programmers might be
3477 tempted to use something like the following version of the class declaration:
3479 class Collects e c where
3481 insert :: e -> c e -> c e
3482 member :: e -> c e -> Bool
3484 The key difference here is that we abstract over the type constructor c that is
3485 used to form the collection type c e, and not over that collection type itself,
3486 represented by ce in the original class declaration. This avoids the immediate
3487 problems that we mentioned above: empty has type <literal>Collects e c => c
3488 e</literal>, which is not ambiguous.
3491 The function f from the previous section has a more accurate type:
3493 f :: (Collects e c) => e -> e -> c e -> c e
3495 The function g from the previous section is now rejected with a type error as
3496 we would hope because the type of f does not allow the two arguments to have
3498 This, then, is an example of a multiple parameter class that does actually work
3499 quite well in practice, without ambiguity problems.
3500 There is, however, a catch. This version of the Collects class is nowhere near
3501 as general as the original class seemed to be: only one of the four instances
3502 for <literal>Collects</literal>
3503 given above can be used with this version of Collects because only one of
3504 them---the instance for lists---has a collection type that can be written in
3505 the form c e, for some type constructor c, and element type e.
3509 <sect4><title>Adding functional dependencies</title>
3512 To get a more useful version of the Collects class, Hugs provides a mechanism
3513 that allows programmers to specify dependencies between the parameters of a
3514 multiple parameter class (For readers with an interest in theoretical
3515 foundations and previous work: The use of dependency information can be seen
3516 both as a generalization of the proposal for `parametric type classes' that was
3517 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3518 later framework for "improvement" of qualified types. The
3519 underlying ideas are also discussed in a more theoretical and abstract setting
3520 in a manuscript [implparam], where they are identified as one point in a
3521 general design space for systems of implicit parameterization.).
3523 To start with an abstract example, consider a declaration such as:
3525 class C a b where ...
3527 which tells us simply that C can be thought of as a binary relation on types
3528 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3529 included in the definition of classes to add information about dependencies
3530 between parameters, as in the following examples:
3532 class D a b | a -> b where ...
3533 class E a b | a -> b, b -> a where ...
3535 The notation <literal>a -> b</literal> used here between the | and where
3536 symbols --- not to be
3537 confused with a function type --- indicates that the a parameter uniquely
3538 determines the b parameter, and might be read as "a determines b." Thus D is
3539 not just a relation, but actually a (partial) function. Similarly, from the two
3540 dependencies that are included in the definition of E, we can see that E
3541 represents a (partial) one-one mapping between types.
3544 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3545 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3546 m>=0, meaning that the y parameters are uniquely determined by the x
3547 parameters. Spaces can be used as separators if more than one variable appears
3548 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3549 annotated with multiple dependencies using commas as separators, as in the
3550 definition of E above. Some dependencies that we can write in this notation are
3551 redundant, and will be rejected because they don't serve any useful
3552 purpose, and may instead indicate an error in the program. Examples of
3553 dependencies like this include <literal>a -> a </literal>,
3554 <literal>a -> a a </literal>,
3555 <literal>a -> </literal>, etc. There can also be
3556 some redundancy if multiple dependencies are given, as in
3557 <literal>a->b</literal>,
3558 <literal>b->c </literal>, <literal>a->c </literal>, and
3559 in which some subset implies the remaining dependencies. Examples like this are
3560 not treated as errors. Note that dependencies appear only in class
3561 declarations, and not in any other part of the language. In particular, the
3562 syntax for instance declarations, class constraints, and types is completely
3566 By including dependencies in a class declaration, we provide a mechanism for
3567 the programmer to specify each multiple parameter class more precisely. The
3568 compiler, on the other hand, is responsible for ensuring that the set of
3569 instances that are in scope at any given point in the program is consistent
3570 with any declared dependencies. For example, the following pair of instance
3571 declarations cannot appear together in the same scope because they violate the
3572 dependency for D, even though either one on its own would be acceptable:
3574 instance D Bool Int where ...
3575 instance D Bool Char where ...
3577 Note also that the following declaration is not allowed, even by itself:
3579 instance D [a] b where ...
3581 The problem here is that this instance would allow one particular choice of [a]
3582 to be associated with more than one choice for b, which contradicts the
3583 dependency specified in the definition of D. More generally, this means that,
3584 in any instance of the form:
3586 instance D t s where ...
3588 for some particular types t and s, the only variables that can appear in s are
3589 the ones that appear in t, and hence, if the type t is known, then s will be
3590 uniquely determined.
3593 The benefit of including dependency information is that it allows us to define
3594 more general multiple parameter classes, without ambiguity problems, and with
3595 the benefit of more accurate types. To illustrate this, we return to the
3596 collection class example, and annotate the original definition of <literal>Collects</literal>
3597 with a simple dependency:
3599 class Collects e ce | ce -> e where
3601 insert :: e -> ce -> ce
3602 member :: e -> ce -> Bool
3604 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3605 determined by the type of the collection ce. Note that both parameters of
3606 Collects are of kind *; there are no constructor classes here. Note too that
3607 all of the instances of Collects that we gave earlier can be used
3608 together with this new definition.
3611 What about the ambiguity problems that we encountered with the original
3612 definition? The empty function still has type Collects e ce => ce, but it is no
3613 longer necessary to regard that as an ambiguous type: Although the variable e
3614 does not appear on the right of the => symbol, the dependency for class
3615 Collects tells us that it is uniquely determined by ce, which does appear on
3616 the right of the => symbol. Hence the context in which empty is used can still
3617 give enough information to determine types for both ce and e, without
3618 ambiguity. More generally, we need only regard a type as ambiguous if it
3619 contains a variable on the left of the => that is not uniquely determined
3620 (either directly or indirectly) by the variables on the right.
3623 Dependencies also help to produce more accurate types for user defined
3624 functions, and hence to provide earlier detection of errors, and less cluttered
3625 types for programmers to work with. Recall the previous definition for a
3628 f x y = insert x y = insert x . insert y
3630 for which we originally obtained a type:
3632 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3634 Given the dependency information that we have for Collects, however, we can
3635 deduce that a and b must be equal because they both appear as the second
3636 parameter in a Collects constraint with the same first parameter c. Hence we
3637 can infer a shorter and more accurate type for f:
3639 f :: (Collects a c) => a -> a -> c -> c
3641 In a similar way, the earlier definition of g will now be flagged as a type error.
3644 Although we have given only a few examples here, it should be clear that the
3645 addition of dependency information can help to make multiple parameter classes
3646 more useful in practice, avoiding ambiguity problems, and allowing more general
3647 sets of instance declarations.
3653 <sect2 id="instance-decls">
3654 <title>Instance declarations</title>
3656 <para>An instance declaration has the form
3658 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 ...
3660 The part before the "<literal>=></literal>" is the
3661 <emphasis>context</emphasis>, while the part after the
3662 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3665 <sect3 id="flexible-instance-head">
3666 <title>Relaxed rules for the instance head</title>
3669 In Haskell 98 the head of an instance declaration
3670 must be of the form <literal>C (T a1 ... an)</literal>, where
3671 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3672 and the <literal>a1 ... an</literal> are distinct type variables.
3673 GHC relaxes these rules in two ways.
3677 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3678 declaration to mention arbitrary nested types.
3679 For example, this becomes a legal instance declaration
3681 instance C (Maybe Int) where ...
3683 See also the <link linkend="instance-overlap">rules on overlap</link>.
3686 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3687 synonyms. As always, using a type synonym is just shorthand for
3688 writing the RHS of the type synonym definition. For example:
3692 type Point = (Int,Int)
3693 instance C Point where ...
3694 instance C [Point] where ...
3698 is legal. However, if you added
3702 instance C (Int,Int) where ...
3706 as well, then the compiler will complain about the overlapping
3707 (actually, identical) instance declarations. As always, type synonyms
3708 must be fully applied. You cannot, for example, write:
3712 instance Monad P where ...
3720 <sect3 id="instance-rules">
3721 <title>Relaxed rules for instance contexts</title>
3723 <para>In Haskell 98, the assertions in the context of the instance declaration
3724 must be of the form <literal>C a</literal> where <literal>a</literal>
3725 is a type variable that occurs in the head.
3729 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3730 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3731 With this flag the context of the instance declaration can each consist of arbitrary
3732 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3736 The Paterson Conditions: for each assertion in the context
3738 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3739 <listitem><para>The assertion has fewer constructors and variables (taken together
3740 and counting repetitions) than the head</para></listitem>
3744 <listitem><para>The Coverage Condition. For each functional dependency,
3745 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3746 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3747 every type variable in
3748 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3749 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3750 substitution mapping each type variable in the class declaration to the
3751 corresponding type in the instance declaration.
3754 These restrictions ensure that context reduction terminates: each reduction
3755 step makes the problem smaller by at least one
3756 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3757 if you give the <option>-XUndecidableInstances</option>
3758 flag (<xref linkend="undecidable-instances"/>).
3759 You can find lots of background material about the reason for these
3760 restrictions in the paper <ulink
3761 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3762 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3765 For example, these are OK:
3767 instance C Int [a] -- Multiple parameters
3768 instance Eq (S [a]) -- Structured type in head
3770 -- Repeated type variable in head
3771 instance C4 a a => C4 [a] [a]
3772 instance Stateful (ST s) (MutVar s)
3774 -- Head can consist of type variables only
3776 instance (Eq a, Show b) => C2 a b
3778 -- Non-type variables in context
3779 instance Show (s a) => Show (Sized s a)
3780 instance C2 Int a => C3 Bool [a]
3781 instance C2 Int a => C3 [a] b
3785 -- Context assertion no smaller than head
3786 instance C a => C a where ...
3787 -- (C b b) has more more occurrences of b than the head
3788 instance C b b => Foo [b] where ...
3793 The same restrictions apply to instances generated by
3794 <literal>deriving</literal> clauses. Thus the following is accepted:
3796 data MinHeap h a = H a (h a)
3799 because the derived instance
3801 instance (Show a, Show (h a)) => Show (MinHeap h a)
3803 conforms to the above rules.
3807 A useful idiom permitted by the above rules is as follows.
3808 If one allows overlapping instance declarations then it's quite
3809 convenient to have a "default instance" declaration that applies if
3810 something more specific does not:
3818 <sect3 id="undecidable-instances">
3819 <title>Undecidable instances</title>
3822 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3823 For example, sometimes you might want to use the following to get the
3824 effect of a "class synonym":
3826 class (C1 a, C2 a, C3 a) => C a where { }
3828 instance (C1 a, C2 a, C3 a) => C a where { }
3830 This allows you to write shorter signatures:
3836 f :: (C1 a, C2 a, C3 a) => ...
3838 The restrictions on functional dependencies (<xref
3839 linkend="functional-dependencies"/>) are particularly troublesome.
3840 It is tempting to introduce type variables in the context that do not appear in
3841 the head, something that is excluded by the normal rules. For example:
3843 class HasConverter a b | a -> b where
3846 data Foo a = MkFoo a
3848 instance (HasConverter a b,Show b) => Show (Foo a) where
3849 show (MkFoo value) = show (convert value)
3851 This is dangerous territory, however. Here, for example, is a program that would make the
3856 instance F [a] [[a]]
3857 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3859 Similarly, it can be tempting to lift the coverage condition:
3861 class Mul a b c | a b -> c where
3862 (.*.) :: a -> b -> c
3864 instance Mul Int Int Int where (.*.) = (*)
3865 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3866 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3868 The third instance declaration does not obey the coverage condition;
3869 and indeed the (somewhat strange) definition:
3871 f = \ b x y -> if b then x .*. [y] else y
3873 makes instance inference go into a loop, because it requires the constraint
3874 <literal>(Mul a [b] b)</literal>.
3877 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3878 the experimental flag <option>-XUndecidableInstances</option>
3879 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3880 both the Paterson Conditions and the Coverage Condition
3881 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3882 fixed-depth recursion stack. If you exceed the stack depth you get a
3883 sort of backtrace, and the opportunity to increase the stack depth
3884 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3890 <sect3 id="instance-overlap">
3891 <title>Overlapping instances</title>
3893 In general, <emphasis>GHC requires that that it be unambiguous which instance
3895 should be used to resolve a type-class constraint</emphasis>. This behaviour
3896 can be modified by two flags: <option>-XOverlappingInstances</option>
3897 <indexterm><primary>-XOverlappingInstances
3898 </primary></indexterm>
3899 and <option>-XIncoherentInstances</option>
3900 <indexterm><primary>-XIncoherentInstances
3901 </primary></indexterm>, as this section discusses. Both these
3902 flags are dynamic flags, and can be set on a per-module basis, using
3903 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3905 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3906 it tries to match every instance declaration against the
3908 by instantiating the head of the instance declaration. For example, consider
3911 instance context1 => C Int a where ... -- (A)
3912 instance context2 => C a Bool where ... -- (B)
3913 instance context3 => C Int [a] where ... -- (C)
3914 instance context4 => C Int [Int] where ... -- (D)
3916 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3917 but (C) and (D) do not. When matching, GHC takes
3918 no account of the context of the instance declaration
3919 (<literal>context1</literal> etc).
3920 GHC's default behaviour is that <emphasis>exactly one instance must match the
3921 constraint it is trying to resolve</emphasis>.
3922 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3923 including both declarations (A) and (B), say); an error is only reported if a
3924 particular constraint matches more than one.
3928 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3929 more than one instance to match, provided there is a most specific one. For
3930 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3931 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3932 most-specific match, the program is rejected.
3935 However, GHC is conservative about committing to an overlapping instance. For example:
3940 Suppose that from the RHS of <literal>f</literal> we get the constraint
3941 <literal>C Int [b]</literal>. But
3942 GHC does not commit to instance (C), because in a particular
3943 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3944 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3945 So GHC rejects the program.
3946 (If you add the flag <option>-XIncoherentInstances</option>,
3947 GHC will instead pick (C), without complaining about
3948 the problem of subsequent instantiations.)
3951 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3952 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3953 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3954 it instead. In this case, GHC will refrain from
3955 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3956 as before) but, rather than rejecting the program, it will infer the type
3958 f :: C Int [b] => [b] -> [b]
3960 That postpones the question of which instance to pick to the
3961 call site for <literal>f</literal>
3962 by which time more is known about the type <literal>b</literal>.
3963 You can write this type signature yourself if you use the
3964 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3968 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3972 instance Foo [b] where
3975 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3976 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3977 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3978 declaration. The solution is to postpone the choice by adding the constraint to the context
3979 of the instance declaration, thus:
3981 instance C Int [b] => Foo [b] where
3984 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3987 Warning: overlapping instances must be used with care. They
3988 can give rise to incoherence (ie different instance choices are made
3989 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
3991 {-# LANGUAGE OverlappingInstances #-}
3994 class MyShow a where
3995 myshow :: a -> String
3997 instance MyShow a => MyShow [a] where
3998 myshow xs = concatMap myshow xs
4000 showHelp :: MyShow a => [a] -> String
4001 showHelp xs = myshow xs
4003 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
4009 instance MyShow T where
4010 myshow x = "Used generic instance"
4012 instance MyShow [T] where
4013 myshow xs = "Used more specific instance"
4015 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
4017 In function <literal>showHelp</literal> GHC sees no overlapping
4018 instances, and so uses the <literal>MyShow [a]</literal> instance
4019 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
4020 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
4021 instance declaration in module <literal>Main</literal>. As a result,
4024 "Used more specific instance"
4025 "Used generic instance"
4027 (An alternative possible behaviour, not currently implemented,
4028 would be to reject module <literal>Help</literal>
4029 on the grounds that a later instance declaration might overlap the local one.)
4032 The willingness to be overlapped or incoherent is a property of
4033 the <emphasis>instance declaration</emphasis> itself, controlled by the
4034 presence or otherwise of the <option>-XOverlappingInstances</option>
4035 and <option>-XIncoherentInstances</option> flags when that module is
4036 being defined. Neither flag is required in a module that imports and uses the
4037 instance declaration. Specifically, during the lookup process:
4040 An instance declaration is ignored during the lookup process if (a) a more specific
4041 match is found, and (b) the instance declaration was compiled with
4042 <option>-XOverlappingInstances</option>. The flag setting for the
4043 more-specific instance does not matter.
4046 Suppose an instance declaration does not match the constraint being looked up, but
4047 does unify with it, so that it might match when the constraint is further
4048 instantiated. Usually GHC will regard this as a reason for not committing to
4049 some other constraint. But if the instance declaration was compiled with
4050 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4051 check for that declaration.
4054 These rules make it possible for a library author to design a library that relies on
4055 overlapping instances without the library client having to know.
4058 If an instance declaration is compiled without
4059 <option>-XOverlappingInstances</option>,
4060 then that instance can never be overlapped. This could perhaps be
4061 inconvenient. Perhaps the rule should instead say that the
4062 <emphasis>overlapping</emphasis> instance declaration should be compiled in
4063 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
4064 at a usage site should be permitted regardless of how the instance declarations
4065 are compiled, if the <option>-XOverlappingInstances</option> flag is
4066 used at the usage site. (Mind you, the exact usage site can occasionally be
4067 hard to pin down.) We are interested to receive feedback on these points.
4069 <para>The <option>-XIncoherentInstances</option> flag implies the
4070 <option>-XOverlappingInstances</option> flag, but not vice versa.
4078 <sect2 id="overloaded-strings">
4079 <title>Overloaded string literals
4083 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4084 string literal has type <literal>String</literal>, but with overloaded string
4085 literals enabled (with <literal>-XOverloadedStrings</literal>)
4086 a string literal has type <literal>(IsString a) => a</literal>.
4089 This means that the usual string syntax can be used, e.g., for packed strings
4090 and other variations of string like types. String literals behave very much
4091 like integer literals, i.e., they can be used in both expressions and patterns.
4092 If used in a pattern the literal with be replaced by an equality test, in the same
4093 way as an integer literal is.
4096 The class <literal>IsString</literal> is defined as:
4098 class IsString a where
4099 fromString :: String -> a
4101 The only predefined instance is the obvious one to make strings work as usual:
4103 instance IsString [Char] where
4106 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4107 it explicitly (for example, to give an instance declaration for it), you can import it
4108 from module <literal>GHC.Exts</literal>.
4111 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4115 Each type in a default declaration must be an
4116 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4120 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4121 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4122 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4123 <emphasis>or</emphasis> <literal>IsString</literal>.
4132 import GHC.Exts( IsString(..) )
4134 newtype MyString = MyString String deriving (Eq, Show)
4135 instance IsString MyString where
4136 fromString = MyString
4138 greet :: MyString -> MyString
4139 greet "hello" = "world"
4143 print $ greet "hello"
4144 print $ greet "fool"
4148 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4149 to work since it gets translated into an equality comparison.
4155 <sect1 id="type-families">
4156 <title>Type families</title>
4159 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4160 facilitate type-level
4161 programming. Type families are a generalisation of <firstterm>associated
4162 data types</firstterm>
4163 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4164 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4165 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4166 Symposium on Principles of Programming Languages (POPL'05)”, pages
4167 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4168 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4169 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4171 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4172 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4173 themselves are described in the paper “<ulink
4174 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4175 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4177 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4178 13th ACM SIGPLAN International Conference on Functional
4179 Programming”, ACM Press, pages 51-62, 2008. Type families
4180 essentially provide type-indexed data types and named functions on types,
4181 which are useful for generic programming and highly parameterised library
4182 interfaces as well as interfaces with enhanced static information, much like
4183 dependent types. They might also be regarded as an alternative to functional
4184 dependencies, but provide a more functional style of type-level programming
4185 than the relational style of functional dependencies.
4188 Indexed type families, or type families for short, are type constructors that
4189 represent sets of types. Set members are denoted by supplying the type family
4190 constructor with type parameters, which are called <firstterm>type
4191 indices</firstterm>. The
4192 difference between vanilla parametrised type constructors and family
4193 constructors is much like between parametrically polymorphic functions and
4194 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4195 behave the same at all type instances, whereas class methods can change their
4196 behaviour in dependence on the class type parameters. Similarly, vanilla type
4197 constructors imply the same data representation for all type instances, but
4198 family constructors can have varying representation types for varying type
4202 Indexed type families come in two flavours: <firstterm>data
4203 families</firstterm> and <firstterm>type synonym
4204 families</firstterm>. They are the indexed family variants of algebraic
4205 data types and type synonyms, respectively. The instances of data families
4206 can be data types and newtypes.
4209 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4210 Additional information on the use of type families in GHC is available on
4211 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4212 Haskell wiki page on type families</ulink>.
4215 <sect2 id="data-families">
4216 <title>Data families</title>
4219 Data families appear in two flavours: (1) they can be defined on the
4221 or (2) they can appear inside type classes (in which case they are known as
4222 associated types). The former is the more general variant, as it lacks the
4223 requirement for the type-indexes to coincide with the class
4224 parameters. However, the latter can lead to more clearly structured code and
4225 compiler warnings if some type instances were - possibly accidentally -
4226 omitted. In the following, we always discuss the general toplevel form first
4227 and then cover the additional constraints placed on associated types.
4230 <sect3 id="data-family-declarations">
4231 <title>Data family declarations</title>
4234 Indexed data families are introduced by a signature, such as
4236 data family GMap k :: * -> *
4238 The special <literal>family</literal> distinguishes family from standard
4239 data declarations. The result kind annotation is optional and, as
4240 usual, defaults to <literal>*</literal> if omitted. An example is
4244 Named arguments can also be given explicit kind signatures if needed.
4246 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4247 declarations] named arguments are entirely optional, so that we can
4248 declare <literal>Array</literal> alternatively with
4250 data family Array :: * -> *
4254 <sect4 id="assoc-data-family-decl">
4255 <title>Associated data family declarations</title>
4257 When a data family is declared as part of a type class, we drop
4258 the <literal>family</literal> special. The <literal>GMap</literal>
4259 declaration takes the following form
4261 class GMapKey k where
4262 data GMap k :: * -> *
4265 In contrast to toplevel declarations, named arguments must be used for
4266 all type parameters that are to be used as type-indexes. Moreover,
4267 the argument names must be class parameters. Each class parameter may
4268 only be used at most once per associated type, but some may be omitted
4269 and they may be in an order other than in the class head. Hence, the
4270 following contrived example is admissible:
4279 <sect3 id="data-instance-declarations">
4280 <title>Data instance declarations</title>
4283 Instance declarations of data and newtype families are very similar to
4284 standard data and newtype declarations. The only two differences are
4285 that the keyword <literal>data</literal> or <literal>newtype</literal>
4286 is followed by <literal>instance</literal> and that some or all of the
4287 type arguments can be non-variable types, but may not contain forall
4288 types or type synonym families. However, data families are generally
4289 allowed in type parameters, and type synonyms are allowed as long as
4290 they are fully applied and expand to a type that is itself admissible -
4291 exactly as this is required for occurrences of type synonyms in class
4292 instance parameters. For example, the <literal>Either</literal>
4293 instance for <literal>GMap</literal> is
4295 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4297 In this example, the declaration has only one variant. In general, it
4301 Data and newtype instance declarations are only permitted when an
4302 appropriate family declaration is in scope - just as a class instance declaratoin
4303 requires the class declaration to be visible. Moreover, each instance
4304 declaration has to conform to the kind determined by its family
4305 declaration. This implies that the number of parameters of an instance
4306 declaration matches the arity determined by the kind of the family.
4309 A data family instance declaration can use the full exprssiveness of
4310 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4312 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4313 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4314 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4317 data instance T Int = T1 Int | T2 Bool
4318 newtype instance T Char = TC Bool
4321 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4322 and indeed can define a GADT. For example:
4325 data instance G [a] b where
4326 G1 :: c -> G [Int] b
4330 <listitem><para> You can use a <literal>deriving</literal> clause on a
4331 <literal>data instance</literal> or <literal>newtype instance</literal>
4338 Even if type families are defined as toplevel declarations, functions
4339 that perform different computations for different family instances may still
4340 need to be defined as methods of type classes. In particular, the
4341 following is not possible:
4344 data instance T Int = A
4345 data instance T Char = B
4347 foo A = 1 -- WRONG: These two equations together...
4348 foo B = 2 -- ...will produce a type error.
4350 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4354 instance Foo Int where
4356 instance Foo Char where
4359 (Given the functionality provided by GADTs (Generalised Algebraic Data
4360 Types), it might seem as if a definition, such as the above, should be
4361 feasible. However, type families are - in contrast to GADTs - are
4362 <emphasis>open;</emphasis> i.e., new instances can always be added,
4364 modules. Supporting pattern matching across different data instances
4365 would require a form of extensible case construct.)
4368 <sect4 id="assoc-data-inst">
4369 <title>Associated data instances</title>
4371 When an associated data family instance is declared within a type
4372 class instance, we drop the <literal>instance</literal> keyword in the
4373 family instance. So, the <literal>Either</literal> instance
4374 for <literal>GMap</literal> becomes:
4376 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4377 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4380 The most important point about associated family instances is that the
4381 type indexes corresponding to class parameters must be identical to
4382 the type given in the instance head; here this is the first argument
4383 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4384 which coincides with the only class parameter. Any parameters to the
4385 family constructor that do not correspond to class parameters, need to
4386 be variables in every instance; here this is the
4387 variable <literal>v</literal>.
4390 Instances for an associated family can only appear as part of
4391 instances declarations of the class in which the family was declared -
4392 just as with the equations of the methods of a class. Also in
4393 correspondence to how methods are handled, declarations of associated
4394 types can be omitted in class instances. If an associated family
4395 instance is omitted, the corresponding instance type is not inhabited;
4396 i.e., only diverging expressions, such
4397 as <literal>undefined</literal>, can assume the type.
4401 <sect4 id="scoping-class-params">
4402 <title>Scoping of class parameters</title>
4404 In the case of multi-parameter type classes, the visibility of class
4405 parameters in the right-hand side of associated family instances
4406 depends <emphasis>solely</emphasis> on the parameters of the data
4407 family. As an example, consider the simple class declaration
4412 Only one of the two class parameters is a parameter to the data
4413 family. Hence, the following instance declaration is invalid:
4415 instance C [c] d where
4416 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4418 Here, the right-hand side of the data instance mentions the type
4419 variable <literal>d</literal> that does not occur in its left-hand
4420 side. We cannot admit such data instances as they would compromise
4425 <sect4 id="family-class-inst">
4426 <title>Type class instances of family instances</title>
4428 Type class instances of instances of data families can be defined as
4429 usual, and in particular data instance declarations can
4430 have <literal>deriving</literal> clauses. For example, we can write
4432 data GMap () v = GMapUnit (Maybe v)
4435 which implicitly defines an instance of the form
4437 instance Show v => Show (GMap () v) where ...
4441 Note that class instances are always for
4442 particular <emphasis>instances</emphasis> of a data family and never
4443 for an entire family as a whole. This is for essentially the same
4444 reasons that we cannot define a toplevel function that performs
4445 pattern matching on the data constructors
4446 of <emphasis>different</emphasis> instances of a single type family.
4447 It would require a form of extensible case construct.
4451 <sect4 id="data-family-overlap">
4452 <title>Overlap of data instances</title>
4454 The instance declarations of a data family used in a single program
4455 may not overlap at all, independent of whether they are associated or
4456 not. In contrast to type class instances, this is not only a matter
4457 of consistency, but one of type safety.
4463 <sect3 id="data-family-import-export">
4464 <title>Import and export</title>
4467 The association of data constructors with type families is more dynamic
4468 than that is the case with standard data and newtype declarations. In
4469 the standard case, the notation <literal>T(..)</literal> in an import or
4470 export list denotes the type constructor and all the data constructors
4471 introduced in its declaration. However, a family declaration never
4472 introduces any data constructors; instead, data constructors are
4473 introduced by family instances. As a result, which data constructors
4474 are associated with a type family depends on the currently visible
4475 instance declarations for that family. Consequently, an import or
4476 export item of the form <literal>T(..)</literal> denotes the family
4477 constructor and all currently visible data constructors - in the case of
4478 an export item, these may be either imported or defined in the current
4479 module. The treatment of import and export items that explicitly list
4480 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4484 <sect4 id="data-family-impexp-assoc">
4485 <title>Associated families</title>
4487 As expected, an import or export item of the
4488 form <literal>C(..)</literal> denotes all of the class' methods and
4489 associated types. However, when associated types are explicitly
4490 listed as subitems of a class, we need some new syntax, as uppercase
4491 identifiers as subitems are usually data constructors, not type
4492 constructors. To clarify that we denote types here, each associated
4493 type name needs to be prefixed by the keyword <literal>type</literal>.
4494 So for example, when explicitly listing the components of
4495 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4496 GMap, empty, lookup, insert)</literal>.
4500 <sect4 id="data-family-impexp-examples">
4501 <title>Examples</title>
4503 Assuming our running <literal>GMapKey</literal> class example, let us
4504 look at some export lists and their meaning:
4507 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4508 just the class name.</para>
4511 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4512 Exports the class, the associated type <literal>GMap</literal>
4514 functions <literal>empty</literal>, <literal>lookup</literal>,
4515 and <literal>insert</literal>. None of the data constructors is
4519 <para><literal>module GMap (GMapKey(..), GMap(..))
4520 where...</literal>: As before, but also exports all the data
4521 constructors <literal>GMapInt</literal>,
4522 <literal>GMapChar</literal>,
4523 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4524 and <literal>GMapUnit</literal>.</para>
4527 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4528 GMap(..)) where...</literal>: As before.</para>
4531 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4532 where...</literal>: As before.</para>
4537 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4538 both the class <literal>GMapKey</literal> as well as its associated
4539 type <literal>GMap</literal>. However, you cannot
4540 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4541 sub-component specifications cannot be nested. To
4542 specify <literal>GMap</literal>'s data constructors, you have to list
4547 <sect4 id="data-family-impexp-instances">
4548 <title>Instances</title>
4550 Family instances are implicitly exported, just like class instances.
4551 However, this applies only to the heads of instances, not to the data
4552 constructors an instance defines.
4560 <sect2 id="synonym-families">
4561 <title>Synonym families</title>
4564 Type families appear in two flavours: (1) they can be defined on the
4565 toplevel or (2) they can appear inside type classes (in which case they
4566 are known as associated type synonyms). The former is the more general
4567 variant, as it lacks the requirement for the type-indexes to coincide with
4568 the class parameters. However, the latter can lead to more clearly
4569 structured code and compiler warnings if some type instances were -
4570 possibly accidentally - omitted. In the following, we always discuss the
4571 general toplevel form first and then cover the additional constraints
4572 placed on associated types.
4575 <sect3 id="type-family-declarations">
4576 <title>Type family declarations</title>
4579 Indexed type families are introduced by a signature, such as
4581 type family Elem c :: *
4583 The special <literal>family</literal> distinguishes family from standard
4584 type declarations. The result kind annotation is optional and, as
4585 usual, defaults to <literal>*</literal> if omitted. An example is
4589 Parameters can also be given explicit kind signatures if needed. We
4590 call the number of parameters in a type family declaration, the family's
4591 arity, and all applications of a type family must be fully saturated
4592 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4593 and it implies that the kind of a type family is not sufficient to
4594 determine a family's arity, and hence in general, also insufficient to
4595 determine whether a type family application is well formed. As an
4596 example, consider the following declaration:
4598 type family F a b :: * -> * -- F's arity is 2,
4599 -- although its overall kind is * -> * -> * -> *
4601 Given this declaration the following are examples of well-formed and
4604 F Char [Int] -- OK! Kind: * -> *
4605 F Char [Int] Bool -- OK! Kind: *
4606 F IO Bool -- WRONG: kind mismatch in the first argument
4607 F Bool -- WRONG: unsaturated application
4611 <sect4 id="assoc-type-family-decl">
4612 <title>Associated type family declarations</title>
4614 When a type family is declared as part of a type class, we drop
4615 the <literal>family</literal> special. The <literal>Elem</literal>
4616 declaration takes the following form
4618 class Collects ce where
4622 The argument names of the type family must be class parameters. Each
4623 class parameter may only be used at most once per associated type, but
4624 some may be omitted and they may be in an order other than in the
4625 class head. Hence, the following contrived example is admissible:
4630 These rules are exactly as for associated data families.
4635 <sect3 id="type-instance-declarations">
4636 <title>Type instance declarations</title>
4638 Instance declarations of type families are very similar to standard type
4639 synonym declarations. The only two differences are that the
4640 keyword <literal>type</literal> is followed
4641 by <literal>instance</literal> and that some or all of the type
4642 arguments can be non-variable types, but may not contain forall types or
4643 type synonym families. However, data families are generally allowed, and
4644 type synonyms are allowed as long as they are fully applied and expand
4645 to a type that is admissible - these are the exact same requirements as
4646 for data instances. For example, the <literal>[e]</literal> instance
4647 for <literal>Elem</literal> is
4649 type instance Elem [e] = e
4653 Type family instance declarations are only legitimate when an
4654 appropriate family declaration is in scope - just like class instances
4655 require the class declaration to be visible. Moreover, each instance
4656 declaration has to conform to the kind determined by its family
4657 declaration, and the number of type parameters in an instance
4658 declaration must match the number of type parameters in the family
4659 declaration. Finally, the right-hand side of a type instance must be a
4660 monotype (i.e., it may not include foralls) and after the expansion of
4661 all saturated vanilla type synonyms, no synonyms, except family synonyms
4662 may remain. Here are some examples of admissible and illegal type
4665 type family F a :: *
4666 type instance F [Int] = Int -- OK!
4667 type instance F String = Char -- OK!
4668 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4669 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4670 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4672 type family G a b :: * -> *
4673 type instance G Int = (,) -- WRONG: must be two type parameters
4674 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4678 <sect4 id="assoc-type-instance">
4679 <title>Associated type instance declarations</title>
4681 When an associated family instance is declared within a type class
4682 instance, we drop the <literal>instance</literal> keyword in the family
4683 instance. So, the <literal>[e]</literal> instance
4684 for <literal>Elem</literal> becomes:
4686 instance (Eq (Elem [e])) => Collects ([e]) where
4690 The most important point about associated family instances is that the
4691 type indexes corresponding to class parameters must be identical to the
4692 type given in the instance head; here this is <literal>[e]</literal>,
4693 which coincides with the only class parameter.
4696 Instances for an associated family can only appear as part of instances
4697 declarations of the class in which the family was declared - just as
4698 with the equations of the methods of a class. Also in correspondence to
4699 how methods are handled, declarations of associated types can be omitted
4700 in class instances. If an associated family instance is omitted, the
4701 corresponding instance type is not inhabited; i.e., only diverging
4702 expressions, such as <literal>undefined</literal>, can assume the type.
4706 <sect4 id="type-family-overlap">
4707 <title>Overlap of type synonym instances</title>
4709 The instance declarations of a type family used in a single program
4710 may only overlap if the right-hand sides of the overlapping instances
4711 coincide for the overlapping types. More formally, two instance
4712 declarations overlap if there is a substitution that makes the
4713 left-hand sides of the instances syntactically the same. Whenever
4714 that is the case, the right-hand sides of the instances must also be
4715 syntactically equal under the same substitution. This condition is
4716 independent of whether the type family is associated or not, and it is
4717 not only a matter of consistency, but one of type safety.
4720 Here are two example to illustrate the condition under which overlap
4723 type instance F (a, Int) = [a]
4724 type instance F (Int, b) = [b] -- overlap permitted
4726 type instance G (a, Int) = [a]
4727 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4732 <sect4 id="type-family-decidability">
4733 <title>Decidability of type synonym instances</title>
4735 In order to guarantee that type inference in the presence of type
4736 families decidable, we need to place a number of additional
4737 restrictions on the formation of type instance declarations (c.f.,
4738 Definition 5 (Relaxed Conditions) of “<ulink
4739 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4740 Checking with Open Type Functions</ulink>”). Instance
4741 declarations have the general form
4743 type instance F t1 .. tn = t
4745 where we require that for every type family application <literal>(G s1
4746 .. sm)</literal> in <literal>t</literal>,
4749 <para><literal>s1 .. sm</literal> do not contain any type family
4750 constructors,</para>
4753 <para>the total number of symbols (data type constructors and type
4754 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4755 in <literal>t1 .. tn</literal>, and</para>
4758 <para>for every type
4759 variable <literal>a</literal>, <literal>a</literal> occurs
4760 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4761 .. tn</literal>.</para>
4764 These restrictions are easily verified and ensure termination of type
4765 inference. However, they are not sufficient to guarantee completeness
4766 of type inference in the presence of, so called, ''loopy equalities'',
4767 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4768 a type variable is underneath a family application and data
4769 constructor application - see the above mentioned paper for details.
4772 If the option <option>-XUndecidableInstances</option> is passed to the
4773 compiler, the above restrictions are not enforced and it is on the
4774 programmer to ensure termination of the normalisation of type families
4775 during type inference.
4780 <sect3 id-="equality-constraints">
4781 <title>Equality constraints</title>
4783 Type context can include equality constraints of the form <literal>t1 ~
4784 t2</literal>, which denote that the types <literal>t1</literal>
4785 and <literal>t2</literal> need to be the same. In the presence of type
4786 families, whether two types are equal cannot generally be decided
4787 locally. Hence, the contexts of function signatures may include
4788 equality constraints, as in the following example:
4790 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4792 where we require that the element type of <literal>c1</literal>
4793 and <literal>c2</literal> are the same. In general, the
4794 types <literal>t1</literal> and <literal>t2</literal> of an equality
4795 constraint may be arbitrary monotypes; i.e., they may not contain any
4796 quantifiers, independent of whether higher-rank types are otherwise
4800 Equality constraints can also appear in class and instance contexts.
4801 The former enable a simple translation of programs using functional
4802 dependencies into programs using family synonyms instead. The general
4803 idea is to rewrite a class declaration of the form
4805 class C a b | a -> b
4809 class (F a ~ b) => C a b where
4812 That is, we represent every functional dependency (FD) <literal>a1 .. an
4813 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4814 superclass context equality <literal>F a1 .. an ~ b</literal>,
4815 essentially giving a name to the functional dependency. In class
4816 instances, we define the type instances of FD families in accordance
4817 with the class head. Method signatures are not affected by that
4821 NB: Equalities in superclass contexts are not fully implemented in
4826 <sect3 id-="ty-fams-in-instances">
4827 <title>Type families and instance declarations</title>
4828 <para>Type families require us to extend the rules for
4829 the form of instance heads, which are given
4830 in <xref linkend="flexible-instance-head"/>.
4833 <listitem><para>Data type families may appear in an instance head</para></listitem>
4834 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4836 The reason for the latter restriction is that there is no way to check for. Consider
4839 type instance F Bool = Int
4846 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4847 The situation is especially bad because the type instance for <literal>F Bool</literal>
4848 might be in another module, or even in a module that is not yet written.
4855 <sect1 id="other-type-extensions">
4856 <title>Other type system extensions</title>
4858 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4860 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4861 is used, the keyword <literal>forall</literal>
4862 allows us to say exactly what this means. For example:
4870 g :: forall b. (b -> b)
4872 The two are treated identically.
4875 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4876 a type variable any more!
4881 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4883 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4884 that the type-class constraints in a type signature must have the
4885 form <emphasis>(class type-variable)</emphasis> or
4886 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4887 With <option>-XFlexibleContexts</option>
4888 these type signatures are perfectly OK
4891 g :: Ord (T a ()) => ...
4893 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4894 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4895 (<xref linkend="instance-rules"/>).
4899 GHC imposes the following restrictions on the constraints in a type signature.
4903 forall tv1..tvn (c1, ...,cn) => type
4906 (Here, we write the "foralls" explicitly, although the Haskell source
4907 language omits them; in Haskell 98, all the free type variables of an
4908 explicit source-language type signature are universally quantified,
4909 except for the class type variables in a class declaration. However,
4910 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4919 <emphasis>Each universally quantified type variable
4920 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4922 A type variable <literal>a</literal> is "reachable" if it appears
4923 in the same constraint as either a type variable free in
4924 <literal>type</literal>, or another reachable type variable.
4925 A value with a type that does not obey
4926 this reachability restriction cannot be used without introducing
4927 ambiguity; that is why the type is rejected.
4928 Here, for example, is an illegal type:
4932 forall a. Eq a => Int
4936 When a value with this type was used, the constraint <literal>Eq tv</literal>
4937 would be introduced where <literal>tv</literal> is a fresh type variable, and
4938 (in the dictionary-translation implementation) the value would be
4939 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4940 can never know which instance of <literal>Eq</literal> to use because we never
4941 get any more information about <literal>tv</literal>.
4945 that the reachability condition is weaker than saying that <literal>a</literal> is
4946 functionally dependent on a type variable free in
4947 <literal>type</literal> (see <xref
4948 linkend="functional-dependencies"/>). The reason for this is there
4949 might be a "hidden" dependency, in a superclass perhaps. So
4950 "reachable" is a conservative approximation to "functionally dependent".
4951 For example, consider:
4953 class C a b | a -> b where ...
4954 class C a b => D a b where ...
4955 f :: forall a b. D a b => a -> a
4957 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4958 but that is not immediately apparent from <literal>f</literal>'s type.
4964 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4965 universally quantified type variables <literal>tvi</literal></emphasis>.
4967 For example, this type is OK because <literal>C a b</literal> mentions the
4968 universally quantified type variable <literal>b</literal>:
4972 forall a. C a b => burble
4976 The next type is illegal because the constraint <literal>Eq b</literal> does not
4977 mention <literal>a</literal>:
4981 forall a. Eq b => burble
4985 The reason for this restriction is milder than the other one. The
4986 excluded types are never useful or necessary (because the offending
4987 context doesn't need to be witnessed at this point; it can be floated
4988 out). Furthermore, floating them out increases sharing. Lastly,
4989 excluding them is a conservative choice; it leaves a patch of
4990 territory free in case we need it later.
5001 <sect2 id="implicit-parameters">
5002 <title>Implicit parameters</title>
5004 <para> Implicit parameters are implemented as described in
5005 "Implicit parameters: dynamic scoping with static types",
5006 J Lewis, MB Shields, E Meijer, J Launchbury,
5007 27th ACM Symposium on Principles of Programming Languages (POPL'00),
5011 <para>(Most of the following, still rather incomplete, documentation is
5012 due to Jeff Lewis.)</para>
5014 <para>Implicit parameter support is enabled with the option
5015 <option>-XImplicitParams</option>.</para>
5018 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
5019 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
5020 context. In Haskell, all variables are statically bound. Dynamic
5021 binding of variables is a notion that goes back to Lisp, but was later
5022 discarded in more modern incarnations, such as Scheme. Dynamic binding
5023 can be very confusing in an untyped language, and unfortunately, typed
5024 languages, in particular Hindley-Milner typed languages like Haskell,
5025 only support static scoping of variables.
5028 However, by a simple extension to the type class system of Haskell, we
5029 can support dynamic binding. Basically, we express the use of a
5030 dynamically bound variable as a constraint on the type. These
5031 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
5032 function uses a dynamically-bound variable <literal>?x</literal>
5033 of type <literal>t'</literal>". For
5034 example, the following expresses the type of a sort function,
5035 implicitly parameterized by a comparison function named <literal>cmp</literal>.
5037 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5039 The dynamic binding constraints are just a new form of predicate in the type class system.
5042 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5043 where <literal>x</literal> is
5044 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5045 Use of this construct also introduces a new
5046 dynamic-binding constraint in the type of the expression.
5047 For example, the following definition
5048 shows how we can define an implicitly parameterized sort function in
5049 terms of an explicitly parameterized <literal>sortBy</literal> function:
5051 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5053 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5059 <title>Implicit-parameter type constraints</title>
5061 Dynamic binding constraints behave just like other type class
5062 constraints in that they are automatically propagated. Thus, when a
5063 function is used, its implicit parameters are inherited by the
5064 function that called it. For example, our <literal>sort</literal> function might be used
5065 to pick out the least value in a list:
5067 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5068 least xs = head (sort xs)
5070 Without lifting a finger, the <literal>?cmp</literal> parameter is
5071 propagated to become a parameter of <literal>least</literal> as well. With explicit
5072 parameters, the default is that parameters must always be explicit
5073 propagated. With implicit parameters, the default is to always
5077 An implicit-parameter type constraint differs from other type class constraints in the
5078 following way: All uses of a particular implicit parameter must have
5079 the same type. This means that the type of <literal>(?x, ?x)</literal>
5080 is <literal>(?x::a) => (a,a)</literal>, and not
5081 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5085 <para> You can't have an implicit parameter in the context of a class or instance
5086 declaration. For example, both these declarations are illegal:
5088 class (?x::Int) => C a where ...
5089 instance (?x::a) => Foo [a] where ...
5091 Reason: exactly which implicit parameter you pick up depends on exactly where
5092 you invoke a function. But the ``invocation'' of instance declarations is done
5093 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5094 Easiest thing is to outlaw the offending types.</para>
5096 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5098 f :: (?x :: [a]) => Int -> Int
5101 g :: (Read a, Show a) => String -> String
5104 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5105 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5106 quite unambiguous, and fixes the type <literal>a</literal>.
5111 <title>Implicit-parameter bindings</title>
5114 An implicit parameter is <emphasis>bound</emphasis> using the standard
5115 <literal>let</literal> or <literal>where</literal> binding forms.
5116 For example, we define the <literal>min</literal> function by binding
5117 <literal>cmp</literal>.
5120 min = let ?cmp = (<=) in least
5124 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5125 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5126 (including in a list comprehension, or do-notation, or pattern guards),
5127 or a <literal>where</literal> clause.
5128 Note the following points:
5131 An implicit-parameter binding group must be a
5132 collection of simple bindings to implicit-style variables (no
5133 function-style bindings, and no type signatures); these bindings are
5134 neither polymorphic or recursive.
5137 You may not mix implicit-parameter bindings with ordinary bindings in a
5138 single <literal>let</literal>
5139 expression; use two nested <literal>let</literal>s instead.
5140 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5144 You may put multiple implicit-parameter bindings in a
5145 single binding group; but they are <emphasis>not</emphasis> treated
5146 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5147 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5148 parameter. The bindings are not nested, and may be re-ordered without changing
5149 the meaning of the program.
5150 For example, consider:
5152 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5154 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5155 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5157 f :: (?x::Int) => Int -> Int
5165 <sect3><title>Implicit parameters and polymorphic recursion</title>
5168 Consider these two definitions:
5171 len1 xs = let ?acc = 0 in len_acc1 xs
5174 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5179 len2 xs = let ?acc = 0 in len_acc2 xs
5181 len_acc2 :: (?acc :: Int) => [a] -> Int
5183 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5185 The only difference between the two groups is that in the second group
5186 <literal>len_acc</literal> is given a type signature.
5187 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5188 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5189 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5190 has a type signature, the recursive call is made to the
5191 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5192 as an implicit parameter. So we get the following results in GHCi:
5199 Adding a type signature dramatically changes the result! This is a rather
5200 counter-intuitive phenomenon, worth watching out for.
5204 <sect3><title>Implicit parameters and monomorphism</title>
5206 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5207 Haskell Report) to implicit parameters. For example, consider:
5215 Since the binding for <literal>y</literal> falls under the Monomorphism
5216 Restriction it is not generalised, so the type of <literal>y</literal> is
5217 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5218 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5219 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5220 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5221 <literal>y</literal> in the body of the <literal>let</literal> will see the
5222 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5223 <literal>14</literal>.
5228 <!-- ======================= COMMENTED OUT ========================
5230 We intend to remove linear implicit parameters, so I'm at least removing
5231 them from the 6.6 user manual
5233 <sect2 id="linear-implicit-parameters">
5234 <title>Linear implicit parameters</title>
5236 Linear implicit parameters are an idea developed by Koen Claessen,
5237 Mark Shields, and Simon PJ. They address the long-standing
5238 problem that monads seem over-kill for certain sorts of problem, notably:
5241 <listitem> <para> distributing a supply of unique names </para> </listitem>
5242 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5243 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5247 Linear implicit parameters are just like ordinary implicit parameters,
5248 except that they are "linear"; that is, they cannot be copied, and
5249 must be explicitly "split" instead. Linear implicit parameters are
5250 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5251 (The '/' in the '%' suggests the split!)
5256 import GHC.Exts( Splittable )
5258 data NameSupply = ...
5260 splitNS :: NameSupply -> (NameSupply, NameSupply)
5261 newName :: NameSupply -> Name
5263 instance Splittable NameSupply where
5267 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5268 f env (Lam x e) = Lam x' (f env e)
5271 env' = extend env x x'
5272 ...more equations for f...
5274 Notice that the implicit parameter %ns is consumed
5276 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5277 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5281 So the translation done by the type checker makes
5282 the parameter explicit:
5284 f :: NameSupply -> Env -> Expr -> Expr
5285 f ns env (Lam x e) = Lam x' (f ns1 env e)
5287 (ns1,ns2) = splitNS ns
5289 env = extend env x x'
5291 Notice the call to 'split' introduced by the type checker.
5292 How did it know to use 'splitNS'? Because what it really did
5293 was to introduce a call to the overloaded function 'split',
5294 defined by the class <literal>Splittable</literal>:
5296 class Splittable a where
5299 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5300 split for name supplies. But we can simply write
5306 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5308 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5309 <literal>GHC.Exts</literal>.
5314 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5315 are entirely distinct implicit parameters: you
5316 can use them together and they won't interfere with each other. </para>
5319 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5321 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5322 in the context of a class or instance declaration. </para></listitem>
5326 <sect3><title>Warnings</title>
5329 The monomorphism restriction is even more important than usual.
5330 Consider the example above:
5332 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5333 f env (Lam x e) = Lam x' (f env e)
5336 env' = extend env x x'
5338 If we replaced the two occurrences of x' by (newName %ns), which is
5339 usually a harmless thing to do, we get:
5341 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5342 f env (Lam x e) = Lam (newName %ns) (f env e)
5344 env' = extend env x (newName %ns)
5346 But now the name supply is consumed in <emphasis>three</emphasis> places
5347 (the two calls to newName,and the recursive call to f), so
5348 the result is utterly different. Urk! We don't even have
5352 Well, this is an experimental change. With implicit
5353 parameters we have already lost beta reduction anyway, and
5354 (as John Launchbury puts it) we can't sensibly reason about
5355 Haskell programs without knowing their typing.
5360 <sect3><title>Recursive functions</title>
5361 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5364 foo :: %x::T => Int -> [Int]
5366 foo n = %x : foo (n-1)
5368 where T is some type in class Splittable.</para>
5370 Do you get a list of all the same T's or all different T's
5371 (assuming that split gives two distinct T's back)?
5373 If you supply the type signature, taking advantage of polymorphic
5374 recursion, you get what you'd probably expect. Here's the
5375 translated term, where the implicit param is made explicit:
5378 foo x n = let (x1,x2) = split x
5379 in x1 : foo x2 (n-1)
5381 But if you don't supply a type signature, GHC uses the Hindley
5382 Milner trick of using a single monomorphic instance of the function
5383 for the recursive calls. That is what makes Hindley Milner type inference
5384 work. So the translation becomes
5388 foom n = x : foom (n-1)
5392 Result: 'x' is not split, and you get a list of identical T's. So the
5393 semantics of the program depends on whether or not foo has a type signature.
5396 You may say that this is a good reason to dislike linear implicit parameters
5397 and you'd be right. That is why they are an experimental feature.
5403 ================ END OF Linear Implicit Parameters commented out -->
5405 <sect2 id="kinding">
5406 <title>Explicitly-kinded quantification</title>
5409 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5410 to give the kind explicitly as (machine-checked) documentation,
5411 just as it is nice to give a type signature for a function. On some occasions,
5412 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5413 John Hughes had to define the data type:
5415 data Set cxt a = Set [a]
5416 | Unused (cxt a -> ())
5418 The only use for the <literal>Unused</literal> constructor was to force the correct
5419 kind for the type variable <literal>cxt</literal>.
5422 GHC now instead allows you to specify the kind of a type variable directly, wherever
5423 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5426 This flag enables kind signatures in the following places:
5428 <listitem><para><literal>data</literal> declarations:
5430 data Set (cxt :: * -> *) a = Set [a]
5431 </screen></para></listitem>
5432 <listitem><para><literal>type</literal> declarations:
5434 type T (f :: * -> *) = f Int
5435 </screen></para></listitem>
5436 <listitem><para><literal>class</literal> declarations:
5438 class (Eq a) => C (f :: * -> *) a where ...
5439 </screen></para></listitem>
5440 <listitem><para><literal>forall</literal>'s in type signatures:
5442 f :: forall (cxt :: * -> *). Set cxt Int
5443 </screen></para></listitem>
5448 The parentheses are required. Some of the spaces are required too, to
5449 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5450 will get a parse error, because "<literal>::*->*</literal>" is a
5451 single lexeme in Haskell.
5455 As part of the same extension, you can put kind annotations in types
5458 f :: (Int :: *) -> Int
5459 g :: forall a. a -> (a :: *)
5463 atype ::= '(' ctype '::' kind ')
5465 The parentheses are required.
5470 <sect2 id="universal-quantification">
5471 <title>Arbitrary-rank polymorphism
5475 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5476 explicit universal quantification in
5478 For example, all the following types are legal:
5480 f1 :: forall a b. a -> b -> a
5481 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5483 f2 :: (forall a. a->a) -> Int -> Int
5484 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5486 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5488 f4 :: Int -> (forall a. a -> a)
5490 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5491 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5492 The <literal>forall</literal> makes explicit the universal quantification that
5493 is implicitly added by Haskell.
5496 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5497 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5498 shows, the polymorphic type on the left of the function arrow can be overloaded.
5501 The function <literal>f3</literal> has a rank-3 type;
5502 it has rank-2 types on the left of a function arrow.
5505 GHC has three flags to control higher-rank types:
5508 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5511 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5514 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5515 That is, you can nest <literal>forall</literal>s
5516 arbitrarily deep in function arrows.
5517 In particular, a forall-type (also called a "type scheme"),
5518 including an operational type class context, is legal:
5520 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5521 of a function arrow </para> </listitem>
5522 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5523 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5524 field type signatures.</para> </listitem>
5525 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5526 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5538 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5539 the types of the constructor arguments. Here are several examples:
5545 data T a = T1 (forall b. b -> b -> b) a
5547 data MonadT m = MkMonad { return :: forall a. a -> m a,
5548 bind :: forall a b. m a -> (a -> m b) -> m b
5551 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5557 The constructors have rank-2 types:
5563 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5564 MkMonad :: forall m. (forall a. a -> m a)
5565 -> (forall a b. m a -> (a -> m b) -> m b)
5567 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5573 Notice that you don't need to use a <literal>forall</literal> if there's an
5574 explicit context. For example in the first argument of the
5575 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5576 prefixed to the argument type. The implicit <literal>forall</literal>
5577 quantifies all type variables that are not already in scope, and are
5578 mentioned in the type quantified over.
5582 As for type signatures, implicit quantification happens for non-overloaded
5583 types too. So if you write this:
5586 data T a = MkT (Either a b) (b -> b)
5589 it's just as if you had written this:
5592 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5595 That is, since the type variable <literal>b</literal> isn't in scope, it's
5596 implicitly universally quantified. (Arguably, it would be better
5597 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5598 where that is what is wanted. Feedback welcomed.)
5602 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5603 the constructor to suitable values, just as usual. For example,
5614 a3 = MkSwizzle reverse
5617 a4 = let r x = Just x
5624 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5625 mkTs f x y = [T1 f x, T1 f y]
5631 The type of the argument can, as usual, be more general than the type
5632 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5633 does not need the <literal>Ord</literal> constraint.)
5637 When you use pattern matching, the bound variables may now have
5638 polymorphic types. For example:
5644 f :: T a -> a -> (a, Char)
5645 f (T1 w k) x = (w k x, w 'c' 'd')
5647 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5648 g (MkSwizzle s) xs f = s (map f (s xs))
5650 h :: MonadT m -> [m a] -> m [a]
5651 h m [] = return m []
5652 h m (x:xs) = bind m x $ \y ->
5653 bind m (h m xs) $ \ys ->
5660 In the function <function>h</function> we use the record selectors <literal>return</literal>
5661 and <literal>bind</literal> to extract the polymorphic bind and return functions
5662 from the <literal>MonadT</literal> data structure, rather than using pattern
5668 <title>Type inference</title>
5671 In general, type inference for arbitrary-rank types is undecidable.
5672 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5673 to get a decidable algorithm by requiring some help from the programmer.
5674 We do not yet have a formal specification of "some help" but the rule is this:
5677 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5678 provides an explicit polymorphic type for x, or GHC's type inference will assume
5679 that x's type has no foralls in it</emphasis>.
5682 What does it mean to "provide" an explicit type for x? You can do that by
5683 giving a type signature for x directly, using a pattern type signature
5684 (<xref linkend="scoped-type-variables"/>), thus:
5686 \ f :: (forall a. a->a) -> (f True, f 'c')
5688 Alternatively, you can give a type signature to the enclosing
5689 context, which GHC can "push down" to find the type for the variable:
5691 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5693 Here the type signature on the expression can be pushed inwards
5694 to give a type signature for f. Similarly, and more commonly,
5695 one can give a type signature for the function itself:
5697 h :: (forall a. a->a) -> (Bool,Char)
5698 h f = (f True, f 'c')
5700 You don't need to give a type signature if the lambda bound variable
5701 is a constructor argument. Here is an example we saw earlier:
5703 f :: T a -> a -> (a, Char)
5704 f (T1 w k) x = (w k x, w 'c' 'd')
5706 Here we do not need to give a type signature to <literal>w</literal>, because
5707 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5714 <sect3 id="implicit-quant">
5715 <title>Implicit quantification</title>
5718 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5719 user-written types, if and only if there is no explicit <literal>forall</literal>,
5720 GHC finds all the type variables mentioned in the type that are not already
5721 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5725 f :: forall a. a -> a
5732 h :: forall b. a -> b -> b
5738 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5741 f :: (a -> a) -> Int
5743 f :: forall a. (a -> a) -> Int
5745 f :: (forall a. a -> a) -> Int
5748 g :: (Ord a => a -> a) -> Int
5749 -- MEANS the illegal type
5750 g :: forall a. (Ord a => a -> a) -> Int
5752 g :: (forall a. Ord a => a -> a) -> Int
5754 The latter produces an illegal type, which you might think is silly,
5755 but at least the rule is simple. If you want the latter type, you
5756 can write your for-alls explicitly. Indeed, doing so is strongly advised
5763 <sect2 id="impredicative-polymorphism">
5764 <title>Impredicative polymorphism
5766 <para><emphasis>NOTE: the impredicative-polymorphism feature is deprecated in GHC 6.12, and
5767 will be removed or replaced in GHC 6.14.</emphasis></para>
5769 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5770 enabled with <option>-XImpredicativeTypes</option>.
5772 that you can call a polymorphic function at a polymorphic type, and
5773 parameterise data structures over polymorphic types. For example:
5775 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5776 f (Just g) = Just (g [3], g "hello")
5779 Notice here that the <literal>Maybe</literal> type is parameterised by the
5780 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5783 <para>The technical details of this extension are described in the paper
5784 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5785 type inference for higher-rank types and impredicativity</ulink>,
5786 which appeared at ICFP 2006.
5790 <sect2 id="scoped-type-variables">
5791 <title>Lexically scoped type variables
5795 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5796 which some type signatures are simply impossible to write. For example:
5798 f :: forall a. [a] -> [a]
5804 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5805 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5806 The type variables bound by a <literal>forall</literal> scope over
5807 the entire definition of the accompanying value declaration.
5808 In this example, the type variable <literal>a</literal> scopes over the whole
5809 definition of <literal>f</literal>, including over
5810 the type signature for <varname>ys</varname>.
5811 In Haskell 98 it is not possible to declare
5812 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5813 it becomes possible to do so.
5815 <para>Lexically-scoped type variables are enabled by
5816 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5818 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5819 variables work, compared to earlier releases. Read this section
5823 <title>Overview</title>
5825 <para>The design follows the following principles
5827 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5828 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5829 design.)</para></listitem>
5830 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5831 type variables. This means that every programmer-written type signature
5832 (including one that contains free scoped type variables) denotes a
5833 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5834 checker, and no inference is involved.</para></listitem>
5835 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5836 changing the program.</para></listitem>
5840 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5842 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5843 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5844 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5845 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5849 In Haskell, a programmer-written type signature is implicitly quantified over
5850 its free type variables (<ulink
5851 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5853 of the Haskell Report).
5854 Lexically scoped type variables affect this implicit quantification rules
5855 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5856 quantified. For example, if type variable <literal>a</literal> is in scope,
5859 (e :: a -> a) means (e :: a -> a)
5860 (e :: b -> b) means (e :: forall b. b->b)
5861 (e :: a -> b) means (e :: forall b. a->b)
5869 <sect3 id="decl-type-sigs">
5870 <title>Declaration type signatures</title>
5871 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5872 quantification (using <literal>forall</literal>) brings into scope the
5873 explicitly-quantified
5874 type variables, in the definition of the named function. For example:
5876 f :: forall a. [a] -> [a]
5877 f (x:xs) = xs ++ [ x :: a ]
5879 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5880 the definition of "<literal>f</literal>".
5882 <para>This only happens if:
5884 <listitem><para> The quantification in <literal>f</literal>'s type
5885 signature is explicit. For example:
5888 g (x:xs) = xs ++ [ x :: a ]
5890 This program will be rejected, because "<literal>a</literal>" does not scope
5891 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5892 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5893 quantification rules.
5895 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5896 not a pattern binding.
5899 f1 :: forall a. [a] -> [a]
5900 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5902 f2 :: forall a. [a] -> [a]
5903 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5905 f3 :: forall a. [a] -> [a]
5906 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5908 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5909 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5910 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5911 the type signature brings <literal>a</literal> into scope.
5917 <sect3 id="exp-type-sigs">
5918 <title>Expression type signatures</title>
5920 <para>An expression type signature that has <emphasis>explicit</emphasis>
5921 quantification (using <literal>forall</literal>) brings into scope the
5922 explicitly-quantified
5923 type variables, in the annotated expression. For example:
5925 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5927 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5928 type variable <literal>s</literal> into scope, in the annotated expression
5929 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5934 <sect3 id="pattern-type-sigs">
5935 <title>Pattern type signatures</title>
5937 A type signature may occur in any pattern; this is a <emphasis>pattern type
5938 signature</emphasis>.
5941 -- f and g assume that 'a' is already in scope
5942 f = \(x::Int, y::a) -> x
5944 h ((x,y) :: (Int,Bool)) = (y,x)
5946 In the case where all the type variables in the pattern type signature are
5947 already in scope (i.e. bound by the enclosing context), matters are simple: the
5948 signature simply constrains the type of the pattern in the obvious way.
5951 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5952 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5953 that are already in scope. For example:
5955 f :: forall a. [a] -> (Int, [a])
5958 (ys::[a], n) = (reverse xs, length xs) -- OK
5959 zs::[a] = xs ++ ys -- OK
5961 Just (v::b) = ... -- Not OK; b is not in scope
5963 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5964 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5968 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5969 type signature may mention a type variable that is not in scope; in this case,
5970 <emphasis>the signature brings that type variable into scope</emphasis>.
5971 This is particularly important for existential data constructors. For example:
5973 data T = forall a. MkT [a]
5976 k (MkT [t::a]) = MkT t3
5980 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5981 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5982 because it is bound by the pattern match. GHC's rule is that in this situation
5983 (and only then), a pattern type signature can mention a type variable that is
5984 not already in scope; the effect is to bring it into scope, standing for the
5985 existentially-bound type variable.
5988 When a pattern type signature binds a type variable in this way, GHC insists that the
5989 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5990 This means that any user-written type signature always stands for a completely known type.
5993 If all this seems a little odd, we think so too. But we must have
5994 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5995 could not name existentially-bound type variables in subsequent type signatures.
5998 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5999 signature is allowed to mention a lexical variable that is not already in
6001 For example, both <literal>f</literal> and <literal>g</literal> would be
6002 illegal if <literal>a</literal> was not already in scope.
6008 <!-- ==================== Commented out part about result type signatures
6010 <sect3 id="result-type-sigs">
6011 <title>Result type signatures</title>
6014 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
6017 {- f assumes that 'a' is already in scope -}
6018 f x y :: [a] = [x,y,x]
6020 g = \ x :: [Int] -> [3,4]
6022 h :: forall a. [a] -> a
6026 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
6027 the result of the function. Similarly, the body of the lambda in the RHS of
6028 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
6029 alternative in <literal>h</literal> is <literal>a</literal>.
6031 <para> A result type signature never brings new type variables into scope.</para>
6033 There are a couple of syntactic wrinkles. First, notice that all three
6034 examples would parse quite differently with parentheses:
6036 {- f assumes that 'a' is already in scope -}
6037 f x (y :: [a]) = [x,y,x]
6039 g = \ (x :: [Int]) -> [3,4]
6041 h :: forall a. [a] -> a
6045 Now the signature is on the <emphasis>pattern</emphasis>; and
6046 <literal>h</literal> would certainly be ill-typed (since the pattern
6047 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6049 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6050 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6051 token or a parenthesised type of some sort). To see why,
6052 consider how one would parse this:
6061 <sect3 id="cls-inst-scoped-tyvars">
6062 <title>Class and instance declarations</title>
6065 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6066 scope over the methods defined in the <literal>where</literal> part. For example:
6084 <sect2 id="typing-binds">
6085 <title>Generalised typing of mutually recursive bindings</title>
6088 The Haskell Report specifies that a group of bindings (at top level, or in a
6089 <literal>let</literal> or <literal>where</literal>) should be sorted into
6090 strongly-connected components, and then type-checked in dependency order
6091 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6092 Report, Section 4.5.1</ulink>).
6093 As each group is type-checked, any binders of the group that
6095 an explicit type signature are put in the type environment with the specified
6097 and all others are monomorphic until the group is generalised
6098 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6101 <para>Following a suggestion of Mark Jones, in his paper
6102 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6104 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6106 <emphasis>the dependency analysis ignores references to variables that have an explicit
6107 type signature</emphasis>.
6108 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6109 typecheck. For example, consider:
6111 f :: Eq a => a -> Bool
6112 f x = (x == x) || g True || g "Yes"
6114 g y = (y <= y) || f True
6116 This is rejected by Haskell 98, but under Jones's scheme the definition for
6117 <literal>g</literal> is typechecked first, separately from that for
6118 <literal>f</literal>,
6119 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6120 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6121 type is generalised, to get
6123 g :: Ord a => a -> Bool
6125 Now, the definition for <literal>f</literal> is typechecked, with this type for
6126 <literal>g</literal> in the type environment.
6130 The same refined dependency analysis also allows the type signatures of
6131 mutually-recursive functions to have different contexts, something that is illegal in
6132 Haskell 98 (Section 4.5.2, last sentence). With
6133 <option>-XRelaxedPolyRec</option>
6134 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6135 type signatures; in practice this means that only variables bound by the same
6136 pattern binding must have the same context. For example, this is fine:
6138 f :: Eq a => a -> Bool
6139 f x = (x == x) || g True
6141 g :: Ord a => a -> Bool
6142 g y = (y <= y) || f True
6147 <sect2 id="mono-local-binds">
6148 <title>Monomorphic local bindings</title>
6150 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6151 The rationale is described in the paper
6152 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6155 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6156 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6157 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6158 If you supply a type signature, then the flag has no effect.
6163 <!-- ==================== End of type system extensions ================= -->
6165 <!-- ====================== TEMPLATE HASKELL ======================= -->
6167 <sect1 id="template-haskell">
6168 <title>Template Haskell</title>
6170 <para>Template Haskell allows you to do compile-time meta-programming in
6173 the main technical innovations is discussed in "<ulink
6174 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6175 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6178 There is a Wiki page about
6179 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6180 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6184 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6185 Haskell library reference material</ulink>
6186 (look for module <literal>Language.Haskell.TH</literal>).
6187 Many changes to the original design are described in
6188 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6189 Notes on Template Haskell version 2</ulink>.
6190 Not all of these changes are in GHC, however.
6193 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6194 as a worked example to help get you started.
6198 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6199 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6204 <title>Syntax</title>
6206 <para> Template Haskell has the following new syntactic
6207 constructions. You need to use the flag
6208 <option>-XTemplateHaskell</option>
6209 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6210 </indexterm>to switch these syntactic extensions on
6211 (<option>-XTemplateHaskell</option> is no longer implied by
6212 <option>-fglasgow-exts</option>).</para>
6216 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6217 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6218 There must be no space between the "$" and the identifier or parenthesis. This use
6219 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6220 of "." as an infix operator. If you want the infix operator, put spaces around it.
6222 <para> A splice can occur in place of
6224 <listitem><para> an expression; the spliced expression must
6225 have type <literal>Q Exp</literal></para></listitem>
6226 <listitem><para> an type; the spliced expression must
6227 have type <literal>Q Typ</literal></para></listitem>
6228 <listitem><para> a list of top-level declarations; the spliced expression
6229 must have type <literal>Q [Dec]</literal></para></listitem>
6231 Note that pattern splices are not supported.
6232 Inside a splice you can can only call functions defined in imported modules,
6233 not functions defined elsewhere in the same module.</para></listitem>
6236 A expression quotation is written in Oxford brackets, thus:
6238 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6239 where the "..." is an expression;
6240 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6241 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6242 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6243 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6244 the quotation has type <literal>Q Type</literal>.</para></listitem>
6245 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6246 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6247 </itemizedlist></para></listitem>
6250 A quasi-quotation can appear in either a pattern context or an
6251 expression context and is also written in Oxford brackets:
6253 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6254 where the "..." is an arbitrary string; a full description of the
6255 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6256 </itemizedlist></para></listitem>
6259 A name can be quoted with either one or two prefix single quotes:
6261 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6262 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6263 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6265 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6266 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6269 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6270 may also be given as an argument to the <literal>reify</literal> function.
6274 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6275 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6282 $(deriveStuff 'f) -- Uses the $(...) notation
6286 deriveStuff 'g -- Omits the $(...)
6290 This abbreviation makes top-level declaration slices quieter and less intimidating.
6295 (Compared to the original paper, there are many differences of detail.
6296 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6297 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6298 Pattern splices and quotations are not implemented.)
6302 <sect2> <title> Using Template Haskell </title>
6306 The data types and monadic constructor functions for Template Haskell are in the library
6307 <literal>Language.Haskell.THSyntax</literal>.
6311 You can only run a function at compile time if it is imported from another module. That is,
6312 you can't define a function in a module, and call it from within a splice in the same module.
6313 (It would make sense to do so, but it's hard to implement.)
6317 You can only run a function at compile time if it is imported
6318 from another module <emphasis>that is not part of a mutually-recursive group of modules
6319 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6320 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6321 splice is to be run.</para>
6323 For example, when compiling module A,
6324 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6325 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6329 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6332 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6333 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6334 compiles and runs a program, and then looks at the result. So it's important that
6335 the program it compiles produces results whose representations are identical to
6336 those of the compiler itself.
6340 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6341 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6346 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6347 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6348 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6355 -- Import our template "pr"
6356 import Printf ( pr )
6358 -- The splice operator $ takes the Haskell source code
6359 -- generated at compile time by "pr" and splices it into
6360 -- the argument of "putStrLn".
6361 main = putStrLn ( $(pr "Hello") )
6367 -- Skeletal printf from the paper.
6368 -- It needs to be in a separate module to the one where
6369 -- you intend to use it.
6371 -- Import some Template Haskell syntax
6372 import Language.Haskell.TH
6374 -- Describe a format string
6375 data Format = D | S | L String
6377 -- Parse a format string. This is left largely to you
6378 -- as we are here interested in building our first ever
6379 -- Template Haskell program and not in building printf.
6380 parse :: String -> [Format]
6383 -- Generate Haskell source code from a parsed representation
6384 -- of the format string. This code will be spliced into
6385 -- the module which calls "pr", at compile time.
6386 gen :: [Format] -> Q Exp
6387 gen [D] = [| \n -> show n |]
6388 gen [S] = [| \s -> s |]
6389 gen [L s] = stringE s
6391 -- Here we generate the Haskell code for the splice
6392 -- from an input format string.
6393 pr :: String -> Q Exp
6394 pr s = gen (parse s)
6397 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6400 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6403 <para>Run "main.exe" and here is your output:</para>
6413 <title>Using Template Haskell with Profiling</title>
6414 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6416 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6417 interpreter to run the splice expressions. The bytecode interpreter
6418 runs the compiled expression on top of the same runtime on which GHC
6419 itself is running; this means that the compiled code referred to by
6420 the interpreted expression must be compatible with this runtime, and
6421 in particular this means that object code that is compiled for
6422 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6423 expression, because profiled object code is only compatible with the
6424 profiling version of the runtime.</para>
6426 <para>This causes difficulties if you have a multi-module program
6427 containing Template Haskell code and you need to compile it for
6428 profiling, because GHC cannot load the profiled object code and use it
6429 when executing the splices. Fortunately GHC provides a workaround.
6430 The basic idea is to compile the program twice:</para>
6434 <para>Compile the program or library first the normal way, without
6435 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6438 <para>Then compile it again with <option>-prof</option>, and
6439 additionally use <option>-osuf
6440 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6441 to name the object files differently (you can choose any suffix
6442 that isn't the normal object suffix here). GHC will automatically
6443 load the object files built in the first step when executing splice
6444 expressions. If you omit the <option>-osuf</option> flag when
6445 building with <option>-prof</option> and Template Haskell is used,
6446 GHC will emit an error message. </para>
6451 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6452 <para>Quasi-quotation allows patterns and expressions to be written using
6453 programmer-defined concrete syntax; the motivation behind the extension and
6454 several examples are documented in
6455 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6456 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6457 2007). The example below shows how to write a quasiquoter for a simple
6458 expression language.</para>
6460 Here are the salient features
6463 A quasi-quote has the form
6464 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6467 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6468 quoter; it cannot be an arbitrary expression.
6471 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6472 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6473 those overlap with Template Haskell quotations.
6476 There must be no spaces in the token
6477 <literal>[<replaceable>quoter</replaceable>|</literal>.
6480 The quoted <replaceable>string</replaceable>
6481 can be arbitrary, and may contain newlines.
6487 A quasiquote may appear in place of
6489 <listitem><para>An expression</para></listitem>
6490 <listitem><para>A pattern</para></listitem>
6491 <listitem><para>A type</para></listitem>
6492 <listitem><para>A top-level declaration</para></listitem>
6494 (Only the first two are described in the paper.)
6498 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6499 which is defined thus:
6501 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6502 quotePat :: String -> Q Pat,
6503 quoteType :: String -> Q Type,
6504 quoteDec :: String -> Q [Dec] }
6506 That is, a quoter is a tuple of four parsers, one for each of the contexts
6507 in which a quasi-quote can occur.
6510 A quasi-quote is expanded by applying the appropriate parser to the string
6511 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6512 type, declaration) determines which of the parsers is called.
6517 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6518 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6519 The example makes use of an antiquoted
6520 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6521 (this syntax for anti-quotation was defined by the parser's
6522 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6523 integer value argument of the constructor <literal>IntExpr</literal> when
6524 pattern matching. Please see the referenced paper for further details regarding
6525 anti-quotation as well as the description of a technique that uses SYB to
6526 leverage a single parser of type <literal>String -> a</literal> to generate both
6527 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6528 pattern parser that returns a value of type <literal>Q Pat</literal>.
6532 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6533 the example, <literal>expr</literal> cannot be defined
6534 in <literal>Main.hs</literal> where it is used, but must be imported.
6538 {- ------------- file Main.hs --------------- -}
6544 main = do { print $ eval [expr|1 + 2|]
6546 { [expr|'int:n|] -> print n
6552 {- ------------- file Expr.hs --------------- -}
6555 import qualified Language.Haskell.TH as TH
6556 import Language.Haskell.TH.Quote
6558 data Expr = IntExpr Integer
6559 | AntiIntExpr String
6560 | BinopExpr BinOp Expr Expr
6562 deriving(Show, Typeable, Data)
6568 deriving(Show, Typeable, Data)
6570 eval :: Expr -> Integer
6571 eval (IntExpr n) = n
6572 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6579 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6581 -- Parse an Expr, returning its representation as
6582 -- either a Q Exp or a Q Pat. See the referenced paper
6583 -- for how to use SYB to do this by writing a single
6584 -- parser of type String -> Expr instead of two
6585 -- separate parsers.
6587 parseExprExp :: String -> Q Exp
6590 parseExprPat :: String -> Q Pat
6594 <para>Now run the compiler:
6596 $ ghc --make -XQuasiQuotes Main.hs -o main
6600 <para>Run "main" and here is your output:
6611 <!-- ===================== Arrow notation =================== -->
6613 <sect1 id="arrow-notation">
6614 <title>Arrow notation
6617 <para>Arrows are a generalization of monads introduced by John Hughes.
6618 For more details, see
6623 “Generalising Monads to Arrows”,
6624 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6625 pp67–111, May 2000.
6626 The paper that introduced arrows: a friendly introduction, motivated with
6627 programming examples.
6633 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6634 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6635 Introduced the notation described here.
6641 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6642 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6649 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6650 John Hughes, in <citetitle>5th International Summer School on
6651 Advanced Functional Programming</citetitle>,
6652 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6654 This paper includes another introduction to the notation,
6655 with practical examples.
6661 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6662 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6663 A terse enumeration of the formal rules used
6664 (extracted from comments in the source code).
6670 The arrows web page at
6671 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6676 With the <option>-XArrows</option> flag, GHC supports the arrow
6677 notation described in the second of these papers,
6678 translating it using combinators from the
6679 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6681 What follows is a brief introduction to the notation;
6682 it won't make much sense unless you've read Hughes's paper.
6685 <para>The extension adds a new kind of expression for defining arrows:
6687 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6688 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6690 where <literal>proc</literal> is a new keyword.
6691 The variables of the pattern are bound in the body of the
6692 <literal>proc</literal>-expression,
6693 which is a new sort of thing called a <firstterm>command</firstterm>.
6694 The syntax of commands is as follows:
6696 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6697 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6698 | <replaceable>cmd</replaceable><superscript>0</superscript>
6700 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6701 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6702 infix operators as for expressions, and
6704 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6705 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6706 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6707 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6708 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6709 | <replaceable>fcmd</replaceable>
6711 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6712 | ( <replaceable>cmd</replaceable> )
6713 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6715 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6716 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6717 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6718 | <replaceable>cmd</replaceable>
6720 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6721 except that the bodies are commands instead of expressions.
6725 Commands produce values, but (like monadic computations)
6726 may yield more than one value,
6727 or none, and may do other things as well.
6728 For the most part, familiarity with monadic notation is a good guide to
6730 However the values of expressions, even monadic ones,
6731 are determined by the values of the variables they contain;
6732 this is not necessarily the case for commands.
6736 A simple example of the new notation is the expression
6738 proc x -> f -< x+1
6740 We call this a <firstterm>procedure</firstterm> or
6741 <firstterm>arrow abstraction</firstterm>.
6742 As with a lambda expression, the variable <literal>x</literal>
6743 is a new variable bound within the <literal>proc</literal>-expression.
6744 It refers to the input to the arrow.
6745 In the above example, <literal>-<</literal> is not an identifier but an
6746 new reserved symbol used for building commands from an expression of arrow
6747 type and an expression to be fed as input to that arrow.
6748 (The weird look will make more sense later.)
6749 It may be read as analogue of application for arrows.
6750 The above example is equivalent to the Haskell expression
6752 arr (\ x -> x+1) >>> f
6754 That would make no sense if the expression to the left of
6755 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6756 More generally, the expression to the left of <literal>-<</literal>
6757 may not involve any <firstterm>local variable</firstterm>,
6758 i.e. a variable bound in the current arrow abstraction.
6759 For such a situation there is a variant <literal>-<<</literal>, as in
6761 proc x -> f x -<< x+1
6763 which is equivalent to
6765 arr (\ x -> (f x, x+1)) >>> app
6767 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6769 Such an arrow is equivalent to a monad, so if you're using this form
6770 you may find a monadic formulation more convenient.
6774 <title>do-notation for commands</title>
6777 Another form of command is a form of <literal>do</literal>-notation.
6778 For example, you can write
6787 You can read this much like ordinary <literal>do</literal>-notation,
6788 but with commands in place of monadic expressions.
6789 The first line sends the value of <literal>x+1</literal> as an input to
6790 the arrow <literal>f</literal>, and matches its output against
6791 <literal>y</literal>.
6792 In the next line, the output is discarded.
6793 The arrow <function>returnA</function> is defined in the
6794 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6795 module as <literal>arr id</literal>.
6796 The above example is treated as an abbreviation for
6798 arr (\ x -> (x, x)) >>>
6799 first (arr (\ x -> x+1) >>> f) >>>
6800 arr (\ (y, x) -> (y, (x, y))) >>>
6801 first (arr (\ y -> 2*y) >>> g) >>>
6803 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6804 first (arr (\ (x, z) -> x*z) >>> h) >>>
6805 arr (\ (t, z) -> t+z) >>>
6808 Note that variables not used later in the composition are projected out.
6809 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6811 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6812 module, this reduces to
6814 arr (\ x -> (x+1, x)) >>>
6816 arr (\ (y, x) -> (2*y, (x, y))) >>>
6818 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6820 arr (\ (t, z) -> t+z)
6822 which is what you might have written by hand.
6823 With arrow notation, GHC keeps track of all those tuples of variables for you.
6827 Note that although the above translation suggests that
6828 <literal>let</literal>-bound variables like <literal>z</literal> must be
6829 monomorphic, the actual translation produces Core,
6830 so polymorphic variables are allowed.
6834 It's also possible to have mutually recursive bindings,
6835 using the new <literal>rec</literal> keyword, as in the following example:
6837 counter :: ArrowCircuit a => a Bool Int
6838 counter = proc reset -> do
6839 rec output <- returnA -< if reset then 0 else next
6840 next <- delay 0 -< output+1
6841 returnA -< output
6843 The translation of such forms uses the <function>loop</function> combinator,
6844 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6850 <title>Conditional commands</title>
6853 In the previous example, we used a conditional expression to construct the
6855 Sometimes we want to conditionally execute different commands, as in
6862 which is translated to
6864 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6865 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6867 Since the translation uses <function>|||</function>,
6868 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6872 There are also <literal>case</literal> commands, like
6878 y <- h -< (x1, x2)
6882 The syntax is the same as for <literal>case</literal> expressions,
6883 except that the bodies of the alternatives are commands rather than expressions.
6884 The translation is similar to that of <literal>if</literal> commands.
6890 <title>Defining your own control structures</title>
6893 As we're seen, arrow notation provides constructs,
6894 modelled on those for expressions,
6895 for sequencing, value recursion and conditionals.
6896 But suitable combinators,
6897 which you can define in ordinary Haskell,
6898 may also be used to build new commands out of existing ones.
6899 The basic idea is that a command defines an arrow from environments to values.
6900 These environments assign values to the free local variables of the command.
6901 Thus combinators that produce arrows from arrows
6902 may also be used to build commands from commands.
6903 For example, the <literal>ArrowChoice</literal> class includes a combinator
6905 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6907 so we can use it to build commands:
6909 expr' = proc x -> do
6912 symbol Plus -< ()
6913 y <- term -< ()
6916 symbol Minus -< ()
6917 y <- term -< ()
6920 (The <literal>do</literal> on the first line is needed to prevent the first
6921 <literal><+> ...</literal> from being interpreted as part of the
6922 expression on the previous line.)
6923 This is equivalent to
6925 expr' = (proc x -> returnA -< x)
6926 <+> (proc x -> do
6927 symbol Plus -< ()
6928 y <- term -< ()
6930 <+> (proc x -> do
6931 symbol Minus -< ()
6932 y <- term -< ()
6935 It is essential that this operator be polymorphic in <literal>e</literal>
6936 (representing the environment input to the command
6937 and thence to its subcommands)
6938 and satisfy the corresponding naturality property
6940 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6942 at least for strict <literal>k</literal>.
6943 (This should be automatic if you're not using <function>seq</function>.)
6944 This ensures that environments seen by the subcommands are environments
6945 of the whole command,
6946 and also allows the translation to safely trim these environments.
6947 The operator must also not use any variable defined within the current
6952 We could define our own operator
6954 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6955 untilA body cond = proc x ->
6956 b <- cond -< x
6957 if b then returnA -< ()
6960 untilA body cond -< x
6962 and use it in the same way.
6963 Of course this infix syntax only makes sense for binary operators;
6964 there is also a more general syntax involving special brackets:
6968 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6975 <title>Primitive constructs</title>
6978 Some operators will need to pass additional inputs to their subcommands.
6979 For example, in an arrow type supporting exceptions,
6980 the operator that attaches an exception handler will wish to pass the
6981 exception that occurred to the handler.
6982 Such an operator might have a type
6984 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6986 where <literal>Ex</literal> is the type of exceptions handled.
6987 You could then use this with arrow notation by writing a command
6989 body `handleA` \ ex -> handler
6991 so that if an exception is raised in the command <literal>body</literal>,
6992 the variable <literal>ex</literal> is bound to the value of the exception
6993 and the command <literal>handler</literal>,
6994 which typically refers to <literal>ex</literal>, is entered.
6995 Though the syntax here looks like a functional lambda,
6996 we are talking about commands, and something different is going on.
6997 The input to the arrow represented by a command consists of values for
6998 the free local variables in the command, plus a stack of anonymous values.
6999 In all the prior examples, this stack was empty.
7000 In the second argument to <function>handleA</function>,
7001 this stack consists of one value, the value of the exception.
7002 The command form of lambda merely gives this value a name.
7007 the values on the stack are paired to the right of the environment.
7008 So operators like <function>handleA</function> that pass
7009 extra inputs to their subcommands can be designed for use with the notation
7010 by pairing the values with the environment in this way.
7011 More precisely, the type of each argument of the operator (and its result)
7012 should have the form
7014 a (...(e,t1), ... tn) t
7016 where <replaceable>e</replaceable> is a polymorphic variable
7017 (representing the environment)
7018 and <replaceable>ti</replaceable> are the types of the values on the stack,
7019 with <replaceable>t1</replaceable> being the <quote>top</quote>.
7020 The polymorphic variable <replaceable>e</replaceable> must not occur in
7021 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
7022 <replaceable>t</replaceable>.
7023 However the arrows involved need not be the same.
7024 Here are some more examples of suitable operators:
7026 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
7027 runReader :: ... => a e c -> a' (e,State) c
7028 runState :: ... => a e c -> a' (e,State) (c,State)
7030 We can supply the extra input required by commands built with the last two
7031 by applying them to ordinary expressions, as in
7035 (|runReader (do { ... })|) s
7037 which adds <literal>s</literal> to the stack of inputs to the command
7038 built using <function>runReader</function>.
7042 The command versions of lambda abstraction and application are analogous to
7043 the expression versions.
7044 In particular, the beta and eta rules describe equivalences of commands.
7045 These three features (operators, lambda abstraction and application)
7046 are the core of the notation; everything else can be built using them,
7047 though the results would be somewhat clumsy.
7048 For example, we could simulate <literal>do</literal>-notation by defining
7050 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7051 u `bind` f = returnA &&& u >>> f
7053 bind_ :: Arrow a => a e b -> a e c -> a e c
7054 u `bind_` f = u `bind` (arr fst >>> f)
7056 We could simulate <literal>if</literal> by defining
7058 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7059 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7066 <title>Differences with the paper</title>
7071 <para>Instead of a single form of arrow application (arrow tail) with two
7072 translations, the implementation provides two forms
7073 <quote><literal>-<</literal></quote> (first-order)
7074 and <quote><literal>-<<</literal></quote> (higher-order).
7079 <para>User-defined operators are flagged with banana brackets instead of
7080 a new <literal>form</literal> keyword.
7089 <title>Portability</title>
7092 Although only GHC implements arrow notation directly,
7093 there is also a preprocessor
7095 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7096 that translates arrow notation into Haskell 98
7097 for use with other Haskell systems.
7098 You would still want to check arrow programs with GHC;
7099 tracing type errors in the preprocessor output is not easy.
7100 Modules intended for both GHC and the preprocessor must observe some
7101 additional restrictions:
7106 The module must import
7107 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7113 The preprocessor cannot cope with other Haskell extensions.
7114 These would have to go in separate modules.
7120 Because the preprocessor targets Haskell (rather than Core),
7121 <literal>let</literal>-bound variables are monomorphic.
7132 <!-- ==================== BANG PATTERNS ================= -->
7134 <sect1 id="bang-patterns">
7135 <title>Bang patterns
7136 <indexterm><primary>Bang patterns</primary></indexterm>
7138 <para>GHC supports an extension of pattern matching called <emphasis>bang
7139 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7140 Bang patterns are under consideration for Haskell Prime.
7142 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7143 prime feature description</ulink> contains more discussion and examples
7144 than the material below.
7147 The key change is the addition of a new rule to the
7148 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7149 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7150 against a value <replaceable>v</replaceable> behaves as follows:
7152 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7153 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7157 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7160 <sect2 id="bang-patterns-informal">
7161 <title>Informal description of bang patterns
7164 The main idea is to add a single new production to the syntax of patterns:
7168 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7169 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7174 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7175 whereas without the bang it would be lazy.
7176 Bang patterns can be nested of course:
7180 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7181 <literal>y</literal>.
7182 A bang only really has an effect if it precedes a variable or wild-card pattern:
7187 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7188 putting a bang before a pattern that
7189 forces evaluation anyway does nothing.
7192 There is one (apparent) exception to this general rule that a bang only
7193 makes a difference when it precedes a variable or wild-card: a bang at the
7194 top level of a <literal>let</literal> or <literal>where</literal>
7195 binding makes the binding strict, regardless of the pattern. For example:
7199 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7200 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7201 (We say "apparent" exception because the Right Way to think of it is that the bang
7202 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7203 is part of the syntax of the <emphasis>binding</emphasis>.)
7204 Nested bangs in a pattern binding behave uniformly with all other forms of
7205 pattern matching. For example
7207 let (!x,[y]) = e in b
7209 is equivalent to this:
7211 let { t = case e of (x,[y]) -> x `seq` (x,y)
7216 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7217 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7218 evaluation of <literal>x</literal>.
7221 Bang patterns work in <literal>case</literal> expressions too, of course:
7223 g5 x = let y = f x in body
7224 g6 x = case f x of { y -> body }
7225 g7 x = case f x of { !y -> body }
7227 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7228 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7229 result, and then evaluates <literal>body</literal>.
7234 <sect2 id="bang-patterns-sem">
7235 <title>Syntax and semantics
7239 We add a single new production to the syntax of patterns:
7243 There is one problem with syntactic ambiguity. Consider:
7247 Is this a definition of the infix function "<literal>(!)</literal>",
7248 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7249 ambiguity in favour of the latter. If you want to define
7250 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7255 The semantics of Haskell pattern matching is described in <ulink
7256 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7257 Section 3.17.2</ulink> of the Haskell Report. To this description add
7258 one extra item 10, saying:
7259 <itemizedlist><listitem><para>Matching
7260 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7261 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7262 <listitem><para>otherwise, <literal>pat</literal> is matched against
7263 <literal>v</literal></para></listitem>
7265 </para></listitem></itemizedlist>
7266 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7267 Section 3.17.3</ulink>, add a new case (t):
7269 case v of { !pat -> e; _ -> e' }
7270 = v `seq` case v of { pat -> e; _ -> e' }
7273 That leaves let expressions, whose translation is given in
7274 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7276 of the Haskell Report.
7277 In the translation box, first apply
7278 the following transformation: for each pattern <literal>pi</literal> that is of
7279 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7280 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7281 have a bang at the top, apply the rules in the existing box.
7283 <para>The effect of the let rule is to force complete matching of the pattern
7284 <literal>qi</literal> before evaluation of the body is begun. The bang is
7285 retained in the translated form in case <literal>qi</literal> is a variable,
7293 The let-binding can be recursive. However, it is much more common for
7294 the let-binding to be non-recursive, in which case the following law holds:
7295 <literal>(let !p = rhs in body)</literal>
7297 <literal>(case rhs of !p -> body)</literal>
7300 A pattern with a bang at the outermost level is not allowed at the top level of
7306 <!-- ==================== ASSERTIONS ================= -->
7308 <sect1 id="assertions">
7310 <indexterm><primary>Assertions</primary></indexterm>
7314 If you want to make use of assertions in your standard Haskell code, you
7315 could define a function like the following:
7321 assert :: Bool -> a -> a
7322 assert False x = error "assertion failed!"
7329 which works, but gives you back a less than useful error message --
7330 an assertion failed, but which and where?
7334 One way out is to define an extended <function>assert</function> function which also
7335 takes a descriptive string to include in the error message and
7336 perhaps combine this with the use of a pre-processor which inserts
7337 the source location where <function>assert</function> was used.
7341 Ghc offers a helping hand here, doing all of this for you. For every
7342 use of <function>assert</function> in the user's source:
7348 kelvinToC :: Double -> Double
7349 kelvinToC k = assert (k >= 0.0) (k+273.15)
7355 Ghc will rewrite this to also include the source location where the
7362 assert pred val ==> assertError "Main.hs|15" pred val
7368 The rewrite is only performed by the compiler when it spots
7369 applications of <function>Control.Exception.assert</function>, so you
7370 can still define and use your own versions of
7371 <function>assert</function>, should you so wish. If not, import
7372 <literal>Control.Exception</literal> to make use
7373 <function>assert</function> in your code.
7377 GHC ignores assertions when optimisation is turned on with the
7378 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7379 <literal>assert pred e</literal> will be rewritten to
7380 <literal>e</literal>. You can also disable assertions using the
7381 <option>-fignore-asserts</option>
7382 option<indexterm><primary><option>-fignore-asserts</option></primary>
7383 </indexterm>.</para>
7386 Assertion failures can be caught, see the documentation for the
7387 <literal>Control.Exception</literal> library for the details.
7393 <!-- =============================== PRAGMAS =========================== -->
7395 <sect1 id="pragmas">
7396 <title>Pragmas</title>
7398 <indexterm><primary>pragma</primary></indexterm>
7400 <para>GHC supports several pragmas, or instructions to the
7401 compiler placed in the source code. Pragmas don't normally affect
7402 the meaning of the program, but they might affect the efficiency
7403 of the generated code.</para>
7405 <para>Pragmas all take the form
7407 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7409 where <replaceable>word</replaceable> indicates the type of
7410 pragma, and is followed optionally by information specific to that
7411 type of pragma. Case is ignored in
7412 <replaceable>word</replaceable>. The various values for
7413 <replaceable>word</replaceable> that GHC understands are described
7414 in the following sections; any pragma encountered with an
7415 unrecognised <replaceable>word</replaceable> is
7416 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7417 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7419 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7423 pragma must precede the <literal>module</literal> keyword in the file.
7426 There can be as many file-header pragmas as you please, and they can be
7427 preceded or followed by comments.
7430 File-header pragmas are read once only, before
7431 pre-processing the file (e.g. with cpp).
7434 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7435 <literal>{-# OPTIONS_GHC #-}</literal>, and
7436 <literal>{-# INCLUDE #-}</literal>.
7441 <sect2 id="language-pragma">
7442 <title>LANGUAGE pragma</title>
7444 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7445 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7447 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7449 It is the intention that all Haskell compilers support the
7450 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7451 all extensions are supported by all compilers, of
7452 course. The <literal>LANGUAGE</literal> pragma should be used instead
7453 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7455 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7457 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7459 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7461 <para>Every language extension can also be turned into a command-line flag
7462 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7463 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7466 <para>A list of all supported language extensions can be obtained by invoking
7467 <literal>ghc --supported-extensions</literal> (see <xref linkend="modes"/>).</para>
7469 <para>Any extension from the <literal>Extension</literal> type defined in
7471 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7472 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7476 <sect2 id="options-pragma">
7477 <title>OPTIONS_GHC pragma</title>
7478 <indexterm><primary>OPTIONS_GHC</primary>
7480 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7483 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7484 additional options that are given to the compiler when compiling
7485 this source file. See <xref linkend="source-file-options"/> for
7488 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7489 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7492 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7494 <sect2 id="include-pragma">
7495 <title>INCLUDE pragma</title>
7497 <para>The <literal>INCLUDE</literal> used to be necessary for
7498 specifying header files to be included when using the FFI and
7499 compiling via C. It is no longer required for GHC, but is
7500 accepted (and ignored) for compatibility with other
7504 <sect2 id="warning-deprecated-pragma">
7505 <title>WARNING and DEPRECATED pragmas</title>
7506 <indexterm><primary>WARNING</primary></indexterm>
7507 <indexterm><primary>DEPRECATED</primary></indexterm>
7509 <para>The WARNING pragma allows you to attach an arbitrary warning
7510 to a particular function, class, or type.
7511 A DEPRECATED pragma lets you specify that
7512 a particular function, class, or type is deprecated.
7513 There are two ways of using these pragmas.
7517 <para>You can work on an entire module thus:</para>
7519 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7524 module Wibble {-# WARNING "This is an unstable interface." #-} where
7527 <para>When you compile any module that import
7528 <literal>Wibble</literal>, GHC will print the specified
7533 <para>You can attach a warning to a function, class, type, or data constructor, with the
7534 following top-level declarations:</para>
7536 {-# DEPRECATED f, C, T "Don't use these" #-}
7537 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7539 <para>When you compile any module that imports and uses any
7540 of the specified entities, GHC will print the specified
7542 <para> You can only attach to entities declared at top level in the module
7543 being compiled, and you can only use unqualified names in the list of
7544 entities. A capitalised name, such as <literal>T</literal>
7545 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7546 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7547 both are in scope. If both are in scope, there is currently no way to
7548 specify one without the other (c.f. fixities
7549 <xref linkend="infix-tycons"/>).</para>
7552 Warnings and deprecations are not reported for
7553 (a) uses within the defining module, and
7554 (b) uses in an export list.
7555 The latter reduces spurious complaints within a library
7556 in which one module gathers together and re-exports
7557 the exports of several others.
7559 <para>You can suppress the warnings with the flag
7560 <option>-fno-warn-warnings-deprecations</option>.</para>
7563 <sect2 id="inline-noinline-pragma">
7564 <title>INLINE and NOINLINE pragmas</title>
7566 <para>These pragmas control the inlining of function
7569 <sect3 id="inline-pragma">
7570 <title>INLINE pragma</title>
7571 <indexterm><primary>INLINE</primary></indexterm>
7573 <para>GHC (with <option>-O</option>, as always) tries to
7574 inline (or “unfold”) functions/values that are
7575 “small enough,” thus avoiding the call overhead
7576 and possibly exposing other more-wonderful optimisations.
7577 Normally, if GHC decides a function is “too
7578 expensive” to inline, it will not do so, nor will it
7579 export that unfolding for other modules to use.</para>
7581 <para>The sledgehammer you can bring to bear is the
7582 <literal>INLINE</literal><indexterm><primary>INLINE
7583 pragma</primary></indexterm> pragma, used thusly:</para>
7586 key_function :: Int -> String -> (Bool, Double)
7587 {-# INLINE key_function #-}
7590 <para>The major effect of an <literal>INLINE</literal> pragma
7591 is to declare a function's “cost” to be very low.
7592 The normal unfolding machinery will then be very keen to
7593 inline it. However, an <literal>INLINE</literal> pragma for a
7594 function "<literal>f</literal>" has a number of other effects:
7597 While GHC is keen to inline the function, it does not do so
7598 blindly. For example, if you write
7602 there really isn't any point in inlining <literal>key_function</literal> to get
7604 map (\x -> <replaceable>body</replaceable>) xs
7606 In general, GHC only inlines the function if there is some reason (no matter
7607 how slight) to supose that it is useful to do so.
7611 Moreover, GHC will only inline the function if it is <emphasis>fully applied</emphasis>,
7612 where "fully applied"
7613 means applied to as many arguments as appear (syntactically)
7614 on the LHS of the function
7615 definition. For example:
7617 comp1 :: (b -> c) -> (a -> b) -> a -> c
7618 {-# INLINE comp1 #-}
7619 comp1 f g = \x -> f (g x)
7621 comp2 :: (b -> c) -> (a -> b) -> a -> c
7622 {-# INLINE comp2 #-}
7623 comp2 f g x = f (g x)
7625 The two functions <literal>comp1</literal> and <literal>comp2</literal> have the
7626 same semantics, but <literal>comp1</literal> will be inlined when applied
7627 to <emphasis>two</emphasis> arguments, while <literal>comp2</literal> requires
7628 <emphasis>three</emphasis>. This might make a big difference if you say
7630 map (not `comp1` not) xs
7632 which will optimise better than the corresponding use of `comp2`.
7636 It is useful for GHC to optimise the definition of an
7637 INLINE function <literal>f</literal> just like any other non-INLINE function,
7638 in case the non-inlined version of <literal>f</literal> is
7639 ultimately called. But we don't want to inline
7640 the <emphasis>optimised</emphasis> version
7641 of <literal>f</literal>;
7642 a major reason for INLINE pragmas is to expose functions
7643 in <literal>f</literal>'s RHS that have
7644 rewrite rules, and it's no good if those functions have been optimised
7648 So <emphasis>GHC guarantees to inline precisely the code that you wrote</emphasis>, no more
7649 and no less. It does this by capturing a copy of the definition of the function to use
7650 for inlining (we call this the "inline-RHS"), which it leaves untouched,
7651 while optimising the ordinarly RHS as usual. For externally-visible functions
7652 the inline-RHS (not the optimised RHS) is recorded in the interface file.
7655 An INLINE function is not worker/wrappered by strictness analysis.
7656 It's going to be inlined wholesale instead.
7660 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7661 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7662 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7663 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7664 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7665 when there is no choice even an INLINE function can be selected, in which case
7666 the INLINE pragma is ignored.
7667 For example, for a self-recursive function, the loop breaker can only be the function
7668 itself, so an INLINE pragma is always ignored.</para>
7670 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7671 function can be put anywhere its type signature could be
7674 <para><literal>INLINE</literal> pragmas are a particularly
7676 <literal>then</literal>/<literal>return</literal> (or
7677 <literal>bind</literal>/<literal>unit</literal>) functions in
7678 a monad. For example, in GHC's own
7679 <literal>UniqueSupply</literal> monad code, we have:</para>
7682 {-# INLINE thenUs #-}
7683 {-# INLINE returnUs #-}
7686 <para>See also the <literal>NOINLINE</literal> (<xref linkend="inlinable-pragma"/>)
7687 and <literal>INLINABLE</literal> (<xref linkend="noinline-pragma"/>)
7690 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7691 so if you want your code to be HBC-compatible you'll have to surround
7692 the pragma with C pre-processor directives
7693 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7697 <sect3 id="inlinable-pragma">
7698 <title>INLINABLE pragma</title>
7700 <para>An INLINABLE pragma works very like an INLINE pragma, except that:
7703 INLINE says "please inline me", but INLINABLE says "feel free to inline me; use your
7704 discretion". In other words the choice is left to GHC, which uses the same
7705 rules as for pragma-free functions. Unlike INLINE, That decision is made at
7706 the <emphasis>call site</emphasis>, and
7707 will therefore be affected by the inlining threshold, optimisation level etc.
7710 Like INLINE, the INLINABLE pragma retains a copy of the original RHS for
7711 inlining purposes, and persists it in the interface file, regardless of
7712 the size of the RHS.
7715 If you use the special function <literal>inline</literal> (<xref linkend="special-ids"/>)
7716 to force inlining at a
7717 call site, you will get a copy of the the original RHS.
7718 Indeed, if you intend to use <literal>inline f</literal> it
7719 is a good idea to mark the definition of <literal>f</literal> INLINABLE,
7720 so that GHC guarantees to expose an unfolding regardless of how big it is.
7727 <sect3 id="noinline-pragma">
7728 <title>NOINLINE pragma</title>
7730 <indexterm><primary>NOINLINE</primary></indexterm>
7731 <indexterm><primary>NOTINLINE</primary></indexterm>
7733 <para>The <literal>NOINLINE</literal> pragma does exactly what
7734 you'd expect: it stops the named function from being inlined
7735 by the compiler. You shouldn't ever need to do this, unless
7736 you're very cautious about code size.</para>
7738 <para><literal>NOTINLINE</literal> is a synonym for
7739 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7740 specified by Haskell 98 as the standard way to disable
7741 inlining, so it should be used if you want your code to be
7745 <sect3 id="conlike-pragma">
7746 <title>CONLIKE modifier</title>
7747 <indexterm><primary>CONLIKE</primary></indexterm>
7748 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7749 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7753 <sect3 id="phase-control">
7754 <title>Phase control</title>
7756 <para> Sometimes you want to control exactly when in GHC's
7757 pipeline the INLINE pragma is switched on. Inlining happens
7758 only during runs of the <emphasis>simplifier</emphasis>. Each
7759 run of the simplifier has a different <emphasis>phase
7760 number</emphasis>; the phase number decreases towards zero.
7761 If you use <option>-dverbose-core2core</option> you'll see the
7762 sequence of phase numbers for successive runs of the
7763 simplifier. In an INLINE pragma you can optionally specify a
7767 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7768 <literal>f</literal>
7769 until phase <literal>k</literal>, but from phase
7770 <literal>k</literal> onwards be very keen to inline it.
7773 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7774 <literal>f</literal>
7775 until phase <literal>k</literal>, but from phase
7776 <literal>k</literal> onwards do not inline it.
7779 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7780 <literal>f</literal>
7781 until phase <literal>k</literal>, but from phase
7782 <literal>k</literal> onwards be willing to inline it (as if
7783 there was no pragma).
7786 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7787 <literal>f</literal>
7788 until phase <literal>k</literal>, but from phase
7789 <literal>k</literal> onwards do not inline it.
7792 The same information is summarised here:
7794 -- Before phase 2 Phase 2 and later
7795 {-# INLINE [2] f #-} -- No Yes
7796 {-# INLINE [~2] f #-} -- Yes No
7797 {-# NOINLINE [2] f #-} -- No Maybe
7798 {-# NOINLINE [~2] f #-} -- Maybe No
7800 {-# INLINE f #-} -- Yes Yes
7801 {-# NOINLINE f #-} -- No No
7803 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7804 function body is small, or it is applied to interesting-looking arguments etc).
7805 Another way to understand the semantics is this:
7807 <listitem><para>For both INLINE and NOINLINE, the phase number says
7808 when inlining is allowed at all.</para></listitem>
7809 <listitem><para>The INLINE pragma has the additional effect of making the
7810 function body look small, so that when inlining is allowed it is very likely to
7815 <para>The same phase-numbering control is available for RULES
7816 (<xref linkend="rewrite-rules"/>).</para>
7820 <sect2 id="annotation-pragmas">
7821 <title>ANN pragmas</title>
7823 <para>GHC offers the ability to annotate various code constructs with additional
7824 data by using three pragmas. This data can then be inspected at a later date by
7825 using GHC-as-a-library.</para>
7827 <sect3 id="ann-pragma">
7828 <title>Annotating values</title>
7830 <indexterm><primary>ANN</primary></indexterm>
7832 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7833 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7834 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7835 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7836 you would do this:</para>
7839 {-# ANN foo (Just "Hello") #-}
7844 A number of restrictions apply to use of annotations:
7846 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7847 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7848 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7849 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7850 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7852 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7853 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7856 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7857 please give the GHC team a shout</ulink>.
7860 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7861 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7864 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7869 <sect3 id="typeann-pragma">
7870 <title>Annotating types</title>
7872 <indexterm><primary>ANN type</primary></indexterm>
7873 <indexterm><primary>ANN</primary></indexterm>
7875 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7878 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7883 <sect3 id="modann-pragma">
7884 <title>Annotating modules</title>
7886 <indexterm><primary>ANN module</primary></indexterm>
7887 <indexterm><primary>ANN</primary></indexterm>
7889 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7892 {-# ANN module (Just "A `Maybe String' annotation") #-}
7897 <sect2 id="line-pragma">
7898 <title>LINE pragma</title>
7900 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7901 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7902 <para>This pragma is similar to C's <literal>#line</literal>
7903 pragma, and is mainly for use in automatically generated Haskell
7904 code. It lets you specify the line number and filename of the
7905 original code; for example</para>
7907 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7909 <para>if you'd generated the current file from something called
7910 <filename>Foo.vhs</filename> and this line corresponds to line
7911 42 in the original. GHC will adjust its error messages to refer
7912 to the line/file named in the <literal>LINE</literal>
7917 <title>RULES pragma</title>
7919 <para>The RULES pragma lets you specify rewrite rules. It is
7920 described in <xref linkend="rewrite-rules"/>.</para>
7923 <sect2 id="specialize-pragma">
7924 <title>SPECIALIZE pragma</title>
7926 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7927 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7928 <indexterm><primary>overloading, death to</primary></indexterm>
7930 <para>(UK spelling also accepted.) For key overloaded
7931 functions, you can create extra versions (NB: more code space)
7932 specialised to particular types. Thus, if you have an
7933 overloaded function:</para>
7936 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7939 <para>If it is heavily used on lists with
7940 <literal>Widget</literal> keys, you could specialise it as
7944 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7947 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7948 be put anywhere its type signature could be put.</para>
7950 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7951 (a) a specialised version of the function and (b) a rewrite rule
7952 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7953 un-specialised function into a call to the specialised one.</para>
7955 <para>The type in a SPECIALIZE pragma can be any type that is less
7956 polymorphic than the type of the original function. In concrete terms,
7957 if the original function is <literal>f</literal> then the pragma
7959 {-# SPECIALIZE f :: <type> #-}
7961 is valid if and only if the definition
7963 f_spec :: <type>
7966 is valid. Here are some examples (where we only give the type signature
7967 for the original function, not its code):
7969 f :: Eq a => a -> b -> b
7970 {-# SPECIALISE f :: Int -> b -> b #-}
7972 g :: (Eq a, Ix b) => a -> b -> b
7973 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7975 h :: Eq a => a -> a -> a
7976 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7978 The last of these examples will generate a
7979 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7980 well. If you use this kind of specialisation, let us know how well it works.
7983 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7984 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7985 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7986 The <literal>INLINE</literal> pragma affects the specialised version of the
7987 function (only), and applies even if the function is recursive. The motivating
7990 -- A GADT for arrays with type-indexed representation
7992 ArrInt :: !Int -> ByteArray# -> Arr Int
7993 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7995 (!:) :: Arr e -> Int -> e
7996 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7997 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7998 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7999 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
8001 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
8002 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
8003 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
8004 the specialised function will be inlined. It has two calls to
8005 <literal>(!:)</literal>,
8006 both at type <literal>Int</literal>. Both these calls fire the first
8007 specialisation, whose body is also inlined. The result is a type-based
8008 unrolling of the indexing function.</para>
8009 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
8010 on an ordinarily-recursive function.</para>
8012 <para>Note: In earlier versions of GHC, it was possible to provide your own
8013 specialised function for a given type:
8016 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
8019 This feature has been removed, as it is now subsumed by the
8020 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
8024 <sect2 id="specialize-instance-pragma">
8025 <title>SPECIALIZE instance pragma
8029 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
8030 <indexterm><primary>overloading, death to</primary></indexterm>
8031 Same idea, except for instance declarations. For example:
8034 instance (Eq a) => Eq (Foo a) where {
8035 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
8039 The pragma must occur inside the <literal>where</literal> part
8040 of the instance declaration.
8043 Compatible with HBC, by the way, except perhaps in the placement
8049 <sect2 id="unpack-pragma">
8050 <title>UNPACK pragma</title>
8052 <indexterm><primary>UNPACK</primary></indexterm>
8054 <para>The <literal>UNPACK</literal> indicates to the compiler
8055 that it should unpack the contents of a constructor field into
8056 the constructor itself, removing a level of indirection. For
8060 data T = T {-# UNPACK #-} !Float
8061 {-# UNPACK #-} !Float
8064 <para>will create a constructor <literal>T</literal> containing
8065 two unboxed floats. This may not always be an optimisation: if
8066 the <function>T</function> constructor is scrutinised and the
8067 floats passed to a non-strict function for example, they will
8068 have to be reboxed (this is done automatically by the
8071 <para>Unpacking constructor fields should only be used in
8072 conjunction with <option>-O</option>, in order to expose
8073 unfoldings to the compiler so the reboxing can be removed as
8074 often as possible. For example:</para>
8078 f (T f1 f2) = f1 + f2
8081 <para>The compiler will avoid reboxing <function>f1</function>
8082 and <function>f2</function> by inlining <function>+</function>
8083 on floats, but only when <option>-O</option> is on.</para>
8085 <para>Any single-constructor data is eligible for unpacking; for
8089 data T = T {-# UNPACK #-} !(Int,Int)
8092 <para>will store the two <literal>Int</literal>s directly in the
8093 <function>T</function> constructor, by flattening the pair.
8094 Multi-level unpacking is also supported:
8097 data T = T {-# UNPACK #-} !S
8098 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8101 will store two unboxed <literal>Int#</literal>s
8102 directly in the <function>T</function> constructor. The
8103 unpacker can see through newtypes, too.</para>
8105 <para>See also the <option>-funbox-strict-fields</option> flag,
8106 which essentially has the effect of adding
8107 <literal>{-# UNPACK #-}</literal> to every strict
8108 constructor field.</para>
8111 <sect2 id="source-pragma">
8112 <title>SOURCE pragma</title>
8114 <indexterm><primary>SOURCE</primary></indexterm>
8115 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8116 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8122 <!-- ======================= REWRITE RULES ======================== -->
8124 <sect1 id="rewrite-rules">
8125 <title>Rewrite rules
8127 <indexterm><primary>RULES pragma</primary></indexterm>
8128 <indexterm><primary>pragma, RULES</primary></indexterm>
8129 <indexterm><primary>rewrite rules</primary></indexterm></title>
8132 The programmer can specify rewrite rules as part of the source program
8138 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8143 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8144 If you need more information, then <option>-ddump-rule-firings</option> shows you
8145 each individual rule firing in detail.
8149 <title>Syntax</title>
8152 From a syntactic point of view:
8158 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8159 may be generated by the layout rule).
8165 The layout rule applies in a pragma.
8166 Currently no new indentation level
8167 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8168 you must lay out the starting in the same column as the enclosing definitions.
8171 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8172 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8175 Furthermore, the closing <literal>#-}</literal>
8176 should start in a column to the right of the opening <literal>{-#</literal>.
8182 Each rule has a name, enclosed in double quotes. The name itself has
8183 no significance at all. It is only used when reporting how many times the rule fired.
8189 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8190 immediately after the name of the rule. Thus:
8193 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8196 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8197 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8206 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8207 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8208 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8209 by spaces, just like in a type <literal>forall</literal>.
8215 A pattern variable may optionally have a type signature.
8216 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8217 For example, here is the <literal>foldr/build</literal> rule:
8220 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8221 foldr k z (build g) = g k z
8224 Since <function>g</function> has a polymorphic type, it must have a type signature.
8231 The left hand side of a rule must consist of a top-level variable applied
8232 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8235 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8236 "wrong2" forall f. f True = True
8239 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8246 A rule does not need to be in the same module as (any of) the
8247 variables it mentions, though of course they need to be in scope.
8253 All rules are implicitly exported from the module, and are therefore
8254 in force in any module that imports the module that defined the rule, directly
8255 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8256 in force when compiling A.) The situation is very similar to that for instance
8264 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8265 any other flag settings. Furthermore, inside a RULE, the language extension
8266 <option>-XScopedTypeVariables</option> is automatically enabled; see
8267 <xref linkend="scoped-type-variables"/>.
8273 Like other pragmas, RULE pragmas are always checked for scope errors, and
8274 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8275 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8276 if the <option>-fenable-rewrite-rules</option> flag is
8277 on (see <xref linkend="rule-semantics"/>).
8286 <sect2 id="rule-semantics">
8287 <title>Semantics</title>
8290 From a semantic point of view:
8295 Rules are enabled (that is, used during optimisation)
8296 by the <option>-fenable-rewrite-rules</option> flag.
8297 This flag is implied by <option>-O</option>, and may be switched
8298 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8299 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8300 may not do what you expect, though, because without <option>-O</option> GHC
8301 ignores all optimisation information in interface files;
8302 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8303 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8304 has no effect on parsing or typechecking.
8310 Rules are regarded as left-to-right rewrite rules.
8311 When GHC finds an expression that is a substitution instance of the LHS
8312 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8313 By "a substitution instance" we mean that the LHS can be made equal to the
8314 expression by substituting for the pattern variables.
8321 GHC makes absolutely no attempt to verify that the LHS and RHS
8322 of a rule have the same meaning. That is undecidable in general, and
8323 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8330 GHC makes no attempt to make sure that the rules are confluent or
8331 terminating. For example:
8334 "loop" forall x y. f x y = f y x
8337 This rule will cause the compiler to go into an infinite loop.
8344 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8350 GHC currently uses a very simple, syntactic, matching algorithm
8351 for matching a rule LHS with an expression. It seeks a substitution
8352 which makes the LHS and expression syntactically equal modulo alpha
8353 conversion. The pattern (rule), but not the expression, is eta-expanded if
8354 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8355 But not beta conversion (that's called higher-order matching).
8359 Matching is carried out on GHC's intermediate language, which includes
8360 type abstractions and applications. So a rule only matches if the
8361 types match too. See <xref linkend="rule-spec"/> below.
8367 GHC keeps trying to apply the rules as it optimises the program.
8368 For example, consider:
8377 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8378 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8379 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8380 not be substituted, and the rule would not fire.
8390 <sect2 id="conlike">
8391 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8394 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8395 results. Consider this (artificial) example
8401 {-# RULES "f" f True = False #-}
8403 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8408 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8410 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8411 would have been a better chance that <literal>f</literal>'s RULE might fire.
8414 The way to get predictable behaviour is to use a NOINLINE
8415 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8416 that it is not inlined until its RULEs have had a chance to fire.
8419 GHC is very cautious about duplicating work. For example, consider
8421 f k z xs = let xs = build g
8422 in ...(foldr k z xs)...sum xs...
8423 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8425 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8426 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8427 duplicated if the rule fired.
8430 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8431 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8432 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8434 {-# INLINE[1] CONLIKE f #-}
8435 f x = <replaceable>blah</replaceable>
8437 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8438 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8439 should be considered cheap enough to duplicate, if such a duplication would make rule
8440 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8441 have such a property.)
8442 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8443 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8444 not going to be inlined before the rule has a chance to fire.
8449 <title>List fusion</title>
8452 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8453 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8454 intermediate list should be eliminated entirely.
8458 The following are good producers:
8470 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8476 Explicit lists (e.g. <literal>[True, False]</literal>)
8482 The cons constructor (e.g <literal>3:4:[]</literal>)
8488 <function>++</function>
8494 <function>map</function>
8500 <function>take</function>, <function>filter</function>
8506 <function>iterate</function>, <function>repeat</function>
8512 <function>zip</function>, <function>zipWith</function>
8521 The following are good consumers:
8533 <function>array</function> (on its second argument)
8539 <function>++</function> (on its first argument)
8545 <function>foldr</function>
8551 <function>map</function>
8557 <function>take</function>, <function>filter</function>
8563 <function>concat</function>
8569 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8575 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8576 will fuse with one but not the other)
8582 <function>partition</function>
8588 <function>head</function>
8594 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8600 <function>sequence_</function>
8606 <function>msum</function>
8612 <function>sortBy</function>
8621 So, for example, the following should generate no intermediate lists:
8624 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8630 This list could readily be extended; if there are Prelude functions that you use
8631 a lot which are not included, please tell us.
8635 If you want to write your own good consumers or producers, look at the
8636 Prelude definitions of the above functions to see how to do so.
8641 <sect2 id="rule-spec">
8642 <title>Specialisation
8646 Rewrite rules can be used to get the same effect as a feature
8647 present in earlier versions of GHC.
8648 For example, suppose that:
8651 genericLookup :: Ord a => Table a b -> a -> b
8652 intLookup :: Table Int b -> Int -> b
8655 where <function>intLookup</function> is an implementation of
8656 <function>genericLookup</function> that works very fast for
8657 keys of type <literal>Int</literal>. You might wish
8658 to tell GHC to use <function>intLookup</function> instead of
8659 <function>genericLookup</function> whenever the latter was called with
8660 type <literal>Table Int b -> Int -> b</literal>.
8661 It used to be possible to write
8664 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8667 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8670 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8673 This slightly odd-looking rule instructs GHC to replace
8674 <function>genericLookup</function> by <function>intLookup</function>
8675 <emphasis>whenever the types match</emphasis>.
8676 What is more, this rule does not need to be in the same
8677 file as <function>genericLookup</function>, unlike the
8678 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8679 have an original definition available to specialise).
8682 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8683 <function>intLookup</function> really behaves as a specialised version
8684 of <function>genericLookup</function>!!!</para>
8686 <para>An example in which using <literal>RULES</literal> for
8687 specialisation will Win Big:
8690 toDouble :: Real a => a -> Double
8691 toDouble = fromRational . toRational
8693 {-# RULES "toDouble/Int" toDouble = i2d #-}
8694 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8697 The <function>i2d</function> function is virtually one machine
8698 instruction; the default conversion—via an intermediate
8699 <literal>Rational</literal>—is obscenely expensive by
8705 <sect2 id="controlling-rules">
8706 <title>Controlling what's going on in rewrite rules</title>
8714 Use <option>-ddump-rules</option> to see the rules that are defined
8715 <emphasis>in this module</emphasis>.
8716 This includes rules generated by the specialisation pass, but excludes
8717 rules imported from other modules.
8723 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8724 If you add <option>-dppr-debug</option> you get a more detailed listing.
8730 Use <option>-ddump-rule-firings</option> to see in great detail what rules are being fired.
8731 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8737 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8740 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8741 {-# INLINE build #-}
8745 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8746 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8747 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8748 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8755 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8756 see how to write rules that will do fusion and yet give an efficient
8757 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8767 <sect2 id="core-pragma">
8768 <title>CORE pragma</title>
8770 <indexterm><primary>CORE pragma</primary></indexterm>
8771 <indexterm><primary>pragma, CORE</primary></indexterm>
8772 <indexterm><primary>core, annotation</primary></indexterm>
8775 The external core format supports <quote>Note</quote> annotations;
8776 the <literal>CORE</literal> pragma gives a way to specify what these
8777 should be in your Haskell source code. Syntactically, core
8778 annotations are attached to expressions and take a Haskell string
8779 literal as an argument. The following function definition shows an
8783 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8786 Semantically, this is equivalent to:
8794 However, when external core is generated (via
8795 <option>-fext-core</option>), there will be Notes attached to the
8796 expressions <function>show</function> and <varname>x</varname>.
8797 The core function declaration for <function>f</function> is:
8801 f :: %forall a . GHCziShow.ZCTShow a ->
8802 a -> GHCziBase.ZMZN GHCziBase.Char =
8803 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8805 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8807 (tpl1::GHCziBase.Int ->
8809 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8811 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8812 (tpl3::GHCziBase.ZMZN a ->
8813 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8821 Here, we can see that the function <function>show</function> (which
8822 has been expanded out to a case expression over the Show dictionary)
8823 has a <literal>%note</literal> attached to it, as does the
8824 expression <varname>eta</varname> (which used to be called
8825 <varname>x</varname>).
8832 <sect1 id="special-ids">
8833 <title>Special built-in functions</title>
8834 <para>GHC has a few built-in functions with special behaviour. These
8835 are now described in the module <ulink
8836 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8837 in the library documentation.
8841 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Ainline"><literal>inline</literal></ulink>
8842 allows control over inlining on a per-call-site basis.
8845 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Alazy"><literal>lazy</literal></ulink>
8846 restrains the strictness analyser.
8849 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3AunsafeCoerce%23"><literal>lazy</literal></ulink>
8850 allows you to fool the type checker.
8857 <sect1 id="generic-classes">
8858 <title>Generic classes</title>
8861 The ideas behind this extension are described in detail in "Derivable type classes",
8862 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8863 An example will give the idea:
8871 fromBin :: [Int] -> (a, [Int])
8873 toBin {| Unit |} Unit = []
8874 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8875 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8876 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8878 fromBin {| Unit |} bs = (Unit, bs)
8879 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8880 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8881 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8882 (y,bs'') = fromBin bs'
8885 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8886 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8887 which are defined thus in the library module <literal>Generics</literal>:
8891 data a :+: b = Inl a | Inr b
8892 data a :*: b = a :*: b
8895 Now you can make a data type into an instance of Bin like this:
8897 instance (Bin a, Bin b) => Bin (a,b)
8898 instance Bin a => Bin [a]
8900 That is, just leave off the "where" clause. Of course, you can put in the
8901 where clause and over-ride whichever methods you please.
8905 <title> Using generics </title>
8906 <para>To use generics you need to</para>
8909 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8910 <option>-XGenerics</option> (to generate extra per-data-type code),
8911 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8915 <para>Import the module <literal>Generics</literal> from the
8916 <literal>lang</literal> package. This import brings into
8917 scope the data types <literal>Unit</literal>,
8918 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8919 don't need this import if you don't mention these types
8920 explicitly; for example, if you are simply giving instance
8921 declarations.)</para>
8926 <sect2> <title> Changes wrt the paper </title>
8928 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8929 can be written infix (indeed, you can now use
8930 any operator starting in a colon as an infix type constructor). Also note that
8931 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8932 Finally, note that the syntax of the type patterns in the class declaration
8933 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8934 alone would ambiguous when they appear on right hand sides (an extension we
8935 anticipate wanting).
8939 <sect2> <title>Terminology and restrictions</title>
8941 Terminology. A "generic default method" in a class declaration
8942 is one that is defined using type patterns as above.
8943 A "polymorphic default method" is a default method defined as in Haskell 98.
8944 A "generic class declaration" is a class declaration with at least one
8945 generic default method.
8953 Alas, we do not yet implement the stuff about constructor names and
8960 A generic class can have only one parameter; you can't have a generic
8961 multi-parameter class.
8967 A default method must be defined entirely using type patterns, or entirely
8968 without. So this is illegal:
8971 op :: a -> (a, Bool)
8972 op {| Unit |} Unit = (Unit, True)
8975 However it is perfectly OK for some methods of a generic class to have
8976 generic default methods and others to have polymorphic default methods.
8982 The type variable(s) in the type pattern for a generic method declaration
8983 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:
8987 op {| p :*: q |} (x :*: y) = op (x :: p)
8995 The type patterns in a generic default method must take one of the forms:
9001 where "a" and "b" are type variables. Furthermore, all the type patterns for
9002 a single type constructor (<literal>:*:</literal>, say) must be identical; they
9003 must use the same type variables. So this is illegal:
9007 op {| a :+: b |} (Inl x) = True
9008 op {| p :+: q |} (Inr y) = False
9010 The type patterns must be identical, even in equations for different methods of the class.
9011 So this too is illegal:
9015 op1 {| a :*: b |} (x :*: y) = True
9018 op2 {| p :*: q |} (x :*: y) = False
9020 (The reason for this restriction is that we gather all the equations for a particular type constructor
9021 into a single generic instance declaration.)
9027 A generic method declaration must give a case for each of the three type constructors.
9033 The type for a generic method can be built only from:
9035 <listitem> <para> Function arrows </para> </listitem>
9036 <listitem> <para> Type variables </para> </listitem>
9037 <listitem> <para> Tuples </para> </listitem>
9038 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
9040 Here are some example type signatures for generic methods:
9043 op2 :: Bool -> (a,Bool)
9044 op3 :: [Int] -> a -> a
9047 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
9051 This restriction is an implementation restriction: we just haven't got around to
9052 implementing the necessary bidirectional maps over arbitrary type constructors.
9053 It would be relatively easy to add specific type constructors, such as Maybe and list,
9054 to the ones that are allowed.</para>
9059 In an instance declaration for a generic class, the idea is that the compiler
9060 will fill in the methods for you, based on the generic templates. However it can only
9065 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
9070 No constructor of the instance type has unboxed fields.
9074 (Of course, these things can only arise if you are already using GHC extensions.)
9075 However, you can still give an instance declarations for types which break these rules,
9076 provided you give explicit code to override any generic default methods.
9084 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9085 what the compiler does with generic declarations.
9090 <sect2> <title> Another example </title>
9092 Just to finish with, here's another example I rather like:
9096 nCons {| Unit |} _ = 1
9097 nCons {| a :*: b |} _ = 1
9098 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9101 tag {| Unit |} _ = 1
9102 tag {| a :*: b |} _ = 1
9103 tag {| a :+: b |} (Inl x) = tag x
9104 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9110 <sect1 id="monomorphism">
9111 <title>Control over monomorphism</title>
9113 <para>GHC supports two flags that control the way in which generalisation is
9114 carried out at let and where bindings.
9118 <title>Switching off the dreaded Monomorphism Restriction</title>
9119 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9121 <para>Haskell's monomorphism restriction (see
9122 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9124 of the Haskell Report)
9125 can be completely switched off by
9126 <option>-XNoMonomorphismRestriction</option>.
9131 <title>Monomorphic pattern bindings</title>
9132 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9133 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9135 <para> As an experimental change, we are exploring the possibility of
9136 making pattern bindings monomorphic; that is, not generalised at all.
9137 A pattern binding is a binding whose LHS has no function arguments,
9138 and is not a simple variable. For example:
9140 f x = x -- Not a pattern binding
9141 f = \x -> x -- Not a pattern binding
9142 f :: Int -> Int = \x -> x -- Not a pattern binding
9144 (g,h) = e -- A pattern binding
9145 (f) = e -- A pattern binding
9146 [x] = e -- A pattern binding
9148 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9149 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
9158 ;;; Local Variables: ***
9159 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
9160 ;;; ispell-local-dictionary: "british" ***
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