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 can all be enabled or disabled by commandline flags
7 or language pragmas. By default GHC understands the most recent Haskell
8 version it supports, plus a handful of extensions.
12 Some of the Glasgow extensions serve to give you access to the
13 underlying facilities with which we implement Haskell. Thus, you can
14 get at the Raw Iron, if you are willing to write some non-portable
15 code at a more primitive level. You need not be “stuck”
16 on performance because of the implementation costs of Haskell's
17 “high-level” features—you can always code
18 “under” them. In an extreme case, you can write all your
19 time-critical code in C, and then just glue it together with Haskell!
23 Before you get too carried away working at the lowest level (e.g.,
24 sloshing <literal>MutableByteArray#</literal>s around your
25 program), you may wish to check if there are libraries that provide a
26 “Haskellised veneer” over the features you want. The
27 separate <ulink url="../libraries/index.html">libraries
28 documentation</ulink> describes all the libraries that come with GHC.
31 <!-- LANGUAGE OPTIONS -->
32 <sect1 id="options-language">
33 <title>Language options</title>
35 <indexterm><primary>language</primary><secondary>option</secondary>
37 <indexterm><primary>options</primary><secondary>language</secondary>
39 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
42 <para>The language option flags control what variation of the language are
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 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 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 (without NewQualifiedOperators 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 (without NewQualifiedOperators 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 without NewQualifiedOperators 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
484 syntax for qualified operators is not accepted, so this
485 option may cause existing 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>-XRebindableSyntax</option>
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>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1295 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1299 <para>"Do" notation is translated using whatever
1300 functions <literal>(>>=)</literal>,
1301 <literal>(>>)</literal>, and <literal>fail</literal>,
1302 are in scope (not the Prelude
1303 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1304 comprehensions, are unaffected. </para></listitem>
1308 notation (see <xref linkend="arrow-notation"/>)
1309 uses whatever <literal>arr</literal>,
1310 <literal>(>>>)</literal>, <literal>first</literal>,
1311 <literal>app</literal>, <literal>(|||)</literal> and
1312 <literal>loop</literal> functions are in scope. But unlike the
1313 other constructs, the types of these functions must match the
1314 Prelude types very closely. Details are in flux; if you want
1318 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1321 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1322 even if that is a little unexpected. For example, the
1323 static semantics of the literal <literal>368</literal>
1324 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1325 <literal>fromInteger</literal> to have any of the types:
1327 fromInteger :: Integer -> Integer
1328 fromInteger :: forall a. Foo a => Integer -> a
1329 fromInteger :: Num a => a -> Integer
1330 fromInteger :: Integer -> Bool -> Bool
1334 <para>Be warned: this is an experimental facility, with
1335 fewer checks than usual. Use <literal>-dcore-lint</literal>
1336 to typecheck the desugared program. If Core Lint is happy
1337 you should be all right.</para>
1341 <sect2 id="postfix-operators">
1342 <title>Postfix operators</title>
1345 The <option>-XPostfixOperators</option> flag enables a small
1346 extension to the syntax of left operator sections, which allows you to
1347 define postfix operators. The extension is this: the left section
1351 is equivalent (from the point of view of both type checking and execution) to the expression
1355 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1356 The strict Haskell 98 interpretation is that the section is equivalent to
1360 That is, the operator must be a function of two arguments. GHC allows it to
1361 take only one argument, and that in turn allows you to write the function
1364 <para>The extension does not extend to the left-hand side of function
1365 definitions; you must define such a function in prefix form.</para>
1369 <sect2 id="tuple-sections">
1370 <title>Tuple sections</title>
1373 The <option>-XTupleSections</option> flag enables Python-style partially applied
1374 tuple constructors. For example, the following program
1378 is considered to be an alternative notation for the more unwieldy alternative
1382 You can omit any combination of arguments to the tuple, as in the following
1384 (, "I", , , "Love", , 1337)
1388 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1393 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1394 will also be available for them, like so
1398 Because there is no unboxed unit tuple, the following expression
1402 continues to stand for the unboxed singleton tuple data constructor.
1407 <sect2 id="disambiguate-fields">
1408 <title>Record field disambiguation</title>
1410 In record construction and record pattern matching
1411 it is entirely unambiguous which field is referred to, even if there are two different
1412 data types in scope with a common field name. For example:
1415 data S = MkS { x :: Int, y :: Bool }
1420 data T = MkT { x :: Int }
1422 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1423 ok2 n = MkT { x = n+1 } -- Unambiguous
1425 bad1 k = k { x = 3 } -- Ambiguous
1426 bad2 k = x k -- Ambiguous
1428 Even though there are two <literal>x</literal>'s in scope,
1429 it is clear that the <literal>x</literal> in the pattern in the
1430 definition of <literal>ok1</literal> can only mean the field
1431 <literal>x</literal> from type <literal>S</literal>. Similarly for
1432 the function <literal>ok2</literal>. However, in the record update
1433 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1434 it is not clear which of the two types is intended.
1437 Haskell 98 regards all four as ambiguous, but with the
1438 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1439 the former two. The rules are precisely the same as those for instance
1440 declarations in Haskell 98, where the method names on the left-hand side
1441 of the method bindings in an instance declaration refer unambiguously
1442 to the method of that class (provided they are in scope at all), even
1443 if there are other variables in scope with the same name.
1444 This reduces the clutter of qualified names when you import two
1445 records from different modules that use the same field name.
1451 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1456 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1461 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1462 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1463 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1466 import qualified M -- Note qualified
1468 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1470 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1471 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1472 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1473 is not. (In effect, it is qualified by the constructor.)
1480 <!-- ===================== Record puns =================== -->
1482 <sect2 id="record-puns">
1487 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1491 When using records, it is common to write a pattern that binds a
1492 variable with the same name as a record field, such as:
1495 data C = C {a :: Int}
1501 Record punning permits the variable name to be elided, so one can simply
1508 to mean the same pattern as above. That is, in a record pattern, the
1509 pattern <literal>a</literal> expands into the pattern <literal>a =
1510 a</literal> for the same name <literal>a</literal>.
1517 Record punning can also be used in an expression, writing, for example,
1523 let a = 1 in C {a = a}
1525 The expansion is purely syntactic, so the expanded right-hand side
1526 expression refers to the nearest enclosing variable that is spelled the
1527 same as the field name.
1531 Puns and other patterns can be mixed in the same record:
1533 data C = C {a :: Int, b :: Int}
1534 f (C {a, b = 4}) = a
1539 Puns can be used wherever record patterns occur (e.g. in
1540 <literal>let</literal> bindings or at the top-level).
1544 A pun on a qualified field name is expanded by stripping off the module qualifier.
1551 f (M.C {M.a = a}) = a
1553 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1554 is only in scope in qualified form.)
1562 <!-- ===================== Record wildcards =================== -->
1564 <sect2 id="record-wildcards">
1565 <title>Record wildcards
1569 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1570 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1574 For records with many fields, it can be tiresome to write out each field
1575 individually in a record pattern, as in
1577 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1578 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1583 Record wildcard syntax permits a "<literal>..</literal>" in a record
1584 pattern, where each elided field <literal>f</literal> is replaced by the
1585 pattern <literal>f = f</literal>. For example, the above pattern can be
1588 f (C {a = 1, ..}) = b + c + d
1596 Wildcards can be mixed with other patterns, including puns
1597 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1598 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1599 wherever record patterns occur, including in <literal>let</literal>
1600 bindings and at the top-level. For example, the top-level binding
1604 defines <literal>b</literal>, <literal>c</literal>, and
1605 <literal>d</literal>.
1609 Record wildcards can also be used in expressions, writing, for example,
1611 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1615 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1617 The expansion is purely syntactic, so the record wildcard
1618 expression refers to the nearest enclosing variables that are spelled
1619 the same as the omitted field names.
1623 The "<literal>..</literal>" expands to the missing
1624 <emphasis>in-scope</emphasis> record fields, where "in scope"
1625 includes both unqualified and qualified-only.
1626 Any fields that are not in scope are not filled in. For example
1629 data R = R { a,b,c :: Int }
1631 import qualified M( R(a,b) )
1634 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1635 omitting <literal>c</literal> since it is not in scope at all.
1642 <!-- ===================== Local fixity declarations =================== -->
1644 <sect2 id="local-fixity-declarations">
1645 <title>Local Fixity Declarations
1648 <para>A careful reading of the Haskell 98 Report reveals that fixity
1649 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1650 <literal>infixr</literal>) are permitted to appear inside local bindings
1651 such those introduced by <literal>let</literal> and
1652 <literal>where</literal>. However, the Haskell Report does not specify
1653 the semantics of such bindings very precisely.
1656 <para>In GHC, a fixity declaration may accompany a local binding:
1663 and the fixity declaration applies wherever the binding is in scope.
1664 For example, in a <literal>let</literal>, it applies in the right-hand
1665 sides of other <literal>let</literal>-bindings and the body of the
1666 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1667 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
1668 declarations of a <literal>let</literal> statement scope over other
1669 statements in the group, just as the bound name does.
1673 Moreover, a local fixity declaration *must* accompany a local binding of
1674 that name: it is not possible to revise the fixity of name bound
1677 let infixr 9 $ in ...
1680 Because local fixity declarations are technically Haskell 98, no flag is
1681 necessary to enable them.
1685 <sect2 id="package-imports">
1686 <title>Package-qualified imports</title>
1688 <para>With the <option>-XPackageImports</option> flag, GHC allows
1689 import declarations to be qualified by the package name that the
1690 module is intended to be imported from. For example:</para>
1693 import "network" Network.Socket
1696 <para>would import the module <literal>Network.Socket</literal> from
1697 the package <literal>network</literal> (any version). This may
1698 be used to disambiguate an import when the same module is
1699 available from multiple packages, or is present in both the
1700 current package being built and an external package.</para>
1702 <para>Note: you probably don't need to use this feature, it was
1703 added mainly so that we can build backwards-compatible versions of
1704 packages when APIs change. It can lead to fragile dependencies in
1705 the common case: modules occasionally move from one package to
1706 another, rendering any package-qualified imports broken.</para>
1709 <sect2 id="syntax-stolen">
1710 <title>Summary of stolen syntax</title>
1712 <para>Turning on an option that enables special syntax
1713 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1714 to compile, perhaps because it uses a variable name which has
1715 become a reserved word. This section lists the syntax that is
1716 "stolen" by language extensions.
1718 notation and nonterminal names from the Haskell 98 lexical syntax
1719 (see the Haskell 98 Report).
1720 We only list syntax changes here that might affect
1721 existing working programs (i.e. "stolen" syntax). Many of these
1722 extensions will also enable new context-free syntax, but in all
1723 cases programs written to use the new syntax would not be
1724 compilable without the option enabled.</para>
1726 <para>There are two classes of special
1731 <para>New reserved words and symbols: character sequences
1732 which are no longer available for use as identifiers in the
1736 <para>Other special syntax: sequences of characters that have
1737 a different meaning when this particular option is turned
1742 The following syntax is stolen:
1747 <literal>forall</literal>
1748 <indexterm><primary><literal>forall</literal></primary></indexterm>
1751 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1752 <option>-XScopedTypeVariables</option>,
1753 <option>-XLiberalTypeSynonyms</option>,
1754 <option>-XRank2Types</option>,
1755 <option>-XRankNTypes</option>,
1756 <option>-XPolymorphicComponents</option>,
1757 <option>-XExistentialQuantification</option>
1763 <literal>mdo</literal>
1764 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1767 Stolen by: <option>-XRecursiveDo</option>,
1773 <literal>foreign</literal>
1774 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1777 Stolen by: <option>-XForeignFunctionInterface</option>,
1783 <literal>rec</literal>,
1784 <literal>proc</literal>, <literal>-<</literal>,
1785 <literal>>-</literal>, <literal>-<<</literal>,
1786 <literal>>>-</literal>, and <literal>(|</literal>,
1787 <literal>|)</literal> brackets
1788 <indexterm><primary><literal>proc</literal></primary></indexterm>
1791 Stolen by: <option>-XArrows</option>,
1797 <literal>?<replaceable>varid</replaceable></literal>,
1798 <literal>%<replaceable>varid</replaceable></literal>
1799 <indexterm><primary>implicit parameters</primary></indexterm>
1802 Stolen by: <option>-XImplicitParams</option>,
1808 <literal>[|</literal>,
1809 <literal>[e|</literal>, <literal>[p|</literal>,
1810 <literal>[d|</literal>, <literal>[t|</literal>,
1811 <literal>$(</literal>,
1812 <literal>$<replaceable>varid</replaceable></literal>
1813 <indexterm><primary>Template Haskell</primary></indexterm>
1816 Stolen by: <option>-XTemplateHaskell</option>,
1822 <literal>[:<replaceable>varid</replaceable>|</literal>
1823 <indexterm><primary>quasi-quotation</primary></indexterm>
1826 Stolen by: <option>-XQuasiQuotes</option>,
1832 <replaceable>varid</replaceable>{<literal>#</literal>},
1833 <replaceable>char</replaceable><literal>#</literal>,
1834 <replaceable>string</replaceable><literal>#</literal>,
1835 <replaceable>integer</replaceable><literal>#</literal>,
1836 <replaceable>float</replaceable><literal>#</literal>,
1837 <replaceable>float</replaceable><literal>##</literal>,
1838 <literal>(#</literal>, <literal>#)</literal>,
1841 Stolen by: <option>-XMagicHash</option>,
1850 <!-- TYPE SYSTEM EXTENSIONS -->
1851 <sect1 id="data-type-extensions">
1852 <title>Extensions to data types and type synonyms</title>
1854 <sect2 id="nullary-types">
1855 <title>Data types with no constructors</title>
1857 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1858 a data type with no constructors. For example:</para>
1862 data T a -- T :: * -> *
1865 <para>Syntactically, the declaration lacks the "= constrs" part. The
1866 type can be parameterised over types of any kind, but if the kind is
1867 not <literal>*</literal> then an explicit kind annotation must be used
1868 (see <xref linkend="kinding"/>).</para>
1870 <para>Such data types have only one value, namely bottom.
1871 Nevertheless, they can be useful when defining "phantom types".</para>
1874 <sect2 id="datatype-contexts">
1875 <title>Data type contexts</title>
1877 <para>Haskell allows datatypes to be given contexts, e.g.</para>
1880 data Eq a => Set a = NilSet | ConsSet a (Set a)
1883 <para>give constructors with types:</para>
1887 ConsSet :: Eq a => a -> Set a -> Set a
1890 <para>In GHC this feature is an extension called
1891 <literal>DatatypeContexts</literal>, and on by default.</para>
1894 <sect2 id="infix-tycons">
1895 <title>Infix type constructors, classes, and type variables</title>
1898 GHC allows type constructors, classes, and type variables to be operators, and
1899 to be written infix, very much like expressions. More specifically:
1902 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1903 The lexical syntax is the same as that for data constructors.
1906 Data type and type-synonym declarations can be written infix, parenthesised
1907 if you want further arguments. E.g.
1909 data a :*: b = Foo a b
1910 type a :+: b = Either a b
1911 class a :=: b where ...
1913 data (a :**: b) x = Baz a b x
1914 type (a :++: b) y = Either (a,b) y
1918 Types, and class constraints, can be written infix. For example
1921 f :: (a :=: b) => a -> b
1925 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1926 The lexical syntax is the same as that for variable operators, excluding "(.)",
1927 "(!)", and "(*)". In a binding position, the operator must be
1928 parenthesised. For example:
1930 type T (+) = Int + Int
1934 liftA2 :: Arrow (~>)
1935 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1941 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1942 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1945 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1946 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1947 sets the fixity for a data constructor and the corresponding type constructor. For example:
1951 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1952 and similarly for <literal>:*:</literal>.
1953 <literal>Int `a` Bool</literal>.
1956 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1963 <sect2 id="type-synonyms">
1964 <title>Liberalised type synonyms</title>
1967 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1968 on individual synonym declarations.
1969 With the <option>-XLiberalTypeSynonyms</option> extension,
1970 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1971 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1974 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1975 in a type synonym, thus:
1977 type Discard a = forall b. Show b => a -> b -> (a, String)
1982 g :: Discard Int -> (Int,String) -- A rank-2 type
1989 If you also use <option>-XUnboxedTuples</option>,
1990 you can write an unboxed tuple in a type synonym:
1992 type Pr = (# Int, Int #)
2000 You can apply a type synonym to a forall type:
2002 type Foo a = a -> a -> Bool
2004 f :: Foo (forall b. b->b)
2006 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2008 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2013 You can apply a type synonym to a partially applied type synonym:
2015 type Generic i o = forall x. i x -> o x
2018 foo :: Generic Id []
2020 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2022 foo :: forall x. x -> [x]
2030 GHC currently does kind checking before expanding synonyms (though even that
2034 After expanding type synonyms, GHC does validity checking on types, looking for
2035 the following mal-formedness which isn't detected simply by kind checking:
2038 Type constructor applied to a type involving for-alls.
2041 Unboxed tuple on left of an arrow.
2044 Partially-applied type synonym.
2048 this will be rejected:
2050 type Pr = (# Int, Int #)
2055 because GHC does not allow unboxed tuples on the left of a function arrow.
2060 <sect2 id="existential-quantification">
2061 <title>Existentially quantified data constructors
2065 The idea of using existential quantification in data type declarations
2066 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2067 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2068 London, 1991). It was later formalised by Laufer and Odersky
2069 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2070 TOPLAS, 16(5), pp1411-1430, 1994).
2071 It's been in Lennart
2072 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2073 proved very useful. Here's the idea. Consider the declaration:
2079 data Foo = forall a. MkFoo a (a -> Bool)
2086 The data type <literal>Foo</literal> has two constructors with types:
2092 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2099 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2100 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2101 For example, the following expression is fine:
2107 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2113 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2114 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2115 isUpper</function> packages a character with a compatible function. These
2116 two things are each of type <literal>Foo</literal> and can be put in a list.
2120 What can we do with a value of type <literal>Foo</literal>?. In particular,
2121 what happens when we pattern-match on <function>MkFoo</function>?
2127 f (MkFoo val fn) = ???
2133 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2134 are compatible, the only (useful) thing we can do with them is to
2135 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2142 f (MkFoo val fn) = fn val
2148 What this allows us to do is to package heterogeneous values
2149 together with a bunch of functions that manipulate them, and then treat
2150 that collection of packages in a uniform manner. You can express
2151 quite a bit of object-oriented-like programming this way.
2154 <sect3 id="existential">
2155 <title>Why existential?
2159 What has this to do with <emphasis>existential</emphasis> quantification?
2160 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2166 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2172 But Haskell programmers can safely think of the ordinary
2173 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2174 adding a new existential quantification construct.
2179 <sect3 id="existential-with-context">
2180 <title>Existentials and type classes</title>
2183 An easy extension is to allow
2184 arbitrary contexts before the constructor. For example:
2190 data Baz = forall a. Eq a => Baz1 a a
2191 | forall b. Show b => Baz2 b (b -> b)
2197 The two constructors have the types you'd expect:
2203 Baz1 :: forall a. Eq a => a -> a -> Baz
2204 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2210 But when pattern matching on <function>Baz1</function> the matched values can be compared
2211 for equality, and when pattern matching on <function>Baz2</function> the first matched
2212 value can be converted to a string (as well as applying the function to it).
2213 So this program is legal:
2220 f (Baz1 p q) | p == q = "Yes"
2222 f (Baz2 v fn) = show (fn v)
2228 Operationally, in a dictionary-passing implementation, the
2229 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2230 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2231 extract it on pattern matching.
2236 <sect3 id="existential-records">
2237 <title>Record Constructors</title>
2240 GHC allows existentials to be used with records syntax as well. For example:
2243 data Counter a = forall self. NewCounter
2245 , _inc :: self -> self
2246 , _display :: self -> IO ()
2250 Here <literal>tag</literal> is a public field, with a well-typed selector
2251 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2252 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2253 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2254 compile-time error. In other words, <emphasis>GHC defines a record selector function
2255 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2256 (This example used an underscore in the fields for which record selectors
2257 will not be defined, but that is only programming style; GHC ignores them.)
2261 To make use of these hidden fields, we need to create some helper functions:
2264 inc :: Counter a -> Counter a
2265 inc (NewCounter x i d t) = NewCounter
2266 { _this = i x, _inc = i, _display = d, tag = t }
2268 display :: Counter a -> IO ()
2269 display NewCounter{ _this = x, _display = d } = d x
2272 Now we can define counters with different underlying implementations:
2275 counterA :: Counter String
2276 counterA = NewCounter
2277 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2279 counterB :: Counter String
2280 counterB = NewCounter
2281 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2284 display (inc counterA) -- prints "1"
2285 display (inc (inc counterB)) -- prints "##"
2288 Record update syntax is supported for existentials (and GADTs):
2290 setTag :: Counter a -> a -> Counter a
2291 setTag obj t = obj{ tag = t }
2293 The rule for record update is this: <emphasis>
2294 the types of the updated fields may
2295 mention only the universally-quantified type variables
2296 of the data constructor. For GADTs, the field may mention only types
2297 that appear as a simple type-variable argument in the constructor's result
2298 type</emphasis>. For example:
2300 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2301 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2302 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2303 -- existentially quantified)
2305 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2306 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2307 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2308 -- type-variable argument in G1's result type)
2316 <title>Restrictions</title>
2319 There are several restrictions on the ways in which existentially-quantified
2320 constructors can be use.
2329 When pattern matching, each pattern match introduces a new,
2330 distinct, type for each existential type variable. These types cannot
2331 be unified with any other type, nor can they escape from the scope of
2332 the pattern match. For example, these fragments are incorrect:
2340 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2341 is the result of <function>f1</function>. One way to see why this is wrong is to
2342 ask what type <function>f1</function> has:
2346 f1 :: Foo -> a -- Weird!
2350 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2355 f1 :: forall a. Foo -> a -- Wrong!
2359 The original program is just plain wrong. Here's another sort of error
2363 f2 (Baz1 a b) (Baz1 p q) = a==q
2367 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2368 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2369 from the two <function>Baz1</function> constructors.
2377 You can't pattern-match on an existentially quantified
2378 constructor in a <literal>let</literal> or <literal>where</literal> group of
2379 bindings. So this is illegal:
2383 f3 x = a==b where { Baz1 a b = x }
2386 Instead, use a <literal>case</literal> expression:
2389 f3 x = case x of Baz1 a b -> a==b
2392 In general, you can only pattern-match
2393 on an existentially-quantified constructor in a <literal>case</literal> expression or
2394 in the patterns of a function definition.
2396 The reason for this restriction is really an implementation one.
2397 Type-checking binding groups is already a nightmare without
2398 existentials complicating the picture. Also an existential pattern
2399 binding at the top level of a module doesn't make sense, because it's
2400 not clear how to prevent the existentially-quantified type "escaping".
2401 So for now, there's a simple-to-state restriction. We'll see how
2409 You can't use existential quantification for <literal>newtype</literal>
2410 declarations. So this is illegal:
2414 newtype T = forall a. Ord a => MkT a
2418 Reason: a value of type <literal>T</literal> must be represented as a
2419 pair of a dictionary for <literal>Ord t</literal> and a value of type
2420 <literal>t</literal>. That contradicts the idea that
2421 <literal>newtype</literal> should have no concrete representation.
2422 You can get just the same efficiency and effect by using
2423 <literal>data</literal> instead of <literal>newtype</literal>. If
2424 there is no overloading involved, then there is more of a case for
2425 allowing an existentially-quantified <literal>newtype</literal>,
2426 because the <literal>data</literal> version does carry an
2427 implementation cost, but single-field existentially quantified
2428 constructors aren't much use. So the simple restriction (no
2429 existential stuff on <literal>newtype</literal>) stands, unless there
2430 are convincing reasons to change it.
2438 You can't use <literal>deriving</literal> to define instances of a
2439 data type with existentially quantified data constructors.
2441 Reason: in most cases it would not make sense. For example:;
2444 data T = forall a. MkT [a] deriving( Eq )
2447 To derive <literal>Eq</literal> in the standard way we would need to have equality
2448 between the single component of two <function>MkT</function> constructors:
2452 (MkT a) == (MkT b) = ???
2455 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2456 It's just about possible to imagine examples in which the derived instance
2457 would make sense, but it seems altogether simpler simply to prohibit such
2458 declarations. Define your own instances!
2469 <!-- ====================== Generalised algebraic data types ======================= -->
2471 <sect2 id="gadt-style">
2472 <title>Declaring data types with explicit constructor signatures</title>
2474 <para>GHC allows you to declare an algebraic data type by
2475 giving the type signatures of constructors explicitly. For example:
2479 Just :: a -> Maybe a
2481 The form is called a "GADT-style declaration"
2482 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2483 can only be declared using this form.</para>
2484 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2485 For example, these two declarations are equivalent:
2487 data Foo = forall a. MkFoo a (a -> Bool)
2488 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2491 <para>Any data type that can be declared in standard Haskell-98 syntax
2492 can also be declared using GADT-style syntax.
2493 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2494 they treat class constraints on the data constructors differently.
2495 Specifically, if the constructor is given a type-class context, that
2496 context is made available by pattern matching. For example:
2499 MkSet :: Eq a => [a] -> Set a
2501 makeSet :: Eq a => [a] -> Set a
2502 makeSet xs = MkSet (nub xs)
2504 insert :: a -> Set a -> Set a
2505 insert a (MkSet as) | a `elem` as = MkSet as
2506 | otherwise = MkSet (a:as)
2508 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2509 gives rise to a <literal>(Eq a)</literal>
2510 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2511 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2512 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2513 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2514 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2515 In the example, the equality dictionary is used to satisfy the equality constraint
2516 generated by the call to <literal>elem</literal>, so that the type of
2517 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2520 For example, one possible application is to reify dictionaries:
2522 data NumInst a where
2523 MkNumInst :: Num a => NumInst a
2525 intInst :: NumInst Int
2528 plus :: NumInst a -> a -> a -> a
2529 plus MkNumInst p q = p + q
2531 Here, a value of type <literal>NumInst a</literal> is equivalent
2532 to an explicit <literal>(Num a)</literal> dictionary.
2535 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2536 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2540 = Num a => MkNumInst (NumInst a)
2542 Notice that, unlike the situation when declaring an existential, there is
2543 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2544 data type's universally quantified type variable <literal>a</literal>.
2545 A constructor may have both universal and existential type variables: for example,
2546 the following two declarations are equivalent:
2549 = forall b. (Num a, Eq b) => MkT1 a b
2551 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2554 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2555 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2556 In Haskell 98 the definition
2558 data Eq a => Set' a = MkSet' [a]
2560 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2561 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2562 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2563 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2564 GHC's behaviour is much more useful, as well as much more intuitive.
2568 The rest of this section gives further details about GADT-style data
2573 The result type of each data constructor must begin with the type constructor being defined.
2574 If the result type of all constructors
2575 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2576 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2577 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2581 As with other type signatures, you can give a single signature for several data constructors.
2582 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2591 The type signature of
2592 each constructor is independent, and is implicitly universally quantified as usual.
2593 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2594 have no scope, and different constructors may have different universally-quantified type variables:
2596 data T a where -- The 'a' has no scope
2597 T1,T2 :: b -> T b -- Means forall b. b -> T b
2598 T3 :: T a -- Means forall a. T a
2603 A constructor signature may mention type class constraints, which can differ for
2604 different constructors. For example, this is fine:
2607 T1 :: Eq b => b -> b -> T b
2608 T2 :: (Show c, Ix c) => c -> [c] -> T c
2610 When patten matching, these constraints are made available to discharge constraints
2611 in the body of the match. For example:
2614 f (T1 x y) | x==y = "yes"
2618 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2619 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2620 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2624 Unlike a Haskell-98-style
2625 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2626 have no scope. Indeed, one can write a kind signature instead:
2628 data Set :: * -> * where ...
2630 or even a mixture of the two:
2632 data Bar a :: (* -> *) -> * where ...
2634 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2637 data Bar a (b :: * -> *) where ...
2643 You can use strictness annotations, in the obvious places
2644 in the constructor type:
2647 Lit :: !Int -> Term Int
2648 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2649 Pair :: Term a -> Term b -> Term (a,b)
2654 You can use a <literal>deriving</literal> clause on a GADT-style data type
2655 declaration. For example, these two declarations are equivalent
2657 data Maybe1 a where {
2658 Nothing1 :: Maybe1 a ;
2659 Just1 :: a -> Maybe1 a
2660 } deriving( Eq, Ord )
2662 data Maybe2 a = Nothing2 | Just2 a
2668 The type signature may have quantified type variables that do not appear
2672 MkFoo :: a -> (a->Bool) -> Foo
2675 Here the type variable <literal>a</literal> does not appear in the result type
2676 of either constructor.
2677 Although it is universally quantified in the type of the constructor, such
2678 a type variable is often called "existential".
2679 Indeed, the above declaration declares precisely the same type as
2680 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2682 The type may contain a class context too, of course:
2685 MkShowable :: Show a => a -> Showable
2690 You can use record syntax on a GADT-style data type declaration:
2694 Adult :: { name :: String, children :: [Person] } -> Person
2695 Child :: Show a => { name :: !String, funny :: a } -> Person
2697 As usual, for every constructor that has a field <literal>f</literal>, the type of
2698 field <literal>f</literal> must be the same (modulo alpha conversion).
2699 The <literal>Child</literal> constructor above shows that the signature
2700 may have a context, existentially-quantified variables, and strictness annotations,
2701 just as in the non-record case. (NB: the "type" that follows the double-colon
2702 is not really a type, because of the record syntax and strictness annotations.
2703 A "type" of this form can appear only in a constructor signature.)
2707 Record updates are allowed with GADT-style declarations,
2708 only fields that have the following property: the type of the field
2709 mentions no existential type variables.
2713 As in the case of existentials declared using the Haskell-98-like record syntax
2714 (<xref linkend="existential-records"/>),
2715 record-selector functions are generated only for those fields that have well-typed
2717 Here is the example of that section, in GADT-style syntax:
2719 data Counter a where
2720 NewCounter { _this :: self
2721 , _inc :: self -> self
2722 , _display :: self -> IO ()
2727 As before, only one selector function is generated here, that for <literal>tag</literal>.
2728 Nevertheless, you can still use all the field names in pattern matching and record construction.
2730 </itemizedlist></para>
2734 <title>Generalised Algebraic Data Types (GADTs)</title>
2736 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2737 by allowing constructors to have richer return types. Here is an example:
2740 Lit :: Int -> Term Int
2741 Succ :: Term Int -> Term Int
2742 IsZero :: Term Int -> Term Bool
2743 If :: Term Bool -> Term a -> Term a -> Term a
2744 Pair :: Term a -> Term b -> Term (a,b)
2746 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2747 case with ordinary data types. This generality allows us to
2748 write a well-typed <literal>eval</literal> function
2749 for these <literal>Terms</literal>:
2753 eval (Succ t) = 1 + eval t
2754 eval (IsZero t) = eval t == 0
2755 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2756 eval (Pair e1 e2) = (eval e1, eval e2)
2758 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2759 For example, in the right hand side of the equation
2764 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2765 A precise specification of the type rules is beyond what this user manual aspires to,
2766 but the design closely follows that described in
2768 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2769 unification-based type inference for GADTs</ulink>,
2771 The general principle is this: <emphasis>type refinement is only carried out
2772 based on user-supplied type annotations</emphasis>.
2773 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2774 and lots of obscure error messages will
2775 occur. However, the refinement is quite general. For example, if we had:
2777 eval :: Term a -> a -> a
2778 eval (Lit i) j = i+j
2780 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2781 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2782 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2785 These and many other examples are given in papers by Hongwei Xi, and
2786 Tim Sheard. There is a longer introduction
2787 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2789 <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
2790 may use different notation to that implemented in GHC.
2793 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2794 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2797 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2798 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2799 The result type of each constructor must begin with the type constructor being defined,
2800 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2801 For example, in the <literal>Term</literal> data
2802 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2803 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2808 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2809 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2810 whose result type is not just <literal>T a b</literal>.
2814 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2815 an ordinary data type.
2819 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2823 Lit { val :: Int } :: Term Int
2824 Succ { num :: Term Int } :: Term Int
2825 Pred { num :: Term Int } :: Term Int
2826 IsZero { arg :: Term Int } :: Term Bool
2827 Pair { arg1 :: Term a
2830 If { cnd :: Term Bool
2835 However, for GADTs there is the following additional constraint:
2836 every constructor that has a field <literal>f</literal> must have
2837 the same result type (modulo alpha conversion)
2838 Hence, in the above example, we cannot merge the <literal>num</literal>
2839 and <literal>arg</literal> fields above into a
2840 single name. Although their field types are both <literal>Term Int</literal>,
2841 their selector functions actually have different types:
2844 num :: Term Int -> Term Int
2845 arg :: Term Bool -> Term Int
2850 When pattern-matching against data constructors drawn from a GADT,
2851 for example in a <literal>case</literal> expression, the following rules apply:
2853 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2854 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2855 <listitem><para>The type of any free variable mentioned in any of
2856 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2858 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2859 way to ensure that a variable a rigid type is to give it a type signature.
2860 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2861 Simple unification-based type inference for GADTs
2862 </ulink>. The criteria implemented by GHC are given in the Appendix.
2872 <!-- ====================== End of Generalised algebraic data types ======================= -->
2874 <sect1 id="deriving">
2875 <title>Extensions to the "deriving" mechanism</title>
2877 <sect2 id="deriving-inferred">
2878 <title>Inferred context for deriving clauses</title>
2881 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2884 data T0 f a = MkT0 a deriving( Eq )
2885 data T1 f a = MkT1 (f a) deriving( Eq )
2886 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2888 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2890 instance Eq a => Eq (T0 f a) where ...
2891 instance Eq (f a) => Eq (T1 f a) where ...
2892 instance Eq (f (f a)) => Eq (T2 f a) where ...
2894 The first of these is obviously fine. The second is still fine, although less obviously.
2895 The third is not Haskell 98, and risks losing termination of instances.
2898 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2899 each constraint in the inferred instance context must consist only of type variables,
2900 with no repetitions.
2903 This rule is applied regardless of flags. If you want a more exotic context, you can write
2904 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2908 <sect2 id="stand-alone-deriving">
2909 <title>Stand-alone deriving declarations</title>
2912 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2914 data Foo a = Bar a | Baz String
2916 deriving instance Eq a => Eq (Foo a)
2918 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2919 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2920 Note the following points:
2923 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2924 exactly as you would in an ordinary instance declaration.
2925 (In contrast, in a <literal>deriving</literal> clause
2926 attached to a data type declaration, the context is inferred.)
2930 A <literal>deriving instance</literal> declaration
2931 must obey the same rules concerning form and termination as ordinary instance declarations,
2932 controlled by the same flags; see <xref linkend="instance-decls"/>.
2936 Unlike a <literal>deriving</literal>
2937 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2938 than the data type (assuming you also use
2939 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2942 data Foo a = Bar a | Baz String
2944 deriving instance Eq a => Eq (Foo [a])
2945 deriving instance Eq a => Eq (Foo (Maybe a))
2947 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2948 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2952 Unlike a <literal>deriving</literal>
2953 declaration attached to a <literal>data</literal> declaration,
2954 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2955 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2956 your problem. (GHC will show you the offending code if it has a type error.)
2957 The merit of this is that you can derive instances for GADTs and other exotic
2958 data types, providing only that the boilerplate code does indeed typecheck. For example:
2964 deriving instance Show (T a)
2966 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2967 data type declaration for <literal>T</literal>,
2968 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2969 the instance declaration using stand-alone deriving.
2974 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2975 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2978 newtype Foo a = MkFoo (State Int a)
2980 deriving instance MonadState Int Foo
2982 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2983 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2985 </itemizedlist></para>
2990 <sect2 id="deriving-typeable">
2991 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2994 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2995 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2996 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2997 classes <literal>Eq</literal>, <literal>Ord</literal>,
2998 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3001 GHC extends this list with several more classes that may be automatically derived:
3003 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
3004 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
3005 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
3007 <para>An instance of <literal>Typeable</literal> can only be derived if the
3008 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3009 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3011 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3012 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3014 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3015 are used, and only <literal>Typeable1</literal> up to
3016 <literal>Typeable7</literal> are provided in the library.)
3017 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3018 class, whose kind suits that of the data type constructor, and
3019 then writing the data type instance by hand.
3023 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3024 the class <literal>Functor</literal>,
3025 defined in <literal>GHC.Base</literal>.
3028 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3029 the class <literal>Foldable</literal>,
3030 defined in <literal>Data.Foldable</literal>.
3033 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3034 the class <literal>Traversable</literal>,
3035 defined in <literal>Data.Traversable</literal>.
3038 In each case the appropriate class must be in scope before it
3039 can be mentioned in the <literal>deriving</literal> clause.
3043 <sect2 id="newtype-deriving">
3044 <title>Generalised derived instances for newtypes</title>
3047 When you define an abstract type using <literal>newtype</literal>, you may want
3048 the new type to inherit some instances from its representation. In
3049 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3050 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3051 other classes you have to write an explicit instance declaration. For
3052 example, if you define
3055 newtype Dollars = Dollars Int
3058 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3059 explicitly define an instance of <literal>Num</literal>:
3062 instance Num Dollars where
3063 Dollars a + Dollars b = Dollars (a+b)
3066 All the instance does is apply and remove the <literal>newtype</literal>
3067 constructor. It is particularly galling that, since the constructor
3068 doesn't appear at run-time, this instance declaration defines a
3069 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3070 dictionary, only slower!
3074 <sect3> <title> Generalising the deriving clause </title>
3076 GHC now permits such instances to be derived instead,
3077 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3080 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3083 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3084 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3085 derives an instance declaration of the form
3088 instance Num Int => Num Dollars
3091 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3095 We can also derive instances of constructor classes in a similar
3096 way. For example, suppose we have implemented state and failure monad
3097 transformers, such that
3100 instance Monad m => Monad (State s m)
3101 instance Monad m => Monad (Failure m)
3103 In Haskell 98, we can define a parsing monad by
3105 type Parser tok m a = State [tok] (Failure m) a
3108 which is automatically a monad thanks to the instance declarations
3109 above. With the extension, we can make the parser type abstract,
3110 without needing to write an instance of class <literal>Monad</literal>, via
3113 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3116 In this case the derived instance declaration is of the form
3118 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3121 Notice that, since <literal>Monad</literal> is a constructor class, the
3122 instance is a <emphasis>partial application</emphasis> of the new type, not the
3123 entire left hand side. We can imagine that the type declaration is
3124 "eta-converted" to generate the context of the instance
3129 We can even derive instances of multi-parameter classes, provided the
3130 newtype is the last class parameter. In this case, a ``partial
3131 application'' of the class appears in the <literal>deriving</literal>
3132 clause. For example, given the class
3135 class StateMonad s m | m -> s where ...
3136 instance Monad m => StateMonad s (State s m) where ...
3138 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3140 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3141 deriving (Monad, StateMonad [tok])
3144 The derived instance is obtained by completing the application of the
3145 class to the new type:
3148 instance StateMonad [tok] (State [tok] (Failure m)) =>
3149 StateMonad [tok] (Parser tok m)
3154 As a result of this extension, all derived instances in newtype
3155 declarations are treated uniformly (and implemented just by reusing
3156 the dictionary for the representation type), <emphasis>except</emphasis>
3157 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3158 the newtype and its representation.
3162 <sect3> <title> A more precise specification </title>
3164 Derived instance declarations are constructed as follows. Consider the
3165 declaration (after expansion of any type synonyms)
3168 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3174 The <literal>ci</literal> are partial applications of
3175 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3176 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3179 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3182 The type <literal>t</literal> is an arbitrary type.
3185 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3186 nor in the <literal>ci</literal>, and
3189 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3190 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3191 should not "look through" the type or its constructor. You can still
3192 derive these classes for a newtype, but it happens in the usual way, not
3193 via this new mechanism.
3196 Then, for each <literal>ci</literal>, the derived instance
3199 instance ci t => ci (T v1...vk)
3201 As an example which does <emphasis>not</emphasis> work, consider
3203 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3205 Here we cannot derive the instance
3207 instance Monad (State s m) => Monad (NonMonad m)
3210 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3211 and so cannot be "eta-converted" away. It is a good thing that this
3212 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3213 not, in fact, a monad --- for the same reason. Try defining
3214 <literal>>>=</literal> with the correct type: you won't be able to.
3218 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3219 important, since we can only derive instances for the last one. If the
3220 <literal>StateMonad</literal> class above were instead defined as
3223 class StateMonad m s | m -> s where ...
3226 then we would not have been able to derive an instance for the
3227 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3228 classes usually have one "main" parameter for which deriving new
3229 instances is most interesting.
3231 <para>Lastly, all of this applies only for classes other than
3232 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3233 and <literal>Data</literal>, for which the built-in derivation applies (section
3234 4.3.3. of the Haskell Report).
3235 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3236 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3237 the standard method is used or the one described here.)
3244 <!-- TYPE SYSTEM EXTENSIONS -->
3245 <sect1 id="type-class-extensions">
3246 <title>Class and instances declarations</title>
3248 <sect2 id="multi-param-type-classes">
3249 <title>Class declarations</title>
3252 This section, and the next one, documents GHC's type-class extensions.
3253 There's lots of background in the paper <ulink
3254 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3255 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3256 Jones, Erik Meijer).
3259 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3263 <title>Multi-parameter type classes</title>
3265 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3270 class Collection c a where
3271 union :: c a -> c a -> c a
3278 <sect3 id="superclass-rules">
3279 <title>The superclasses of a class declaration</title>
3282 In Haskell 98 the context of a class declaration (which introduces superclasses)
3283 must be simple; that is, each predicate must consist of a class applied to
3284 type variables. The flag <option>-XFlexibleContexts</option>
3285 (<xref linkend="flexible-contexts"/>)
3286 lifts this restriction,
3287 so that the only restriction on the context in a class declaration is
3288 that the class hierarchy must be acyclic. So these class declarations are OK:
3292 class Functor (m k) => FiniteMap m k where
3295 class (Monad m, Monad (t m)) => Transform t m where
3296 lift :: m a -> (t m) a
3302 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3303 of "acyclic" involves only the superclass relationships. For example,
3309 op :: D b => a -> b -> b
3312 class C a => D a where { ... }
3316 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3317 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3318 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3325 <sect3 id="class-method-types">
3326 <title>Class method types</title>
3329 Haskell 98 prohibits class method types to mention constraints on the
3330 class type variable, thus:
3333 fromList :: [a] -> s a
3334 elem :: Eq a => a -> s a -> Bool
3336 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3337 contains the constraint <literal>Eq a</literal>, constrains only the
3338 class type variable (in this case <literal>a</literal>).
3339 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3346 <sect2 id="functional-dependencies">
3347 <title>Functional dependencies
3350 <para> Functional dependencies are implemented as described by Mark Jones
3351 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3352 In Proceedings of the 9th European Symposium on Programming,
3353 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3357 Functional dependencies are introduced by a vertical bar in the syntax of a
3358 class declaration; e.g.
3360 class (Monad m) => MonadState s m | m -> s where ...
3362 class Foo a b c | a b -> c where ...
3364 There should be more documentation, but there isn't (yet). Yell if you need it.
3367 <sect3><title>Rules for functional dependencies </title>
3369 In a class declaration, all of the class type variables must be reachable (in the sense
3370 mentioned in <xref linkend="flexible-contexts"/>)
3371 from the free variables of each method type.
3375 class Coll s a where
3377 insert :: s -> a -> s
3380 is not OK, because the type of <literal>empty</literal> doesn't mention
3381 <literal>a</literal>. Functional dependencies can make the type variable
3384 class Coll s a | s -> a where
3386 insert :: s -> a -> s
3389 Alternatively <literal>Coll</literal> might be rewritten
3392 class Coll s a where
3394 insert :: s a -> a -> s a
3398 which makes the connection between the type of a collection of
3399 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3400 Occasionally this really doesn't work, in which case you can split the
3408 class CollE s => Coll s a where
3409 insert :: s -> a -> s
3416 <title>Background on functional dependencies</title>
3418 <para>The following description of the motivation and use of functional dependencies is taken
3419 from the Hugs user manual, reproduced here (with minor changes) by kind
3420 permission of Mark Jones.
3423 Consider the following class, intended as part of a
3424 library for collection types:
3426 class Collects e ce where
3428 insert :: e -> ce -> ce
3429 member :: e -> ce -> Bool
3431 The type variable e used here represents the element type, while ce is the type
3432 of the container itself. Within this framework, we might want to define
3433 instances of this class for lists or characteristic functions (both of which
3434 can be used to represent collections of any equality type), bit sets (which can
3435 be used to represent collections of characters), or hash tables (which can be
3436 used to represent any collection whose elements have a hash function). Omitting
3437 standard implementation details, this would lead to the following declarations:
3439 instance Eq e => Collects e [e] where ...
3440 instance Eq e => Collects e (e -> Bool) where ...
3441 instance Collects Char BitSet where ...
3442 instance (Hashable e, Collects a ce)
3443 => Collects e (Array Int ce) where ...
3445 All this looks quite promising; we have a class and a range of interesting
3446 implementations. Unfortunately, there are some serious problems with the class
3447 declaration. First, the empty function has an ambiguous type:
3449 empty :: Collects e ce => ce
3451 By "ambiguous" we mean that there is a type variable e that appears on the left
3452 of the <literal>=></literal> symbol, but not on the right. The problem with
3453 this is that, according to the theoretical foundations of Haskell overloading,
3454 we cannot guarantee a well-defined semantics for any term with an ambiguous
3458 We can sidestep this specific problem by removing the empty member from the
3459 class declaration. However, although the remaining members, insert and member,
3460 do not have ambiguous types, we still run into problems when we try to use
3461 them. For example, consider the following two functions:
3463 f x y = insert x . insert y
3466 for which GHC infers the following types:
3468 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3469 g :: (Collects Bool c, Collects Char c) => c -> c
3471 Notice that the type for f allows the two parameters x and y to be assigned
3472 different types, even though it attempts to insert each of the two values, one
3473 after the other, into the same collection. If we're trying to model collections
3474 that contain only one type of value, then this is clearly an inaccurate
3475 type. Worse still, the definition for g is accepted, without causing a type
3476 error. As a result, the error in this code will not be flagged at the point
3477 where it appears. Instead, it will show up only when we try to use g, which
3478 might even be in a different module.
3481 <sect4><title>An attempt to use constructor classes</title>
3484 Faced with the problems described above, some Haskell programmers might be
3485 tempted to use something like the following version of the class declaration:
3487 class Collects e c where
3489 insert :: e -> c e -> c e
3490 member :: e -> c e -> Bool
3492 The key difference here is that we abstract over the type constructor c that is
3493 used to form the collection type c e, and not over that collection type itself,
3494 represented by ce in the original class declaration. This avoids the immediate
3495 problems that we mentioned above: empty has type <literal>Collects e c => c
3496 e</literal>, which is not ambiguous.
3499 The function f from the previous section has a more accurate type:
3501 f :: (Collects e c) => e -> e -> c e -> c e
3503 The function g from the previous section is now rejected with a type error as
3504 we would hope because the type of f does not allow the two arguments to have
3506 This, then, is an example of a multiple parameter class that does actually work
3507 quite well in practice, without ambiguity problems.
3508 There is, however, a catch. This version of the Collects class is nowhere near
3509 as general as the original class seemed to be: only one of the four instances
3510 for <literal>Collects</literal>
3511 given above can be used with this version of Collects because only one of
3512 them---the instance for lists---has a collection type that can be written in
3513 the form c e, for some type constructor c, and element type e.
3517 <sect4><title>Adding functional dependencies</title>
3520 To get a more useful version of the Collects class, Hugs provides a mechanism
3521 that allows programmers to specify dependencies between the parameters of a
3522 multiple parameter class (For readers with an interest in theoretical
3523 foundations and previous work: The use of dependency information can be seen
3524 both as a generalization of the proposal for `parametric type classes' that was
3525 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3526 later framework for "improvement" of qualified types. The
3527 underlying ideas are also discussed in a more theoretical and abstract setting
3528 in a manuscript [implparam], where they are identified as one point in a
3529 general design space for systems of implicit parameterization.).
3531 To start with an abstract example, consider a declaration such as:
3533 class C a b where ...
3535 which tells us simply that C can be thought of as a binary relation on types
3536 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3537 included in the definition of classes to add information about dependencies
3538 between parameters, as in the following examples:
3540 class D a b | a -> b where ...
3541 class E a b | a -> b, b -> a where ...
3543 The notation <literal>a -> b</literal> used here between the | and where
3544 symbols --- not to be
3545 confused with a function type --- indicates that the a parameter uniquely
3546 determines the b parameter, and might be read as "a determines b." Thus D is
3547 not just a relation, but actually a (partial) function. Similarly, from the two
3548 dependencies that are included in the definition of E, we can see that E
3549 represents a (partial) one-one mapping between types.
3552 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3553 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3554 m>=0, meaning that the y parameters are uniquely determined by the x
3555 parameters. Spaces can be used as separators if more than one variable appears
3556 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3557 annotated with multiple dependencies using commas as separators, as in the
3558 definition of E above. Some dependencies that we can write in this notation are
3559 redundant, and will be rejected because they don't serve any useful
3560 purpose, and may instead indicate an error in the program. Examples of
3561 dependencies like this include <literal>a -> a </literal>,
3562 <literal>a -> a a </literal>,
3563 <literal>a -> </literal>, etc. There can also be
3564 some redundancy if multiple dependencies are given, as in
3565 <literal>a->b</literal>,
3566 <literal>b->c </literal>, <literal>a->c </literal>, and
3567 in which some subset implies the remaining dependencies. Examples like this are
3568 not treated as errors. Note that dependencies appear only in class
3569 declarations, and not in any other part of the language. In particular, the
3570 syntax for instance declarations, class constraints, and types is completely
3574 By including dependencies in a class declaration, we provide a mechanism for
3575 the programmer to specify each multiple parameter class more precisely. The
3576 compiler, on the other hand, is responsible for ensuring that the set of
3577 instances that are in scope at any given point in the program is consistent
3578 with any declared dependencies. For example, the following pair of instance
3579 declarations cannot appear together in the same scope because they violate the
3580 dependency for D, even though either one on its own would be acceptable:
3582 instance D Bool Int where ...
3583 instance D Bool Char where ...
3585 Note also that the following declaration is not allowed, even by itself:
3587 instance D [a] b where ...
3589 The problem here is that this instance would allow one particular choice of [a]
3590 to be associated with more than one choice for b, which contradicts the
3591 dependency specified in the definition of D. More generally, this means that,
3592 in any instance of the form:
3594 instance D t s where ...
3596 for some particular types t and s, the only variables that can appear in s are
3597 the ones that appear in t, and hence, if the type t is known, then s will be
3598 uniquely determined.
3601 The benefit of including dependency information is that it allows us to define
3602 more general multiple parameter classes, without ambiguity problems, and with
3603 the benefit of more accurate types. To illustrate this, we return to the
3604 collection class example, and annotate the original definition of <literal>Collects</literal>
3605 with a simple dependency:
3607 class Collects e ce | ce -> e where
3609 insert :: e -> ce -> ce
3610 member :: e -> ce -> Bool
3612 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3613 determined by the type of the collection ce. Note that both parameters of
3614 Collects are of kind *; there are no constructor classes here. Note too that
3615 all of the instances of Collects that we gave earlier can be used
3616 together with this new definition.
3619 What about the ambiguity problems that we encountered with the original
3620 definition? The empty function still has type Collects e ce => ce, but it is no
3621 longer necessary to regard that as an ambiguous type: Although the variable e
3622 does not appear on the right of the => symbol, the dependency for class
3623 Collects tells us that it is uniquely determined by ce, which does appear on
3624 the right of the => symbol. Hence the context in which empty is used can still
3625 give enough information to determine types for both ce and e, without
3626 ambiguity. More generally, we need only regard a type as ambiguous if it
3627 contains a variable on the left of the => that is not uniquely determined
3628 (either directly or indirectly) by the variables on the right.
3631 Dependencies also help to produce more accurate types for user defined
3632 functions, and hence to provide earlier detection of errors, and less cluttered
3633 types for programmers to work with. Recall the previous definition for a
3636 f x y = insert x y = insert x . insert y
3638 for which we originally obtained a type:
3640 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3642 Given the dependency information that we have for Collects, however, we can
3643 deduce that a and b must be equal because they both appear as the second
3644 parameter in a Collects constraint with the same first parameter c. Hence we
3645 can infer a shorter and more accurate type for f:
3647 f :: (Collects a c) => a -> a -> c -> c
3649 In a similar way, the earlier definition of g will now be flagged as a type error.
3652 Although we have given only a few examples here, it should be clear that the
3653 addition of dependency information can help to make multiple parameter classes
3654 more useful in practice, avoiding ambiguity problems, and allowing more general
3655 sets of instance declarations.
3661 <sect2 id="instance-decls">
3662 <title>Instance declarations</title>
3664 <para>An instance declaration has the form
3666 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 ...
3668 The part before the "<literal>=></literal>" is the
3669 <emphasis>context</emphasis>, while the part after the
3670 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3673 <sect3 id="flexible-instance-head">
3674 <title>Relaxed rules for the instance head</title>
3677 In Haskell 98 the head of an instance declaration
3678 must be of the form <literal>C (T a1 ... an)</literal>, where
3679 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3680 and the <literal>a1 ... an</literal> are distinct type variables.
3681 GHC relaxes these rules in two ways.
3685 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3686 declaration to mention arbitrary nested types.
3687 For example, this becomes a legal instance declaration
3689 instance C (Maybe Int) where ...
3691 See also the <link linkend="instance-overlap">rules on overlap</link>.
3694 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3695 synonyms. As always, using a type synonym is just shorthand for
3696 writing the RHS of the type synonym definition. For example:
3700 type Point = (Int,Int)
3701 instance C Point where ...
3702 instance C [Point] where ...
3706 is legal. However, if you added
3710 instance C (Int,Int) where ...
3714 as well, then the compiler will complain about the overlapping
3715 (actually, identical) instance declarations. As always, type synonyms
3716 must be fully applied. You cannot, for example, write:
3720 instance Monad P where ...
3728 <sect3 id="instance-rules">
3729 <title>Relaxed rules for instance contexts</title>
3731 <para>In Haskell 98, the assertions in the context of the instance declaration
3732 must be of the form <literal>C a</literal> where <literal>a</literal>
3733 is a type variable that occurs in the head.
3737 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3738 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3739 With this flag the context of the instance declaration can each consist of arbitrary
3740 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3744 The Paterson Conditions: for each assertion in the context
3746 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3747 <listitem><para>The assertion has fewer constructors and variables (taken together
3748 and counting repetitions) than the head</para></listitem>
3752 <listitem><para>The Coverage Condition. For each functional dependency,
3753 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3754 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3755 every type variable in
3756 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3757 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3758 substitution mapping each type variable in the class declaration to the
3759 corresponding type in the instance declaration.
3762 These restrictions ensure that context reduction terminates: each reduction
3763 step makes the problem smaller by at least one
3764 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3765 if you give the <option>-XUndecidableInstances</option>
3766 flag (<xref linkend="undecidable-instances"/>).
3767 You can find lots of background material about the reason for these
3768 restrictions in the paper <ulink
3769 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3770 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3773 For example, these are OK:
3775 instance C Int [a] -- Multiple parameters
3776 instance Eq (S [a]) -- Structured type in head
3778 -- Repeated type variable in head
3779 instance C4 a a => C4 [a] [a]
3780 instance Stateful (ST s) (MutVar s)
3782 -- Head can consist of type variables only
3784 instance (Eq a, Show b) => C2 a b
3786 -- Non-type variables in context
3787 instance Show (s a) => Show (Sized s a)
3788 instance C2 Int a => C3 Bool [a]
3789 instance C2 Int a => C3 [a] b
3793 -- Context assertion no smaller than head
3794 instance C a => C a where ...
3795 -- (C b b) has more more occurrences of b than the head
3796 instance C b b => Foo [b] where ...
3801 The same restrictions apply to instances generated by
3802 <literal>deriving</literal> clauses. Thus the following is accepted:
3804 data MinHeap h a = H a (h a)
3807 because the derived instance
3809 instance (Show a, Show (h a)) => Show (MinHeap h a)
3811 conforms to the above rules.
3815 A useful idiom permitted by the above rules is as follows.
3816 If one allows overlapping instance declarations then it's quite
3817 convenient to have a "default instance" declaration that applies if
3818 something more specific does not:
3826 <sect3 id="undecidable-instances">
3827 <title>Undecidable instances</title>
3830 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3831 For example, sometimes you might want to use the following to get the
3832 effect of a "class synonym":
3834 class (C1 a, C2 a, C3 a) => C a where { }
3836 instance (C1 a, C2 a, C3 a) => C a where { }
3838 This allows you to write shorter signatures:
3844 f :: (C1 a, C2 a, C3 a) => ...
3846 The restrictions on functional dependencies (<xref
3847 linkend="functional-dependencies"/>) are particularly troublesome.
3848 It is tempting to introduce type variables in the context that do not appear in
3849 the head, something that is excluded by the normal rules. For example:
3851 class HasConverter a b | a -> b where
3854 data Foo a = MkFoo a
3856 instance (HasConverter a b,Show b) => Show (Foo a) where
3857 show (MkFoo value) = show (convert value)
3859 This is dangerous territory, however. Here, for example, is a program that would make the
3864 instance F [a] [[a]]
3865 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3867 Similarly, it can be tempting to lift the coverage condition:
3869 class Mul a b c | a b -> c where
3870 (.*.) :: a -> b -> c
3872 instance Mul Int Int Int where (.*.) = (*)
3873 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3874 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3876 The third instance declaration does not obey the coverage condition;
3877 and indeed the (somewhat strange) definition:
3879 f = \ b x y -> if b then x .*. [y] else y
3881 makes instance inference go into a loop, because it requires the constraint
3882 <literal>(Mul a [b] b)</literal>.
3885 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3886 the experimental flag <option>-XUndecidableInstances</option>
3887 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3888 both the Paterson Conditions and the Coverage Condition
3889 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3890 fixed-depth recursion stack. If you exceed the stack depth you get a
3891 sort of backtrace, and the opportunity to increase the stack depth
3892 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3898 <sect3 id="instance-overlap">
3899 <title>Overlapping instances</title>
3901 In general, <emphasis>GHC requires that that it be unambiguous which instance
3903 should be used to resolve a type-class constraint</emphasis>. This behaviour
3904 can be modified by two flags: <option>-XOverlappingInstances</option>
3905 <indexterm><primary>-XOverlappingInstances
3906 </primary></indexterm>
3907 and <option>-XIncoherentInstances</option>
3908 <indexterm><primary>-XIncoherentInstances
3909 </primary></indexterm>, as this section discusses. Both these
3910 flags are dynamic flags, and can be set on a per-module basis, using
3911 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3913 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3914 it tries to match every instance declaration against the
3916 by instantiating the head of the instance declaration. For example, consider
3919 instance context1 => C Int a where ... -- (A)
3920 instance context2 => C a Bool where ... -- (B)
3921 instance context3 => C Int [a] where ... -- (C)
3922 instance context4 => C Int [Int] where ... -- (D)
3924 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3925 but (C) and (D) do not. When matching, GHC takes
3926 no account of the context of the instance declaration
3927 (<literal>context1</literal> etc).
3928 GHC's default behaviour is that <emphasis>exactly one instance must match the
3929 constraint it is trying to resolve</emphasis>.
3930 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3931 including both declarations (A) and (B), say); an error is only reported if a
3932 particular constraint matches more than one.
3936 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3937 more than one instance to match, provided there is a most specific one. For
3938 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3939 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3940 most-specific match, the program is rejected.
3943 However, GHC is conservative about committing to an overlapping instance. For example:
3948 Suppose that from the RHS of <literal>f</literal> we get the constraint
3949 <literal>C Int [b]</literal>. But
3950 GHC does not commit to instance (C), because in a particular
3951 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3952 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3953 So GHC rejects the program.
3954 (If you add the flag <option>-XIncoherentInstances</option>,
3955 GHC will instead pick (C), without complaining about
3956 the problem of subsequent instantiations.)
3959 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3960 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3961 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3962 it instead. In this case, GHC will refrain from
3963 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3964 as before) but, rather than rejecting the program, it will infer the type
3966 f :: C Int [b] => [b] -> [b]
3968 That postpones the question of which instance to pick to the
3969 call site for <literal>f</literal>
3970 by which time more is known about the type <literal>b</literal>.
3971 You can write this type signature yourself if you use the
3972 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3976 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3980 instance Foo [b] where
3983 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3984 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3985 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3986 declaration. The solution is to postpone the choice by adding the constraint to the context
3987 of the instance declaration, thus:
3989 instance C Int [b] => Foo [b] where
3992 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3995 Warning: overlapping instances must be used with care. They
3996 can give rise to incoherence (ie different instance choices are made
3997 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
3999 {-# LANGUAGE OverlappingInstances #-}
4002 class MyShow a where
4003 myshow :: a -> String
4005 instance MyShow a => MyShow [a] where
4006 myshow xs = concatMap myshow xs
4008 showHelp :: MyShow a => [a] -> String
4009 showHelp xs = myshow xs
4011 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
4017 instance MyShow T where
4018 myshow x = "Used generic instance"
4020 instance MyShow [T] where
4021 myshow xs = "Used more specific instance"
4023 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
4025 In function <literal>showHelp</literal> GHC sees no overlapping
4026 instances, and so uses the <literal>MyShow [a]</literal> instance
4027 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
4028 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
4029 instance declaration in module <literal>Main</literal>. As a result,
4032 "Used more specific instance"
4033 "Used generic instance"
4035 (An alternative possible behaviour, not currently implemented,
4036 would be to reject module <literal>Help</literal>
4037 on the grounds that a later instance declaration might overlap the local one.)
4040 The willingness to be overlapped or incoherent is a property of
4041 the <emphasis>instance declaration</emphasis> itself, controlled by the
4042 presence or otherwise of the <option>-XOverlappingInstances</option>
4043 and <option>-XIncoherentInstances</option> flags when that module is
4044 being defined. Neither flag is required in a module that imports and uses the
4045 instance declaration. Specifically, during the lookup process:
4048 An instance declaration is ignored during the lookup process if (a) a more specific
4049 match is found, and (b) the instance declaration was compiled with
4050 <option>-XOverlappingInstances</option>. The flag setting for the
4051 more-specific instance does not matter.
4054 Suppose an instance declaration does not match the constraint being looked up, but
4055 does unify with it, so that it might match when the constraint is further
4056 instantiated. Usually GHC will regard this as a reason for not committing to
4057 some other constraint. But if the instance declaration was compiled with
4058 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4059 check for that declaration.
4062 These rules make it possible for a library author to design a library that relies on
4063 overlapping instances without the library client having to know.
4066 If an instance declaration is compiled without
4067 <option>-XOverlappingInstances</option>,
4068 then that instance can never be overlapped. This could perhaps be
4069 inconvenient. Perhaps the rule should instead say that the
4070 <emphasis>overlapping</emphasis> instance declaration should be compiled in
4071 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
4072 at a usage site should be permitted regardless of how the instance declarations
4073 are compiled, if the <option>-XOverlappingInstances</option> flag is
4074 used at the usage site. (Mind you, the exact usage site can occasionally be
4075 hard to pin down.) We are interested to receive feedback on these points.
4077 <para>The <option>-XIncoherentInstances</option> flag implies the
4078 <option>-XOverlappingInstances</option> flag, but not vice versa.
4086 <sect2 id="overloaded-strings">
4087 <title>Overloaded string literals
4091 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4092 string literal has type <literal>String</literal>, but with overloaded string
4093 literals enabled (with <literal>-XOverloadedStrings</literal>)
4094 a string literal has type <literal>(IsString a) => a</literal>.
4097 This means that the usual string syntax can be used, e.g., for packed strings
4098 and other variations of string like types. String literals behave very much
4099 like integer literals, i.e., they can be used in both expressions and patterns.
4100 If used in a pattern the literal with be replaced by an equality test, in the same
4101 way as an integer literal is.
4104 The class <literal>IsString</literal> is defined as:
4106 class IsString a where
4107 fromString :: String -> a
4109 The only predefined instance is the obvious one to make strings work as usual:
4111 instance IsString [Char] where
4114 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4115 it explicitly (for example, to give an instance declaration for it), you can import it
4116 from module <literal>GHC.Exts</literal>.
4119 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4123 Each type in a default declaration must be an
4124 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4128 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4129 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4130 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4131 <emphasis>or</emphasis> <literal>IsString</literal>.
4140 import GHC.Exts( IsString(..) )
4142 newtype MyString = MyString String deriving (Eq, Show)
4143 instance IsString MyString where
4144 fromString = MyString
4146 greet :: MyString -> MyString
4147 greet "hello" = "world"
4151 print $ greet "hello"
4152 print $ greet "fool"
4156 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4157 to work since it gets translated into an equality comparison.
4163 <sect1 id="type-families">
4164 <title>Type families</title>
4167 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4168 facilitate type-level
4169 programming. Type families are a generalisation of <firstterm>associated
4170 data types</firstterm>
4171 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4172 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4173 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4174 Symposium on Principles of Programming Languages (POPL'05)”, pages
4175 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4176 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4177 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4179 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4180 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4181 themselves are described in the paper “<ulink
4182 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4183 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4185 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4186 13th ACM SIGPLAN International Conference on Functional
4187 Programming”, ACM Press, pages 51-62, 2008. Type families
4188 essentially provide type-indexed data types and named functions on types,
4189 which are useful for generic programming and highly parameterised library
4190 interfaces as well as interfaces with enhanced static information, much like
4191 dependent types. They might also be regarded as an alternative to functional
4192 dependencies, but provide a more functional style of type-level programming
4193 than the relational style of functional dependencies.
4196 Indexed type families, or type families for short, are type constructors that
4197 represent sets of types. Set members are denoted by supplying the type family
4198 constructor with type parameters, which are called <firstterm>type
4199 indices</firstterm>. The
4200 difference between vanilla parametrised type constructors and family
4201 constructors is much like between parametrically polymorphic functions and
4202 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4203 behave the same at all type instances, whereas class methods can change their
4204 behaviour in dependence on the class type parameters. Similarly, vanilla type
4205 constructors imply the same data representation for all type instances, but
4206 family constructors can have varying representation types for varying type
4210 Indexed type families come in two flavours: <firstterm>data
4211 families</firstterm> and <firstterm>type synonym
4212 families</firstterm>. They are the indexed family variants of algebraic
4213 data types and type synonyms, respectively. The instances of data families
4214 can be data types and newtypes.
4217 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4218 Additional information on the use of type families in GHC is available on
4219 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4220 Haskell wiki page on type families</ulink>.
4223 <sect2 id="data-families">
4224 <title>Data families</title>
4227 Data families appear in two flavours: (1) they can be defined on the
4229 or (2) they can appear inside type classes (in which case they are known as
4230 associated types). The former is the more general variant, as it lacks the
4231 requirement for the type-indexes to coincide with the class
4232 parameters. However, the latter can lead to more clearly structured code and
4233 compiler warnings if some type instances were - possibly accidentally -
4234 omitted. In the following, we always discuss the general toplevel form first
4235 and then cover the additional constraints placed on associated types.
4238 <sect3 id="data-family-declarations">
4239 <title>Data family declarations</title>
4242 Indexed data families are introduced by a signature, such as
4244 data family GMap k :: * -> *
4246 The special <literal>family</literal> distinguishes family from standard
4247 data declarations. The result kind annotation is optional and, as
4248 usual, defaults to <literal>*</literal> if omitted. An example is
4252 Named arguments can also be given explicit kind signatures if needed.
4254 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4255 declarations] named arguments are entirely optional, so that we can
4256 declare <literal>Array</literal> alternatively with
4258 data family Array :: * -> *
4262 <sect4 id="assoc-data-family-decl">
4263 <title>Associated data family declarations</title>
4265 When a data family is declared as part of a type class, we drop
4266 the <literal>family</literal> special. The <literal>GMap</literal>
4267 declaration takes the following form
4269 class GMapKey k where
4270 data GMap k :: * -> *
4273 In contrast to toplevel declarations, named arguments must be used for
4274 all type parameters that are to be used as type-indexes. Moreover,
4275 the argument names must be class parameters. Each class parameter may
4276 only be used at most once per associated type, but some may be omitted
4277 and they may be in an order other than in the class head. Hence, the
4278 following contrived example is admissible:
4287 <sect3 id="data-instance-declarations">
4288 <title>Data instance declarations</title>
4291 Instance declarations of data and newtype families are very similar to
4292 standard data and newtype declarations. The only two differences are
4293 that the keyword <literal>data</literal> or <literal>newtype</literal>
4294 is followed by <literal>instance</literal> and that some or all of the
4295 type arguments can be non-variable types, but may not contain forall
4296 types or type synonym families. However, data families are generally
4297 allowed in type parameters, and type synonyms are allowed as long as
4298 they are fully applied and expand to a type that is itself admissible -
4299 exactly as this is required for occurrences of type synonyms in class
4300 instance parameters. For example, the <literal>Either</literal>
4301 instance for <literal>GMap</literal> is
4303 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4305 In this example, the declaration has only one variant. In general, it
4309 Data and newtype instance declarations are only permitted when an
4310 appropriate family declaration is in scope - just as a class instance declaratoin
4311 requires the class declaration to be visible. Moreover, each instance
4312 declaration has to conform to the kind determined by its family
4313 declaration. This implies that the number of parameters of an instance
4314 declaration matches the arity determined by the kind of the family.
4317 A data family instance declaration can use the full exprssiveness of
4318 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4320 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4321 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4322 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4325 data instance T Int = T1 Int | T2 Bool
4326 newtype instance T Char = TC Bool
4329 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4330 and indeed can define a GADT. For example:
4333 data instance G [a] b where
4334 G1 :: c -> G [Int] b
4338 <listitem><para> You can use a <literal>deriving</literal> clause on a
4339 <literal>data instance</literal> or <literal>newtype instance</literal>
4346 Even if type families are defined as toplevel declarations, functions
4347 that perform different computations for different family instances may still
4348 need to be defined as methods of type classes. In particular, the
4349 following is not possible:
4352 data instance T Int = A
4353 data instance T Char = B
4355 foo A = 1 -- WRONG: These two equations together...
4356 foo B = 2 -- ...will produce a type error.
4358 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4362 instance Foo Int where
4364 instance Foo Char where
4367 (Given the functionality provided by GADTs (Generalised Algebraic Data
4368 Types), it might seem as if a definition, such as the above, should be
4369 feasible. However, type families are - in contrast to GADTs - are
4370 <emphasis>open;</emphasis> i.e., new instances can always be added,
4372 modules. Supporting pattern matching across different data instances
4373 would require a form of extensible case construct.)
4376 <sect4 id="assoc-data-inst">
4377 <title>Associated data instances</title>
4379 When an associated data family instance is declared within a type
4380 class instance, we drop the <literal>instance</literal> keyword in the
4381 family instance. So, the <literal>Either</literal> instance
4382 for <literal>GMap</literal> becomes:
4384 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4385 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4388 The most important point about associated family instances is that the
4389 type indexes corresponding to class parameters must be identical to
4390 the type given in the instance head; here this is the first argument
4391 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4392 which coincides with the only class parameter. Any parameters to the
4393 family constructor that do not correspond to class parameters, need to
4394 be variables in every instance; here this is the
4395 variable <literal>v</literal>.
4398 Instances for an associated family can only appear as part of
4399 instances declarations of the class in which the family was declared -
4400 just as with the equations of the methods of a class. Also in
4401 correspondence to how methods are handled, declarations of associated
4402 types can be omitted in class instances. If an associated family
4403 instance is omitted, the corresponding instance type is not inhabited;
4404 i.e., only diverging expressions, such
4405 as <literal>undefined</literal>, can assume the type.
4409 <sect4 id="scoping-class-params">
4410 <title>Scoping of class parameters</title>
4412 In the case of multi-parameter type classes, the visibility of class
4413 parameters in the right-hand side of associated family instances
4414 depends <emphasis>solely</emphasis> on the parameters of the data
4415 family. As an example, consider the simple class declaration
4420 Only one of the two class parameters is a parameter to the data
4421 family. Hence, the following instance declaration is invalid:
4423 instance C [c] d where
4424 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4426 Here, the right-hand side of the data instance mentions the type
4427 variable <literal>d</literal> that does not occur in its left-hand
4428 side. We cannot admit such data instances as they would compromise
4433 <sect4 id="family-class-inst">
4434 <title>Type class instances of family instances</title>
4436 Type class instances of instances of data families can be defined as
4437 usual, and in particular data instance declarations can
4438 have <literal>deriving</literal> clauses. For example, we can write
4440 data GMap () v = GMapUnit (Maybe v)
4443 which implicitly defines an instance of the form
4445 instance Show v => Show (GMap () v) where ...
4449 Note that class instances are always for
4450 particular <emphasis>instances</emphasis> of a data family and never
4451 for an entire family as a whole. This is for essentially the same
4452 reasons that we cannot define a toplevel function that performs
4453 pattern matching on the data constructors
4454 of <emphasis>different</emphasis> instances of a single type family.
4455 It would require a form of extensible case construct.
4459 <sect4 id="data-family-overlap">
4460 <title>Overlap of data instances</title>
4462 The instance declarations of a data family used in a single program
4463 may not overlap at all, independent of whether they are associated or
4464 not. In contrast to type class instances, this is not only a matter
4465 of consistency, but one of type safety.
4471 <sect3 id="data-family-import-export">
4472 <title>Import and export</title>
4475 The association of data constructors with type families is more dynamic
4476 than that is the case with standard data and newtype declarations. In
4477 the standard case, the notation <literal>T(..)</literal> in an import or
4478 export list denotes the type constructor and all the data constructors
4479 introduced in its declaration. However, a family declaration never
4480 introduces any data constructors; instead, data constructors are
4481 introduced by family instances. As a result, which data constructors
4482 are associated with a type family depends on the currently visible
4483 instance declarations for that family. Consequently, an import or
4484 export item of the form <literal>T(..)</literal> denotes the family
4485 constructor and all currently visible data constructors - in the case of
4486 an export item, these may be either imported or defined in the current
4487 module. The treatment of import and export items that explicitly list
4488 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4492 <sect4 id="data-family-impexp-assoc">
4493 <title>Associated families</title>
4495 As expected, an import or export item of the
4496 form <literal>C(..)</literal> denotes all of the class' methods and
4497 associated types. However, when associated types are explicitly
4498 listed as subitems of a class, we need some new syntax, as uppercase
4499 identifiers as subitems are usually data constructors, not type
4500 constructors. To clarify that we denote types here, each associated
4501 type name needs to be prefixed by the keyword <literal>type</literal>.
4502 So for example, when explicitly listing the components of
4503 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4504 GMap, empty, lookup, insert)</literal>.
4508 <sect4 id="data-family-impexp-examples">
4509 <title>Examples</title>
4511 Assuming our running <literal>GMapKey</literal> class example, let us
4512 look at some export lists and their meaning:
4515 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4516 just the class name.</para>
4519 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4520 Exports the class, the associated type <literal>GMap</literal>
4522 functions <literal>empty</literal>, <literal>lookup</literal>,
4523 and <literal>insert</literal>. None of the data constructors is
4527 <para><literal>module GMap (GMapKey(..), GMap(..))
4528 where...</literal>: As before, but also exports all the data
4529 constructors <literal>GMapInt</literal>,
4530 <literal>GMapChar</literal>,
4531 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4532 and <literal>GMapUnit</literal>.</para>
4535 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4536 GMap(..)) where...</literal>: As before.</para>
4539 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4540 where...</literal>: As before.</para>
4545 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4546 both the class <literal>GMapKey</literal> as well as its associated
4547 type <literal>GMap</literal>. However, you cannot
4548 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4549 sub-component specifications cannot be nested. To
4550 specify <literal>GMap</literal>'s data constructors, you have to list
4555 <sect4 id="data-family-impexp-instances">
4556 <title>Instances</title>
4558 Family instances are implicitly exported, just like class instances.
4559 However, this applies only to the heads of instances, not to the data
4560 constructors an instance defines.
4568 <sect2 id="synonym-families">
4569 <title>Synonym families</title>
4572 Type families appear in two flavours: (1) they can be defined on the
4573 toplevel or (2) they can appear inside type classes (in which case they
4574 are known as associated type synonyms). The former is the more general
4575 variant, as it lacks the requirement for the type-indexes to coincide with
4576 the class parameters. However, the latter can lead to more clearly
4577 structured code and compiler warnings if some type instances were -
4578 possibly accidentally - omitted. In the following, we always discuss the
4579 general toplevel form first and then cover the additional constraints
4580 placed on associated types.
4583 <sect3 id="type-family-declarations">
4584 <title>Type family declarations</title>
4587 Indexed type families are introduced by a signature, such as
4589 type family Elem c :: *
4591 The special <literal>family</literal> distinguishes family from standard
4592 type declarations. The result kind annotation is optional and, as
4593 usual, defaults to <literal>*</literal> if omitted. An example is
4597 Parameters can also be given explicit kind signatures if needed. We
4598 call the number of parameters in a type family declaration, the family's
4599 arity, and all applications of a type family must be fully saturated
4600 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4601 and it implies that the kind of a type family is not sufficient to
4602 determine a family's arity, and hence in general, also insufficient to
4603 determine whether a type family application is well formed. As an
4604 example, consider the following declaration:
4606 type family F a b :: * -> * -- F's arity is 2,
4607 -- although its overall kind is * -> * -> * -> *
4609 Given this declaration the following are examples of well-formed and
4612 F Char [Int] -- OK! Kind: * -> *
4613 F Char [Int] Bool -- OK! Kind: *
4614 F IO Bool -- WRONG: kind mismatch in the first argument
4615 F Bool -- WRONG: unsaturated application
4619 <sect4 id="assoc-type-family-decl">
4620 <title>Associated type family declarations</title>
4622 When a type family is declared as part of a type class, we drop
4623 the <literal>family</literal> special. The <literal>Elem</literal>
4624 declaration takes the following form
4626 class Collects ce where
4630 The argument names of the type family must be class parameters. Each
4631 class parameter may only be used at most once per associated type, but
4632 some may be omitted and they may be in an order other than in the
4633 class head. Hence, the following contrived example is admissible:
4638 These rules are exactly as for associated data families.
4643 <sect3 id="type-instance-declarations">
4644 <title>Type instance declarations</title>
4646 Instance declarations of type families are very similar to standard type
4647 synonym declarations. The only two differences are that the
4648 keyword <literal>type</literal> is followed
4649 by <literal>instance</literal> and that some or all of the type
4650 arguments can be non-variable types, but may not contain forall types or
4651 type synonym families. However, data families are generally allowed, and
4652 type synonyms are allowed as long as they are fully applied and expand
4653 to a type that is admissible - these are the exact same requirements as
4654 for data instances. For example, the <literal>[e]</literal> instance
4655 for <literal>Elem</literal> is
4657 type instance Elem [e] = e
4661 Type family instance declarations are only legitimate when an
4662 appropriate family declaration is in scope - just like class instances
4663 require the class declaration to be visible. Moreover, each instance
4664 declaration has to conform to the kind determined by its family
4665 declaration, and the number of type parameters in an instance
4666 declaration must match the number of type parameters in the family
4667 declaration. Finally, the right-hand side of a type instance must be a
4668 monotype (i.e., it may not include foralls) and after the expansion of
4669 all saturated vanilla type synonyms, no synonyms, except family synonyms
4670 may remain. Here are some examples of admissible and illegal type
4673 type family F a :: *
4674 type instance F [Int] = Int -- OK!
4675 type instance F String = Char -- OK!
4676 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4677 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4678 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4680 type family G a b :: * -> *
4681 type instance G Int = (,) -- WRONG: must be two type parameters
4682 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4686 <sect4 id="assoc-type-instance">
4687 <title>Associated type instance declarations</title>
4689 When an associated family instance is declared within a type class
4690 instance, we drop the <literal>instance</literal> keyword in the family
4691 instance. So, the <literal>[e]</literal> instance
4692 for <literal>Elem</literal> becomes:
4694 instance (Eq (Elem [e])) => Collects ([e]) where
4698 The most important point about associated family instances is that the
4699 type indexes corresponding to class parameters must be identical to the
4700 type given in the instance head; here this is <literal>[e]</literal>,
4701 which coincides with the only class parameter.
4704 Instances for an associated family can only appear as part of instances
4705 declarations of the class in which the family was declared - just as
4706 with the equations of the methods of a class. Also in correspondence to
4707 how methods are handled, declarations of associated types can be omitted
4708 in class instances. If an associated family instance is omitted, the
4709 corresponding instance type is not inhabited; i.e., only diverging
4710 expressions, such as <literal>undefined</literal>, can assume the type.
4714 <sect4 id="type-family-overlap">
4715 <title>Overlap of type synonym instances</title>
4717 The instance declarations of a type family used in a single program
4718 may only overlap if the right-hand sides of the overlapping instances
4719 coincide for the overlapping types. More formally, two instance
4720 declarations overlap if there is a substitution that makes the
4721 left-hand sides of the instances syntactically the same. Whenever
4722 that is the case, the right-hand sides of the instances must also be
4723 syntactically equal under the same substitution. This condition is
4724 independent of whether the type family is associated or not, and it is
4725 not only a matter of consistency, but one of type safety.
4728 Here are two example to illustrate the condition under which overlap
4731 type instance F (a, Int) = [a]
4732 type instance F (Int, b) = [b] -- overlap permitted
4734 type instance G (a, Int) = [a]
4735 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4740 <sect4 id="type-family-decidability">
4741 <title>Decidability of type synonym instances</title>
4743 In order to guarantee that type inference in the presence of type
4744 families decidable, we need to place a number of additional
4745 restrictions on the formation of type instance declarations (c.f.,
4746 Definition 5 (Relaxed Conditions) of “<ulink
4747 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4748 Checking with Open Type Functions</ulink>”). Instance
4749 declarations have the general form
4751 type instance F t1 .. tn = t
4753 where we require that for every type family application <literal>(G s1
4754 .. sm)</literal> in <literal>t</literal>,
4757 <para><literal>s1 .. sm</literal> do not contain any type family
4758 constructors,</para>
4761 <para>the total number of symbols (data type constructors and type
4762 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4763 in <literal>t1 .. tn</literal>, and</para>
4766 <para>for every type
4767 variable <literal>a</literal>, <literal>a</literal> occurs
4768 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4769 .. tn</literal>.</para>
4772 These restrictions are easily verified and ensure termination of type
4773 inference. However, they are not sufficient to guarantee completeness
4774 of type inference in the presence of, so called, ''loopy equalities'',
4775 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4776 a type variable is underneath a family application and data
4777 constructor application - see the above mentioned paper for details.
4780 If the option <option>-XUndecidableInstances</option> is passed to the
4781 compiler, the above restrictions are not enforced and it is on the
4782 programmer to ensure termination of the normalisation of type families
4783 during type inference.
4788 <sect3 id-="equality-constraints">
4789 <title>Equality constraints</title>
4791 Type context can include equality constraints of the form <literal>t1 ~
4792 t2</literal>, which denote that the types <literal>t1</literal>
4793 and <literal>t2</literal> need to be the same. In the presence of type
4794 families, whether two types are equal cannot generally be decided
4795 locally. Hence, the contexts of function signatures may include
4796 equality constraints, as in the following example:
4798 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4800 where we require that the element type of <literal>c1</literal>
4801 and <literal>c2</literal> are the same. In general, the
4802 types <literal>t1</literal> and <literal>t2</literal> of an equality
4803 constraint may be arbitrary monotypes; i.e., they may not contain any
4804 quantifiers, independent of whether higher-rank types are otherwise
4808 Equality constraints can also appear in class and instance contexts.
4809 The former enable a simple translation of programs using functional
4810 dependencies into programs using family synonyms instead. The general
4811 idea is to rewrite a class declaration of the form
4813 class C a b | a -> b
4817 class (F a ~ b) => C a b where
4820 That is, we represent every functional dependency (FD) <literal>a1 .. an
4821 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4822 superclass context equality <literal>F a1 .. an ~ b</literal>,
4823 essentially giving a name to the functional dependency. In class
4824 instances, we define the type instances of FD families in accordance
4825 with the class head. Method signatures are not affected by that
4829 NB: Equalities in superclass contexts are not fully implemented in
4834 <sect3 id-="ty-fams-in-instances">
4835 <title>Type families and instance declarations</title>
4836 <para>Type families require us to extend the rules for
4837 the form of instance heads, which are given
4838 in <xref linkend="flexible-instance-head"/>.
4841 <listitem><para>Data type families may appear in an instance head</para></listitem>
4842 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4844 The reason for the latter restriction is that there is no way to check for. Consider
4847 type instance F Bool = Int
4854 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4855 The situation is especially bad because the type instance for <literal>F Bool</literal>
4856 might be in another module, or even in a module that is not yet written.
4863 <sect1 id="other-type-extensions">
4864 <title>Other type system extensions</title>
4866 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4868 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4869 is used, the keyword <literal>forall</literal>
4870 allows us to say exactly what this means. For example:
4878 g :: forall b. (b -> b)
4880 The two are treated identically.
4883 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4884 a type variable any more!
4889 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4891 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4892 that the type-class constraints in a type signature must have the
4893 form <emphasis>(class type-variable)</emphasis> or
4894 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4895 With <option>-XFlexibleContexts</option>
4896 these type signatures are perfectly OK
4899 g :: Ord (T a ()) => ...
4901 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4902 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4903 (<xref linkend="instance-rules"/>).
4907 GHC imposes the following restrictions on the constraints in a type signature.
4911 forall tv1..tvn (c1, ...,cn) => type
4914 (Here, we write the "foralls" explicitly, although the Haskell source
4915 language omits them; in Haskell 98, all the free type variables of an
4916 explicit source-language type signature are universally quantified,
4917 except for the class type variables in a class declaration. However,
4918 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4927 <emphasis>Each universally quantified type variable
4928 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4930 A type variable <literal>a</literal> is "reachable" if it appears
4931 in the same constraint as either a type variable free in
4932 <literal>type</literal>, or another reachable type variable.
4933 A value with a type that does not obey
4934 this reachability restriction cannot be used without introducing
4935 ambiguity; that is why the type is rejected.
4936 Here, for example, is an illegal type:
4940 forall a. Eq a => Int
4944 When a value with this type was used, the constraint <literal>Eq tv</literal>
4945 would be introduced where <literal>tv</literal> is a fresh type variable, and
4946 (in the dictionary-translation implementation) the value would be
4947 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4948 can never know which instance of <literal>Eq</literal> to use because we never
4949 get any more information about <literal>tv</literal>.
4953 that the reachability condition is weaker than saying that <literal>a</literal> is
4954 functionally dependent on a type variable free in
4955 <literal>type</literal> (see <xref
4956 linkend="functional-dependencies"/>). The reason for this is there
4957 might be a "hidden" dependency, in a superclass perhaps. So
4958 "reachable" is a conservative approximation to "functionally dependent".
4959 For example, consider:
4961 class C a b | a -> b where ...
4962 class C a b => D a b where ...
4963 f :: forall a b. D a b => a -> a
4965 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4966 but that is not immediately apparent from <literal>f</literal>'s type.
4972 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4973 universally quantified type variables <literal>tvi</literal></emphasis>.
4975 For example, this type is OK because <literal>C a b</literal> mentions the
4976 universally quantified type variable <literal>b</literal>:
4980 forall a. C a b => burble
4984 The next type is illegal because the constraint <literal>Eq b</literal> does not
4985 mention <literal>a</literal>:
4989 forall a. Eq b => burble
4993 The reason for this restriction is milder than the other one. The
4994 excluded types are never useful or necessary (because the offending
4995 context doesn't need to be witnessed at this point; it can be floated
4996 out). Furthermore, floating them out increases sharing. Lastly,
4997 excluding them is a conservative choice; it leaves a patch of
4998 territory free in case we need it later.
5009 <sect2 id="implicit-parameters">
5010 <title>Implicit parameters</title>
5012 <para> Implicit parameters are implemented as described in
5013 "Implicit parameters: dynamic scoping with static types",
5014 J Lewis, MB Shields, E Meijer, J Launchbury,
5015 27th ACM Symposium on Principles of Programming Languages (POPL'00),
5019 <para>(Most of the following, still rather incomplete, documentation is
5020 due to Jeff Lewis.)</para>
5022 <para>Implicit parameter support is enabled with the option
5023 <option>-XImplicitParams</option>.</para>
5026 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
5027 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
5028 context. In Haskell, all variables are statically bound. Dynamic
5029 binding of variables is a notion that goes back to Lisp, but was later
5030 discarded in more modern incarnations, such as Scheme. Dynamic binding
5031 can be very confusing in an untyped language, and unfortunately, typed
5032 languages, in particular Hindley-Milner typed languages like Haskell,
5033 only support static scoping of variables.
5036 However, by a simple extension to the type class system of Haskell, we
5037 can support dynamic binding. Basically, we express the use of a
5038 dynamically bound variable as a constraint on the type. These
5039 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
5040 function uses a dynamically-bound variable <literal>?x</literal>
5041 of type <literal>t'</literal>". For
5042 example, the following expresses the type of a sort function,
5043 implicitly parameterized by a comparison function named <literal>cmp</literal>.
5045 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5047 The dynamic binding constraints are just a new form of predicate in the type class system.
5050 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5051 where <literal>x</literal> is
5052 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5053 Use of this construct also introduces a new
5054 dynamic-binding constraint in the type of the expression.
5055 For example, the following definition
5056 shows how we can define an implicitly parameterized sort function in
5057 terms of an explicitly parameterized <literal>sortBy</literal> function:
5059 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5061 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5067 <title>Implicit-parameter type constraints</title>
5069 Dynamic binding constraints behave just like other type class
5070 constraints in that they are automatically propagated. Thus, when a
5071 function is used, its implicit parameters are inherited by the
5072 function that called it. For example, our <literal>sort</literal> function might be used
5073 to pick out the least value in a list:
5075 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5076 least xs = head (sort xs)
5078 Without lifting a finger, the <literal>?cmp</literal> parameter is
5079 propagated to become a parameter of <literal>least</literal> as well. With explicit
5080 parameters, the default is that parameters must always be explicit
5081 propagated. With implicit parameters, the default is to always
5085 An implicit-parameter type constraint differs from other type class constraints in the
5086 following way: All uses of a particular implicit parameter must have
5087 the same type. This means that the type of <literal>(?x, ?x)</literal>
5088 is <literal>(?x::a) => (a,a)</literal>, and not
5089 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5093 <para> You can't have an implicit parameter in the context of a class or instance
5094 declaration. For example, both these declarations are illegal:
5096 class (?x::Int) => C a where ...
5097 instance (?x::a) => Foo [a] where ...
5099 Reason: exactly which implicit parameter you pick up depends on exactly where
5100 you invoke a function. But the ``invocation'' of instance declarations is done
5101 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5102 Easiest thing is to outlaw the offending types.</para>
5104 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5106 f :: (?x :: [a]) => Int -> Int
5109 g :: (Read a, Show a) => String -> String
5112 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5113 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5114 quite unambiguous, and fixes the type <literal>a</literal>.
5119 <title>Implicit-parameter bindings</title>
5122 An implicit parameter is <emphasis>bound</emphasis> using the standard
5123 <literal>let</literal> or <literal>where</literal> binding forms.
5124 For example, we define the <literal>min</literal> function by binding
5125 <literal>cmp</literal>.
5128 min = let ?cmp = (<=) in least
5132 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5133 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5134 (including in a list comprehension, or do-notation, or pattern guards),
5135 or a <literal>where</literal> clause.
5136 Note the following points:
5139 An implicit-parameter binding group must be a
5140 collection of simple bindings to implicit-style variables (no
5141 function-style bindings, and no type signatures); these bindings are
5142 neither polymorphic or recursive.
5145 You may not mix implicit-parameter bindings with ordinary bindings in a
5146 single <literal>let</literal>
5147 expression; use two nested <literal>let</literal>s instead.
5148 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5152 You may put multiple implicit-parameter bindings in a
5153 single binding group; but they are <emphasis>not</emphasis> treated
5154 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5155 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5156 parameter. The bindings are not nested, and may be re-ordered without changing
5157 the meaning of the program.
5158 For example, consider:
5160 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5162 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5163 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5165 f :: (?x::Int) => Int -> Int
5173 <sect3><title>Implicit parameters and polymorphic recursion</title>
5176 Consider these two definitions:
5179 len1 xs = let ?acc = 0 in len_acc1 xs
5182 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5187 len2 xs = let ?acc = 0 in len_acc2 xs
5189 len_acc2 :: (?acc :: Int) => [a] -> Int
5191 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5193 The only difference between the two groups is that in the second group
5194 <literal>len_acc</literal> is given a type signature.
5195 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5196 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5197 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5198 has a type signature, the recursive call is made to the
5199 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5200 as an implicit parameter. So we get the following results in GHCi:
5207 Adding a type signature dramatically changes the result! This is a rather
5208 counter-intuitive phenomenon, worth watching out for.
5212 <sect3><title>Implicit parameters and monomorphism</title>
5214 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5215 Haskell Report) to implicit parameters. For example, consider:
5223 Since the binding for <literal>y</literal> falls under the Monomorphism
5224 Restriction it is not generalised, so the type of <literal>y</literal> is
5225 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5226 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5227 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5228 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5229 <literal>y</literal> in the body of the <literal>let</literal> will see the
5230 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5231 <literal>14</literal>.
5236 <!-- ======================= COMMENTED OUT ========================
5238 We intend to remove linear implicit parameters, so I'm at least removing
5239 them from the 6.6 user manual
5241 <sect2 id="linear-implicit-parameters">
5242 <title>Linear implicit parameters</title>
5244 Linear implicit parameters are an idea developed by Koen Claessen,
5245 Mark Shields, and Simon PJ. They address the long-standing
5246 problem that monads seem over-kill for certain sorts of problem, notably:
5249 <listitem> <para> distributing a supply of unique names </para> </listitem>
5250 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5251 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5255 Linear implicit parameters are just like ordinary implicit parameters,
5256 except that they are "linear"; that is, they cannot be copied, and
5257 must be explicitly "split" instead. Linear implicit parameters are
5258 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5259 (The '/' in the '%' suggests the split!)
5264 import GHC.Exts( Splittable )
5266 data NameSupply = ...
5268 splitNS :: NameSupply -> (NameSupply, NameSupply)
5269 newName :: NameSupply -> Name
5271 instance Splittable NameSupply where
5275 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5276 f env (Lam x e) = Lam x' (f env e)
5279 env' = extend env x x'
5280 ...more equations for f...
5282 Notice that the implicit parameter %ns is consumed
5284 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5285 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5289 So the translation done by the type checker makes
5290 the parameter explicit:
5292 f :: NameSupply -> Env -> Expr -> Expr
5293 f ns env (Lam x e) = Lam x' (f ns1 env e)
5295 (ns1,ns2) = splitNS ns
5297 env = extend env x x'
5299 Notice the call to 'split' introduced by the type checker.
5300 How did it know to use 'splitNS'? Because what it really did
5301 was to introduce a call to the overloaded function 'split',
5302 defined by the class <literal>Splittable</literal>:
5304 class Splittable a where
5307 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5308 split for name supplies. But we can simply write
5314 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5316 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5317 <literal>GHC.Exts</literal>.
5322 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5323 are entirely distinct implicit parameters: you
5324 can use them together and they won't interfere with each other. </para>
5327 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5329 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5330 in the context of a class or instance declaration. </para></listitem>
5334 <sect3><title>Warnings</title>
5337 The monomorphism restriction is even more important than usual.
5338 Consider the example above:
5340 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5341 f env (Lam x e) = Lam x' (f env e)
5344 env' = extend env x x'
5346 If we replaced the two occurrences of x' by (newName %ns), which is
5347 usually a harmless thing to do, we get:
5349 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5350 f env (Lam x e) = Lam (newName %ns) (f env e)
5352 env' = extend env x (newName %ns)
5354 But now the name supply is consumed in <emphasis>three</emphasis> places
5355 (the two calls to newName,and the recursive call to f), so
5356 the result is utterly different. Urk! We don't even have
5360 Well, this is an experimental change. With implicit
5361 parameters we have already lost beta reduction anyway, and
5362 (as John Launchbury puts it) we can't sensibly reason about
5363 Haskell programs without knowing their typing.
5368 <sect3><title>Recursive functions</title>
5369 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5372 foo :: %x::T => Int -> [Int]
5374 foo n = %x : foo (n-1)
5376 where T is some type in class Splittable.</para>
5378 Do you get a list of all the same T's or all different T's
5379 (assuming that split gives two distinct T's back)?
5381 If you supply the type signature, taking advantage of polymorphic
5382 recursion, you get what you'd probably expect. Here's the
5383 translated term, where the implicit param is made explicit:
5386 foo x n = let (x1,x2) = split x
5387 in x1 : foo x2 (n-1)
5389 But if you don't supply a type signature, GHC uses the Hindley
5390 Milner trick of using a single monomorphic instance of the function
5391 for the recursive calls. That is what makes Hindley Milner type inference
5392 work. So the translation becomes
5396 foom n = x : foom (n-1)
5400 Result: 'x' is not split, and you get a list of identical T's. So the
5401 semantics of the program depends on whether or not foo has a type signature.
5404 You may say that this is a good reason to dislike linear implicit parameters
5405 and you'd be right. That is why they are an experimental feature.
5411 ================ END OF Linear Implicit Parameters commented out -->
5413 <sect2 id="kinding">
5414 <title>Explicitly-kinded quantification</title>
5417 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5418 to give the kind explicitly as (machine-checked) documentation,
5419 just as it is nice to give a type signature for a function. On some occasions,
5420 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5421 John Hughes had to define the data type:
5423 data Set cxt a = Set [a]
5424 | Unused (cxt a -> ())
5426 The only use for the <literal>Unused</literal> constructor was to force the correct
5427 kind for the type variable <literal>cxt</literal>.
5430 GHC now instead allows you to specify the kind of a type variable directly, wherever
5431 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5434 This flag enables kind signatures in the following places:
5436 <listitem><para><literal>data</literal> declarations:
5438 data Set (cxt :: * -> *) a = Set [a]
5439 </screen></para></listitem>
5440 <listitem><para><literal>type</literal> declarations:
5442 type T (f :: * -> *) = f Int
5443 </screen></para></listitem>
5444 <listitem><para><literal>class</literal> declarations:
5446 class (Eq a) => C (f :: * -> *) a where ...
5447 </screen></para></listitem>
5448 <listitem><para><literal>forall</literal>'s in type signatures:
5450 f :: forall (cxt :: * -> *). Set cxt Int
5451 </screen></para></listitem>
5456 The parentheses are required. Some of the spaces are required too, to
5457 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5458 will get a parse error, because "<literal>::*->*</literal>" is a
5459 single lexeme in Haskell.
5463 As part of the same extension, you can put kind annotations in types
5466 f :: (Int :: *) -> Int
5467 g :: forall a. a -> (a :: *)
5471 atype ::= '(' ctype '::' kind ')
5473 The parentheses are required.
5478 <sect2 id="universal-quantification">
5479 <title>Arbitrary-rank polymorphism
5483 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5484 explicit universal quantification in
5486 For example, all the following types are legal:
5488 f1 :: forall a b. a -> b -> a
5489 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5491 f2 :: (forall a. a->a) -> Int -> Int
5492 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5494 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5496 f4 :: Int -> (forall a. a -> a)
5498 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5499 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5500 The <literal>forall</literal> makes explicit the universal quantification that
5501 is implicitly added by Haskell.
5504 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5505 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5506 shows, the polymorphic type on the left of the function arrow can be overloaded.
5509 The function <literal>f3</literal> has a rank-3 type;
5510 it has rank-2 types on the left of a function arrow.
5513 GHC has three flags to control higher-rank types:
5516 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5519 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5522 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5523 That is, you can nest <literal>forall</literal>s
5524 arbitrarily deep in function arrows.
5525 In particular, a forall-type (also called a "type scheme"),
5526 including an operational type class context, is legal:
5528 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5529 of a function arrow </para> </listitem>
5530 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5531 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5532 field type signatures.</para> </listitem>
5533 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5534 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5546 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5547 the types of the constructor arguments. Here are several examples:
5553 data T a = T1 (forall b. b -> b -> b) a
5555 data MonadT m = MkMonad { return :: forall a. a -> m a,
5556 bind :: forall a b. m a -> (a -> m b) -> m b
5559 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5565 The constructors have rank-2 types:
5571 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5572 MkMonad :: forall m. (forall a. a -> m a)
5573 -> (forall a b. m a -> (a -> m b) -> m b)
5575 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5581 Notice that you don't need to use a <literal>forall</literal> if there's an
5582 explicit context. For example in the first argument of the
5583 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5584 prefixed to the argument type. The implicit <literal>forall</literal>
5585 quantifies all type variables that are not already in scope, and are
5586 mentioned in the type quantified over.
5590 As for type signatures, implicit quantification happens for non-overloaded
5591 types too. So if you write this:
5594 data T a = MkT (Either a b) (b -> b)
5597 it's just as if you had written this:
5600 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5603 That is, since the type variable <literal>b</literal> isn't in scope, it's
5604 implicitly universally quantified. (Arguably, it would be better
5605 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5606 where that is what is wanted. Feedback welcomed.)
5610 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5611 the constructor to suitable values, just as usual. For example,
5622 a3 = MkSwizzle reverse
5625 a4 = let r x = Just x
5632 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5633 mkTs f x y = [T1 f x, T1 f y]
5639 The type of the argument can, as usual, be more general than the type
5640 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5641 does not need the <literal>Ord</literal> constraint.)
5645 When you use pattern matching, the bound variables may now have
5646 polymorphic types. For example:
5652 f :: T a -> a -> (a, Char)
5653 f (T1 w k) x = (w k x, w 'c' 'd')
5655 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5656 g (MkSwizzle s) xs f = s (map f (s xs))
5658 h :: MonadT m -> [m a] -> m [a]
5659 h m [] = return m []
5660 h m (x:xs) = bind m x $ \y ->
5661 bind m (h m xs) $ \ys ->
5668 In the function <function>h</function> we use the record selectors <literal>return</literal>
5669 and <literal>bind</literal> to extract the polymorphic bind and return functions
5670 from the <literal>MonadT</literal> data structure, rather than using pattern
5676 <title>Type inference</title>
5679 In general, type inference for arbitrary-rank types is undecidable.
5680 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5681 to get a decidable algorithm by requiring some help from the programmer.
5682 We do not yet have a formal specification of "some help" but the rule is this:
5685 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5686 provides an explicit polymorphic type for x, or GHC's type inference will assume
5687 that x's type has no foralls in it</emphasis>.
5690 What does it mean to "provide" an explicit type for x? You can do that by
5691 giving a type signature for x directly, using a pattern type signature
5692 (<xref linkend="scoped-type-variables"/>), thus:
5694 \ f :: (forall a. a->a) -> (f True, f 'c')
5696 Alternatively, you can give a type signature to the enclosing
5697 context, which GHC can "push down" to find the type for the variable:
5699 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5701 Here the type signature on the expression can be pushed inwards
5702 to give a type signature for f. Similarly, and more commonly,
5703 one can give a type signature for the function itself:
5705 h :: (forall a. a->a) -> (Bool,Char)
5706 h f = (f True, f 'c')
5708 You don't need to give a type signature if the lambda bound variable
5709 is a constructor argument. Here is an example we saw earlier:
5711 f :: T a -> a -> (a, Char)
5712 f (T1 w k) x = (w k x, w 'c' 'd')
5714 Here we do not need to give a type signature to <literal>w</literal>, because
5715 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5722 <sect3 id="implicit-quant">
5723 <title>Implicit quantification</title>
5726 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5727 user-written types, if and only if there is no explicit <literal>forall</literal>,
5728 GHC finds all the type variables mentioned in the type that are not already
5729 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5733 f :: forall a. a -> a
5740 h :: forall b. a -> b -> b
5746 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5749 f :: (a -> a) -> Int
5751 f :: forall a. (a -> a) -> Int
5753 f :: (forall a. a -> a) -> Int
5756 g :: (Ord a => a -> a) -> Int
5757 -- MEANS the illegal type
5758 g :: forall a. (Ord a => a -> a) -> Int
5760 g :: (forall a. Ord a => a -> a) -> Int
5762 The latter produces an illegal type, which you might think is silly,
5763 but at least the rule is simple. If you want the latter type, you
5764 can write your for-alls explicitly. Indeed, doing so is strongly advised
5771 <sect2 id="impredicative-polymorphism">
5772 <title>Impredicative polymorphism
5774 <para><emphasis>NOTE: the impredicative-polymorphism feature is deprecated in GHC 6.12, and
5775 will be removed or replaced in GHC 6.14.</emphasis></para>
5777 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5778 enabled with <option>-XImpredicativeTypes</option>.
5780 that you can call a polymorphic function at a polymorphic type, and
5781 parameterise data structures over polymorphic types. For example:
5783 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5784 f (Just g) = Just (g [3], g "hello")
5787 Notice here that the <literal>Maybe</literal> type is parameterised by the
5788 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5791 <para>The technical details of this extension are described in the paper
5792 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5793 type inference for higher-rank types and impredicativity</ulink>,
5794 which appeared at ICFP 2006.
5798 <sect2 id="scoped-type-variables">
5799 <title>Lexically scoped type variables
5803 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5804 which some type signatures are simply impossible to write. For example:
5806 f :: forall a. [a] -> [a]
5812 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5813 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5814 The type variables bound by a <literal>forall</literal> scope over
5815 the entire definition of the accompanying value declaration.
5816 In this example, the type variable <literal>a</literal> scopes over the whole
5817 definition of <literal>f</literal>, including over
5818 the type signature for <varname>ys</varname>.
5819 In Haskell 98 it is not possible to declare
5820 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5821 it becomes possible to do so.
5823 <para>Lexically-scoped type variables are enabled by
5824 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5826 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5827 variables work, compared to earlier releases. Read this section
5831 <title>Overview</title>
5833 <para>The design follows the following principles
5835 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5836 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5837 design.)</para></listitem>
5838 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5839 type variables. This means that every programmer-written type signature
5840 (including one that contains free scoped type variables) denotes a
5841 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5842 checker, and no inference is involved.</para></listitem>
5843 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5844 changing the program.</para></listitem>
5848 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5850 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5851 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5852 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5853 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5857 In Haskell, a programmer-written type signature is implicitly quantified over
5858 its free type variables (<ulink
5859 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5861 of the Haskell Report).
5862 Lexically scoped type variables affect this implicit quantification rules
5863 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5864 quantified. For example, if type variable <literal>a</literal> is in scope,
5867 (e :: a -> a) means (e :: a -> a)
5868 (e :: b -> b) means (e :: forall b. b->b)
5869 (e :: a -> b) means (e :: forall b. a->b)
5877 <sect3 id="decl-type-sigs">
5878 <title>Declaration type signatures</title>
5879 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5880 quantification (using <literal>forall</literal>) brings into scope the
5881 explicitly-quantified
5882 type variables, in the definition of the named function. For example:
5884 f :: forall a. [a] -> [a]
5885 f (x:xs) = xs ++ [ x :: a ]
5887 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5888 the definition of "<literal>f</literal>".
5890 <para>This only happens if:
5892 <listitem><para> The quantification in <literal>f</literal>'s type
5893 signature is explicit. For example:
5896 g (x:xs) = xs ++ [ x :: a ]
5898 This program will be rejected, because "<literal>a</literal>" does not scope
5899 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5900 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5901 quantification rules.
5903 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5904 not a pattern binding.
5907 f1 :: forall a. [a] -> [a]
5908 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5910 f2 :: forall a. [a] -> [a]
5911 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5913 f3 :: forall a. [a] -> [a]
5914 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5916 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5917 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5918 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5919 the type signature brings <literal>a</literal> into scope.
5925 <sect3 id="exp-type-sigs">
5926 <title>Expression type signatures</title>
5928 <para>An expression type signature that has <emphasis>explicit</emphasis>
5929 quantification (using <literal>forall</literal>) brings into scope the
5930 explicitly-quantified
5931 type variables, in the annotated expression. For example:
5933 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5935 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5936 type variable <literal>s</literal> into scope, in the annotated expression
5937 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5942 <sect3 id="pattern-type-sigs">
5943 <title>Pattern type signatures</title>
5945 A type signature may occur in any pattern; this is a <emphasis>pattern type
5946 signature</emphasis>.
5949 -- f and g assume that 'a' is already in scope
5950 f = \(x::Int, y::a) -> x
5952 h ((x,y) :: (Int,Bool)) = (y,x)
5954 In the case where all the type variables in the pattern type signature are
5955 already in scope (i.e. bound by the enclosing context), matters are simple: the
5956 signature simply constrains the type of the pattern in the obvious way.
5959 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5960 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5961 that are already in scope. For example:
5963 f :: forall a. [a] -> (Int, [a])
5966 (ys::[a], n) = (reverse xs, length xs) -- OK
5967 zs::[a] = xs ++ ys -- OK
5969 Just (v::b) = ... -- Not OK; b is not in scope
5971 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5972 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5976 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5977 type signature may mention a type variable that is not in scope; in this case,
5978 <emphasis>the signature brings that type variable into scope</emphasis>.
5979 This is particularly important for existential data constructors. For example:
5981 data T = forall a. MkT [a]
5984 k (MkT [t::a]) = MkT t3
5988 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5989 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5990 because it is bound by the pattern match. GHC's rule is that in this situation
5991 (and only then), a pattern type signature can mention a type variable that is
5992 not already in scope; the effect is to bring it into scope, standing for the
5993 existentially-bound type variable.
5996 When a pattern type signature binds a type variable in this way, GHC insists that the
5997 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5998 This means that any user-written type signature always stands for a completely known type.
6001 If all this seems a little odd, we think so too. But we must have
6002 <emphasis>some</emphasis> way to bring such type variables into scope, else we
6003 could not name existentially-bound type variables in subsequent type signatures.
6006 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
6007 signature is allowed to mention a lexical variable that is not already in
6009 For example, both <literal>f</literal> and <literal>g</literal> would be
6010 illegal if <literal>a</literal> was not already in scope.
6016 <!-- ==================== Commented out part about result type signatures
6018 <sect3 id="result-type-sigs">
6019 <title>Result type signatures</title>
6022 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
6025 {- f assumes that 'a' is already in scope -}
6026 f x y :: [a] = [x,y,x]
6028 g = \ x :: [Int] -> [3,4]
6030 h :: forall a. [a] -> a
6034 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
6035 the result of the function. Similarly, the body of the lambda in the RHS of
6036 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
6037 alternative in <literal>h</literal> is <literal>a</literal>.
6039 <para> A result type signature never brings new type variables into scope.</para>
6041 There are a couple of syntactic wrinkles. First, notice that all three
6042 examples would parse quite differently with parentheses:
6044 {- f assumes that 'a' is already in scope -}
6045 f x (y :: [a]) = [x,y,x]
6047 g = \ (x :: [Int]) -> [3,4]
6049 h :: forall a. [a] -> a
6053 Now the signature is on the <emphasis>pattern</emphasis>; and
6054 <literal>h</literal> would certainly be ill-typed (since the pattern
6055 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6057 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6058 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6059 token or a parenthesised type of some sort). To see why,
6060 consider how one would parse this:
6069 <sect3 id="cls-inst-scoped-tyvars">
6070 <title>Class and instance declarations</title>
6073 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6074 scope over the methods defined in the <literal>where</literal> part. For example:
6092 <sect2 id="typing-binds">
6093 <title>Generalised typing of mutually recursive bindings</title>
6096 The Haskell Report specifies that a group of bindings (at top level, or in a
6097 <literal>let</literal> or <literal>where</literal>) should be sorted into
6098 strongly-connected components, and then type-checked in dependency order
6099 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6100 Report, Section 4.5.1</ulink>).
6101 As each group is type-checked, any binders of the group that
6103 an explicit type signature are put in the type environment with the specified
6105 and all others are monomorphic until the group is generalised
6106 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6109 <para>Following a suggestion of Mark Jones, in his paper
6110 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6112 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6114 <emphasis>the dependency analysis ignores references to variables that have an explicit
6115 type signature</emphasis>.
6116 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6117 typecheck. For example, consider:
6119 f :: Eq a => a -> Bool
6120 f x = (x == x) || g True || g "Yes"
6122 g y = (y <= y) || f True
6124 This is rejected by Haskell 98, but under Jones's scheme the definition for
6125 <literal>g</literal> is typechecked first, separately from that for
6126 <literal>f</literal>,
6127 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6128 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6129 type is generalised, to get
6131 g :: Ord a => a -> Bool
6133 Now, the definition for <literal>f</literal> is typechecked, with this type for
6134 <literal>g</literal> in the type environment.
6138 The same refined dependency analysis also allows the type signatures of
6139 mutually-recursive functions to have different contexts, something that is illegal in
6140 Haskell 98 (Section 4.5.2, last sentence). With
6141 <option>-XRelaxedPolyRec</option>
6142 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6143 type signatures; in practice this means that only variables bound by the same
6144 pattern binding must have the same context. For example, this is fine:
6146 f :: Eq a => a -> Bool
6147 f x = (x == x) || g True
6149 g :: Ord a => a -> Bool
6150 g y = (y <= y) || f True
6155 <sect2 id="mono-local-binds">
6156 <title>Monomorphic local bindings</title>
6158 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6159 The rationale is described in the paper
6160 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6163 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6164 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6165 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6166 If you supply a type signature, then the flag has no effect.
6171 <!-- ==================== End of type system extensions ================= -->
6173 <!-- ====================== TEMPLATE HASKELL ======================= -->
6175 <sect1 id="template-haskell">
6176 <title>Template Haskell</title>
6178 <para>Template Haskell allows you to do compile-time meta-programming in
6181 the main technical innovations is discussed in "<ulink
6182 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6183 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6186 There is a Wiki page about
6187 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6188 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6192 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6193 Haskell library reference material</ulink>
6194 (look for module <literal>Language.Haskell.TH</literal>).
6195 Many changes to the original design are described in
6196 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6197 Notes on Template Haskell version 2</ulink>.
6198 Not all of these changes are in GHC, however.
6201 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6202 as a worked example to help get you started.
6206 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6207 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6212 <title>Syntax</title>
6214 <para> Template Haskell has the following new syntactic
6215 constructions. You need to use the flag
6216 <option>-XTemplateHaskell</option>
6217 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6218 </indexterm>to switch these syntactic extensions on
6219 (<option>-XTemplateHaskell</option> is no longer implied by
6220 <option>-fglasgow-exts</option>).</para>
6224 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6225 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6226 There must be no space between the "$" and the identifier or parenthesis. This use
6227 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6228 of "." as an infix operator. If you want the infix operator, put spaces around it.
6230 <para> A splice can occur in place of
6232 <listitem><para> an expression; the spliced expression must
6233 have type <literal>Q Exp</literal></para></listitem>
6234 <listitem><para> an type; the spliced expression must
6235 have type <literal>Q Typ</literal></para></listitem>
6236 <listitem><para> a list of top-level declarations; the spliced expression
6237 must have type <literal>Q [Dec]</literal></para></listitem>
6239 Note that pattern splices are not supported.
6240 Inside a splice you can can only call functions defined in imported modules,
6241 not functions defined elsewhere in the same module.</para></listitem>
6244 A expression quotation is written in Oxford brackets, thus:
6246 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6247 where the "..." is an expression;
6248 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6249 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6250 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6251 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6252 the quotation has type <literal>Q Type</literal>.</para></listitem>
6253 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6254 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6255 </itemizedlist></para></listitem>
6258 A quasi-quotation can appear in either a pattern context or an
6259 expression context and is also written in Oxford brackets:
6261 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6262 where the "..." is an arbitrary string; a full description of the
6263 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6264 </itemizedlist></para></listitem>
6267 A name can be quoted with either one or two prefix single quotes:
6269 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6270 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6271 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6273 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6274 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6277 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6278 may also be given as an argument to the <literal>reify</literal> function.
6282 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6283 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6290 $(deriveStuff 'f) -- Uses the $(...) notation
6294 deriveStuff 'g -- Omits the $(...)
6298 This abbreviation makes top-level declaration slices quieter and less intimidating.
6303 (Compared to the original paper, there are many differences of detail.
6304 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6305 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6306 Pattern splices and quotations are not implemented.)
6310 <sect2> <title> Using Template Haskell </title>
6314 The data types and monadic constructor functions for Template Haskell are in the library
6315 <literal>Language.Haskell.THSyntax</literal>.
6319 You can only run a function at compile time if it is imported from another module. That is,
6320 you can't define a function in a module, and call it from within a splice in the same module.
6321 (It would make sense to do so, but it's hard to implement.)
6325 You can only run a function at compile time if it is imported
6326 from another module <emphasis>that is not part of a mutually-recursive group of modules
6327 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6328 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6329 splice is to be run.</para>
6331 For example, when compiling module A,
6332 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6333 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6337 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6340 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6341 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6342 compiles and runs a program, and then looks at the result. So it's important that
6343 the program it compiles produces results whose representations are identical to
6344 those of the compiler itself.
6348 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6349 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6354 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6355 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6356 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6363 -- Import our template "pr"
6364 import Printf ( pr )
6366 -- The splice operator $ takes the Haskell source code
6367 -- generated at compile time by "pr" and splices it into
6368 -- the argument of "putStrLn".
6369 main = putStrLn ( $(pr "Hello") )
6375 -- Skeletal printf from the paper.
6376 -- It needs to be in a separate module to the one where
6377 -- you intend to use it.
6379 -- Import some Template Haskell syntax
6380 import Language.Haskell.TH
6382 -- Describe a format string
6383 data Format = D | S | L String
6385 -- Parse a format string. This is left largely to you
6386 -- as we are here interested in building our first ever
6387 -- Template Haskell program and not in building printf.
6388 parse :: String -> [Format]
6391 -- Generate Haskell source code from a parsed representation
6392 -- of the format string. This code will be spliced into
6393 -- the module which calls "pr", at compile time.
6394 gen :: [Format] -> Q Exp
6395 gen [D] = [| \n -> show n |]
6396 gen [S] = [| \s -> s |]
6397 gen [L s] = stringE s
6399 -- Here we generate the Haskell code for the splice
6400 -- from an input format string.
6401 pr :: String -> Q Exp
6402 pr s = gen (parse s)
6405 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6408 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6411 <para>Run "main.exe" and here is your output:</para>
6421 <title>Using Template Haskell with Profiling</title>
6422 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6424 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6425 interpreter to run the splice expressions. The bytecode interpreter
6426 runs the compiled expression on top of the same runtime on which GHC
6427 itself is running; this means that the compiled code referred to by
6428 the interpreted expression must be compatible with this runtime, and
6429 in particular this means that object code that is compiled for
6430 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6431 expression, because profiled object code is only compatible with the
6432 profiling version of the runtime.</para>
6434 <para>This causes difficulties if you have a multi-module program
6435 containing Template Haskell code and you need to compile it for
6436 profiling, because GHC cannot load the profiled object code and use it
6437 when executing the splices. Fortunately GHC provides a workaround.
6438 The basic idea is to compile the program twice:</para>
6442 <para>Compile the program or library first the normal way, without
6443 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6446 <para>Then compile it again with <option>-prof</option>, and
6447 additionally use <option>-osuf
6448 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6449 to name the object files differently (you can choose any suffix
6450 that isn't the normal object suffix here). GHC will automatically
6451 load the object files built in the first step when executing splice
6452 expressions. If you omit the <option>-osuf</option> flag when
6453 building with <option>-prof</option> and Template Haskell is used,
6454 GHC will emit an error message. </para>
6459 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6460 <para>Quasi-quotation allows patterns and expressions to be written using
6461 programmer-defined concrete syntax; the motivation behind the extension and
6462 several examples are documented in
6463 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6464 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6465 2007). The example below shows how to write a quasiquoter for a simple
6466 expression language.</para>
6468 Here are the salient features
6471 A quasi-quote has the form
6472 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6475 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6476 quoter; it cannot be an arbitrary expression.
6479 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6480 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6481 those overlap with Template Haskell quotations.
6484 There must be no spaces in the token
6485 <literal>[<replaceable>quoter</replaceable>|</literal>.
6488 The quoted <replaceable>string</replaceable>
6489 can be arbitrary, and may contain newlines.
6495 A quasiquote may appear in place of
6497 <listitem><para>An expression</para></listitem>
6498 <listitem><para>A pattern</para></listitem>
6499 <listitem><para>A type</para></listitem>
6500 <listitem><para>A top-level declaration</para></listitem>
6502 (Only the first two are described in the paper.)
6506 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6507 which is defined thus:
6509 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6510 quotePat :: String -> Q Pat,
6511 quoteType :: String -> Q Type,
6512 quoteDec :: String -> Q [Dec] }
6514 That is, a quoter is a tuple of four parsers, one for each of the contexts
6515 in which a quasi-quote can occur.
6518 A quasi-quote is expanded by applying the appropriate parser to the string
6519 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6520 type, declaration) determines which of the parsers is called.
6525 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6526 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6527 The example makes use of an antiquoted
6528 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6529 (this syntax for anti-quotation was defined by the parser's
6530 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6531 integer value argument of the constructor <literal>IntExpr</literal> when
6532 pattern matching. Please see the referenced paper for further details regarding
6533 anti-quotation as well as the description of a technique that uses SYB to
6534 leverage a single parser of type <literal>String -> a</literal> to generate both
6535 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6536 pattern parser that returns a value of type <literal>Q Pat</literal>.
6540 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6541 the example, <literal>expr</literal> cannot be defined
6542 in <literal>Main.hs</literal> where it is used, but must be imported.
6546 {- ------------- file Main.hs --------------- -}
6552 main = do { print $ eval [expr|1 + 2|]
6554 { [expr|'int:n|] -> print n
6560 {- ------------- file Expr.hs --------------- -}
6563 import qualified Language.Haskell.TH as TH
6564 import Language.Haskell.TH.Quote
6566 data Expr = IntExpr Integer
6567 | AntiIntExpr String
6568 | BinopExpr BinOp Expr Expr
6570 deriving(Show, Typeable, Data)
6576 deriving(Show, Typeable, Data)
6578 eval :: Expr -> Integer
6579 eval (IntExpr n) = n
6580 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6587 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6589 -- Parse an Expr, returning its representation as
6590 -- either a Q Exp or a Q Pat. See the referenced paper
6591 -- for how to use SYB to do this by writing a single
6592 -- parser of type String -> Expr instead of two
6593 -- separate parsers.
6595 parseExprExp :: String -> Q Exp
6598 parseExprPat :: String -> Q Pat
6602 <para>Now run the compiler:
6604 $ ghc --make -XQuasiQuotes Main.hs -o main
6608 <para>Run "main" and here is your output:
6619 <!-- ===================== Arrow notation =================== -->
6621 <sect1 id="arrow-notation">
6622 <title>Arrow notation
6625 <para>Arrows are a generalization of monads introduced by John Hughes.
6626 For more details, see
6631 “Generalising Monads to Arrows”,
6632 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6633 pp67–111, May 2000.
6634 The paper that introduced arrows: a friendly introduction, motivated with
6635 programming examples.
6641 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6642 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6643 Introduced the notation described here.
6649 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6650 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6657 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6658 John Hughes, in <citetitle>5th International Summer School on
6659 Advanced Functional Programming</citetitle>,
6660 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6662 This paper includes another introduction to the notation,
6663 with practical examples.
6669 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6670 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6671 A terse enumeration of the formal rules used
6672 (extracted from comments in the source code).
6678 The arrows web page at
6679 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6684 With the <option>-XArrows</option> flag, GHC supports the arrow
6685 notation described in the second of these papers,
6686 translating it using combinators from the
6687 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6689 What follows is a brief introduction to the notation;
6690 it won't make much sense unless you've read Hughes's paper.
6693 <para>The extension adds a new kind of expression for defining arrows:
6695 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6696 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6698 where <literal>proc</literal> is a new keyword.
6699 The variables of the pattern are bound in the body of the
6700 <literal>proc</literal>-expression,
6701 which is a new sort of thing called a <firstterm>command</firstterm>.
6702 The syntax of commands is as follows:
6704 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6705 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6706 | <replaceable>cmd</replaceable><superscript>0</superscript>
6708 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6709 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6710 infix operators as for expressions, and
6712 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6713 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6714 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6715 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6716 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6717 | <replaceable>fcmd</replaceable>
6719 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6720 | ( <replaceable>cmd</replaceable> )
6721 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6723 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6724 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6725 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6726 | <replaceable>cmd</replaceable>
6728 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6729 except that the bodies are commands instead of expressions.
6733 Commands produce values, but (like monadic computations)
6734 may yield more than one value,
6735 or none, and may do other things as well.
6736 For the most part, familiarity with monadic notation is a good guide to
6738 However the values of expressions, even monadic ones,
6739 are determined by the values of the variables they contain;
6740 this is not necessarily the case for commands.
6744 A simple example of the new notation is the expression
6746 proc x -> f -< x+1
6748 We call this a <firstterm>procedure</firstterm> or
6749 <firstterm>arrow abstraction</firstterm>.
6750 As with a lambda expression, the variable <literal>x</literal>
6751 is a new variable bound within the <literal>proc</literal>-expression.
6752 It refers to the input to the arrow.
6753 In the above example, <literal>-<</literal> is not an identifier but an
6754 new reserved symbol used for building commands from an expression of arrow
6755 type and an expression to be fed as input to that arrow.
6756 (The weird look will make more sense later.)
6757 It may be read as analogue of application for arrows.
6758 The above example is equivalent to the Haskell expression
6760 arr (\ x -> x+1) >>> f
6762 That would make no sense if the expression to the left of
6763 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6764 More generally, the expression to the left of <literal>-<</literal>
6765 may not involve any <firstterm>local variable</firstterm>,
6766 i.e. a variable bound in the current arrow abstraction.
6767 For such a situation there is a variant <literal>-<<</literal>, as in
6769 proc x -> f x -<< x+1
6771 which is equivalent to
6773 arr (\ x -> (f x, x+1)) >>> app
6775 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6777 Such an arrow is equivalent to a monad, so if you're using this form
6778 you may find a monadic formulation more convenient.
6782 <title>do-notation for commands</title>
6785 Another form of command is a form of <literal>do</literal>-notation.
6786 For example, you can write
6795 You can read this much like ordinary <literal>do</literal>-notation,
6796 but with commands in place of monadic expressions.
6797 The first line sends the value of <literal>x+1</literal> as an input to
6798 the arrow <literal>f</literal>, and matches its output against
6799 <literal>y</literal>.
6800 In the next line, the output is discarded.
6801 The arrow <function>returnA</function> is defined in the
6802 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6803 module as <literal>arr id</literal>.
6804 The above example is treated as an abbreviation for
6806 arr (\ x -> (x, x)) >>>
6807 first (arr (\ x -> x+1) >>> f) >>>
6808 arr (\ (y, x) -> (y, (x, y))) >>>
6809 first (arr (\ y -> 2*y) >>> g) >>>
6811 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6812 first (arr (\ (x, z) -> x*z) >>> h) >>>
6813 arr (\ (t, z) -> t+z) >>>
6816 Note that variables not used later in the composition are projected out.
6817 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6819 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6820 module, this reduces to
6822 arr (\ x -> (x+1, x)) >>>
6824 arr (\ (y, x) -> (2*y, (x, y))) >>>
6826 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6828 arr (\ (t, z) -> t+z)
6830 which is what you might have written by hand.
6831 With arrow notation, GHC keeps track of all those tuples of variables for you.
6835 Note that although the above translation suggests that
6836 <literal>let</literal>-bound variables like <literal>z</literal> must be
6837 monomorphic, the actual translation produces Core,
6838 so polymorphic variables are allowed.
6842 It's also possible to have mutually recursive bindings,
6843 using the new <literal>rec</literal> keyword, as in the following example:
6845 counter :: ArrowCircuit a => a Bool Int
6846 counter = proc reset -> do
6847 rec output <- returnA -< if reset then 0 else next
6848 next <- delay 0 -< output+1
6849 returnA -< output
6851 The translation of such forms uses the <function>loop</function> combinator,
6852 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6858 <title>Conditional commands</title>
6861 In the previous example, we used a conditional expression to construct the
6863 Sometimes we want to conditionally execute different commands, as in
6870 which is translated to
6872 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6873 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6875 Since the translation uses <function>|||</function>,
6876 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6880 There are also <literal>case</literal> commands, like
6886 y <- h -< (x1, x2)
6890 The syntax is the same as for <literal>case</literal> expressions,
6891 except that the bodies of the alternatives are commands rather than expressions.
6892 The translation is similar to that of <literal>if</literal> commands.
6898 <title>Defining your own control structures</title>
6901 As we're seen, arrow notation provides constructs,
6902 modelled on those for expressions,
6903 for sequencing, value recursion and conditionals.
6904 But suitable combinators,
6905 which you can define in ordinary Haskell,
6906 may also be used to build new commands out of existing ones.
6907 The basic idea is that a command defines an arrow from environments to values.
6908 These environments assign values to the free local variables of the command.
6909 Thus combinators that produce arrows from arrows
6910 may also be used to build commands from commands.
6911 For example, the <literal>ArrowChoice</literal> class includes a combinator
6913 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6915 so we can use it to build commands:
6917 expr' = proc x -> do
6920 symbol Plus -< ()
6921 y <- term -< ()
6924 symbol Minus -< ()
6925 y <- term -< ()
6928 (The <literal>do</literal> on the first line is needed to prevent the first
6929 <literal><+> ...</literal> from being interpreted as part of the
6930 expression on the previous line.)
6931 This is equivalent to
6933 expr' = (proc x -> returnA -< x)
6934 <+> (proc x -> do
6935 symbol Plus -< ()
6936 y <- term -< ()
6938 <+> (proc x -> do
6939 symbol Minus -< ()
6940 y <- term -< ()
6943 It is essential that this operator be polymorphic in <literal>e</literal>
6944 (representing the environment input to the command
6945 and thence to its subcommands)
6946 and satisfy the corresponding naturality property
6948 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6950 at least for strict <literal>k</literal>.
6951 (This should be automatic if you're not using <function>seq</function>.)
6952 This ensures that environments seen by the subcommands are environments
6953 of the whole command,
6954 and also allows the translation to safely trim these environments.
6955 The operator must also not use any variable defined within the current
6960 We could define our own operator
6962 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6963 untilA body cond = proc x ->
6964 b <- cond -< x
6965 if b then returnA -< ()
6968 untilA body cond -< x
6970 and use it in the same way.
6971 Of course this infix syntax only makes sense for binary operators;
6972 there is also a more general syntax involving special brackets:
6976 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6983 <title>Primitive constructs</title>
6986 Some operators will need to pass additional inputs to their subcommands.
6987 For example, in an arrow type supporting exceptions,
6988 the operator that attaches an exception handler will wish to pass the
6989 exception that occurred to the handler.
6990 Such an operator might have a type
6992 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6994 where <literal>Ex</literal> is the type of exceptions handled.
6995 You could then use this with arrow notation by writing a command
6997 body `handleA` \ ex -> handler
6999 so that if an exception is raised in the command <literal>body</literal>,
7000 the variable <literal>ex</literal> is bound to the value of the exception
7001 and the command <literal>handler</literal>,
7002 which typically refers to <literal>ex</literal>, is entered.
7003 Though the syntax here looks like a functional lambda,
7004 we are talking about commands, and something different is going on.
7005 The input to the arrow represented by a command consists of values for
7006 the free local variables in the command, plus a stack of anonymous values.
7007 In all the prior examples, this stack was empty.
7008 In the second argument to <function>handleA</function>,
7009 this stack consists of one value, the value of the exception.
7010 The command form of lambda merely gives this value a name.
7015 the values on the stack are paired to the right of the environment.
7016 So operators like <function>handleA</function> that pass
7017 extra inputs to their subcommands can be designed for use with the notation
7018 by pairing the values with the environment in this way.
7019 More precisely, the type of each argument of the operator (and its result)
7020 should have the form
7022 a (...(e,t1), ... tn) t
7024 where <replaceable>e</replaceable> is a polymorphic variable
7025 (representing the environment)
7026 and <replaceable>ti</replaceable> are the types of the values on the stack,
7027 with <replaceable>t1</replaceable> being the <quote>top</quote>.
7028 The polymorphic variable <replaceable>e</replaceable> must not occur in
7029 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
7030 <replaceable>t</replaceable>.
7031 However the arrows involved need not be the same.
7032 Here are some more examples of suitable operators:
7034 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
7035 runReader :: ... => a e c -> a' (e,State) c
7036 runState :: ... => a e c -> a' (e,State) (c,State)
7038 We can supply the extra input required by commands built with the last two
7039 by applying them to ordinary expressions, as in
7043 (|runReader (do { ... })|) s
7045 which adds <literal>s</literal> to the stack of inputs to the command
7046 built using <function>runReader</function>.
7050 The command versions of lambda abstraction and application are analogous to
7051 the expression versions.
7052 In particular, the beta and eta rules describe equivalences of commands.
7053 These three features (operators, lambda abstraction and application)
7054 are the core of the notation; everything else can be built using them,
7055 though the results would be somewhat clumsy.
7056 For example, we could simulate <literal>do</literal>-notation by defining
7058 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7059 u `bind` f = returnA &&& u >>> f
7061 bind_ :: Arrow a => a e b -> a e c -> a e c
7062 u `bind_` f = u `bind` (arr fst >>> f)
7064 We could simulate <literal>if</literal> by defining
7066 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7067 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7074 <title>Differences with the paper</title>
7079 <para>Instead of a single form of arrow application (arrow tail) with two
7080 translations, the implementation provides two forms
7081 <quote><literal>-<</literal></quote> (first-order)
7082 and <quote><literal>-<<</literal></quote> (higher-order).
7087 <para>User-defined operators are flagged with banana brackets instead of
7088 a new <literal>form</literal> keyword.
7097 <title>Portability</title>
7100 Although only GHC implements arrow notation directly,
7101 there is also a preprocessor
7103 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7104 that translates arrow notation into Haskell 98
7105 for use with other Haskell systems.
7106 You would still want to check arrow programs with GHC;
7107 tracing type errors in the preprocessor output is not easy.
7108 Modules intended for both GHC and the preprocessor must observe some
7109 additional restrictions:
7114 The module must import
7115 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7121 The preprocessor cannot cope with other Haskell extensions.
7122 These would have to go in separate modules.
7128 Because the preprocessor targets Haskell (rather than Core),
7129 <literal>let</literal>-bound variables are monomorphic.
7140 <!-- ==================== BANG PATTERNS ================= -->
7142 <sect1 id="bang-patterns">
7143 <title>Bang patterns
7144 <indexterm><primary>Bang patterns</primary></indexterm>
7146 <para>GHC supports an extension of pattern matching called <emphasis>bang
7147 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7148 Bang patterns are under consideration for Haskell Prime.
7150 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7151 prime feature description</ulink> contains more discussion and examples
7152 than the material below.
7155 The key change is the addition of a new rule to the
7156 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7157 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7158 against a value <replaceable>v</replaceable> behaves as follows:
7160 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7161 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7165 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7168 <sect2 id="bang-patterns-informal">
7169 <title>Informal description of bang patterns
7172 The main idea is to add a single new production to the syntax of patterns:
7176 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7177 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7182 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7183 whereas without the bang it would be lazy.
7184 Bang patterns can be nested of course:
7188 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7189 <literal>y</literal>.
7190 A bang only really has an effect if it precedes a variable or wild-card pattern:
7195 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7196 putting a bang before a pattern that
7197 forces evaluation anyway does nothing.
7200 There is one (apparent) exception to this general rule that a bang only
7201 makes a difference when it precedes a variable or wild-card: a bang at the
7202 top level of a <literal>let</literal> or <literal>where</literal>
7203 binding makes the binding strict, regardless of the pattern.
7204 (We say "apparent" exception because the Right Way to think of it is that the bang
7205 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7206 is part of the syntax of the <emphasis>binding</emphasis>,
7207 creating a "bang-pattern binding".)
7212 is a bang-pattern binding. Operationally, it behaves just like a case expression:
7214 case e of [x,y] -> b
7216 Like a case expression, a bang-pattern binding must be non-recursive, and
7219 However, <emphasis>nested</emphasis> bangs in a pattern binding behave uniformly with all other forms of
7220 pattern matching. For example
7222 let (!x,[y]) = e in b
7224 is equivalent to this:
7226 let { t = case e of (x,[y]) -> x `seq` (x,y)
7231 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7232 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7233 evaluation of <literal>x</literal>.
7236 Bang patterns work in <literal>case</literal> expressions too, of course:
7238 g5 x = let y = f x in body
7239 g6 x = case f x of { y -> body }
7240 g7 x = case f x of { !y -> body }
7242 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7243 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7244 result, and then evaluates <literal>body</literal>.
7249 <sect2 id="bang-patterns-sem">
7250 <title>Syntax and semantics
7254 We add a single new production to the syntax of patterns:
7258 There is one problem with syntactic ambiguity. Consider:
7262 Is this a definition of the infix function "<literal>(!)</literal>",
7263 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7264 ambiguity in favour of the latter. If you want to define
7265 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7270 The semantics of Haskell pattern matching is described in <ulink
7271 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7272 Section 3.17.2</ulink> of the Haskell Report. To this description add
7273 one extra item 10, saying:
7274 <itemizedlist><listitem><para>Matching
7275 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7276 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7277 <listitem><para>otherwise, <literal>pat</literal> is matched against
7278 <literal>v</literal></para></listitem>
7280 </para></listitem></itemizedlist>
7281 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7282 Section 3.17.3</ulink>, add a new case (t):
7284 case v of { !pat -> e; _ -> e' }
7285 = v `seq` case v of { pat -> e; _ -> e' }
7288 That leaves let expressions, whose translation is given in
7289 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7291 of the Haskell Report.
7292 In the translation box, first apply
7293 the following transformation: for each pattern <literal>pi</literal> that is of
7294 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7295 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7296 have a bang at the top, apply the rules in the existing box.
7298 <para>The effect of the let rule is to force complete matching of the pattern
7299 <literal>qi</literal> before evaluation of the body is begun. The bang is
7300 retained in the translated form in case <literal>qi</literal> is a variable,
7308 The let-binding can be recursive. However, it is much more common for
7309 the let-binding to be non-recursive, in which case the following law holds:
7310 <literal>(let !p = rhs in body)</literal>
7312 <literal>(case rhs of !p -> body)</literal>
7315 A pattern with a bang at the outermost level is not allowed at the top level of
7321 <!-- ==================== ASSERTIONS ================= -->
7323 <sect1 id="assertions">
7325 <indexterm><primary>Assertions</primary></indexterm>
7329 If you want to make use of assertions in your standard Haskell code, you
7330 could define a function like the following:
7336 assert :: Bool -> a -> a
7337 assert False x = error "assertion failed!"
7344 which works, but gives you back a less than useful error message --
7345 an assertion failed, but which and where?
7349 One way out is to define an extended <function>assert</function> function which also
7350 takes a descriptive string to include in the error message and
7351 perhaps combine this with the use of a pre-processor which inserts
7352 the source location where <function>assert</function> was used.
7356 Ghc offers a helping hand here, doing all of this for you. For every
7357 use of <function>assert</function> in the user's source:
7363 kelvinToC :: Double -> Double
7364 kelvinToC k = assert (k >= 0.0) (k+273.15)
7370 Ghc will rewrite this to also include the source location where the
7377 assert pred val ==> assertError "Main.hs|15" pred val
7383 The rewrite is only performed by the compiler when it spots
7384 applications of <function>Control.Exception.assert</function>, so you
7385 can still define and use your own versions of
7386 <function>assert</function>, should you so wish. If not, import
7387 <literal>Control.Exception</literal> to make use
7388 <function>assert</function> in your code.
7392 GHC ignores assertions when optimisation is turned on with the
7393 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7394 <literal>assert pred e</literal> will be rewritten to
7395 <literal>e</literal>. You can also disable assertions using the
7396 <option>-fignore-asserts</option>
7397 option<indexterm><primary><option>-fignore-asserts</option></primary>
7398 </indexterm>.</para>
7401 Assertion failures can be caught, see the documentation for the
7402 <literal>Control.Exception</literal> library for the details.
7408 <!-- =============================== PRAGMAS =========================== -->
7410 <sect1 id="pragmas">
7411 <title>Pragmas</title>
7413 <indexterm><primary>pragma</primary></indexterm>
7415 <para>GHC supports several pragmas, or instructions to the
7416 compiler placed in the source code. Pragmas don't normally affect
7417 the meaning of the program, but they might affect the efficiency
7418 of the generated code.</para>
7420 <para>Pragmas all take the form
7422 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7424 where <replaceable>word</replaceable> indicates the type of
7425 pragma, and is followed optionally by information specific to that
7426 type of pragma. Case is ignored in
7427 <replaceable>word</replaceable>. The various values for
7428 <replaceable>word</replaceable> that GHC understands are described
7429 in the following sections; any pragma encountered with an
7430 unrecognised <replaceable>word</replaceable> is
7431 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7432 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7434 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7438 pragma must precede the <literal>module</literal> keyword in the file.
7441 There can be as many file-header pragmas as you please, and they can be
7442 preceded or followed by comments.
7445 File-header pragmas are read once only, before
7446 pre-processing the file (e.g. with cpp).
7449 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7450 <literal>{-# OPTIONS_GHC #-}</literal>, and
7451 <literal>{-# INCLUDE #-}</literal>.
7456 <sect2 id="language-pragma">
7457 <title>LANGUAGE pragma</title>
7459 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7460 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7462 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7464 It is the intention that all Haskell compilers support the
7465 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7466 all extensions are supported by all compilers, of
7467 course. The <literal>LANGUAGE</literal> pragma should be used instead
7468 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7470 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7472 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7474 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7476 <para>Every language extension can also be turned into a command-line flag
7477 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7478 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7481 <para>A list of all supported language extensions can be obtained by invoking
7482 <literal>ghc --supported-extensions</literal> (see <xref linkend="modes"/>).</para>
7484 <para>Any extension from the <literal>Extension</literal> type defined in
7486 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7487 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7491 <sect2 id="options-pragma">
7492 <title>OPTIONS_GHC pragma</title>
7493 <indexterm><primary>OPTIONS_GHC</primary>
7495 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7498 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7499 additional options that are given to the compiler when compiling
7500 this source file. See <xref linkend="source-file-options"/> for
7503 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7504 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7507 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7509 <sect2 id="include-pragma">
7510 <title>INCLUDE pragma</title>
7512 <para>The <literal>INCLUDE</literal> used to be necessary for
7513 specifying header files to be included when using the FFI and
7514 compiling via C. It is no longer required for GHC, but is
7515 accepted (and ignored) for compatibility with other
7519 <sect2 id="warning-deprecated-pragma">
7520 <title>WARNING and DEPRECATED pragmas</title>
7521 <indexterm><primary>WARNING</primary></indexterm>
7522 <indexterm><primary>DEPRECATED</primary></indexterm>
7524 <para>The WARNING pragma allows you to attach an arbitrary warning
7525 to a particular function, class, or type.
7526 A DEPRECATED pragma lets you specify that
7527 a particular function, class, or type is deprecated.
7528 There are two ways of using these pragmas.
7532 <para>You can work on an entire module thus:</para>
7534 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7539 module Wibble {-# WARNING "This is an unstable interface." #-} where
7542 <para>When you compile any module that import
7543 <literal>Wibble</literal>, GHC will print the specified
7548 <para>You can attach a warning to a function, class, type, or data constructor, with the
7549 following top-level declarations:</para>
7551 {-# DEPRECATED f, C, T "Don't use these" #-}
7552 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7554 <para>When you compile any module that imports and uses any
7555 of the specified entities, GHC will print the specified
7557 <para> You can only attach to entities declared at top level in the module
7558 being compiled, and you can only use unqualified names in the list of
7559 entities. A capitalised name, such as <literal>T</literal>
7560 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7561 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7562 both are in scope. If both are in scope, there is currently no way to
7563 specify one without the other (c.f. fixities
7564 <xref linkend="infix-tycons"/>).</para>
7567 Warnings and deprecations are not reported for
7568 (a) uses within the defining module, and
7569 (b) uses in an export list.
7570 The latter reduces spurious complaints within a library
7571 in which one module gathers together and re-exports
7572 the exports of several others.
7574 <para>You can suppress the warnings with the flag
7575 <option>-fno-warn-warnings-deprecations</option>.</para>
7578 <sect2 id="inline-noinline-pragma">
7579 <title>INLINE and NOINLINE pragmas</title>
7581 <para>These pragmas control the inlining of function
7584 <sect3 id="inline-pragma">
7585 <title>INLINE pragma</title>
7586 <indexterm><primary>INLINE</primary></indexterm>
7588 <para>GHC (with <option>-O</option>, as always) tries to
7589 inline (or “unfold”) functions/values that are
7590 “small enough,” thus avoiding the call overhead
7591 and possibly exposing other more-wonderful optimisations.
7592 Normally, if GHC decides a function is “too
7593 expensive” to inline, it will not do so, nor will it
7594 export that unfolding for other modules to use.</para>
7596 <para>The sledgehammer you can bring to bear is the
7597 <literal>INLINE</literal><indexterm><primary>INLINE
7598 pragma</primary></indexterm> pragma, used thusly:</para>
7601 key_function :: Int -> String -> (Bool, Double)
7602 {-# INLINE key_function #-}
7605 <para>The major effect of an <literal>INLINE</literal> pragma
7606 is to declare a function's “cost” to be very low.
7607 The normal unfolding machinery will then be very keen to
7608 inline it. However, an <literal>INLINE</literal> pragma for a
7609 function "<literal>f</literal>" has a number of other effects:
7612 While GHC is keen to inline the function, it does not do so
7613 blindly. For example, if you write
7617 there really isn't any point in inlining <literal>key_function</literal> to get
7619 map (\x -> <replaceable>body</replaceable>) xs
7621 In general, GHC only inlines the function if there is some reason (no matter
7622 how slight) to supose that it is useful to do so.
7626 Moreover, GHC will only inline the function if it is <emphasis>fully applied</emphasis>,
7627 where "fully applied"
7628 means applied to as many arguments as appear (syntactically)
7629 on the LHS of the function
7630 definition. For example:
7632 comp1 :: (b -> c) -> (a -> b) -> a -> c
7633 {-# INLINE comp1 #-}
7634 comp1 f g = \x -> f (g x)
7636 comp2 :: (b -> c) -> (a -> b) -> a -> c
7637 {-# INLINE comp2 #-}
7638 comp2 f g x = f (g x)
7640 The two functions <literal>comp1</literal> and <literal>comp2</literal> have the
7641 same semantics, but <literal>comp1</literal> will be inlined when applied
7642 to <emphasis>two</emphasis> arguments, while <literal>comp2</literal> requires
7643 <emphasis>three</emphasis>. This might make a big difference if you say
7645 map (not `comp1` not) xs
7647 which will optimise better than the corresponding use of `comp2`.
7651 It is useful for GHC to optimise the definition of an
7652 INLINE function <literal>f</literal> just like any other non-INLINE function,
7653 in case the non-inlined version of <literal>f</literal> is
7654 ultimately called. But we don't want to inline
7655 the <emphasis>optimised</emphasis> version
7656 of <literal>f</literal>;
7657 a major reason for INLINE pragmas is to expose functions
7658 in <literal>f</literal>'s RHS that have
7659 rewrite rules, and it's no good if those functions have been optimised
7663 So <emphasis>GHC guarantees to inline precisely the code that you wrote</emphasis>, no more
7664 and no less. It does this by capturing a copy of the definition of the function to use
7665 for inlining (we call this the "inline-RHS"), which it leaves untouched,
7666 while optimising the ordinarly RHS as usual. For externally-visible functions
7667 the inline-RHS (not the optimised RHS) is recorded in the interface file.
7670 An INLINE function is not worker/wrappered by strictness analysis.
7671 It's going to be inlined wholesale instead.
7675 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7676 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7677 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7678 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7679 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7680 when there is no choice even an INLINE function can be selected, in which case
7681 the INLINE pragma is ignored.
7682 For example, for a self-recursive function, the loop breaker can only be the function
7683 itself, so an INLINE pragma is always ignored.</para>
7685 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7686 function can be put anywhere its type signature could be
7689 <para><literal>INLINE</literal> pragmas are a particularly
7691 <literal>then</literal>/<literal>return</literal> (or
7692 <literal>bind</literal>/<literal>unit</literal>) functions in
7693 a monad. For example, in GHC's own
7694 <literal>UniqueSupply</literal> monad code, we have:</para>
7697 {-# INLINE thenUs #-}
7698 {-# INLINE returnUs #-}
7701 <para>See also the <literal>NOINLINE</literal> (<xref linkend="inlinable-pragma"/>)
7702 and <literal>INLINABLE</literal> (<xref linkend="noinline-pragma"/>)
7705 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7706 so if you want your code to be HBC-compatible you'll have to surround
7707 the pragma with C pre-processor directives
7708 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7712 <sect3 id="inlinable-pragma">
7713 <title>INLINABLE pragma</title>
7715 <para>An <literal>{-# INLINABLE f #-}</literal> pragma on a
7716 function <literal>f</literal> has the following behaviour:
7719 While <literal>INLINE</literal> says "please inline me", the <literal>INLINABLE</literal>
7720 says "feel free to inline me; use your
7721 discretion". In other words the choice is left to GHC, which uses the same
7722 rules as for pragma-free functions. Unlike <literal>INLINE</literal>, that decision is made at
7723 the <emphasis>call site</emphasis>, and
7724 will therefore be affected by the inlining threshold, optimisation level etc.
7727 Like <literal>INLINE</literal>, the <literal>INLINABLE</literal> pragma retains a
7728 copy of the original RHS for
7729 inlining purposes, and persists it in the interface file, regardless of
7730 the size of the RHS.
7734 One way to use <literal>INLINABLE</literal> is in conjunction with
7735 the special function <literal>inline</literal> (<xref linkend="special-ids"/>).
7736 The call <literal>inline f</literal> tries very hard to inline <literal>f</literal>.
7737 To make sure that <literal>f</literal> can be inlined,
7738 it is a good idea to mark the definition
7739 of <literal>f</literal> as <literal>INLINABLE</literal>,
7740 so that GHC guarantees to expose an unfolding regardless of how big it is.
7741 Moreover, by annotating <literal>f</literal> as <literal>INLINABLE</literal>,
7742 you ensure that <literal>f</literal>'s original RHS is inlined, rather than
7743 whatever random optimised version of <literal>f</literal> GHC's optimiser
7748 The <literal>INLINABLE</literal> pragma also works with <literal>SPECIALISE</literal>:
7749 if you mark function <literal>f</literal> as <literal>INLINABLE</literal>, then
7750 you can subsequently <literal>SPECIALISE</literal> in another module
7751 (see <xref linkend="specialize-pragma"/>).</para></listitem>
7754 Unlike <literal>INLINE</literal>, it is OK to use
7755 an <literal>INLINABLE</literal> pragma on a recursive function.
7756 The principal reason do to so to allow later use of <literal>SPECIALISE</literal>
7763 <sect3 id="noinline-pragma">
7764 <title>NOINLINE pragma</title>
7766 <indexterm><primary>NOINLINE</primary></indexterm>
7767 <indexterm><primary>NOTINLINE</primary></indexterm>
7769 <para>The <literal>NOINLINE</literal> pragma does exactly what
7770 you'd expect: it stops the named function from being inlined
7771 by the compiler. You shouldn't ever need to do this, unless
7772 you're very cautious about code size.</para>
7774 <para><literal>NOTINLINE</literal> is a synonym for
7775 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7776 specified by Haskell 98 as the standard way to disable
7777 inlining, so it should be used if you want your code to be
7781 <sect3 id="conlike-pragma">
7782 <title>CONLIKE modifier</title>
7783 <indexterm><primary>CONLIKE</primary></indexterm>
7784 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7785 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7789 <sect3 id="phase-control">
7790 <title>Phase control</title>
7792 <para> Sometimes you want to control exactly when in GHC's
7793 pipeline the INLINE pragma is switched on. Inlining happens
7794 only during runs of the <emphasis>simplifier</emphasis>. Each
7795 run of the simplifier has a different <emphasis>phase
7796 number</emphasis>; the phase number decreases towards zero.
7797 If you use <option>-dverbose-core2core</option> you'll see the
7798 sequence of phase numbers for successive runs of the
7799 simplifier. In an INLINE pragma you can optionally specify a
7803 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7804 <literal>f</literal>
7805 until phase <literal>k</literal>, but from phase
7806 <literal>k</literal> onwards be very keen to inline it.
7809 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7810 <literal>f</literal>
7811 until phase <literal>k</literal>, but from phase
7812 <literal>k</literal> onwards do not inline it.
7815 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7816 <literal>f</literal>
7817 until phase <literal>k</literal>, but from phase
7818 <literal>k</literal> onwards be willing to inline it (as if
7819 there was no pragma).
7822 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7823 <literal>f</literal>
7824 until phase <literal>k</literal>, but from phase
7825 <literal>k</literal> onwards do not inline it.
7828 The same information is summarised here:
7830 -- Before phase 2 Phase 2 and later
7831 {-# INLINE [2] f #-} -- No Yes
7832 {-# INLINE [~2] f #-} -- Yes No
7833 {-# NOINLINE [2] f #-} -- No Maybe
7834 {-# NOINLINE [~2] f #-} -- Maybe No
7836 {-# INLINE f #-} -- Yes Yes
7837 {-# NOINLINE f #-} -- No No
7839 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7840 function body is small, or it is applied to interesting-looking arguments etc).
7841 Another way to understand the semantics is this:
7843 <listitem><para>For both INLINE and NOINLINE, the phase number says
7844 when inlining is allowed at all.</para></listitem>
7845 <listitem><para>The INLINE pragma has the additional effect of making the
7846 function body look small, so that when inlining is allowed it is very likely to
7851 <para>The same phase-numbering control is available for RULES
7852 (<xref linkend="rewrite-rules"/>).</para>
7856 <sect2 id="annotation-pragmas">
7857 <title>ANN pragmas</title>
7859 <para>GHC offers the ability to annotate various code constructs with additional
7860 data by using three pragmas. This data can then be inspected at a later date by
7861 using GHC-as-a-library.</para>
7863 <sect3 id="ann-pragma">
7864 <title>Annotating values</title>
7866 <indexterm><primary>ANN</primary></indexterm>
7868 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7869 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7870 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7871 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7872 you would do this:</para>
7875 {-# ANN foo (Just "Hello") #-}
7880 A number of restrictions apply to use of annotations:
7882 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7883 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7884 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7885 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7886 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7888 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7889 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7892 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7893 please give the GHC team a shout</ulink>.
7896 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7897 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7900 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7905 <sect3 id="typeann-pragma">
7906 <title>Annotating types</title>
7908 <indexterm><primary>ANN type</primary></indexterm>
7909 <indexterm><primary>ANN</primary></indexterm>
7911 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7914 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7919 <sect3 id="modann-pragma">
7920 <title>Annotating modules</title>
7922 <indexterm><primary>ANN module</primary></indexterm>
7923 <indexterm><primary>ANN</primary></indexterm>
7925 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7928 {-# ANN module (Just "A `Maybe String' annotation") #-}
7933 <sect2 id="line-pragma">
7934 <title>LINE pragma</title>
7936 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7937 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7938 <para>This pragma is similar to C's <literal>#line</literal>
7939 pragma, and is mainly for use in automatically generated Haskell
7940 code. It lets you specify the line number and filename of the
7941 original code; for example</para>
7943 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7945 <para>if you'd generated the current file from something called
7946 <filename>Foo.vhs</filename> and this line corresponds to line
7947 42 in the original. GHC will adjust its error messages to refer
7948 to the line/file named in the <literal>LINE</literal>
7953 <title>RULES pragma</title>
7955 <para>The RULES pragma lets you specify rewrite rules. It is
7956 described in <xref linkend="rewrite-rules"/>.</para>
7959 <sect2 id="specialize-pragma">
7960 <title>SPECIALIZE pragma</title>
7962 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7963 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7964 <indexterm><primary>overloading, death to</primary></indexterm>
7966 <para>(UK spelling also accepted.) For key overloaded
7967 functions, you can create extra versions (NB: more code space)
7968 specialised to particular types. Thus, if you have an
7969 overloaded function:</para>
7972 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7975 <para>If it is heavily used on lists with
7976 <literal>Widget</literal> keys, you could specialise it as
7980 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7983 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7984 be put anywhere its type signature could be put.</para>
7986 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7987 (a) a specialised version of the function and (b) a rewrite rule
7988 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7989 un-specialised function into a call to the specialised one.</para>
7991 <para>The type in a SPECIALIZE pragma can be any type that is less
7992 polymorphic than the type of the original function. In concrete terms,
7993 if the original function is <literal>f</literal> then the pragma
7995 {-# SPECIALIZE f :: <type> #-}
7997 is valid if and only if the definition
7999 f_spec :: <type>
8002 is valid. Here are some examples (where we only give the type signature
8003 for the original function, not its code):
8005 f :: Eq a => a -> b -> b
8006 {-# SPECIALISE f :: Int -> b -> b #-}
8008 g :: (Eq a, Ix b) => a -> b -> b
8009 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
8011 h :: Eq a => a -> a -> a
8012 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
8014 The last of these examples will generate a
8015 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
8016 well. If you use this kind of specialisation, let us know how well it works.
8019 <sect3 id="specialize-inline">
8020 <title>SPECIALIZE INLINE</title>
8022 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
8023 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
8024 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
8025 The <literal>INLINE</literal> pragma affects the specialised version of the
8026 function (only), and applies even if the function is recursive. The motivating
8029 -- A GADT for arrays with type-indexed representation
8031 ArrInt :: !Int -> ByteArray# -> Arr Int
8032 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
8034 (!:) :: Arr e -> Int -> e
8035 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
8036 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
8037 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
8038 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
8040 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
8041 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
8042 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
8043 the specialised function will be inlined. It has two calls to
8044 <literal>(!:)</literal>,
8045 both at type <literal>Int</literal>. Both these calls fire the first
8046 specialisation, whose body is also inlined. The result is a type-based
8047 unrolling of the indexing function.</para>
8048 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
8049 on an ordinarily-recursive function.</para>
8052 <sect3><title>SPECIALIZE for imported functions</title>
8055 Generally, you can only give a <literal>SPECIALIZE</literal> pragma
8056 for a function defined in the same module.
8057 However if a function <literal>f</literal> is given an <literal>INLINABLE</literal>
8058 pragma at its definition site, then it can subequently be specialised by
8059 importing modules (see <xref linkend="inlinable-pragma"/>).
8062 module Map( lookup, blah blah ) where
8063 lookup :: Ord key => [(key,a)] -> key -> Maybe a
8065 {-# INLINABLE lookup #-}
8068 import Map( lookup )
8070 data T = T1 | T2 deriving( Eq, Ord )
8071 {-# SPECIALISE lookup :: [(T,a)] -> T -> Maybe a
8073 Here, <literal>lookup</literal> is declared <literal>INLINABLE</literal>, but
8074 it cannot be specialised for type <literal>T</literal> at its definition site,
8075 because that type does not exist yet. Instead a client module can define <literal>T</literal>
8076 and then specialise <literal>lookup</literal> at that type.
8079 Moreover, every module that imports <literal>Client</literal> (or imports a module
8080 that imports <literal>Client</literal>, transitively) will "see", and make use of,
8081 the specialised version of <literal>lookup</literal>. You don't need to put
8082 a <literal>SPECIALIZE</literal> pragma in every module.
8085 Moreover you often don't even need the <literal>SPECIALIZE</literal> pragma in the
8086 first place. When compiling a module M,
8087 GHC's optimiser (with -O) automatically considers each top-level
8088 overloaded function declared in M, and specialises it
8089 for the different types at which it is called in M. The optimiser
8090 <emphasis>also</emphasis> considers each <emphasis>imported</emphasis>
8091 <literal>INLINABLE</literal> overloaded function, and specialises it
8092 for the different types at which it is called in M.
8093 So in our example, it would be enough for <literal>lookup</literal> to
8094 be called at type <literal>T</literal>:
8097 import Map( lookup )
8099 data T = T1 | T2 deriving( Eq, Ord )
8101 findT1 :: [(T,a)] -> Maybe a
8102 findT1 m = lookup m T1 -- A call of lookup at type T
8104 However, sometimes there are no such calls, in which case the
8105 pragma can be useful.
8109 <sect3><title>Obselete SPECIALIZE syntax</title>
8111 <para>Note: In earlier versions of GHC, it was possible to provide your own
8112 specialised function for a given type:
8115 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
8118 This feature has been removed, as it is now subsumed by the
8119 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
8124 <sect2 id="specialize-instance-pragma">
8125 <title>SPECIALIZE instance pragma
8129 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
8130 <indexterm><primary>overloading, death to</primary></indexterm>
8131 Same idea, except for instance declarations. For example:
8134 instance (Eq a) => Eq (Foo a) where {
8135 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
8139 The pragma must occur inside the <literal>where</literal> part
8140 of the instance declaration.
8143 Compatible with HBC, by the way, except perhaps in the placement
8149 <sect2 id="unpack-pragma">
8150 <title>UNPACK pragma</title>
8152 <indexterm><primary>UNPACK</primary></indexterm>
8154 <para>The <literal>UNPACK</literal> indicates to the compiler
8155 that it should unpack the contents of a constructor field into
8156 the constructor itself, removing a level of indirection. For
8160 data T = T {-# UNPACK #-} !Float
8161 {-# UNPACK #-} !Float
8164 <para>will create a constructor <literal>T</literal> containing
8165 two unboxed floats. This may not always be an optimisation: if
8166 the <function>T</function> constructor is scrutinised and the
8167 floats passed to a non-strict function for example, they will
8168 have to be reboxed (this is done automatically by the
8171 <para>Unpacking constructor fields should only be used in
8172 conjunction with <option>-O</option>, in order to expose
8173 unfoldings to the compiler so the reboxing can be removed as
8174 often as possible. For example:</para>
8178 f (T f1 f2) = f1 + f2
8181 <para>The compiler will avoid reboxing <function>f1</function>
8182 and <function>f2</function> by inlining <function>+</function>
8183 on floats, but only when <option>-O</option> is on.</para>
8185 <para>Any single-constructor data is eligible for unpacking; for
8189 data T = T {-# UNPACK #-} !(Int,Int)
8192 <para>will store the two <literal>Int</literal>s directly in the
8193 <function>T</function> constructor, by flattening the pair.
8194 Multi-level unpacking is also supported:
8197 data T = T {-# UNPACK #-} !S
8198 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8201 will store two unboxed <literal>Int#</literal>s
8202 directly in the <function>T</function> constructor. The
8203 unpacker can see through newtypes, too.</para>
8205 <para>See also the <option>-funbox-strict-fields</option> flag,
8206 which essentially has the effect of adding
8207 <literal>{-# UNPACK #-}</literal> to every strict
8208 constructor field.</para>
8211 <sect2 id="source-pragma">
8212 <title>SOURCE pragma</title>
8214 <indexterm><primary>SOURCE</primary></indexterm>
8215 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8216 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8222 <!-- ======================= REWRITE RULES ======================== -->
8224 <sect1 id="rewrite-rules">
8225 <title>Rewrite rules
8227 <indexterm><primary>RULES pragma</primary></indexterm>
8228 <indexterm><primary>pragma, RULES</primary></indexterm>
8229 <indexterm><primary>rewrite rules</primary></indexterm></title>
8232 The programmer can specify rewrite rules as part of the source program
8238 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8243 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8244 If you need more information, then <option>-ddump-rule-firings</option> shows you
8245 each individual rule firing and <option>-ddump-rule-rewrites</option> also shows what the code looks like before and after the rewrite.
8249 <title>Syntax</title>
8252 From a syntactic point of view:
8258 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8259 may be generated by the layout rule).
8265 The layout rule applies in a pragma.
8266 Currently no new indentation level
8267 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8268 you must lay out the starting in the same column as the enclosing definitions.
8271 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8272 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8275 Furthermore, the closing <literal>#-}</literal>
8276 should start in a column to the right of the opening <literal>{-#</literal>.
8282 Each rule has a name, enclosed in double quotes. The name itself has
8283 no significance at all. It is only used when reporting how many times the rule fired.
8289 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8290 immediately after the name of the rule. Thus:
8293 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8296 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8297 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8306 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8307 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8308 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8309 by spaces, just like in a type <literal>forall</literal>.
8315 A pattern variable may optionally have a type signature.
8316 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8317 For example, here is the <literal>foldr/build</literal> rule:
8320 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8321 foldr k z (build g) = g k z
8324 Since <function>g</function> has a polymorphic type, it must have a type signature.
8331 The left hand side of a rule must consist of a top-level variable applied
8332 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8335 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8336 "wrong2" forall f. f True = True
8339 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8346 A rule does not need to be in the same module as (any of) the
8347 variables it mentions, though of course they need to be in scope.
8353 All rules are implicitly exported from the module, and are therefore
8354 in force in any module that imports the module that defined the rule, directly
8355 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8356 in force when compiling A.) The situation is very similar to that for instance
8364 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8365 any other flag settings. Furthermore, inside a RULE, the language extension
8366 <option>-XScopedTypeVariables</option> is automatically enabled; see
8367 <xref linkend="scoped-type-variables"/>.
8373 Like other pragmas, RULE pragmas are always checked for scope errors, and
8374 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8375 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8376 if the <option>-fenable-rewrite-rules</option> flag is
8377 on (see <xref linkend="rule-semantics"/>).
8386 <sect2 id="rule-semantics">
8387 <title>Semantics</title>
8390 From a semantic point of view:
8395 Rules are enabled (that is, used during optimisation)
8396 by the <option>-fenable-rewrite-rules</option> flag.
8397 This flag is implied by <option>-O</option>, and may be switched
8398 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8399 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8400 may not do what you expect, though, because without <option>-O</option> GHC
8401 ignores all optimisation information in interface files;
8402 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8403 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8404 has no effect on parsing or typechecking.
8410 Rules are regarded as left-to-right rewrite rules.
8411 When GHC finds an expression that is a substitution instance of the LHS
8412 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8413 By "a substitution instance" we mean that the LHS can be made equal to the
8414 expression by substituting for the pattern variables.
8421 GHC makes absolutely no attempt to verify that the LHS and RHS
8422 of a rule have the same meaning. That is undecidable in general, and
8423 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8430 GHC makes no attempt to make sure that the rules are confluent or
8431 terminating. For example:
8434 "loop" forall x y. f x y = f y x
8437 This rule will cause the compiler to go into an infinite loop.
8444 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8450 GHC currently uses a very simple, syntactic, matching algorithm
8451 for matching a rule LHS with an expression. It seeks a substitution
8452 which makes the LHS and expression syntactically equal modulo alpha
8453 conversion. The pattern (rule), but not the expression, is eta-expanded if
8454 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8455 But not beta conversion (that's called higher-order matching).
8459 Matching is carried out on GHC's intermediate language, which includes
8460 type abstractions and applications. So a rule only matches if the
8461 types match too. See <xref linkend="rule-spec"/> below.
8467 GHC keeps trying to apply the rules as it optimises the program.
8468 For example, consider:
8477 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8478 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8479 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8480 not be substituted, and the rule would not fire.
8490 <sect2 id="conlike">
8491 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8494 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8495 results. Consider this (artificial) example
8501 {-# RULES "f" f True = False #-}
8503 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8508 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8510 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8511 would have been a better chance that <literal>f</literal>'s RULE might fire.
8514 The way to get predictable behaviour is to use a NOINLINE
8515 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8516 that it is not inlined until its RULEs have had a chance to fire.
8519 GHC is very cautious about duplicating work. For example, consider
8521 f k z xs = let xs = build g
8522 in ...(foldr k z xs)...sum xs...
8523 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8525 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8526 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8527 duplicated if the rule fired.
8530 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8531 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8532 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8534 {-# INLINE[1] CONLIKE f #-}
8535 f x = <replaceable>blah</replaceable>
8537 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8538 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8539 should be considered cheap enough to duplicate, if such a duplication would make rule
8540 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8541 have such a property.)
8542 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8543 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8544 not going to be inlined before the rule has a chance to fire.
8549 <title>List fusion</title>
8552 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8553 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8554 intermediate list should be eliminated entirely.
8558 The following are good producers:
8570 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8576 Explicit lists (e.g. <literal>[True, False]</literal>)
8582 The cons constructor (e.g <literal>3:4:[]</literal>)
8588 <function>++</function>
8594 <function>map</function>
8600 <function>take</function>, <function>filter</function>
8606 <function>iterate</function>, <function>repeat</function>
8612 <function>zip</function>, <function>zipWith</function>
8621 The following are good consumers:
8633 <function>array</function> (on its second argument)
8639 <function>++</function> (on its first argument)
8645 <function>foldr</function>
8651 <function>map</function>
8657 <function>take</function>, <function>filter</function>
8663 <function>concat</function>
8669 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8675 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8676 will fuse with one but not the other)
8682 <function>partition</function>
8688 <function>head</function>
8694 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8700 <function>sequence_</function>
8706 <function>msum</function>
8712 <function>sortBy</function>
8721 So, for example, the following should generate no intermediate lists:
8724 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8730 This list could readily be extended; if there are Prelude functions that you use
8731 a lot which are not included, please tell us.
8735 If you want to write your own good consumers or producers, look at the
8736 Prelude definitions of the above functions to see how to do so.
8741 <sect2 id="rule-spec">
8742 <title>Specialisation
8746 Rewrite rules can be used to get the same effect as a feature
8747 present in earlier versions of GHC.
8748 For example, suppose that:
8751 genericLookup :: Ord a => Table a b -> a -> b
8752 intLookup :: Table Int b -> Int -> b
8755 where <function>intLookup</function> is an implementation of
8756 <function>genericLookup</function> that works very fast for
8757 keys of type <literal>Int</literal>. You might wish
8758 to tell GHC to use <function>intLookup</function> instead of
8759 <function>genericLookup</function> whenever the latter was called with
8760 type <literal>Table Int b -> Int -> b</literal>.
8761 It used to be possible to write
8764 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8767 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8770 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8773 This slightly odd-looking rule instructs GHC to replace
8774 <function>genericLookup</function> by <function>intLookup</function>
8775 <emphasis>whenever the types match</emphasis>.
8776 What is more, this rule does not need to be in the same
8777 file as <function>genericLookup</function>, unlike the
8778 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8779 have an original definition available to specialise).
8782 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8783 <function>intLookup</function> really behaves as a specialised version
8784 of <function>genericLookup</function>!!!</para>
8786 <para>An example in which using <literal>RULES</literal> for
8787 specialisation will Win Big:
8790 toDouble :: Real a => a -> Double
8791 toDouble = fromRational . toRational
8793 {-# RULES "toDouble/Int" toDouble = i2d #-}
8794 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8797 The <function>i2d</function> function is virtually one machine
8798 instruction; the default conversion—via an intermediate
8799 <literal>Rational</literal>—is obscenely expensive by
8805 <sect2 id="controlling-rules">
8806 <title>Controlling what's going on in rewrite rules</title>
8814 Use <option>-ddump-rules</option> to see the rules that are defined
8815 <emphasis>in this module</emphasis>.
8816 This includes rules generated by the specialisation pass, but excludes
8817 rules imported from other modules.
8823 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8824 If you add <option>-dppr-debug</option> you get a more detailed listing.
8830 Use <option>-ddump-rule-firings</option> or <option>-ddump-rule-rewrites</option>
8831 to see in great detail what rules are being fired.
8832 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8838 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8841 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8842 {-# INLINE build #-}
8846 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8847 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8848 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8849 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8856 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8857 see how to write rules that will do fusion and yet give an efficient
8858 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8868 <sect2 id="core-pragma">
8869 <title>CORE pragma</title>
8871 <indexterm><primary>CORE pragma</primary></indexterm>
8872 <indexterm><primary>pragma, CORE</primary></indexterm>
8873 <indexterm><primary>core, annotation</primary></indexterm>
8876 The external core format supports <quote>Note</quote> annotations;
8877 the <literal>CORE</literal> pragma gives a way to specify what these
8878 should be in your Haskell source code. Syntactically, core
8879 annotations are attached to expressions and take a Haskell string
8880 literal as an argument. The following function definition shows an
8884 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8887 Semantically, this is equivalent to:
8895 However, when external core is generated (via
8896 <option>-fext-core</option>), there will be Notes attached to the
8897 expressions <function>show</function> and <varname>x</varname>.
8898 The core function declaration for <function>f</function> is:
8902 f :: %forall a . GHCziShow.ZCTShow a ->
8903 a -> GHCziBase.ZMZN GHCziBase.Char =
8904 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8906 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8908 (tpl1::GHCziBase.Int ->
8910 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8912 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8913 (tpl3::GHCziBase.ZMZN a ->
8914 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8922 Here, we can see that the function <function>show</function> (which
8923 has been expanded out to a case expression over the Show dictionary)
8924 has a <literal>%note</literal> attached to it, as does the
8925 expression <varname>eta</varname> (which used to be called
8926 <varname>x</varname>).
8933 <sect1 id="special-ids">
8934 <title>Special built-in functions</title>
8935 <para>GHC has a few built-in functions with special behaviour. These
8936 are now described in the module <ulink
8937 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8938 in the library documentation.
8942 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Ainline"><literal>inline</literal></ulink>
8943 allows control over inlining on a per-call-site basis.
8946 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Alazy"><literal>lazy</literal></ulink>
8947 restrains the strictness analyser.
8950 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3AunsafeCoerce%23"><literal>lazy</literal></ulink>
8951 allows you to fool the type checker.
8958 <sect1 id="generic-classes">
8959 <title>Generic classes</title>
8962 The ideas behind this extension are described in detail in "Derivable type classes",
8963 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8964 An example will give the idea:
8972 fromBin :: [Int] -> (a, [Int])
8974 toBin {| Unit |} Unit = []
8975 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8976 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8977 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8979 fromBin {| Unit |} bs = (Unit, bs)
8980 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8981 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8982 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8983 (y,bs'') = fromBin bs'
8986 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8987 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8988 which are defined thus in the library module <literal>Generics</literal>:
8992 data a :+: b = Inl a | Inr b
8993 data a :*: b = a :*: b
8996 Now you can make a data type into an instance of Bin like this:
8998 instance (Bin a, Bin b) => Bin (a,b)
8999 instance Bin a => Bin [a]
9001 That is, just leave off the "where" clause. Of course, you can put in the
9002 where clause and over-ride whichever methods you please.
9006 <title> Using generics </title>
9007 <para>To use generics you need to</para>
9010 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
9011 <option>-XGenerics</option> (to generate extra per-data-type code),
9012 and <option>-package lang</option> (to make the <literal>Generics</literal> library
9016 <para>Import the module <literal>Generics</literal> from the
9017 <literal>lang</literal> package. This import brings into
9018 scope the data types <literal>Unit</literal>,
9019 <literal>:*:</literal>, and <literal>:+:</literal>. (You
9020 don't need this import if you don't mention these types
9021 explicitly; for example, if you are simply giving instance
9022 declarations.)</para>
9027 <sect2> <title> Changes wrt the paper </title>
9029 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
9030 can be written infix (indeed, you can now use
9031 any operator starting in a colon as an infix type constructor). Also note that
9032 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
9033 Finally, note that the syntax of the type patterns in the class declaration
9034 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
9035 alone would ambiguous when they appear on right hand sides (an extension we
9036 anticipate wanting).
9040 <sect2> <title>Terminology and restrictions</title>
9042 Terminology. A "generic default method" in a class declaration
9043 is one that is defined using type patterns as above.
9044 A "polymorphic default method" is a default method defined as in Haskell 98.
9045 A "generic class declaration" is a class declaration with at least one
9046 generic default method.
9054 Alas, we do not yet implement the stuff about constructor names and
9061 A generic class can have only one parameter; you can't have a generic
9062 multi-parameter class.
9068 A default method must be defined entirely using type patterns, or entirely
9069 without. So this is illegal:
9072 op :: a -> (a, Bool)
9073 op {| Unit |} Unit = (Unit, True)
9076 However it is perfectly OK for some methods of a generic class to have
9077 generic default methods and others to have polymorphic default methods.
9083 The type variable(s) in the type pattern for a generic method declaration
9084 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:
9088 op {| p :*: q |} (x :*: y) = op (x :: p)
9096 The type patterns in a generic default method must take one of the forms:
9102 where "a" and "b" are type variables. Furthermore, all the type patterns for
9103 a single type constructor (<literal>:*:</literal>, say) must be identical; they
9104 must use the same type variables. So this is illegal:
9108 op {| a :+: b |} (Inl x) = True
9109 op {| p :+: q |} (Inr y) = False
9111 The type patterns must be identical, even in equations for different methods of the class.
9112 So this too is illegal:
9116 op1 {| a :*: b |} (x :*: y) = True
9119 op2 {| p :*: q |} (x :*: y) = False
9121 (The reason for this restriction is that we gather all the equations for a particular type constructor
9122 into a single generic instance declaration.)
9128 A generic method declaration must give a case for each of the three type constructors.
9134 The type for a generic method can be built only from:
9136 <listitem> <para> Function arrows </para> </listitem>
9137 <listitem> <para> Type variables </para> </listitem>
9138 <listitem> <para> Tuples </para> </listitem>
9139 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
9141 Here are some example type signatures for generic methods:
9144 op2 :: Bool -> (a,Bool)
9145 op3 :: [Int] -> a -> a
9148 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
9152 This restriction is an implementation restriction: we just haven't got around to
9153 implementing the necessary bidirectional maps over arbitrary type constructors.
9154 It would be relatively easy to add specific type constructors, such as Maybe and list,
9155 to the ones that are allowed.</para>
9160 In an instance declaration for a generic class, the idea is that the compiler
9161 will fill in the methods for you, based on the generic templates. However it can only
9166 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
9171 No constructor of the instance type has unboxed fields.
9175 (Of course, these things can only arise if you are already using GHC extensions.)
9176 However, you can still give an instance declarations for types which break these rules,
9177 provided you give explicit code to override any generic default methods.
9185 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9186 what the compiler does with generic declarations.
9191 <sect2> <title> Another example </title>
9193 Just to finish with, here's another example I rather like:
9197 nCons {| Unit |} _ = 1
9198 nCons {| a :*: b |} _ = 1
9199 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9202 tag {| Unit |} _ = 1
9203 tag {| a :*: b |} _ = 1
9204 tag {| a :+: b |} (Inl x) = tag x
9205 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9211 <sect1 id="monomorphism">
9212 <title>Control over monomorphism</title>
9214 <para>GHC supports two flags that control the way in which generalisation is
9215 carried out at let and where bindings.
9219 <title>Switching off the dreaded Monomorphism Restriction</title>
9220 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9222 <para>Haskell's monomorphism restriction (see
9223 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9225 of the Haskell Report)
9226 can be completely switched off by
9227 <option>-XNoMonomorphismRestriction</option>.
9232 <title>Monomorphic pattern bindings</title>
9233 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9234 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9236 <para> As an experimental change, we are exploring the possibility of
9237 making pattern bindings monomorphic; that is, not generalised at all.
9238 A pattern binding is a binding whose LHS has no function arguments,
9239 and is not a simple variable. For example:
9241 f x = x -- Not a pattern binding
9242 f = \x -> x -- Not a pattern binding
9243 f :: Int -> Int = \x -> x -- Not a pattern binding
9245 (g,h) = e -- A pattern binding
9246 (f) = e -- A pattern binding
9247 [x] = e -- A pattern binding
9249 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9250 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
9259 ;;; Local Variables: ***
9260 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
9261 ;;; ispell-local-dictionary: "british" ***
projects / ghc-hetmet.git / blob