1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Language options can be controlled in two ways:
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
54 </itemizedlist></para>
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 <option>-XPrintExplicitForalls</option>,
60 <option>-XForeignFunctionInterface</option>,
61 <option>-XUnliftedFFITypes</option>,
62 <option>-XGADTs</option>,
63 <option>-XImplicitParams</option>,
64 <option>-XScopedTypeVariables</option>,
65 <option>-XUnboxedTuples</option>,
66 <option>-XTypeSynonymInstances</option>,
67 <option>-XStandaloneDeriving</option>,
68 <option>-XDeriveDataTypeable</option>,
69 <option>-XFlexibleContexts</option>,
70 <option>-XFlexibleInstances</option>,
71 <option>-XConstrainedClassMethods</option>,
72 <option>-XMultiParamTypeClasses</option>,
73 <option>-XFunctionalDependencies</option>,
74 <option>-XMagicHash</option>,
75 <option>-XPolymorphicComponents</option>,
76 <option>-XExistentialQuantification</option>,
77 <option>-XUnicodeSyntax</option>,
78 <option>-XPostfixOperators</option>,
79 <option>-XPatternGuards</option>,
80 <option>-XLiberalTypeSynonyms</option>,
81 <option>-XRankNTypes</option>,
82 <option>-XImpredicativeTypes</option>,
83 <option>-XTypeOperators</option>,
84 <option>-XRecursiveDo</option>,
85 <option>-XParallelListComp</option>,
86 <option>-XEmptyDataDecls</option>,
87 <option>-XKindSignatures</option>,
88 <option>-XGeneralizedNewtypeDeriving</option>,
89 <option>-XTypeFamilies</option>.
90 Enabling these options is the <emphasis>only</emphasis>
91 effect of <option>-fglasgow-exts</option>.
92 We are trying to move away from this portmanteau flag,
93 and towards enabling features individually.</para>
97 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
98 <sect1 id="primitives">
99 <title>Unboxed types and primitive operations</title>
101 <para>GHC is built on a raft of primitive data types and operations;
102 "primitive" in the sense that they cannot be defined in Haskell itself.
103 While you really can use this stuff to write fast code,
104 we generally find it a lot less painful, and more satisfying in the
105 long run, to use higher-level language features and libraries. With
106 any luck, the code you write will be optimised to the efficient
107 unboxed version in any case. And if it isn't, we'd like to know
110 <para>All these primitive data types and operations are exported by the
111 library <literal>GHC.Prim</literal>, for which there is
112 <ulink url="../libraries/ghc-prim/GHC-Prim.html">detailed online documentation</ulink>.
113 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
116 If you want to mention any of the primitive data types or operations in your
117 program, you must first import <literal>GHC.Prim</literal> to bring them
118 into scope. Many of them have names ending in "#", and to mention such
119 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
122 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
123 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
124 we briefly summarise here. </para>
126 <sect2 id="glasgow-unboxed">
131 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
134 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
135 that values of that type are represented by a pointer to a heap
136 object. The representation of a Haskell <literal>Int</literal>, for
137 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
138 type, however, is represented by the value itself, no pointers or heap
139 allocation are involved.
143 Unboxed types correspond to the “raw machine” types you
144 would use in C: <literal>Int#</literal> (long int),
145 <literal>Double#</literal> (double), <literal>Addr#</literal>
146 (void *), etc. The <emphasis>primitive operations</emphasis>
147 (PrimOps) on these types are what you might expect; e.g.,
148 <literal>(+#)</literal> is addition on
149 <literal>Int#</literal>s, and is the machine-addition that we all
150 know and love—usually one instruction.
154 Primitive (unboxed) types cannot be defined in Haskell, and are
155 therefore built into the language and compiler. Primitive types are
156 always unlifted; that is, a value of a primitive type cannot be
157 bottom. We use the convention (but it is only a convention)
158 that primitive types, values, and
159 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
160 For some primitive types we have special syntax for literals, also
161 described in the <link linkend="magic-hash">same section</link>.
165 Primitive values are often represented by a simple bit-pattern, such
166 as <literal>Int#</literal>, <literal>Float#</literal>,
167 <literal>Double#</literal>. But this is not necessarily the case:
168 a primitive value might be represented by a pointer to a
169 heap-allocated object. Examples include
170 <literal>Array#</literal>, the type of primitive arrays. A
171 primitive array is heap-allocated because it is too big a value to fit
172 in a register, and would be too expensive to copy around; in a sense,
173 it is accidental that it is represented by a pointer. If a pointer
174 represents a primitive value, then it really does point to that value:
175 no unevaluated thunks, no indirections…nothing can be at the
176 other end of the pointer than the primitive value.
177 A numerically-intensive program using unboxed types can
178 go a <emphasis>lot</emphasis> faster than its “standard”
179 counterpart—we saw a threefold speedup on one example.
183 There are some restrictions on the use of primitive types:
185 <listitem><para>The main restriction
186 is that you can't pass a primitive value to a polymorphic
187 function or store one in a polymorphic data type. This rules out
188 things like <literal>[Int#]</literal> (i.e. lists of primitive
189 integers). The reason for this restriction is that polymorphic
190 arguments and constructor fields are assumed to be pointers: if an
191 unboxed integer is stored in one of these, the garbage collector would
192 attempt to follow it, leading to unpredictable space leaks. Or a
193 <function>seq</function> operation on the polymorphic component may
194 attempt to dereference the pointer, with disastrous results. Even
195 worse, the unboxed value might be larger than a pointer
196 (<literal>Double#</literal> for instance).
199 <listitem><para> You cannot define a newtype whose representation type
200 (the argument type of the data constructor) is an unboxed type. Thus,
206 <listitem><para> You cannot bind a variable with an unboxed type
207 in a <emphasis>top-level</emphasis> binding.
209 <listitem><para> You cannot bind a variable with an unboxed type
210 in a <emphasis>recursive</emphasis> binding.
212 <listitem><para> You may bind unboxed variables in a (non-recursive,
213 non-top-level) pattern binding, but you must make any such pattern-match
214 strict. For example, rather than:
216 data Foo = Foo Int Int#
218 f x = let (Foo a b, w) = ..rhs.. in ..body..
222 data Foo = Foo Int Int#
224 f x = let !(Foo a b, w) = ..rhs.. in ..body..
226 since <literal>b</literal> has type <literal>Int#</literal>.
234 <sect2 id="unboxed-tuples">
235 <title>Unboxed Tuples
239 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
240 they're available by default with <option>-fglasgow-exts</option>. An
241 unboxed tuple looks like this:
253 where <literal>e_1..e_n</literal> are expressions of any
254 type (primitive or non-primitive). The type of an unboxed tuple looks
259 Unboxed tuples are used for functions that need to return multiple
260 values, but they avoid the heap allocation normally associated with
261 using fully-fledged tuples. When an unboxed tuple is returned, the
262 components are put directly into registers or on the stack; the
263 unboxed tuple itself does not have a composite representation. Many
264 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
266 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
267 tuples to avoid unnecessary allocation during sequences of operations.
271 There are some pretty stringent restrictions on the use of unboxed tuples:
276 Values of unboxed tuple types are subject to the same restrictions as
277 other unboxed types; i.e. they may not be stored in polymorphic data
278 structures or passed to polymorphic functions.
285 No variable can have an unboxed tuple type, nor may a constructor or function
286 argument have an unboxed tuple type. The following are all illegal:
290 data Foo = Foo (# Int, Int #)
292 f :: (# Int, Int #) -> (# Int, Int #)
295 g :: (# Int, Int #) -> Int
298 h x = let y = (# x,x #) in ...
305 The typical use of unboxed tuples is simply to return multiple values,
306 binding those multiple results with a <literal>case</literal> expression, thus:
308 f x y = (# x+1, y-1 #)
309 g x = case f x x of { (# a, b #) -> a + b }
311 You can have an unboxed tuple in a pattern binding, thus
313 f x = let (# p,q #) = h x in ..body..
315 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
316 the resulting binding is lazy like any other Haskell pattern binding. The
317 above example desugars like this:
319 f x = let t = case h x o f{ (# p,q #) -> (p,q)
324 Indeed, the bindings can even be recursive.
331 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
333 <sect1 id="syntax-extns">
334 <title>Syntactic extensions</title>
336 <sect2 id="unicode-syntax">
337 <title>Unicode syntax</title>
339 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
340 enables Unicode characters to be used to stand for certain ASCII
341 character sequences. The following alternatives are provided:</para>
344 <tgroup cols="2" align="left" colsep="1" rowsep="1">
348 <entry>Unicode alternative</entry>
349 <entry>Code point</entry>
355 <entry><literal>::</literal></entry>
356 <entry>::</entry> <!-- no special char, apparently -->
357 <entry>0x2237</entry>
358 <entry>PROPORTION</entry>
363 <entry><literal>=></literal></entry>
364 <entry>⇒</entry>
365 <entry>0x21D2</entry>
366 <entry>RIGHTWARDS DOUBLE ARROW</entry>
371 <entry><literal>forall</literal></entry>
372 <entry>∀</entry>
373 <entry>0x2200</entry>
374 <entry>FOR ALL</entry>
379 <entry><literal>-></literal></entry>
380 <entry>→</entry>
381 <entry>0x2192</entry>
382 <entry>RIGHTWARDS ARROW</entry>
387 <entry><literal><-</literal></entry>
388 <entry>←</entry>
389 <entry>0x2190</entry>
390 <entry>LEFTWARDS ARROW</entry>
396 <entry>…</entry>
397 <entry>0x22EF</entry>
398 <entry>MIDLINE HORIZONTAL ELLIPSIS</entry>
405 <sect2 id="magic-hash">
406 <title>The magic hash</title>
407 <para>The language extension <option>-XMagicHash</option> allows "#" as a
408 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
409 a valid type constructor or data constructor.</para>
411 <para>The hash sign does not change sematics at all. We tend to use variable
412 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
413 but there is no requirement to do so; they are just plain ordinary variables.
414 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
415 For example, to bring <literal>Int#</literal> into scope you must
416 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
417 the <option>-XMagicHash</option> extension
418 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
419 that is now in scope.</para>
420 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
422 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
423 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
424 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
425 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
426 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
427 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
428 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
429 is a <literal>Word#</literal>. </para> </listitem>
430 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
431 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
436 <sect2 id="new-qualified-operators">
437 <title>New qualified operator syntax</title>
439 <para>A new syntax for referencing qualified operators is
440 planned to be introduced by Haskell', and is enabled in GHC
442 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
443 option. In the new syntax, the prefix form of a qualified
445 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
446 (in Haskell 98 this would
447 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
448 and the infix form is
449 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
450 (in Haskell 98 this would
451 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
454 add x y = Prelude.(+) x y
455 subtract y = (`Prelude.(-)` y)
457 The new form of qualified operators is intended to regularise
458 the syntax by eliminating odd cases
459 like <literal>Prelude..</literal>. For example,
460 when <literal>NewQualifiedOperators</literal> is on, it is possible to
461 write the enumerated sequence <literal>[Monday..]</literal>
462 without spaces, whereas in Haskell 98 this would be a
463 reference to the operator ‘<literal>.</literal>‘
464 from module <literal>Monday</literal>.</para>
466 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
467 98 syntax for qualified operators is not accepted, so this
468 option may cause existing Haskell 98 code to break.</para>
473 <!-- ====================== HIERARCHICAL MODULES ======================= -->
476 <sect2 id="hierarchical-modules">
477 <title>Hierarchical Modules</title>
479 <para>GHC supports a small extension to the syntax of module
480 names: a module name is allowed to contain a dot
481 <literal>‘.’</literal>. This is also known as the
482 “hierarchical module namespace” extension, because
483 it extends the normally flat Haskell module namespace into a
484 more flexible hierarchy of modules.</para>
486 <para>This extension has very little impact on the language
487 itself; modules names are <emphasis>always</emphasis> fully
488 qualified, so you can just think of the fully qualified module
489 name as <quote>the module name</quote>. In particular, this
490 means that the full module name must be given after the
491 <literal>module</literal> keyword at the beginning of the
492 module; for example, the module <literal>A.B.C</literal> must
495 <programlisting>module A.B.C</programlisting>
498 <para>It is a common strategy to use the <literal>as</literal>
499 keyword to save some typing when using qualified names with
500 hierarchical modules. For example:</para>
503 import qualified Control.Monad.ST.Strict as ST
506 <para>For details on how GHC searches for source and interface
507 files in the presence of hierarchical modules, see <xref
508 linkend="search-path"/>.</para>
510 <para>GHC comes with a large collection of libraries arranged
511 hierarchically; see the accompanying <ulink
512 url="../libraries/index.html">library
513 documentation</ulink>. More libraries to install are available
515 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
518 <!-- ====================== PATTERN GUARDS ======================= -->
520 <sect2 id="pattern-guards">
521 <title>Pattern guards</title>
524 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
525 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
529 Suppose we have an abstract data type of finite maps, with a
533 lookup :: FiniteMap -> Int -> Maybe Int
536 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
537 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
541 clunky env var1 var2 | ok1 && ok2 = val1 + val2
542 | otherwise = var1 + var2
553 The auxiliary functions are
557 maybeToBool :: Maybe a -> Bool
558 maybeToBool (Just x) = True
559 maybeToBool Nothing = False
561 expectJust :: Maybe a -> a
562 expectJust (Just x) = x
563 expectJust Nothing = error "Unexpected Nothing"
567 What is <function>clunky</function> doing? The guard <literal>ok1 &&
568 ok2</literal> checks that both lookups succeed, using
569 <function>maybeToBool</function> to convert the <function>Maybe</function>
570 types to booleans. The (lazily evaluated) <function>expectJust</function>
571 calls extract the values from the results of the lookups, and binds the
572 returned values to <varname>val1</varname> and <varname>val2</varname>
573 respectively. If either lookup fails, then clunky takes the
574 <literal>otherwise</literal> case and returns the sum of its arguments.
578 This is certainly legal Haskell, but it is a tremendously verbose and
579 un-obvious way to achieve the desired effect. Arguably, a more direct way
580 to write clunky would be to use case expressions:
584 clunky env var1 var2 = case lookup env var1 of
586 Just val1 -> case lookup env var2 of
588 Just val2 -> val1 + val2
594 This is a bit shorter, but hardly better. Of course, we can rewrite any set
595 of pattern-matching, guarded equations as case expressions; that is
596 precisely what the compiler does when compiling equations! The reason that
597 Haskell provides guarded equations is because they allow us to write down
598 the cases we want to consider, one at a time, independently of each other.
599 This structure is hidden in the case version. Two of the right-hand sides
600 are really the same (<function>fail</function>), and the whole expression
601 tends to become more and more indented.
605 Here is how I would write clunky:
610 | Just val1 <- lookup env var1
611 , Just val2 <- lookup env var2
613 ...other equations for clunky...
617 The semantics should be clear enough. The qualifiers are matched in order.
618 For a <literal><-</literal> qualifier, which I call a pattern guard, the
619 right hand side is evaluated and matched against the pattern on the left.
620 If the match fails then the whole guard fails and the next equation is
621 tried. If it succeeds, then the appropriate binding takes place, and the
622 next qualifier is matched, in the augmented environment. Unlike list
623 comprehensions, however, the type of the expression to the right of the
624 <literal><-</literal> is the same as the type of the pattern to its
625 left. The bindings introduced by pattern guards scope over all the
626 remaining guard qualifiers, and over the right hand side of the equation.
630 Just as with list comprehensions, boolean expressions can be freely mixed
631 with among the pattern guards. For example:
642 Haskell's current guards therefore emerge as a special case, in which the
643 qualifier list has just one element, a boolean expression.
647 <!-- ===================== View patterns =================== -->
649 <sect2 id="view-patterns">
654 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
655 More information and examples of view patterns can be found on the
656 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
661 View patterns are somewhat like pattern guards that can be nested inside
662 of other patterns. They are a convenient way of pattern-matching
663 against values of abstract types. For example, in a programming language
664 implementation, we might represent the syntax of the types of the
673 view :: Type -> TypeView
675 -- additional operations for constructing Typ's ...
678 The representation of Typ is held abstract, permitting implementations
679 to use a fancy representation (e.g., hash-consing to manage sharing).
681 Without view patterns, using this signature a little inconvenient:
683 size :: Typ -> Integer
684 size t = case view t of
686 Arrow t1 t2 -> size t1 + size t2
689 It is necessary to iterate the case, rather than using an equational
690 function definition. And the situation is even worse when the matching
691 against <literal>t</literal> is buried deep inside another pattern.
695 View patterns permit calling the view function inside the pattern and
696 matching against the result:
698 size (view -> Unit) = 1
699 size (view -> Arrow t1 t2) = size t1 + size t2
702 That is, we add a new form of pattern, written
703 <replaceable>expression</replaceable> <literal>-></literal>
704 <replaceable>pattern</replaceable> that means "apply the expression to
705 whatever we're trying to match against, and then match the result of
706 that application against the pattern". The expression can be any Haskell
707 expression of function type, and view patterns can be used wherever
712 The semantics of a pattern <literal>(</literal>
713 <replaceable>exp</replaceable> <literal>-></literal>
714 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
720 <para>The variables bound by the view pattern are the variables bound by
721 <replaceable>pat</replaceable>.
725 Any variables in <replaceable>exp</replaceable> are bound occurrences,
726 but variables bound "to the left" in a pattern are in scope. This
727 feature permits, for example, one argument to a function to be used in
728 the view of another argument. For example, the function
729 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
730 written using view patterns as follows:
733 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
734 ...other equations for clunky...
739 More precisely, the scoping rules are:
743 In a single pattern, variables bound by patterns to the left of a view
744 pattern expression are in scope. For example:
746 example :: Maybe ((String -> Integer,Integer), String) -> Bool
747 example Just ((f,_), f -> 4) = True
750 Additionally, in function definitions, variables bound by matching earlier curried
751 arguments may be used in view pattern expressions in later arguments:
753 example :: (String -> Integer) -> String -> Bool
754 example f (f -> 4) = True
756 That is, the scoping is the same as it would be if the curried arguments
757 were collected into a tuple.
763 In mutually recursive bindings, such as <literal>let</literal>,
764 <literal>where</literal>, or the top level, view patterns in one
765 declaration may not mention variables bound by other declarations. That
766 is, each declaration must be self-contained. For example, the following
767 program is not allowed:
774 restriction in the future; the only cost is that type checking patterns
775 would get a little more complicated.)
785 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
786 <replaceable>T1</replaceable> <literal>-></literal>
787 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
788 a <replaceable>T2</replaceable>, then the whole view pattern matches a
789 <replaceable>T1</replaceable>.
792 <listitem><para> Matching: To the equations in Section 3.17.3 of the
793 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
794 Report</ulink>, add the following:
796 case v of { (e -> p) -> e1 ; _ -> e2 }
798 case (e v) of { p -> e1 ; _ -> e2 }
800 That is, to match a variable <replaceable>v</replaceable> against a pattern
801 <literal>(</literal> <replaceable>exp</replaceable>
802 <literal>-></literal> <replaceable>pat</replaceable>
803 <literal>)</literal>, evaluate <literal>(</literal>
804 <replaceable>exp</replaceable> <replaceable> v</replaceable>
805 <literal>)</literal> and match the result against
806 <replaceable>pat</replaceable>.
809 <listitem><para> Efficiency: When the same view function is applied in
810 multiple branches of a function definition or a case expression (e.g.,
811 in <literal>size</literal> above), GHC makes an attempt to collect these
812 applications into a single nested case expression, so that the view
813 function is only applied once. Pattern compilation in GHC follows the
814 matrix algorithm described in Chapter 4 of <ulink
815 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
816 Implementation of Functional Programming Languages</ulink>. When the
817 top rows of the first column of a matrix are all view patterns with the
818 "same" expression, these patterns are transformed into a single nested
819 case. This includes, for example, adjacent view patterns that line up
822 f ((view -> A, p1), p2) = e1
823 f ((view -> B, p3), p4) = e2
827 <para> The current notion of when two view pattern expressions are "the
828 same" is very restricted: it is not even full syntactic equality.
829 However, it does include variables, literals, applications, and tuples;
830 e.g., two instances of <literal>view ("hi", "there")</literal> will be
831 collected. However, the current implementation does not compare up to
832 alpha-equivalence, so two instances of <literal>(x, view x ->
833 y)</literal> will not be coalesced.
843 <!-- ===================== n+k patterns =================== -->
845 <sect2 id="n-k-patterns">
846 <title>n+k patterns</title>
847 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
850 <literal>n+k</literal> pattern support is enabled by default. To disable
851 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
856 <!-- ===================== Recursive do-notation =================== -->
858 <sect2 id="mdo-notation">
859 <title>The recursive do-notation
862 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
863 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
864 by Levent Erkok, John Launchbury,
865 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
866 This paper is essential reading for anyone making non-trivial use of mdo-notation,
867 and we do not repeat it here.
870 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
871 that is, the variables bound in a do-expression are visible only in the textually following
872 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
873 group. It turns out that several applications can benefit from recursive bindings in
874 the do-notation, and this extension provides the necessary syntactic support.
877 Here is a simple (yet contrived) example:
880 import Control.Monad.Fix
882 justOnes = mdo xs <- Just (1:xs)
886 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
890 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. Its definition is:
893 class Monad m => MonadFix m where
894 mfix :: (a -> m a) -> m a
897 The function <literal>mfix</literal>
898 dictates how the required recursion operation should be performed. For example,
899 <literal>justOnes</literal> desugars as follows:
901 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
903 For full details of the way in which mdo is typechecked and desugared, see
904 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
905 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
908 If recursive bindings are required for a monad,
909 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
910 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
911 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
912 for Haskell's internal state monad (strict and lazy, respectively).
915 Here are some important points in using the recursive-do notation:
918 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
919 than <literal>do</literal>).
923 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
924 <literal>-fglasgow-exts</literal>.
928 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
929 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
930 be distinct (Section 3.3 of the paper).
934 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
935 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
936 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
937 and improve termination (Section 3.2 of the paper).
943 Historical note: The old implementation of the mdo-notation (and most
944 of the existing documents) used the name
945 <literal>MonadRec</literal> for the class and the corresponding library.
946 This name is not supported by GHC.
952 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
954 <sect2 id="parallel-list-comprehensions">
955 <title>Parallel List Comprehensions</title>
956 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
958 <indexterm><primary>parallel list comprehensions</primary>
961 <para>Parallel list comprehensions are a natural extension to list
962 comprehensions. List comprehensions can be thought of as a nice
963 syntax for writing maps and filters. Parallel comprehensions
964 extend this to include the zipWith family.</para>
966 <para>A parallel list comprehension has multiple independent
967 branches of qualifier lists, each separated by a `|' symbol. For
968 example, the following zips together two lists:</para>
971 [ (x, y) | x <- xs | y <- ys ]
974 <para>The behavior of parallel list comprehensions follows that of
975 zip, in that the resulting list will have the same length as the
976 shortest branch.</para>
978 <para>We can define parallel list comprehensions by translation to
979 regular comprehensions. Here's the basic idea:</para>
981 <para>Given a parallel comprehension of the form: </para>
984 [ e | p1 <- e11, p2 <- e12, ...
985 | q1 <- e21, q2 <- e22, ...
990 <para>This will be translated to: </para>
993 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
994 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
999 <para>where `zipN' is the appropriate zip for the given number of
1004 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1006 <sect2 id="generalised-list-comprehensions">
1007 <title>Generalised (SQL-Like) List Comprehensions</title>
1008 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1010 <indexterm><primary>extended list comprehensions</primary>
1012 <indexterm><primary>group</primary></indexterm>
1013 <indexterm><primary>sql</primary></indexterm>
1016 <para>Generalised list comprehensions are a further enhancement to the
1017 list comprehension syntactic sugar to allow operations such as sorting
1018 and grouping which are familiar from SQL. They are fully described in the
1019 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1020 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1021 except that the syntax we use differs slightly from the paper.</para>
1022 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1023 <para>Here is an example:
1025 employees = [ ("Simon", "MS", 80)
1026 , ("Erik", "MS", 100)
1027 , ("Phil", "Ed", 40)
1028 , ("Gordon", "Ed", 45)
1029 , ("Paul", "Yale", 60)]
1031 output = [ (the dept, sum salary)
1032 | (name, dept, salary) <- employees
1033 , then group by dept
1034 , then sortWith by (sum salary)
1037 In this example, the list <literal>output</literal> would take on
1041 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1044 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1045 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1046 function that is exported by <literal>GHC.Exts</literal>.)</para>
1048 <para>There are five new forms of comprehension qualifier,
1049 all introduced by the (existing) keyword <literal>then</literal>:
1057 This statement requires that <literal>f</literal> have the type <literal>
1058 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1059 motivating example, as this form is used to apply <literal>take 5</literal>.
1070 This form is similar to the previous one, but allows you to create a function
1071 which will be passed as the first argument to f. As a consequence f must have
1072 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1073 from the type, this function lets f "project out" some information
1074 from the elements of the list it is transforming.</para>
1076 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1077 is supplied with a function that lets it find out the <literal>sum salary</literal>
1078 for any item in the list comprehension it transforms.</para>
1086 then group by e using f
1089 <para>This is the most general of the grouping-type statements. In this form,
1090 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1091 As with the <literal>then f by e</literal> case above, the first argument
1092 is a function supplied to f by the compiler which lets it compute e on every
1093 element of the list being transformed. However, unlike the non-grouping case,
1094 f additionally partitions the list into a number of sublists: this means that
1095 at every point after this statement, binders occurring before it in the comprehension
1096 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1097 this, let's look at an example:</para>
1100 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1101 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1102 groupRuns f = groupBy (\x y -> f x == f y)
1104 output = [ (the x, y)
1105 | x <- ([1..3] ++ [1..2])
1107 , then group by x using groupRuns ]
1110 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1113 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1116 <para>Note that we have used the <literal>the</literal> function to change the type
1117 of x from a list to its original numeric type. The variable y, in contrast, is left
1118 unchanged from the list form introduced by the grouping.</para>
1128 <para>This form of grouping is essentially the same as the one described above. However,
1129 since no function to use for the grouping has been supplied it will fall back on the
1130 <literal>groupWith</literal> function defined in
1131 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1132 is the form of the group statement that we made use of in the opening example.</para>
1143 <para>With this form of the group statement, f is required to simply have the type
1144 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1145 comprehension so far directly. An example of this form is as follows:</para>
1151 , then group using inits]
1154 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1157 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1165 <!-- ===================== REBINDABLE SYNTAX =================== -->
1167 <sect2 id="rebindable-syntax">
1168 <title>Rebindable syntax and the implicit Prelude import</title>
1170 <para><indexterm><primary>-XNoImplicitPrelude
1171 option</primary></indexterm> GHC normally imports
1172 <filename>Prelude.hi</filename> files for you. If you'd
1173 rather it didn't, then give it a
1174 <option>-XNoImplicitPrelude</option> option. The idea is
1175 that you can then import a Prelude of your own. (But don't
1176 call it <literal>Prelude</literal>; the Haskell module
1177 namespace is flat, and you must not conflict with any
1178 Prelude module.)</para>
1180 <para>Suppose you are importing a Prelude of your own
1181 in order to define your own numeric class
1182 hierarchy. It completely defeats that purpose if the
1183 literal "1" means "<literal>Prelude.fromInteger
1184 1</literal>", which is what the Haskell Report specifies.
1185 So the <option>-XNoImplicitPrelude</option>
1186 flag <emphasis>also</emphasis> causes
1187 the following pieces of built-in syntax to refer to
1188 <emphasis>whatever is in scope</emphasis>, not the Prelude
1192 <para>An integer literal <literal>368</literal> means
1193 "<literal>fromInteger (368::Integer)</literal>", rather than
1194 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1197 <listitem><para>Fractional literals are handed in just the same way,
1198 except that the translation is
1199 <literal>fromRational (3.68::Rational)</literal>.
1202 <listitem><para>The equality test in an overloaded numeric pattern
1203 uses whatever <literal>(==)</literal> is in scope.
1206 <listitem><para>The subtraction operation, and the
1207 greater-than-or-equal test, in <literal>n+k</literal> patterns
1208 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1212 <para>Negation (e.g. "<literal>- (f x)</literal>")
1213 means "<literal>negate (f x)</literal>", both in numeric
1214 patterns, and expressions.
1218 <para>"Do" notation is translated using whatever
1219 functions <literal>(>>=)</literal>,
1220 <literal>(>>)</literal>, and <literal>fail</literal>,
1221 are in scope (not the Prelude
1222 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1223 comprehensions, are unaffected. </para></listitem>
1227 notation (see <xref linkend="arrow-notation"/>)
1228 uses whatever <literal>arr</literal>,
1229 <literal>(>>>)</literal>, <literal>first</literal>,
1230 <literal>app</literal>, <literal>(|||)</literal> and
1231 <literal>loop</literal> functions are in scope. But unlike the
1232 other constructs, the types of these functions must match the
1233 Prelude types very closely. Details are in flux; if you want
1237 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1238 even if that is a little unexpected. For example, the
1239 static semantics of the literal <literal>368</literal>
1240 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1241 <literal>fromInteger</literal> to have any of the types:
1243 fromInteger :: Integer -> Integer
1244 fromInteger :: forall a. Foo a => Integer -> a
1245 fromInteger :: Num a => a -> Integer
1246 fromInteger :: Integer -> Bool -> Bool
1250 <para>Be warned: this is an experimental facility, with
1251 fewer checks than usual. Use <literal>-dcore-lint</literal>
1252 to typecheck the desugared program. If Core Lint is happy
1253 you should be all right.</para>
1257 <sect2 id="postfix-operators">
1258 <title>Postfix operators</title>
1261 The <option>-XPostfixOperators</option> flag enables a small
1262 extension to the syntax of left operator sections, which allows you to
1263 define postfix operators. The extension is this: the left section
1267 is equivalent (from the point of view of both type checking and execution) to the expression
1271 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1272 The strict Haskell 98 interpretation is that the section is equivalent to
1276 That is, the operator must be a function of two arguments. GHC allows it to
1277 take only one argument, and that in turn allows you to write the function
1280 <para>The extension does not extend to the left-hand side of function
1281 definitions; you must define such a function in prefix form.</para>
1285 <sect2 id="tuple-sections">
1286 <title>Tuple sections</title>
1289 The <option>-XTupleSections</option> flag enables Python-style partially applied
1290 tuple constructors. For example, the following program
1294 is considered to be an alternative notation for the more unwieldy alternative
1298 You can omit any combination of arguments to the tuple, as in the following
1300 (, "I", , , "Love", , 1337)
1304 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1309 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1310 will also be available for them, like so
1314 Because there is no unboxed unit tuple, the following expression
1318 continues to stand for the unboxed singleton tuple data constructor.
1323 <sect2 id="disambiguate-fields">
1324 <title>Record field disambiguation</title>
1326 In record construction and record pattern matching
1327 it is entirely unambiguous which field is referred to, even if there are two different
1328 data types in scope with a common field name. For example:
1331 data S = MkS { x :: Int, y :: Bool }
1336 data T = MkT { x :: Int }
1338 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1340 ok2 n = MkT { x = n+1 } -- Unambiguous
1342 bad1 k = k { x = 3 } -- Ambiguous
1343 bad2 k = x k -- Ambiguous
1345 Even though there are two <literal>x</literal>'s in scope,
1346 it is clear that the <literal>x</literal> in the pattern in the
1347 definition of <literal>ok1</literal> can only mean the field
1348 <literal>x</literal> from type <literal>S</literal>. Similarly for
1349 the function <literal>ok2</literal>. However, in the record update
1350 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1351 it is not clear which of the two types is intended.
1354 Haskell 98 regards all four as ambiguous, but with the
1355 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1356 the former two. The rules are precisely the same as those for instance
1357 declarations in Haskell 98, where the method names on the left-hand side
1358 of the method bindings in an instance declaration refer unambiguously
1359 to the method of that class (provided they are in scope at all), even
1360 if there are other variables in scope with the same name.
1361 This reduces the clutter of qualified names when you import two
1362 records from different modules that use the same field name.
1366 <!-- ===================== Record puns =================== -->
1368 <sect2 id="record-puns">
1373 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1377 When using records, it is common to write a pattern that binds a
1378 variable with the same name as a record field, such as:
1381 data C = C {a :: Int}
1387 Record punning permits the variable name to be elided, so one can simply
1394 to mean the same pattern as above. That is, in a record pattern, the
1395 pattern <literal>a</literal> expands into the pattern <literal>a =
1396 a</literal> for the same name <literal>a</literal>.
1400 Note that puns and other patterns can be mixed in the same record:
1402 data C = C {a :: Int, b :: Int}
1403 f (C {a, b = 4}) = a
1405 and that puns can be used wherever record patterns occur (e.g. in
1406 <literal>let</literal> bindings or at the top-level).
1410 Record punning can also be used in an expression, writing, for example,
1416 let a = 1 in C {a = a}
1419 Note that this expansion is purely syntactic, so the record pun
1420 expression refers to the nearest enclosing variable that is spelled the
1421 same as the field name.
1426 <!-- ===================== Record wildcards =================== -->
1428 <sect2 id="record-wildcards">
1429 <title>Record wildcards
1433 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1437 For records with many fields, it can be tiresome to write out each field
1438 individually in a record pattern, as in
1440 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1441 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1446 Record wildcard syntax permits a (<literal>..</literal>) in a record
1447 pattern, where each elided field <literal>f</literal> is replaced by the
1448 pattern <literal>f = f</literal>. For example, the above pattern can be
1451 f (C {a = 1, ..}) = b + c + d
1456 Note that wildcards can be mixed with other patterns, including puns
1457 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1458 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1459 wherever record patterns occur, including in <literal>let</literal>
1460 bindings and at the top-level. For example, the top-level binding
1464 defines <literal>b</literal>, <literal>c</literal>, and
1465 <literal>d</literal>.
1469 Record wildcards can also be used in expressions, writing, for example,
1472 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1478 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1481 Note that this expansion is purely syntactic, so the record wildcard
1482 expression refers to the nearest enclosing variables that are spelled
1483 the same as the omitted field names.
1488 <!-- ===================== Local fixity declarations =================== -->
1490 <sect2 id="local-fixity-declarations">
1491 <title>Local Fixity Declarations
1494 <para>A careful reading of the Haskell 98 Report reveals that fixity
1495 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1496 <literal>infixr</literal>) are permitted to appear inside local bindings
1497 such those introduced by <literal>let</literal> and
1498 <literal>where</literal>. However, the Haskell Report does not specify
1499 the semantics of such bindings very precisely.
1502 <para>In GHC, a fixity declaration may accompany a local binding:
1509 and the fixity declaration applies wherever the binding is in scope.
1510 For example, in a <literal>let</literal>, it applies in the right-hand
1511 sides of other <literal>let</literal>-bindings and the body of the
1512 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1513 expressions (<xref linkend="mdo-notation"/>), the local fixity
1514 declarations of a <literal>let</literal> statement scope over other
1515 statements in the group, just as the bound name does.
1519 Moreover, a local fixity declaration *must* accompany a local binding of
1520 that name: it is not possible to revise the fixity of name bound
1523 let infixr 9 $ in ...
1526 Because local fixity declarations are technically Haskell 98, no flag is
1527 necessary to enable them.
1531 <sect2 id="package-imports">
1532 <title>Package-qualified imports</title>
1534 <para>With the <option>-XPackageImports</option> flag, GHC allows
1535 import declarations to be qualified by the package name that the
1536 module is intended to be imported from. For example:</para>
1539 import "network" Network.Socket
1542 <para>would import the module <literal>Network.Socket</literal> from
1543 the package <literal>network</literal> (any version). This may
1544 be used to disambiguate an import when the same module is
1545 available from multiple packages, or is present in both the
1546 current package being built and an external package.</para>
1548 <para>Note: you probably don't need to use this feature, it was
1549 added mainly so that we can build backwards-compatible versions of
1550 packages when APIs change. It can lead to fragile dependencies in
1551 the common case: modules occasionally move from one package to
1552 another, rendering any package-qualified imports broken.</para>
1555 <sect2 id="syntax-stolen">
1556 <title>Summary of stolen syntax</title>
1558 <para>Turning on an option that enables special syntax
1559 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1560 to compile, perhaps because it uses a variable name which has
1561 become a reserved word. This section lists the syntax that is
1562 "stolen" by language extensions.
1564 notation and nonterminal names from the Haskell 98 lexical syntax
1565 (see the Haskell 98 Report).
1566 We only list syntax changes here that might affect
1567 existing working programs (i.e. "stolen" syntax). Many of these
1568 extensions will also enable new context-free syntax, but in all
1569 cases programs written to use the new syntax would not be
1570 compilable without the option enabled.</para>
1572 <para>There are two classes of special
1577 <para>New reserved words and symbols: character sequences
1578 which are no longer available for use as identifiers in the
1582 <para>Other special syntax: sequences of characters that have
1583 a different meaning when this particular option is turned
1588 The following syntax is stolen:
1593 <literal>forall</literal>
1594 <indexterm><primary><literal>forall</literal></primary></indexterm>
1597 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1598 <option>-XLiberalTypeSynonyms</option>,
1599 <option>-XRank2Types</option>,
1600 <option>-XRankNTypes</option>,
1601 <option>-XPolymorphicComponents</option>,
1602 <option>-XExistentialQuantification</option>
1608 <literal>mdo</literal>
1609 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1612 Stolen by: <option>-XRecursiveDo</option>,
1618 <literal>foreign</literal>
1619 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1622 Stolen by: <option>-XForeignFunctionInterface</option>,
1628 <literal>rec</literal>,
1629 <literal>proc</literal>, <literal>-<</literal>,
1630 <literal>>-</literal>, <literal>-<<</literal>,
1631 <literal>>>-</literal>, and <literal>(|</literal>,
1632 <literal>|)</literal> brackets
1633 <indexterm><primary><literal>proc</literal></primary></indexterm>
1636 Stolen by: <option>-XArrows</option>,
1642 <literal>?<replaceable>varid</replaceable></literal>,
1643 <literal>%<replaceable>varid</replaceable></literal>
1644 <indexterm><primary>implicit parameters</primary></indexterm>
1647 Stolen by: <option>-XImplicitParams</option>,
1653 <literal>[|</literal>,
1654 <literal>[e|</literal>, <literal>[p|</literal>,
1655 <literal>[d|</literal>, <literal>[t|</literal>,
1656 <literal>$(</literal>,
1657 <literal>$<replaceable>varid</replaceable></literal>
1658 <indexterm><primary>Template Haskell</primary></indexterm>
1661 Stolen by: <option>-XTemplateHaskell</option>,
1667 <literal>[:<replaceable>varid</replaceable>|</literal>
1668 <indexterm><primary>quasi-quotation</primary></indexterm>
1671 Stolen by: <option>-XQuasiQuotes</option>,
1677 <replaceable>varid</replaceable>{<literal>#</literal>},
1678 <replaceable>char</replaceable><literal>#</literal>,
1679 <replaceable>string</replaceable><literal>#</literal>,
1680 <replaceable>integer</replaceable><literal>#</literal>,
1681 <replaceable>float</replaceable><literal>#</literal>,
1682 <replaceable>float</replaceable><literal>##</literal>,
1683 <literal>(#</literal>, <literal>#)</literal>,
1686 Stolen by: <option>-XMagicHash</option>,
1695 <!-- TYPE SYSTEM EXTENSIONS -->
1696 <sect1 id="data-type-extensions">
1697 <title>Extensions to data types and type synonyms</title>
1699 <sect2 id="nullary-types">
1700 <title>Data types with no constructors</title>
1702 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1703 a data type with no constructors. For example:</para>
1707 data T a -- T :: * -> *
1710 <para>Syntactically, the declaration lacks the "= constrs" part. The
1711 type can be parameterised over types of any kind, but if the kind is
1712 not <literal>*</literal> then an explicit kind annotation must be used
1713 (see <xref linkend="kinding"/>).</para>
1715 <para>Such data types have only one value, namely bottom.
1716 Nevertheless, they can be useful when defining "phantom types".</para>
1719 <sect2 id="infix-tycons">
1720 <title>Infix type constructors, classes, and type variables</title>
1723 GHC allows type constructors, classes, and type variables to be operators, and
1724 to be written infix, very much like expressions. More specifically:
1727 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1728 The lexical syntax is the same as that for data constructors.
1731 Data type and type-synonym declarations can be written infix, parenthesised
1732 if you want further arguments. E.g.
1734 data a :*: b = Foo a b
1735 type a :+: b = Either a b
1736 class a :=: b where ...
1738 data (a :**: b) x = Baz a b x
1739 type (a :++: b) y = Either (a,b) y
1743 Types, and class constraints, can be written infix. For example
1746 f :: (a :=: b) => a -> b
1750 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1751 The lexical syntax is the same as that for variable operators, excluding "(.)",
1752 "(!)", and "(*)". In a binding position, the operator must be
1753 parenthesised. For example:
1755 type T (+) = Int + Int
1759 liftA2 :: Arrow (~>)
1760 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1766 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1767 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1770 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1771 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1772 sets the fixity for a data constructor and the corresponding type constructor. For example:
1776 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1777 and similarly for <literal>:*:</literal>.
1778 <literal>Int `a` Bool</literal>.
1781 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1788 <sect2 id="type-synonyms">
1789 <title>Liberalised type synonyms</title>
1792 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1793 on individual synonym declarations.
1794 With the <option>-XLiberalTypeSynonyms</option> extension,
1795 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1796 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1799 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1800 in a type synonym, thus:
1802 type Discard a = forall b. Show b => a -> b -> (a, String)
1807 g :: Discard Int -> (Int,String) -- A rank-2 type
1814 If you also use <option>-XUnboxedTuples</option>,
1815 you can write an unboxed tuple in a type synonym:
1817 type Pr = (# Int, Int #)
1825 You can apply a type synonym to a forall type:
1827 type Foo a = a -> a -> Bool
1829 f :: Foo (forall b. b->b)
1831 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1833 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1838 You can apply a type synonym to a partially applied type synonym:
1840 type Generic i o = forall x. i x -> o x
1843 foo :: Generic Id []
1845 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1847 foo :: forall x. x -> [x]
1855 GHC currently does kind checking before expanding synonyms (though even that
1859 After expanding type synonyms, GHC does validity checking on types, looking for
1860 the following mal-formedness which isn't detected simply by kind checking:
1863 Type constructor applied to a type involving for-alls.
1866 Unboxed tuple on left of an arrow.
1869 Partially-applied type synonym.
1873 this will be rejected:
1875 type Pr = (# Int, Int #)
1880 because GHC does not allow unboxed tuples on the left of a function arrow.
1885 <sect2 id="existential-quantification">
1886 <title>Existentially quantified data constructors
1890 The idea of using existential quantification in data type declarations
1891 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1892 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1893 London, 1991). It was later formalised by Laufer and Odersky
1894 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1895 TOPLAS, 16(5), pp1411-1430, 1994).
1896 It's been in Lennart
1897 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1898 proved very useful. Here's the idea. Consider the declaration:
1904 data Foo = forall a. MkFoo a (a -> Bool)
1911 The data type <literal>Foo</literal> has two constructors with types:
1917 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1924 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1925 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1926 For example, the following expression is fine:
1932 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1938 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1939 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1940 isUpper</function> packages a character with a compatible function. These
1941 two things are each of type <literal>Foo</literal> and can be put in a list.
1945 What can we do with a value of type <literal>Foo</literal>?. In particular,
1946 what happens when we pattern-match on <function>MkFoo</function>?
1952 f (MkFoo val fn) = ???
1958 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1959 are compatible, the only (useful) thing we can do with them is to
1960 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1967 f (MkFoo val fn) = fn val
1973 What this allows us to do is to package heterogeneous values
1974 together with a bunch of functions that manipulate them, and then treat
1975 that collection of packages in a uniform manner. You can express
1976 quite a bit of object-oriented-like programming this way.
1979 <sect3 id="existential">
1980 <title>Why existential?
1984 What has this to do with <emphasis>existential</emphasis> quantification?
1985 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1991 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1997 But Haskell programmers can safely think of the ordinary
1998 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1999 adding a new existential quantification construct.
2004 <sect3 id="existential-with-context">
2005 <title>Existentials and type classes</title>
2008 An easy extension is to allow
2009 arbitrary contexts before the constructor. For example:
2015 data Baz = forall a. Eq a => Baz1 a a
2016 | forall b. Show b => Baz2 b (b -> b)
2022 The two constructors have the types you'd expect:
2028 Baz1 :: forall a. Eq a => a -> a -> Baz
2029 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2035 But when pattern matching on <function>Baz1</function> the matched values can be compared
2036 for equality, and when pattern matching on <function>Baz2</function> the first matched
2037 value can be converted to a string (as well as applying the function to it).
2038 So this program is legal:
2045 f (Baz1 p q) | p == q = "Yes"
2047 f (Baz2 v fn) = show (fn v)
2053 Operationally, in a dictionary-passing implementation, the
2054 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2055 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2056 extract it on pattern matching.
2061 <sect3 id="existential-records">
2062 <title>Record Constructors</title>
2065 GHC allows existentials to be used with records syntax as well. For example:
2068 data Counter a = forall self. NewCounter
2070 , _inc :: self -> self
2071 , _display :: self -> IO ()
2075 Here <literal>tag</literal> is a public field, with a well-typed selector
2076 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2077 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2078 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2079 compile-time error. In other words, <emphasis>GHC defines a record selector function
2080 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2081 (This example used an underscore in the fields for which record selectors
2082 will not be defined, but that is only programming style; GHC ignores them.)
2086 To make use of these hidden fields, we need to create some helper functions:
2089 inc :: Counter a -> Counter a
2090 inc (NewCounter x i d t) = NewCounter
2091 { _this = i x, _inc = i, _display = d, tag = t }
2093 display :: Counter a -> IO ()
2094 display NewCounter{ _this = x, _display = d } = d x
2097 Now we can define counters with different underlying implementations:
2100 counterA :: Counter String
2101 counterA = NewCounter
2102 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2104 counterB :: Counter String
2105 counterB = NewCounter
2106 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2109 display (inc counterA) -- prints "1"
2110 display (inc (inc counterB)) -- prints "##"
2113 Record update syntax is supported for existentials (and GADTs):
2115 setTag :: Counter a -> a -> Counter a
2116 setTag obj t = obj{ tag = t }
2118 The rule for record update is this: <emphasis>
2119 the types of the updated fields may
2120 mention only the universally-quantified type variables
2121 of the data constructor. For GADTs, the field may mention only types
2122 that appear as a simple type-variable argument in the constructor's result
2123 type</emphasis>. For example:
2125 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2126 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2127 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2128 -- existentially quantified)
2130 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2131 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2132 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2133 -- type-variable argument in G1's result type)
2141 <title>Restrictions</title>
2144 There are several restrictions on the ways in which existentially-quantified
2145 constructors can be use.
2154 When pattern matching, each pattern match introduces a new,
2155 distinct, type for each existential type variable. These types cannot
2156 be unified with any other type, nor can they escape from the scope of
2157 the pattern match. For example, these fragments are incorrect:
2165 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2166 is the result of <function>f1</function>. One way to see why this is wrong is to
2167 ask what type <function>f1</function> has:
2171 f1 :: Foo -> a -- Weird!
2175 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2180 f1 :: forall a. Foo -> a -- Wrong!
2184 The original program is just plain wrong. Here's another sort of error
2188 f2 (Baz1 a b) (Baz1 p q) = a==q
2192 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2193 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2194 from the two <function>Baz1</function> constructors.
2202 You can't pattern-match on an existentially quantified
2203 constructor in a <literal>let</literal> or <literal>where</literal> group of
2204 bindings. So this is illegal:
2208 f3 x = a==b where { Baz1 a b = x }
2211 Instead, use a <literal>case</literal> expression:
2214 f3 x = case x of Baz1 a b -> a==b
2217 In general, you can only pattern-match
2218 on an existentially-quantified constructor in a <literal>case</literal> expression or
2219 in the patterns of a function definition.
2221 The reason for this restriction is really an implementation one.
2222 Type-checking binding groups is already a nightmare without
2223 existentials complicating the picture. Also an existential pattern
2224 binding at the top level of a module doesn't make sense, because it's
2225 not clear how to prevent the existentially-quantified type "escaping".
2226 So for now, there's a simple-to-state restriction. We'll see how
2234 You can't use existential quantification for <literal>newtype</literal>
2235 declarations. So this is illegal:
2239 newtype T = forall a. Ord a => MkT a
2243 Reason: a value of type <literal>T</literal> must be represented as a
2244 pair of a dictionary for <literal>Ord t</literal> and a value of type
2245 <literal>t</literal>. That contradicts the idea that
2246 <literal>newtype</literal> should have no concrete representation.
2247 You can get just the same efficiency and effect by using
2248 <literal>data</literal> instead of <literal>newtype</literal>. If
2249 there is no overloading involved, then there is more of a case for
2250 allowing an existentially-quantified <literal>newtype</literal>,
2251 because the <literal>data</literal> version does carry an
2252 implementation cost, but single-field existentially quantified
2253 constructors aren't much use. So the simple restriction (no
2254 existential stuff on <literal>newtype</literal>) stands, unless there
2255 are convincing reasons to change it.
2263 You can't use <literal>deriving</literal> to define instances of a
2264 data type with existentially quantified data constructors.
2266 Reason: in most cases it would not make sense. For example:;
2269 data T = forall a. MkT [a] deriving( Eq )
2272 To derive <literal>Eq</literal> in the standard way we would need to have equality
2273 between the single component of two <function>MkT</function> constructors:
2277 (MkT a) == (MkT b) = ???
2280 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2281 It's just about possible to imagine examples in which the derived instance
2282 would make sense, but it seems altogether simpler simply to prohibit such
2283 declarations. Define your own instances!
2294 <!-- ====================== Generalised algebraic data types ======================= -->
2296 <sect2 id="gadt-style">
2297 <title>Declaring data types with explicit constructor signatures</title>
2299 <para>GHC allows you to declare an algebraic data type by
2300 giving the type signatures of constructors explicitly. For example:
2304 Just :: a -> Maybe a
2306 The form is called a "GADT-style declaration"
2307 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2308 can only be declared using this form.</para>
2309 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2310 For example, these two declarations are equivalent:
2312 data Foo = forall a. MkFoo a (a -> Bool)
2313 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2316 <para>Any data type that can be declared in standard Haskell-98 syntax
2317 can also be declared using GADT-style syntax.
2318 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2319 they treat class constraints on the data constructors differently.
2320 Specifically, if the constructor is given a type-class context, that
2321 context is made available by pattern matching. For example:
2324 MkSet :: Eq a => [a] -> Set a
2326 makeSet :: Eq a => [a] -> Set a
2327 makeSet xs = MkSet (nub xs)
2329 insert :: a -> Set a -> Set a
2330 insert a (MkSet as) | a `elem` as = MkSet as
2331 | otherwise = MkSet (a:as)
2333 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2334 gives rise to a <literal>(Eq a)</literal>
2335 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2336 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2337 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2338 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2339 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2340 In the example, the equality dictionary is used to satisfy the equality constraint
2341 generated by the call to <literal>elem</literal>, so that the type of
2342 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2345 For example, one possible application is to reify dictionaries:
2347 data NumInst a where
2348 MkNumInst :: Num a => NumInst a
2350 intInst :: NumInst Int
2353 plus :: NumInst a -> a -> a -> a
2354 plus MkNumInst p q = p + q
2356 Here, a value of type <literal>NumInst a</literal> is equivalent
2357 to an explicit <literal>(Num a)</literal> dictionary.
2360 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2361 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2365 = Num a => MkNumInst (NumInst a)
2367 Notice that, unlike the situation when declaring an existential, there is
2368 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2369 data type's universally quantified type variable <literal>a</literal>.
2370 A constructor may have both universal and existential type variables: for example,
2371 the following two declarations are equivalent:
2374 = forall b. (Num a, Eq b) => MkT1 a b
2376 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2379 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2380 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2381 In Haskell 98 the definition
2383 data Eq a => Set' a = MkSet' [a]
2385 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2386 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2387 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2388 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2389 GHC's behaviour is much more useful, as well as much more intuitive.
2393 The rest of this section gives further details about GADT-style data
2398 The result type of each data constructor must begin with the type constructor being defined.
2399 If the result type of all constructors
2400 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2401 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2402 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2406 As with other type signatures, you can give a single signature for several data constructors.
2407 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2416 The type signature of
2417 each constructor is independent, and is implicitly universally quantified as usual.
2418 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2419 have no scope, and different constructors may have different universally-quantified type variables:
2421 data T a where -- The 'a' has no scope
2422 T1,T2 :: b -> T b -- Means forall b. b -> T b
2423 T3 :: T a -- Means forall a. T a
2428 A constructor signature may mention type class constraints, which can differ for
2429 different constructors. For example, this is fine:
2432 T1 :: Eq b => b -> b -> T b
2433 T2 :: (Show c, Ix c) => c -> [c] -> T c
2435 When patten matching, these constraints are made available to discharge constraints
2436 in the body of the match. For example:
2439 f (T1 x y) | x==y = "yes"
2443 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2444 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2445 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2449 Unlike a Haskell-98-style
2450 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2451 have no scope. Indeed, one can write a kind signature instead:
2453 data Set :: * -> * where ...
2455 or even a mixture of the two:
2457 data Bar a :: (* -> *) -> * where ...
2459 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2462 data Bar a (b :: * -> *) where ...
2468 You can use strictness annotations, in the obvious places
2469 in the constructor type:
2472 Lit :: !Int -> Term Int
2473 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2474 Pair :: Term a -> Term b -> Term (a,b)
2479 You can use a <literal>deriving</literal> clause on a GADT-style data type
2480 declaration. For example, these two declarations are equivalent
2482 data Maybe1 a where {
2483 Nothing1 :: Maybe1 a ;
2484 Just1 :: a -> Maybe1 a
2485 } deriving( Eq, Ord )
2487 data Maybe2 a = Nothing2 | Just2 a
2493 The type signature may have quantified type variables that do not appear
2497 MkFoo :: a -> (a->Bool) -> Foo
2500 Here the type variable <literal>a</literal> does not appear in the result type
2501 of either constructor.
2502 Although it is universally quantified in the type of the constructor, such
2503 a type variable is often called "existential".
2504 Indeed, the above declaration declares precisely the same type as
2505 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2507 The type may contain a class context too, of course:
2510 MkShowable :: Show a => a -> Showable
2515 You can use record syntax on a GADT-style data type declaration:
2519 Adult :: { name :: String, children :: [Person] } -> Person
2520 Child :: Show a => { name :: !String, funny :: a } -> Person
2522 As usual, for every constructor that has a field <literal>f</literal>, the type of
2523 field <literal>f</literal> must be the same (modulo alpha conversion).
2524 The <literal>Child</literal> constructor above shows that the signature
2525 may have a context, existentially-quantified variables, and strictness annotations,
2526 just as in the non-record case. (NB: the "type" that follows the double-colon
2527 is not really a type, because of the record syntax and strictness annotations.
2528 A "type" of this form can appear only in a constructor signature.)
2532 Record updates are allowed with GADT-style declarations,
2533 only fields that have the following property: the type of the field
2534 mentions no existential type variables.
2538 As in the case of existentials declared using the Haskell-98-like record syntax
2539 (<xref linkend="existential-records"/>),
2540 record-selector functions are generated only for those fields that have well-typed
2542 Here is the example of that section, in GADT-style syntax:
2544 data Counter a where
2545 NewCounter { _this :: self
2546 , _inc :: self -> self
2547 , _display :: self -> IO ()
2552 As before, only one selector function is generated here, that for <literal>tag</literal>.
2553 Nevertheless, you can still use all the field names in pattern matching and record construction.
2555 </itemizedlist></para>
2559 <title>Generalised Algebraic Data Types (GADTs)</title>
2561 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2562 by allowing constructors to have richer return types. Here is an example:
2565 Lit :: Int -> Term Int
2566 Succ :: Term Int -> Term Int
2567 IsZero :: Term Int -> Term Bool
2568 If :: Term Bool -> Term a -> Term a -> Term a
2569 Pair :: Term a -> Term b -> Term (a,b)
2571 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2572 case with ordinary data types. This generality allows us to
2573 write a well-typed <literal>eval</literal> function
2574 for these <literal>Terms</literal>:
2578 eval (Succ t) = 1 + eval t
2579 eval (IsZero t) = eval t == 0
2580 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2581 eval (Pair e1 e2) = (eval e1, eval e2)
2583 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2584 For example, in the right hand side of the equation
2589 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2590 A precise specification of the type rules is beyond what this user manual aspires to,
2591 but the design closely follows that described in
2593 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2594 unification-based type inference for GADTs</ulink>,
2596 The general principle is this: <emphasis>type refinement is only carried out
2597 based on user-supplied type annotations</emphasis>.
2598 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2599 and lots of obscure error messages will
2600 occur. However, the refinement is quite general. For example, if we had:
2602 eval :: Term a -> a -> a
2603 eval (Lit i) j = i+j
2605 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2606 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2607 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2610 These and many other examples are given in papers by Hongwei Xi, and
2611 Tim Sheard. There is a longer introduction
2612 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2614 <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
2615 may use different notation to that implemented in GHC.
2618 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2619 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2622 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2623 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2624 The result type of each constructor must begin with the type constructor being defined,
2625 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2626 For example, in the <literal>Term</literal> data
2627 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2628 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2633 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2634 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2635 whose result type is not just <literal>T a b</literal>.
2639 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2640 an ordinary data type.
2644 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2648 Lit { val :: Int } :: Term Int
2649 Succ { num :: Term Int } :: Term Int
2650 Pred { num :: Term Int } :: Term Int
2651 IsZero { arg :: Term Int } :: Term Bool
2652 Pair { arg1 :: Term a
2655 If { cnd :: Term Bool
2660 However, for GADTs there is the following additional constraint:
2661 every constructor that has a field <literal>f</literal> must have
2662 the same result type (modulo alpha conversion)
2663 Hence, in the above example, we cannot merge the <literal>num</literal>
2664 and <literal>arg</literal> fields above into a
2665 single name. Although their field types are both <literal>Term Int</literal>,
2666 their selector functions actually have different types:
2669 num :: Term Int -> Term Int
2670 arg :: Term Bool -> Term Int
2675 When pattern-matching against data constructors drawn from a GADT,
2676 for example in a <literal>case</literal> expression, the following rules apply:
2678 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2679 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2680 <listitem><para>The type of any free variable mentioned in any of
2681 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2683 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2684 way to ensure that a variable a rigid type is to give it a type signature.
2685 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2686 Simple unification-based type inference for GADTs
2687 </ulink>. The criteria implemented by GHC are given in the Appendix.
2697 <!-- ====================== End of Generalised algebraic data types ======================= -->
2699 <sect1 id="deriving">
2700 <title>Extensions to the "deriving" mechanism</title>
2702 <sect2 id="deriving-inferred">
2703 <title>Inferred context for deriving clauses</title>
2706 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2709 data T0 f a = MkT0 a deriving( Eq )
2710 data T1 f a = MkT1 (f a) deriving( Eq )
2711 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2713 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2715 instance Eq a => Eq (T0 f a) where ...
2716 instance Eq (f a) => Eq (T1 f a) where ...
2717 instance Eq (f (f a)) => Eq (T2 f a) where ...
2719 The first of these is obviously fine. The second is still fine, although less obviously.
2720 The third is not Haskell 98, and risks losing termination of instances.
2723 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2724 each constraint in the inferred instance context must consist only of type variables,
2725 with no repetitions.
2728 This rule is applied regardless of flags. If you want a more exotic context, you can write
2729 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2733 <sect2 id="stand-alone-deriving">
2734 <title>Stand-alone deriving declarations</title>
2737 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2739 data Foo a = Bar a | Baz String
2741 deriving instance Eq a => Eq (Foo a)
2743 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2744 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2745 Note the following points:
2748 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2749 exactly as you would in an ordinary instance declaration.
2750 (In contrast, in a <literal>deriving</literal> clause
2751 attached to a data type declaration, the context is inferred.)
2755 A <literal>deriving instance</literal> declaration
2756 must obey the same rules concerning form and termination as ordinary instance declarations,
2757 controlled by the same flags; see <xref linkend="instance-decls"/>.
2761 Unlike a <literal>deriving</literal>
2762 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2763 than the data type (assuming you also use
2764 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2767 data Foo a = Bar a | Baz String
2769 deriving instance Eq a => Eq (Foo [a])
2770 deriving instance Eq a => Eq (Foo (Maybe a))
2772 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2773 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2777 Unlike a <literal>deriving</literal>
2778 declaration attached to a <literal>data</literal> declaration,
2779 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2780 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2781 your problem. (GHC will show you the offending code if it has a type error.)
2782 The merit of this is that you can derive instances for GADTs and other exotic
2783 data types, providing only that the boilerplate code does indeed typecheck. For example:
2789 deriving instance Show (T a)
2791 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2792 data type declaration for <literal>T</literal>,
2793 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2794 the instance declaration using stand-alone deriving.
2799 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2800 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2803 newtype Foo a = MkFoo (State Int a)
2805 deriving instance MonadState Int Foo
2807 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2808 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2810 </itemizedlist></para>
2815 <sect2 id="deriving-typeable">
2816 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2819 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2820 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2821 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2822 classes <literal>Eq</literal>, <literal>Ord</literal>,
2823 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2826 GHC extends this list with several more classes that may be automatically derived:
2828 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2829 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2830 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2832 <para>An instance of <literal>Typeable</literal> can only be derived if the
2833 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2834 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2836 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2837 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2839 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2840 are used, and only <literal>Typeable1</literal> up to
2841 <literal>Typeable7</literal> are provided in the library.)
2842 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2843 class, whose kind suits that of the data type constructor, and
2844 then writing the data type instance by hand.
2848 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2849 the class <literal>Functor</literal>,
2850 defined in <literal>GHC.Base</literal>.
2853 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2854 the class <literal>Foldable</literal>,
2855 defined in <literal>Data.Foldable</literal>.
2858 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2859 the class <literal>Traversable</literal>,
2860 defined in <literal>Data.Traversable</literal>.
2863 In each case the appropriate class must be in scope before it
2864 can be mentioned in the <literal>deriving</literal> clause.
2868 <sect2 id="newtype-deriving">
2869 <title>Generalised derived instances for newtypes</title>
2872 When you define an abstract type using <literal>newtype</literal>, you may want
2873 the new type to inherit some instances from its representation. In
2874 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2875 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2876 other classes you have to write an explicit instance declaration. For
2877 example, if you define
2880 newtype Dollars = Dollars Int
2883 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2884 explicitly define an instance of <literal>Num</literal>:
2887 instance Num Dollars where
2888 Dollars a + Dollars b = Dollars (a+b)
2891 All the instance does is apply and remove the <literal>newtype</literal>
2892 constructor. It is particularly galling that, since the constructor
2893 doesn't appear at run-time, this instance declaration defines a
2894 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2895 dictionary, only slower!
2899 <sect3> <title> Generalising the deriving clause </title>
2901 GHC now permits such instances to be derived instead,
2902 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2905 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2908 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2909 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2910 derives an instance declaration of the form
2913 instance Num Int => Num Dollars
2916 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2920 We can also derive instances of constructor classes in a similar
2921 way. For example, suppose we have implemented state and failure monad
2922 transformers, such that
2925 instance Monad m => Monad (State s m)
2926 instance Monad m => Monad (Failure m)
2928 In Haskell 98, we can define a parsing monad by
2930 type Parser tok m a = State [tok] (Failure m) a
2933 which is automatically a monad thanks to the instance declarations
2934 above. With the extension, we can make the parser type abstract,
2935 without needing to write an instance of class <literal>Monad</literal>, via
2938 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2941 In this case the derived instance declaration is of the form
2943 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2946 Notice that, since <literal>Monad</literal> is a constructor class, the
2947 instance is a <emphasis>partial application</emphasis> of the new type, not the
2948 entire left hand side. We can imagine that the type declaration is
2949 "eta-converted" to generate the context of the instance
2954 We can even derive instances of multi-parameter classes, provided the
2955 newtype is the last class parameter. In this case, a ``partial
2956 application'' of the class appears in the <literal>deriving</literal>
2957 clause. For example, given the class
2960 class StateMonad s m | m -> s where ...
2961 instance Monad m => StateMonad s (State s m) where ...
2963 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2965 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2966 deriving (Monad, StateMonad [tok])
2969 The derived instance is obtained by completing the application of the
2970 class to the new type:
2973 instance StateMonad [tok] (State [tok] (Failure m)) =>
2974 StateMonad [tok] (Parser tok m)
2979 As a result of this extension, all derived instances in newtype
2980 declarations are treated uniformly (and implemented just by reusing
2981 the dictionary for the representation type), <emphasis>except</emphasis>
2982 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2983 the newtype and its representation.
2987 <sect3> <title> A more precise specification </title>
2989 Derived instance declarations are constructed as follows. Consider the
2990 declaration (after expansion of any type synonyms)
2993 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2999 The <literal>ci</literal> are partial applications of
3000 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3001 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3004 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3007 The type <literal>t</literal> is an arbitrary type.
3010 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3011 nor in the <literal>ci</literal>, and
3014 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3015 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3016 should not "look through" the type or its constructor. You can still
3017 derive these classes for a newtype, but it happens in the usual way, not
3018 via this new mechanism.
3021 Then, for each <literal>ci</literal>, the derived instance
3024 instance ci t => ci (T v1...vk)
3026 As an example which does <emphasis>not</emphasis> work, consider
3028 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3030 Here we cannot derive the instance
3032 instance Monad (State s m) => Monad (NonMonad m)
3035 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3036 and so cannot be "eta-converted" away. It is a good thing that this
3037 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3038 not, in fact, a monad --- for the same reason. Try defining
3039 <literal>>>=</literal> with the correct type: you won't be able to.
3043 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3044 important, since we can only derive instances for the last one. If the
3045 <literal>StateMonad</literal> class above were instead defined as
3048 class StateMonad m s | m -> s where ...
3051 then we would not have been able to derive an instance for the
3052 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3053 classes usually have one "main" parameter for which deriving new
3054 instances is most interesting.
3056 <para>Lastly, all of this applies only for classes other than
3057 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3058 and <literal>Data</literal>, for which the built-in derivation applies (section
3059 4.3.3. of the Haskell Report).
3060 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3061 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3062 the standard method is used or the one described here.)
3069 <!-- TYPE SYSTEM EXTENSIONS -->
3070 <sect1 id="type-class-extensions">
3071 <title>Class and instances declarations</title>
3073 <sect2 id="multi-param-type-classes">
3074 <title>Class declarations</title>
3077 This section, and the next one, documents GHC's type-class extensions.
3078 There's lots of background in the paper <ulink
3079 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3080 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3081 Jones, Erik Meijer).
3084 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3088 <title>Multi-parameter type classes</title>
3090 Multi-parameter type classes are permitted. For example:
3094 class Collection c a where
3095 union :: c a -> c a -> c a
3103 <title>The superclasses of a class declaration</title>
3106 There are no restrictions on the context in a class declaration
3107 (which introduces superclasses), except that the class hierarchy must
3108 be acyclic. So these class declarations are OK:
3112 class Functor (m k) => FiniteMap m k where
3115 class (Monad m, Monad (t m)) => Transform t m where
3116 lift :: m a -> (t m) a
3122 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3123 of "acyclic" involves only the superclass relationships. For example,
3129 op :: D b => a -> b -> b
3132 class C a => D a where { ... }
3136 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3137 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3138 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3145 <sect3 id="class-method-types">
3146 <title>Class method types</title>
3149 Haskell 98 prohibits class method types to mention constraints on the
3150 class type variable, thus:
3153 fromList :: [a] -> s a
3154 elem :: Eq a => a -> s a -> Bool
3156 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3157 contains the constraint <literal>Eq a</literal>, constrains only the
3158 class type variable (in this case <literal>a</literal>).
3159 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3166 <sect2 id="functional-dependencies">
3167 <title>Functional dependencies
3170 <para> Functional dependencies are implemented as described by Mark Jones
3171 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3172 In Proceedings of the 9th European Symposium on Programming,
3173 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3177 Functional dependencies are introduced by a vertical bar in the syntax of a
3178 class declaration; e.g.
3180 class (Monad m) => MonadState s m | m -> s where ...
3182 class Foo a b c | a b -> c where ...
3184 There should be more documentation, but there isn't (yet). Yell if you need it.
3187 <sect3><title>Rules for functional dependencies </title>
3189 In a class declaration, all of the class type variables must be reachable (in the sense
3190 mentioned in <xref linkend="type-restrictions"/>)
3191 from the free variables of each method type.
3195 class Coll s a where
3197 insert :: s -> a -> s
3200 is not OK, because the type of <literal>empty</literal> doesn't mention
3201 <literal>a</literal>. Functional dependencies can make the type variable
3204 class Coll s a | s -> a where
3206 insert :: s -> a -> s
3209 Alternatively <literal>Coll</literal> might be rewritten
3212 class Coll s a where
3214 insert :: s a -> a -> s a
3218 which makes the connection between the type of a collection of
3219 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3220 Occasionally this really doesn't work, in which case you can split the
3228 class CollE s => Coll s a where
3229 insert :: s -> a -> s
3236 <title>Background on functional dependencies</title>
3238 <para>The following description of the motivation and use of functional dependencies is taken
3239 from the Hugs user manual, reproduced here (with minor changes) by kind
3240 permission of Mark Jones.
3243 Consider the following class, intended as part of a
3244 library for collection types:
3246 class Collects e ce where
3248 insert :: e -> ce -> ce
3249 member :: e -> ce -> Bool
3251 The type variable e used here represents the element type, while ce is the type
3252 of the container itself. Within this framework, we might want to define
3253 instances of this class for lists or characteristic functions (both of which
3254 can be used to represent collections of any equality type), bit sets (which can
3255 be used to represent collections of characters), or hash tables (which can be
3256 used to represent any collection whose elements have a hash function). Omitting
3257 standard implementation details, this would lead to the following declarations:
3259 instance Eq e => Collects e [e] where ...
3260 instance Eq e => Collects e (e -> Bool) where ...
3261 instance Collects Char BitSet where ...
3262 instance (Hashable e, Collects a ce)
3263 => Collects e (Array Int ce) where ...
3265 All this looks quite promising; we have a class and a range of interesting
3266 implementations. Unfortunately, there are some serious problems with the class
3267 declaration. First, the empty function has an ambiguous type:
3269 empty :: Collects e ce => ce
3271 By "ambiguous" we mean that there is a type variable e that appears on the left
3272 of the <literal>=></literal> symbol, but not on the right. The problem with
3273 this is that, according to the theoretical foundations of Haskell overloading,
3274 we cannot guarantee a well-defined semantics for any term with an ambiguous
3278 We can sidestep this specific problem by removing the empty member from the
3279 class declaration. However, although the remaining members, insert and member,
3280 do not have ambiguous types, we still run into problems when we try to use
3281 them. For example, consider the following two functions:
3283 f x y = insert x . insert y
3286 for which GHC infers the following types:
3288 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3289 g :: (Collects Bool c, Collects Char c) => c -> c
3291 Notice that the type for f allows the two parameters x and y to be assigned
3292 different types, even though it attempts to insert each of the two values, one
3293 after the other, into the same collection. If we're trying to model collections
3294 that contain only one type of value, then this is clearly an inaccurate
3295 type. Worse still, the definition for g is accepted, without causing a type
3296 error. As a result, the error in this code will not be flagged at the point
3297 where it appears. Instead, it will show up only when we try to use g, which
3298 might even be in a different module.
3301 <sect4><title>An attempt to use constructor classes</title>
3304 Faced with the problems described above, some Haskell programmers might be
3305 tempted to use something like the following version of the class declaration:
3307 class Collects e c where
3309 insert :: e -> c e -> c e
3310 member :: e -> c e -> Bool
3312 The key difference here is that we abstract over the type constructor c that is
3313 used to form the collection type c e, and not over that collection type itself,
3314 represented by ce in the original class declaration. This avoids the immediate
3315 problems that we mentioned above: empty has type <literal>Collects e c => c
3316 e</literal>, which is not ambiguous.
3319 The function f from the previous section has a more accurate type:
3321 f :: (Collects e c) => e -> e -> c e -> c e
3323 The function g from the previous section is now rejected with a type error as
3324 we would hope because the type of f does not allow the two arguments to have
3326 This, then, is an example of a multiple parameter class that does actually work
3327 quite well in practice, without ambiguity problems.
3328 There is, however, a catch. This version of the Collects class is nowhere near
3329 as general as the original class seemed to be: only one of the four instances
3330 for <literal>Collects</literal>
3331 given above can be used with this version of Collects because only one of
3332 them---the instance for lists---has a collection type that can be written in
3333 the form c e, for some type constructor c, and element type e.
3337 <sect4><title>Adding functional dependencies</title>
3340 To get a more useful version of the Collects class, Hugs provides a mechanism
3341 that allows programmers to specify dependencies between the parameters of a
3342 multiple parameter class (For readers with an interest in theoretical
3343 foundations and previous work: The use of dependency information can be seen
3344 both as a generalization of the proposal for `parametric type classes' that was
3345 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3346 later framework for "improvement" of qualified types. The
3347 underlying ideas are also discussed in a more theoretical and abstract setting
3348 in a manuscript [implparam], where they are identified as one point in a
3349 general design space for systems of implicit parameterization.).
3351 To start with an abstract example, consider a declaration such as:
3353 class C a b where ...
3355 which tells us simply that C can be thought of as a binary relation on types
3356 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3357 included in the definition of classes to add information about dependencies
3358 between parameters, as in the following examples:
3360 class D a b | a -> b where ...
3361 class E a b | a -> b, b -> a where ...
3363 The notation <literal>a -> b</literal> used here between the | and where
3364 symbols --- not to be
3365 confused with a function type --- indicates that the a parameter uniquely
3366 determines the b parameter, and might be read as "a determines b." Thus D is
3367 not just a relation, but actually a (partial) function. Similarly, from the two
3368 dependencies that are included in the definition of E, we can see that E
3369 represents a (partial) one-one mapping between types.
3372 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3373 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3374 m>=0, meaning that the y parameters are uniquely determined by the x
3375 parameters. Spaces can be used as separators if more than one variable appears
3376 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3377 annotated with multiple dependencies using commas as separators, as in the
3378 definition of E above. Some dependencies that we can write in this notation are
3379 redundant, and will be rejected because they don't serve any useful
3380 purpose, and may instead indicate an error in the program. Examples of
3381 dependencies like this include <literal>a -> a </literal>,
3382 <literal>a -> a a </literal>,
3383 <literal>a -> </literal>, etc. There can also be
3384 some redundancy if multiple dependencies are given, as in
3385 <literal>a->b</literal>,
3386 <literal>b->c </literal>, <literal>a->c </literal>, and
3387 in which some subset implies the remaining dependencies. Examples like this are
3388 not treated as errors. Note that dependencies appear only in class
3389 declarations, and not in any other part of the language. In particular, the
3390 syntax for instance declarations, class constraints, and types is completely
3394 By including dependencies in a class declaration, we provide a mechanism for
3395 the programmer to specify each multiple parameter class more precisely. The
3396 compiler, on the other hand, is responsible for ensuring that the set of
3397 instances that are in scope at any given point in the program is consistent
3398 with any declared dependencies. For example, the following pair of instance
3399 declarations cannot appear together in the same scope because they violate the
3400 dependency for D, even though either one on its own would be acceptable:
3402 instance D Bool Int where ...
3403 instance D Bool Char where ...
3405 Note also that the following declaration is not allowed, even by itself:
3407 instance D [a] b where ...
3409 The problem here is that this instance would allow one particular choice of [a]
3410 to be associated with more than one choice for b, which contradicts the
3411 dependency specified in the definition of D. More generally, this means that,
3412 in any instance of the form:
3414 instance D t s where ...
3416 for some particular types t and s, the only variables that can appear in s are
3417 the ones that appear in t, and hence, if the type t is known, then s will be
3418 uniquely determined.
3421 The benefit of including dependency information is that it allows us to define
3422 more general multiple parameter classes, without ambiguity problems, and with
3423 the benefit of more accurate types. To illustrate this, we return to the
3424 collection class example, and annotate the original definition of <literal>Collects</literal>
3425 with a simple dependency:
3427 class Collects e ce | ce -> e where
3429 insert :: e -> ce -> ce
3430 member :: e -> ce -> Bool
3432 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3433 determined by the type of the collection ce. Note that both parameters of
3434 Collects are of kind *; there are no constructor classes here. Note too that
3435 all of the instances of Collects that we gave earlier can be used
3436 together with this new definition.
3439 What about the ambiguity problems that we encountered with the original
3440 definition? The empty function still has type Collects e ce => ce, but it is no
3441 longer necessary to regard that as an ambiguous type: Although the variable e
3442 does not appear on the right of the => symbol, the dependency for class
3443 Collects tells us that it is uniquely determined by ce, which does appear on
3444 the right of the => symbol. Hence the context in which empty is used can still
3445 give enough information to determine types for both ce and e, without
3446 ambiguity. More generally, we need only regard a type as ambiguous if it
3447 contains a variable on the left of the => that is not uniquely determined
3448 (either directly or indirectly) by the variables on the right.
3451 Dependencies also help to produce more accurate types for user defined
3452 functions, and hence to provide earlier detection of errors, and less cluttered
3453 types for programmers to work with. Recall the previous definition for a
3456 f x y = insert x y = insert x . insert y
3458 for which we originally obtained a type:
3460 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3462 Given the dependency information that we have for Collects, however, we can
3463 deduce that a and b must be equal because they both appear as the second
3464 parameter in a Collects constraint with the same first parameter c. Hence we
3465 can infer a shorter and more accurate type for f:
3467 f :: (Collects a c) => a -> a -> c -> c
3469 In a similar way, the earlier definition of g will now be flagged as a type error.
3472 Although we have given only a few examples here, it should be clear that the
3473 addition of dependency information can help to make multiple parameter classes
3474 more useful in practice, avoiding ambiguity problems, and allowing more general
3475 sets of instance declarations.
3481 <sect2 id="instance-decls">
3482 <title>Instance declarations</title>
3484 <para>An instance declaration has the form
3486 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 ...
3488 The part before the "<literal>=></literal>" is the
3489 <emphasis>context</emphasis>, while the part after the
3490 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3493 <sect3 id="flexible-instance-head">
3494 <title>Relaxed rules for the instance head</title>
3497 In Haskell 98 the head of an instance declaration
3498 must be of the form <literal>C (T a1 ... an)</literal>, where
3499 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3500 and the <literal>a1 ... an</literal> are distinct type variables.
3501 GHC relaxes these rules in two ways.
3505 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3506 declaration to mention arbitrary nested types.
3507 For example, this becomes a legal instance declaration
3509 instance C (Maybe Int) where ...
3511 See also the <link linkend="instance-overlap">rules on overlap</link>.
3514 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3515 synonyms. As always, using a type synonym is just shorthand for
3516 writing the RHS of the type synonym definition. For example:
3520 type Point = (Int,Int)
3521 instance C Point where ...
3522 instance C [Point] where ...
3526 is legal. However, if you added
3530 instance C (Int,Int) where ...
3534 as well, then the compiler will complain about the overlapping
3535 (actually, identical) instance declarations. As always, type synonyms
3536 must be fully applied. You cannot, for example, write:
3540 instance Monad P where ...
3548 <sect3 id="instance-rules">
3549 <title>Relaxed rules for instance contexts</title>
3551 <para>In Haskell 98, the assertions in the context of the instance declaration
3552 must be of the form <literal>C a</literal> where <literal>a</literal>
3553 is a type variable that occurs in the head.
3557 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3558 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3559 With this flag the context of the instance declaration can each consist of arbitrary
3560 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3564 The Paterson Conditions: for each assertion in the context
3566 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3567 <listitem><para>The assertion has fewer constructors and variables (taken together
3568 and counting repetitions) than the head</para></listitem>
3572 <listitem><para>The Coverage Condition. For each functional dependency,
3573 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3574 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3575 every type variable in
3576 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3577 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3578 substitution mapping each type variable in the class declaration to the
3579 corresponding type in the instance declaration.
3582 These restrictions ensure that context reduction terminates: each reduction
3583 step makes the problem smaller by at least one
3584 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3585 if you give the <option>-XUndecidableInstances</option>
3586 flag (<xref linkend="undecidable-instances"/>).
3587 You can find lots of background material about the reason for these
3588 restrictions in the paper <ulink
3589 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3590 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3593 For example, these are OK:
3595 instance C Int [a] -- Multiple parameters
3596 instance Eq (S [a]) -- Structured type in head
3598 -- Repeated type variable in head
3599 instance C4 a a => C4 [a] [a]
3600 instance Stateful (ST s) (MutVar s)
3602 -- Head can consist of type variables only
3604 instance (Eq a, Show b) => C2 a b
3606 -- Non-type variables in context
3607 instance Show (s a) => Show (Sized s a)
3608 instance C2 Int a => C3 Bool [a]
3609 instance C2 Int a => C3 [a] b
3613 -- Context assertion no smaller than head
3614 instance C a => C a where ...
3615 -- (C b b) has more more occurrences of b than the head
3616 instance C b b => Foo [b] where ...
3621 The same restrictions apply to instances generated by
3622 <literal>deriving</literal> clauses. Thus the following is accepted:
3624 data MinHeap h a = H a (h a)
3627 because the derived instance
3629 instance (Show a, Show (h a)) => Show (MinHeap h a)
3631 conforms to the above rules.
3635 A useful idiom permitted by the above rules is as follows.
3636 If one allows overlapping instance declarations then it's quite
3637 convenient to have a "default instance" declaration that applies if
3638 something more specific does not:
3646 <sect3 id="undecidable-instances">
3647 <title>Undecidable instances</title>
3650 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3651 For example, sometimes you might want to use the following to get the
3652 effect of a "class synonym":
3654 class (C1 a, C2 a, C3 a) => C a where { }
3656 instance (C1 a, C2 a, C3 a) => C a where { }
3658 This allows you to write shorter signatures:
3664 f :: (C1 a, C2 a, C3 a) => ...
3666 The restrictions on functional dependencies (<xref
3667 linkend="functional-dependencies"/>) are particularly troublesome.
3668 It is tempting to introduce type variables in the context that do not appear in
3669 the head, something that is excluded by the normal rules. For example:
3671 class HasConverter a b | a -> b where
3674 data Foo a = MkFoo a
3676 instance (HasConverter a b,Show b) => Show (Foo a) where
3677 show (MkFoo value) = show (convert value)
3679 This is dangerous territory, however. Here, for example, is a program that would make the
3684 instance F [a] [[a]]
3685 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3687 Similarly, it can be tempting to lift the coverage condition:
3689 class Mul a b c | a b -> c where
3690 (.*.) :: a -> b -> c
3692 instance Mul Int Int Int where (.*.) = (*)
3693 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3694 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3696 The third instance declaration does not obey the coverage condition;
3697 and indeed the (somewhat strange) definition:
3699 f = \ b x y -> if b then x .*. [y] else y
3701 makes instance inference go into a loop, because it requires the constraint
3702 <literal>(Mul a [b] b)</literal>.
3705 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3706 the experimental flag <option>-XUndecidableInstances</option>
3707 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3708 both the Paterson Conditions and the Coverage Condition
3709 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3710 fixed-depth recursion stack. If you exceed the stack depth you get a
3711 sort of backtrace, and the opportunity to increase the stack depth
3712 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3718 <sect3 id="instance-overlap">
3719 <title>Overlapping instances</title>
3721 In general, <emphasis>GHC requires that that it be unambiguous which instance
3723 should be used to resolve a type-class constraint</emphasis>. This behaviour
3724 can be modified by two flags: <option>-XOverlappingInstances</option>
3725 <indexterm><primary>-XOverlappingInstances
3726 </primary></indexterm>
3727 and <option>-XIncoherentInstances</option>
3728 <indexterm><primary>-XIncoherentInstances
3729 </primary></indexterm>, as this section discusses. Both these
3730 flags are dynamic flags, and can be set on a per-module basis, using
3731 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3733 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3734 it tries to match every instance declaration against the
3736 by instantiating the head of the instance declaration. For example, consider
3739 instance context1 => C Int a where ... -- (A)
3740 instance context2 => C a Bool where ... -- (B)
3741 instance context3 => C Int [a] where ... -- (C)
3742 instance context4 => C Int [Int] where ... -- (D)
3744 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3745 but (C) and (D) do not. When matching, GHC takes
3746 no account of the context of the instance declaration
3747 (<literal>context1</literal> etc).
3748 GHC's default behaviour is that <emphasis>exactly one instance must match the
3749 constraint it is trying to resolve</emphasis>.
3750 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3751 including both declarations (A) and (B), say); an error is only reported if a
3752 particular constraint matches more than one.
3756 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3757 more than one instance to match, provided there is a most specific one. For
3758 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3759 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3760 most-specific match, the program is rejected.
3763 However, GHC is conservative about committing to an overlapping instance. For example:
3768 Suppose that from the RHS of <literal>f</literal> we get the constraint
3769 <literal>C Int [b]</literal>. But
3770 GHC does not commit to instance (C), because in a particular
3771 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3772 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3773 So GHC rejects the program.
3774 (If you add the flag <option>-XIncoherentInstances</option>,
3775 GHC will instead pick (C), without complaining about
3776 the problem of subsequent instantiations.)
3779 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3780 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3781 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3782 it instead. In this case, GHC will refrain from
3783 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3784 as before) but, rather than rejecting the program, it will infer the type
3786 f :: C Int [b] => [b] -> [b]
3788 That postpones the question of which instance to pick to the
3789 call site for <literal>f</literal>
3790 by which time more is known about the type <literal>b</literal>.
3791 You can write this type signature yourself if you use the
3792 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3796 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3800 instance Foo [b] where
3803 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3804 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3805 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3806 declaration. The solution is to postpone the choice by adding the constraint to the context
3807 of the instance declaration, thus:
3809 instance C Int [b] => Foo [b] where
3812 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3815 The willingness to be overlapped or incoherent is a property of
3816 the <emphasis>instance declaration</emphasis> itself, controlled by the
3817 presence or otherwise of the <option>-XOverlappingInstances</option>
3818 and <option>-XIncoherentInstances</option> flags when that module is
3819 being defined. Neither flag is required in a module that imports and uses the
3820 instance declaration. Specifically, during the lookup process:
3823 An instance declaration is ignored during the lookup process if (a) a more specific
3824 match is found, and (b) the instance declaration was compiled with
3825 <option>-XOverlappingInstances</option>. The flag setting for the
3826 more-specific instance does not matter.
3829 Suppose an instance declaration does not match the constraint being looked up, but
3830 does unify with it, so that it might match when the constraint is further
3831 instantiated. Usually GHC will regard this as a reason for not committing to
3832 some other constraint. But if the instance declaration was compiled with
3833 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3834 check for that declaration.
3837 These rules make it possible for a library author to design a library that relies on
3838 overlapping instances without the library client having to know.
3841 If an instance declaration is compiled without
3842 <option>-XOverlappingInstances</option>,
3843 then that instance can never be overlapped. This could perhaps be
3844 inconvenient. Perhaps the rule should instead say that the
3845 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3846 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3847 at a usage site should be permitted regardless of how the instance declarations
3848 are compiled, if the <option>-XOverlappingInstances</option> flag is
3849 used at the usage site. (Mind you, the exact usage site can occasionally be
3850 hard to pin down.) We are interested to receive feedback on these points.
3852 <para>The <option>-XIncoherentInstances</option> flag implies the
3853 <option>-XOverlappingInstances</option> flag, but not vice versa.
3861 <sect2 id="overloaded-strings">
3862 <title>Overloaded string literals
3866 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3867 string literal has type <literal>String</literal>, but with overloaded string
3868 literals enabled (with <literal>-XOverloadedStrings</literal>)
3869 a string literal has type <literal>(IsString a) => a</literal>.
3872 This means that the usual string syntax can be used, e.g., for packed strings
3873 and other variations of string like types. String literals behave very much
3874 like integer literals, i.e., they can be used in both expressions and patterns.
3875 If used in a pattern the literal with be replaced by an equality test, in the same
3876 way as an integer literal is.
3879 The class <literal>IsString</literal> is defined as:
3881 class IsString a where
3882 fromString :: String -> a
3884 The only predefined instance is the obvious one to make strings work as usual:
3886 instance IsString [Char] where
3889 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3890 it explicitly (for example, to give an instance declaration for it), you can import it
3891 from module <literal>GHC.Exts</literal>.
3894 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3898 Each type in a default declaration must be an
3899 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3903 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3904 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3905 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3906 <emphasis>or</emphasis> <literal>IsString</literal>.
3915 import GHC.Exts( IsString(..) )
3917 newtype MyString = MyString String deriving (Eq, Show)
3918 instance IsString MyString where
3919 fromString = MyString
3921 greet :: MyString -> MyString
3922 greet "hello" = "world"
3926 print $ greet "hello"
3927 print $ greet "fool"
3931 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3932 to work since it gets translated into an equality comparison.
3938 <sect1 id="type-families">
3939 <title>Type families</title>
3942 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3943 facilitate type-level
3944 programming. Type families are a generalisation of <firstterm>associated
3945 data types</firstterm>
3946 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3947 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3948 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3949 Symposium on Principles of Programming Languages (POPL'05)”, pages
3950 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3951 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3952 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3954 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3955 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3956 themselves are described in the paper “<ulink
3957 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3958 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3960 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3961 13th ACM SIGPLAN International Conference on Functional
3962 Programming”, ACM Press, pages 51-62, 2008. Type families
3963 essentially provide type-indexed data types and named functions on types,
3964 which are useful for generic programming and highly parameterised library
3965 interfaces as well as interfaces with enhanced static information, much like
3966 dependent types. They might also be regarded as an alternative to functional
3967 dependencies, but provide a more functional style of type-level programming
3968 than the relational style of functional dependencies.
3971 Indexed type families, or type families for short, are type constructors that
3972 represent sets of types. Set members are denoted by supplying the type family
3973 constructor with type parameters, which are called <firstterm>type
3974 indices</firstterm>. The
3975 difference between vanilla parametrised type constructors and family
3976 constructors is much like between parametrically polymorphic functions and
3977 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3978 behave the same at all type instances, whereas class methods can change their
3979 behaviour in dependence on the class type parameters. Similarly, vanilla type
3980 constructors imply the same data representation for all type instances, but
3981 family constructors can have varying representation types for varying type
3985 Indexed type families come in two flavours: <firstterm>data
3986 families</firstterm> and <firstterm>type synonym
3987 families</firstterm>. They are the indexed family variants of algebraic
3988 data types and type synonyms, respectively. The instances of data families
3989 can be data types and newtypes.
3992 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3993 Additional information on the use of type families in GHC is available on
3994 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3995 Haskell wiki page on type families</ulink>.
3998 <sect2 id="data-families">
3999 <title>Data families</title>
4002 Data families appear in two flavours: (1) they can be defined on the
4004 or (2) they can appear inside type classes (in which case they are known as
4005 associated types). The former is the more general variant, as it lacks the
4006 requirement for the type-indexes to coincide with the class
4007 parameters. However, the latter can lead to more clearly structured code and
4008 compiler warnings if some type instances were - possibly accidentally -
4009 omitted. In the following, we always discuss the general toplevel form first
4010 and then cover the additional constraints placed on associated types.
4013 <sect3 id="data-family-declarations">
4014 <title>Data family declarations</title>
4017 Indexed data families are introduced by a signature, such as
4019 data family GMap k :: * -> *
4021 The special <literal>family</literal> distinguishes family from standard
4022 data declarations. The result kind annotation is optional and, as
4023 usual, defaults to <literal>*</literal> if omitted. An example is
4027 Named arguments can also be given explicit kind signatures if needed.
4029 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4030 declarations] named arguments are entirely optional, so that we can
4031 declare <literal>Array</literal> alternatively with
4033 data family Array :: * -> *
4037 <sect4 id="assoc-data-family-decl">
4038 <title>Associated data family declarations</title>
4040 When a data family is declared as part of a type class, we drop
4041 the <literal>family</literal> special. The <literal>GMap</literal>
4042 declaration takes the following form
4044 class GMapKey k where
4045 data GMap k :: * -> *
4048 In contrast to toplevel declarations, named arguments must be used for
4049 all type parameters that are to be used as type-indexes. Moreover,
4050 the argument names must be class parameters. Each class parameter may
4051 only be used at most once per associated type, but some may be omitted
4052 and they may be in an order other than in the class head. Hence, the
4053 following contrived example is admissible:
4062 <sect3 id="data-instance-declarations">
4063 <title>Data instance declarations</title>
4066 Instance declarations of data and newtype families are very similar to
4067 standard data and newtype declarations. The only two differences are
4068 that the keyword <literal>data</literal> or <literal>newtype</literal>
4069 is followed by <literal>instance</literal> and that some or all of the
4070 type arguments can be non-variable types, but may not contain forall
4071 types or type synonym families. However, data families are generally
4072 allowed in type parameters, and type synonyms are allowed as long as
4073 they are fully applied and expand to a type that is itself admissible -
4074 exactly as this is required for occurrences of type synonyms in class
4075 instance parameters. For example, the <literal>Either</literal>
4076 instance for <literal>GMap</literal> is
4078 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4080 In this example, the declaration has only one variant. In general, it
4084 Data and newtype instance declarations are only permitted when an
4085 appropriate family declaration is in scope - just as a class instance declaratoin
4086 requires the class declaration to be visible. Moreover, each instance
4087 declaration has to conform to the kind determined by its family
4088 declaration. This implies that the number of parameters of an instance
4089 declaration matches the arity determined by the kind of the family.
4092 A data family instance declaration can use the full exprssiveness of
4093 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4095 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4096 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4097 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4100 data instance T Int = T1 Int | T2 Bool
4101 newtype instance T Char = TC Bool
4104 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4105 and indeed can define a GADT. For example:
4108 data instance G [a] b where
4109 G1 :: c -> G [Int] b
4113 <listitem><para> You can use a <literal>deriving</literal> clause on a
4114 <literal>data instance</literal> or <literal>newtype instance</literal>
4121 Even if type families are defined as toplevel declarations, functions
4122 that perform different computations for different family instances may still
4123 need to be defined as methods of type classes. In particular, the
4124 following is not possible:
4127 data instance T Int = A
4128 data instance T Char = B
4130 foo A = 1 -- WRONG: These two equations together...
4131 foo B = 2 -- ...will produce a type error.
4133 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4137 instance Foo Int where
4139 instance Foo Char where
4142 (Given the functionality provided by GADTs (Generalised Algebraic Data
4143 Types), it might seem as if a definition, such as the above, should be
4144 feasible. However, type families are - in contrast to GADTs - are
4145 <emphasis>open;</emphasis> i.e., new instances can always be added,
4147 modules. Supporting pattern matching across different data instances
4148 would require a form of extensible case construct.)
4151 <sect4 id="assoc-data-inst">
4152 <title>Associated data instances</title>
4154 When an associated data family instance is declared within a type
4155 class instance, we drop the <literal>instance</literal> keyword in the
4156 family instance. So, the <literal>Either</literal> instance
4157 for <literal>GMap</literal> becomes:
4159 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4160 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4163 The most important point about associated family instances is that the
4164 type indexes corresponding to class parameters must be identical to
4165 the type given in the instance head; here this is the first argument
4166 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4167 which coincides with the only class parameter. Any parameters to the
4168 family constructor that do not correspond to class parameters, need to
4169 be variables in every instance; here this is the
4170 variable <literal>v</literal>.
4173 Instances for an associated family can only appear as part of
4174 instances declarations of the class in which the family was declared -
4175 just as with the equations of the methods of a class. Also in
4176 correspondence to how methods are handled, declarations of associated
4177 types can be omitted in class instances. If an associated family
4178 instance is omitted, the corresponding instance type is not inhabited;
4179 i.e., only diverging expressions, such
4180 as <literal>undefined</literal>, can assume the type.
4184 <sect4 id="scoping-class-params">
4185 <title>Scoping of class parameters</title>
4187 In the case of multi-parameter type classes, the visibility of class
4188 parameters in the right-hand side of associated family instances
4189 depends <emphasis>solely</emphasis> on the parameters of the data
4190 family. As an example, consider the simple class declaration
4195 Only one of the two class parameters is a parameter to the data
4196 family. Hence, the following instance declaration is invalid:
4198 instance C [c] d where
4199 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4201 Here, the right-hand side of the data instance mentions the type
4202 variable <literal>d</literal> that does not occur in its left-hand
4203 side. We cannot admit such data instances as they would compromise
4208 <sect4 id="family-class-inst">
4209 <title>Type class instances of family instances</title>
4211 Type class instances of instances of data families can be defined as
4212 usual, and in particular data instance declarations can
4213 have <literal>deriving</literal> clauses. For example, we can write
4215 data GMap () v = GMapUnit (Maybe v)
4218 which implicitly defines an instance of the form
4220 instance Show v => Show (GMap () v) where ...
4224 Note that class instances are always for
4225 particular <emphasis>instances</emphasis> of a data family and never
4226 for an entire family as a whole. This is for essentially the same
4227 reasons that we cannot define a toplevel function that performs
4228 pattern matching on the data constructors
4229 of <emphasis>different</emphasis> instances of a single type family.
4230 It would require a form of extensible case construct.
4234 <sect4 id="data-family-overlap">
4235 <title>Overlap of data instances</title>
4237 The instance declarations of a data family used in a single program
4238 may not overlap at all, independent of whether they are associated or
4239 not. In contrast to type class instances, this is not only a matter
4240 of consistency, but one of type safety.
4246 <sect3 id="data-family-import-export">
4247 <title>Import and export</title>
4250 The association of data constructors with type families is more dynamic
4251 than that is the case with standard data and newtype declarations. In
4252 the standard case, the notation <literal>T(..)</literal> in an import or
4253 export list denotes the type constructor and all the data constructors
4254 introduced in its declaration. However, a family declaration never
4255 introduces any data constructors; instead, data constructors are
4256 introduced by family instances. As a result, which data constructors
4257 are associated with a type family depends on the currently visible
4258 instance declarations for that family. Consequently, an import or
4259 export item of the form <literal>T(..)</literal> denotes the family
4260 constructor and all currently visible data constructors - in the case of
4261 an export item, these may be either imported or defined in the current
4262 module. The treatment of import and export items that explicitly list
4263 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4267 <sect4 id="data-family-impexp-assoc">
4268 <title>Associated families</title>
4270 As expected, an import or export item of the
4271 form <literal>C(..)</literal> denotes all of the class' methods and
4272 associated types. However, when associated types are explicitly
4273 listed as subitems of a class, we need some new syntax, as uppercase
4274 identifiers as subitems are usually data constructors, not type
4275 constructors. To clarify that we denote types here, each associated
4276 type name needs to be prefixed by the keyword <literal>type</literal>.
4277 So for example, when explicitly listing the components of
4278 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4279 GMap, empty, lookup, insert)</literal>.
4283 <sect4 id="data-family-impexp-examples">
4284 <title>Examples</title>
4286 Assuming our running <literal>GMapKey</literal> class example, let us
4287 look at some export lists and their meaning:
4290 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4291 just the class name.</para>
4294 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4295 Exports the class, the associated type <literal>GMap</literal>
4297 functions <literal>empty</literal>, <literal>lookup</literal>,
4298 and <literal>insert</literal>. None of the data constructors is
4302 <para><literal>module GMap (GMapKey(..), GMap(..))
4303 where...</literal>: As before, but also exports all the data
4304 constructors <literal>GMapInt</literal>,
4305 <literal>GMapChar</literal>,
4306 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4307 and <literal>GMapUnit</literal>.</para>
4310 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4311 GMap(..)) where...</literal>: As before.</para>
4314 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4315 where...</literal>: As before.</para>
4320 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4321 both the class <literal>GMapKey</literal> as well as its associated
4322 type <literal>GMap</literal>. However, you cannot
4323 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4324 sub-component specifications cannot be nested. To
4325 specify <literal>GMap</literal>'s data constructors, you have to list
4330 <sect4 id="data-family-impexp-instances">
4331 <title>Instances</title>
4333 Family instances are implicitly exported, just like class instances.
4334 However, this applies only to the heads of instances, not to the data
4335 constructors an instance defines.
4343 <sect2 id="synonym-families">
4344 <title>Synonym families</title>
4347 Type families appear in two flavours: (1) they can be defined on the
4348 toplevel or (2) they can appear inside type classes (in which case they
4349 are known as associated type synonyms). The former is the more general
4350 variant, as it lacks the requirement for the type-indexes to coincide with
4351 the class parameters. However, the latter can lead to more clearly
4352 structured code and compiler warnings if some type instances were -
4353 possibly accidentally - omitted. In the following, we always discuss the
4354 general toplevel form first and then cover the additional constraints
4355 placed on associated types.
4358 <sect3 id="type-family-declarations">
4359 <title>Type family declarations</title>
4362 Indexed type families are introduced by a signature, such as
4364 type family Elem c :: *
4366 The special <literal>family</literal> distinguishes family from standard
4367 type declarations. The result kind annotation is optional and, as
4368 usual, defaults to <literal>*</literal> if omitted. An example is
4372 Parameters can also be given explicit kind signatures if needed. We
4373 call the number of parameters in a type family declaration, the family's
4374 arity, and all applications of a type family must be fully saturated
4375 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4376 and it implies that the kind of a type family is not sufficient to
4377 determine a family's arity, and hence in general, also insufficient to
4378 determine whether a type family application is well formed. As an
4379 example, consider the following declaration:
4381 type family F a b :: * -> * -- F's arity is 2,
4382 -- although its overall kind is * -> * -> * -> *
4384 Given this declaration the following are examples of well-formed and
4387 F Char [Int] -- OK! Kind: * -> *
4388 F Char [Int] Bool -- OK! Kind: *
4389 F IO Bool -- WRONG: kind mismatch in the first argument
4390 F Bool -- WRONG: unsaturated application
4394 <sect4 id="assoc-type-family-decl">
4395 <title>Associated type family declarations</title>
4397 When a type family is declared as part of a type class, we drop
4398 the <literal>family</literal> special. The <literal>Elem</literal>
4399 declaration takes the following form
4401 class Collects ce where
4405 The argument names of the type family must be class parameters. Each
4406 class parameter may only be used at most once per associated type, but
4407 some may be omitted and they may be in an order other than in the
4408 class head. Hence, the following contrived example is admissible:
4413 These rules are exactly as for associated data families.
4418 <sect3 id="type-instance-declarations">
4419 <title>Type instance declarations</title>
4421 Instance declarations of type families are very similar to standard type
4422 synonym declarations. The only two differences are that the
4423 keyword <literal>type</literal> is followed
4424 by <literal>instance</literal> and that some or all of the type
4425 arguments can be non-variable types, but may not contain forall types or
4426 type synonym families. However, data families are generally allowed, and
4427 type synonyms are allowed as long as they are fully applied and expand
4428 to a type that is admissible - these are the exact same requirements as
4429 for data instances. For example, the <literal>[e]</literal> instance
4430 for <literal>Elem</literal> is
4432 type instance Elem [e] = e
4436 Type family instance declarations are only legitimate when an
4437 appropriate family declaration is in scope - just like class instances
4438 require the class declaration to be visible. Moreover, each instance
4439 declaration has to conform to the kind determined by its family
4440 declaration, and the number of type parameters in an instance
4441 declaration must match the number of type parameters in the family
4442 declaration. Finally, the right-hand side of a type instance must be a
4443 monotype (i.e., it may not include foralls) and after the expansion of
4444 all saturated vanilla type synonyms, no synonyms, except family synonyms
4445 may remain. Here are some examples of admissible and illegal type
4448 type family F a :: *
4449 type instance F [Int] = Int -- OK!
4450 type instance F String = Char -- OK!
4451 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4452 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4453 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4455 type family G a b :: * -> *
4456 type instance G Int = (,) -- WRONG: must be two type parameters
4457 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4461 <sect4 id="assoc-type-instance">
4462 <title>Associated type instance declarations</title>
4464 When an associated family instance is declared within a type class
4465 instance, we drop the <literal>instance</literal> keyword in the family
4466 instance. So, the <literal>[e]</literal> instance
4467 for <literal>Elem</literal> becomes:
4469 instance (Eq (Elem [e])) => Collects ([e]) where
4473 The most important point about associated family instances is that the
4474 type indexes corresponding to class parameters must be identical to the
4475 type given in the instance head; here this is <literal>[e]</literal>,
4476 which coincides with the only class parameter.
4479 Instances for an associated family can only appear as part of instances
4480 declarations of the class in which the family was declared - just as
4481 with the equations of the methods of a class. Also in correspondence to
4482 how methods are handled, declarations of associated types can be omitted
4483 in class instances. If an associated family instance is omitted, the
4484 corresponding instance type is not inhabited; i.e., only diverging
4485 expressions, such as <literal>undefined</literal>, can assume the type.
4489 <sect4 id="type-family-overlap">
4490 <title>Overlap of type synonym instances</title>
4492 The instance declarations of a type family used in a single program
4493 may only overlap if the right-hand sides of the overlapping instances
4494 coincide for the overlapping types. More formally, two instance
4495 declarations overlap if there is a substitution that makes the
4496 left-hand sides of the instances syntactically the same. Whenever
4497 that is the case, the right-hand sides of the instances must also be
4498 syntactically equal under the same substitution. This condition is
4499 independent of whether the type family is associated or not, and it is
4500 not only a matter of consistency, but one of type safety.
4503 Here are two example to illustrate the condition under which overlap
4506 type instance F (a, Int) = [a]
4507 type instance F (Int, b) = [b] -- overlap permitted
4509 type instance G (a, Int) = [a]
4510 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4515 <sect4 id="type-family-decidability">
4516 <title>Decidability of type synonym instances</title>
4518 In order to guarantee that type inference in the presence of type
4519 families decidable, we need to place a number of additional
4520 restrictions on the formation of type instance declarations (c.f.,
4521 Definition 5 (Relaxed Conditions) of “<ulink
4522 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4523 Checking with Open Type Functions</ulink>”). Instance
4524 declarations have the general form
4526 type instance F t1 .. tn = t
4528 where we require that for every type family application <literal>(G s1
4529 .. sm)</literal> in <literal>t</literal>,
4532 <para><literal>s1 .. sm</literal> do not contain any type family
4533 constructors,</para>
4536 <para>the total number of symbols (data type constructors and type
4537 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4538 in <literal>t1 .. tn</literal>, and</para>
4541 <para>for every type
4542 variable <literal>a</literal>, <literal>a</literal> occurs
4543 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4544 .. tn</literal>.</para>
4547 These restrictions are easily verified and ensure termination of type
4548 inference. However, they are not sufficient to guarantee completeness
4549 of type inference in the presence of, so called, ''loopy equalities'',
4550 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4551 a type variable is underneath a family application and data
4552 constructor application - see the above mentioned paper for details.
4555 If the option <option>-XUndecidableInstances</option> is passed to the
4556 compiler, the above restrictions are not enforced and it is on the
4557 programmer to ensure termination of the normalisation of type families
4558 during type inference.
4563 <sect3 id-="equality-constraints">
4564 <title>Equality constraints</title>
4566 Type context can include equality constraints of the form <literal>t1 ~
4567 t2</literal>, which denote that the types <literal>t1</literal>
4568 and <literal>t2</literal> need to be the same. In the presence of type
4569 families, whether two types are equal cannot generally be decided
4570 locally. Hence, the contexts of function signatures may include
4571 equality constraints, as in the following example:
4573 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4575 where we require that the element type of <literal>c1</literal>
4576 and <literal>c2</literal> are the same. In general, the
4577 types <literal>t1</literal> and <literal>t2</literal> of an equality
4578 constraint may be arbitrary monotypes; i.e., they may not contain any
4579 quantifiers, independent of whether higher-rank types are otherwise
4583 Equality constraints can also appear in class and instance contexts.
4584 The former enable a simple translation of programs using functional
4585 dependencies into programs using family synonyms instead. The general
4586 idea is to rewrite a class declaration of the form
4588 class C a b | a -> b
4592 class (F a ~ b) => C a b where
4595 That is, we represent every functional dependency (FD) <literal>a1 .. an
4596 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4597 superclass context equality <literal>F a1 .. an ~ b</literal>,
4598 essentially giving a name to the functional dependency. In class
4599 instances, we define the type instances of FD families in accordance
4600 with the class head. Method signatures are not affected by that
4604 NB: Equalities in superclass contexts are not fully implemented in
4609 <sect3 id-="ty-fams-in-instances">
4610 <title>Type families and instance declarations</title>
4611 <para>Type families require us to extend the rules for
4612 the form of instance heads, which are given
4613 in <xref linkend="flexible-instance-head"/>.
4616 <listitem><para>Data type families may appear in an instance head</para></listitem>
4617 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4619 The reason for the latter restriction is that there is no way to check for. Consider
4622 type instance F Bool = Int
4629 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4630 The situation is especially bad because the type instance for <literal>F Bool</literal>
4631 might be in another module, or even in a module that is not yet written.
4638 <sect1 id="other-type-extensions">
4639 <title>Other type system extensions</title>
4641 <sect2 id="type-restrictions">
4642 <title>Type signatures</title>
4644 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4646 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4647 that the type-class constraints in a type signature must have the
4648 form <emphasis>(class type-variable)</emphasis> or
4649 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4650 With <option>-XFlexibleContexts</option>
4651 these type signatures are perfectly OK
4654 g :: Ord (T a ()) => ...
4658 GHC imposes the following restrictions on the constraints in a type signature.
4662 forall tv1..tvn (c1, ...,cn) => type
4665 (Here, we write the "foralls" explicitly, although the Haskell source
4666 language omits them; in Haskell 98, all the free type variables of an
4667 explicit source-language type signature are universally quantified,
4668 except for the class type variables in a class declaration. However,
4669 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4678 <emphasis>Each universally quantified type variable
4679 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4681 A type variable <literal>a</literal> is "reachable" if it appears
4682 in the same constraint as either a type variable free in
4683 <literal>type</literal>, or another reachable type variable.
4684 A value with a type that does not obey
4685 this reachability restriction cannot be used without introducing
4686 ambiguity; that is why the type is rejected.
4687 Here, for example, is an illegal type:
4691 forall a. Eq a => Int
4695 When a value with this type was used, the constraint <literal>Eq tv</literal>
4696 would be introduced where <literal>tv</literal> is a fresh type variable, and
4697 (in the dictionary-translation implementation) the value would be
4698 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4699 can never know which instance of <literal>Eq</literal> to use because we never
4700 get any more information about <literal>tv</literal>.
4704 that the reachability condition is weaker than saying that <literal>a</literal> is
4705 functionally dependent on a type variable free in
4706 <literal>type</literal> (see <xref
4707 linkend="functional-dependencies"/>). The reason for this is there
4708 might be a "hidden" dependency, in a superclass perhaps. So
4709 "reachable" is a conservative approximation to "functionally dependent".
4710 For example, consider:
4712 class C a b | a -> b where ...
4713 class C a b => D a b where ...
4714 f :: forall a b. D a b => a -> a
4716 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4717 but that is not immediately apparent from <literal>f</literal>'s type.
4723 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4724 universally quantified type variables <literal>tvi</literal></emphasis>.
4726 For example, this type is OK because <literal>C a b</literal> mentions the
4727 universally quantified type variable <literal>b</literal>:
4731 forall a. C a b => burble
4735 The next type is illegal because the constraint <literal>Eq b</literal> does not
4736 mention <literal>a</literal>:
4740 forall a. Eq b => burble
4744 The reason for this restriction is milder than the other one. The
4745 excluded types are never useful or necessary (because the offending
4746 context doesn't need to be witnessed at this point; it can be floated
4747 out). Furthermore, floating them out increases sharing. Lastly,
4748 excluding them is a conservative choice; it leaves a patch of
4749 territory free in case we need it later.
4763 <sect2 id="implicit-parameters">
4764 <title>Implicit parameters</title>
4766 <para> Implicit parameters are implemented as described in
4767 "Implicit parameters: dynamic scoping with static types",
4768 J Lewis, MB Shields, E Meijer, J Launchbury,
4769 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4773 <para>(Most of the following, still rather incomplete, documentation is
4774 due to Jeff Lewis.)</para>
4776 <para>Implicit parameter support is enabled with the option
4777 <option>-XImplicitParams</option>.</para>
4780 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4781 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4782 context. In Haskell, all variables are statically bound. Dynamic
4783 binding of variables is a notion that goes back to Lisp, but was later
4784 discarded in more modern incarnations, such as Scheme. Dynamic binding
4785 can be very confusing in an untyped language, and unfortunately, typed
4786 languages, in particular Hindley-Milner typed languages like Haskell,
4787 only support static scoping of variables.
4790 However, by a simple extension to the type class system of Haskell, we
4791 can support dynamic binding. Basically, we express the use of a
4792 dynamically bound variable as a constraint on the type. These
4793 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4794 function uses a dynamically-bound variable <literal>?x</literal>
4795 of type <literal>t'</literal>". For
4796 example, the following expresses the type of a sort function,
4797 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4799 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4801 The dynamic binding constraints are just a new form of predicate in the type class system.
4804 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4805 where <literal>x</literal> is
4806 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4807 Use of this construct also introduces a new
4808 dynamic-binding constraint in the type of the expression.
4809 For example, the following definition
4810 shows how we can define an implicitly parameterized sort function in
4811 terms of an explicitly parameterized <literal>sortBy</literal> function:
4813 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4815 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4821 <title>Implicit-parameter type constraints</title>
4823 Dynamic binding constraints behave just like other type class
4824 constraints in that they are automatically propagated. Thus, when a
4825 function is used, its implicit parameters are inherited by the
4826 function that called it. For example, our <literal>sort</literal> function might be used
4827 to pick out the least value in a list:
4829 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4830 least xs = head (sort xs)
4832 Without lifting a finger, the <literal>?cmp</literal> parameter is
4833 propagated to become a parameter of <literal>least</literal> as well. With explicit
4834 parameters, the default is that parameters must always be explicit
4835 propagated. With implicit parameters, the default is to always
4839 An implicit-parameter type constraint differs from other type class constraints in the
4840 following way: All uses of a particular implicit parameter must have
4841 the same type. This means that the type of <literal>(?x, ?x)</literal>
4842 is <literal>(?x::a) => (a,a)</literal>, and not
4843 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4847 <para> You can't have an implicit parameter in the context of a class or instance
4848 declaration. For example, both these declarations are illegal:
4850 class (?x::Int) => C a where ...
4851 instance (?x::a) => Foo [a] where ...
4853 Reason: exactly which implicit parameter you pick up depends on exactly where
4854 you invoke a function. But the ``invocation'' of instance declarations is done
4855 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4856 Easiest thing is to outlaw the offending types.</para>
4858 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4860 f :: (?x :: [a]) => Int -> Int
4863 g :: (Read a, Show a) => String -> String
4866 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4867 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4868 quite unambiguous, and fixes the type <literal>a</literal>.
4873 <title>Implicit-parameter bindings</title>
4876 An implicit parameter is <emphasis>bound</emphasis> using the standard
4877 <literal>let</literal> or <literal>where</literal> binding forms.
4878 For example, we define the <literal>min</literal> function by binding
4879 <literal>cmp</literal>.
4882 min = let ?cmp = (<=) in least
4886 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4887 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4888 (including in a list comprehension, or do-notation, or pattern guards),
4889 or a <literal>where</literal> clause.
4890 Note the following points:
4893 An implicit-parameter binding group must be a
4894 collection of simple bindings to implicit-style variables (no
4895 function-style bindings, and no type signatures); these bindings are
4896 neither polymorphic or recursive.
4899 You may not mix implicit-parameter bindings with ordinary bindings in a
4900 single <literal>let</literal>
4901 expression; use two nested <literal>let</literal>s instead.
4902 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4906 You may put multiple implicit-parameter bindings in a
4907 single binding group; but they are <emphasis>not</emphasis> treated
4908 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4909 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4910 parameter. The bindings are not nested, and may be re-ordered without changing
4911 the meaning of the program.
4912 For example, consider:
4914 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4916 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4917 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4919 f :: (?x::Int) => Int -> Int
4927 <sect3><title>Implicit parameters and polymorphic recursion</title>
4930 Consider these two definitions:
4933 len1 xs = let ?acc = 0 in len_acc1 xs
4936 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4941 len2 xs = let ?acc = 0 in len_acc2 xs
4943 len_acc2 :: (?acc :: Int) => [a] -> Int
4945 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4947 The only difference between the two groups is that in the second group
4948 <literal>len_acc</literal> is given a type signature.
4949 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4950 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4951 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4952 has a type signature, the recursive call is made to the
4953 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4954 as an implicit parameter. So we get the following results in GHCi:
4961 Adding a type signature dramatically changes the result! This is a rather
4962 counter-intuitive phenomenon, worth watching out for.
4966 <sect3><title>Implicit parameters and monomorphism</title>
4968 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4969 Haskell Report) to implicit parameters. For example, consider:
4977 Since the binding for <literal>y</literal> falls under the Monomorphism
4978 Restriction it is not generalised, so the type of <literal>y</literal> is
4979 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4980 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4981 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4982 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4983 <literal>y</literal> in the body of the <literal>let</literal> will see the
4984 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4985 <literal>14</literal>.
4990 <!-- ======================= COMMENTED OUT ========================
4992 We intend to remove linear implicit parameters, so I'm at least removing
4993 them from the 6.6 user manual
4995 <sect2 id="linear-implicit-parameters">
4996 <title>Linear implicit parameters</title>
4998 Linear implicit parameters are an idea developed by Koen Claessen,
4999 Mark Shields, and Simon PJ. They address the long-standing
5000 problem that monads seem over-kill for certain sorts of problem, notably:
5003 <listitem> <para> distributing a supply of unique names </para> </listitem>
5004 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5005 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5009 Linear implicit parameters are just like ordinary implicit parameters,
5010 except that they are "linear"; that is, they cannot be copied, and
5011 must be explicitly "split" instead. Linear implicit parameters are
5012 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5013 (The '/' in the '%' suggests the split!)
5018 import GHC.Exts( Splittable )
5020 data NameSupply = ...
5022 splitNS :: NameSupply -> (NameSupply, NameSupply)
5023 newName :: NameSupply -> Name
5025 instance Splittable NameSupply where
5029 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5030 f env (Lam x e) = Lam x' (f env e)
5033 env' = extend env x x'
5034 ...more equations for f...
5036 Notice that the implicit parameter %ns is consumed
5038 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5039 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5043 So the translation done by the type checker makes
5044 the parameter explicit:
5046 f :: NameSupply -> Env -> Expr -> Expr
5047 f ns env (Lam x e) = Lam x' (f ns1 env e)
5049 (ns1,ns2) = splitNS ns
5051 env = extend env x x'
5053 Notice the call to 'split' introduced by the type checker.
5054 How did it know to use 'splitNS'? Because what it really did
5055 was to introduce a call to the overloaded function 'split',
5056 defined by the class <literal>Splittable</literal>:
5058 class Splittable a where
5061 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5062 split for name supplies. But we can simply write
5068 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5070 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5071 <literal>GHC.Exts</literal>.
5076 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5077 are entirely distinct implicit parameters: you
5078 can use them together and they won't interfere with each other. </para>
5081 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5083 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5084 in the context of a class or instance declaration. </para></listitem>
5088 <sect3><title>Warnings</title>
5091 The monomorphism restriction is even more important than usual.
5092 Consider the example above:
5094 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5095 f env (Lam x e) = Lam x' (f env e)
5098 env' = extend env x x'
5100 If we replaced the two occurrences of x' by (newName %ns), which is
5101 usually a harmless thing to do, we get:
5103 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5104 f env (Lam x e) = Lam (newName %ns) (f env e)
5106 env' = extend env x (newName %ns)
5108 But now the name supply is consumed in <emphasis>three</emphasis> places
5109 (the two calls to newName,and the recursive call to f), so
5110 the result is utterly different. Urk! We don't even have
5114 Well, this is an experimental change. With implicit
5115 parameters we have already lost beta reduction anyway, and
5116 (as John Launchbury puts it) we can't sensibly reason about
5117 Haskell programs without knowing their typing.
5122 <sect3><title>Recursive functions</title>
5123 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5126 foo :: %x::T => Int -> [Int]
5128 foo n = %x : foo (n-1)
5130 where T is some type in class Splittable.</para>
5132 Do you get a list of all the same T's or all different T's
5133 (assuming that split gives two distinct T's back)?
5135 If you supply the type signature, taking advantage of polymorphic
5136 recursion, you get what you'd probably expect. Here's the
5137 translated term, where the implicit param is made explicit:
5140 foo x n = let (x1,x2) = split x
5141 in x1 : foo x2 (n-1)
5143 But if you don't supply a type signature, GHC uses the Hindley
5144 Milner trick of using a single monomorphic instance of the function
5145 for the recursive calls. That is what makes Hindley Milner type inference
5146 work. So the translation becomes
5150 foom n = x : foom (n-1)
5154 Result: 'x' is not split, and you get a list of identical T's. So the
5155 semantics of the program depends on whether or not foo has a type signature.
5158 You may say that this is a good reason to dislike linear implicit parameters
5159 and you'd be right. That is why they are an experimental feature.
5165 ================ END OF Linear Implicit Parameters commented out -->
5167 <sect2 id="kinding">
5168 <title>Explicitly-kinded quantification</title>
5171 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5172 to give the kind explicitly as (machine-checked) documentation,
5173 just as it is nice to give a type signature for a function. On some occasions,
5174 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5175 John Hughes had to define the data type:
5177 data Set cxt a = Set [a]
5178 | Unused (cxt a -> ())
5180 The only use for the <literal>Unused</literal> constructor was to force the correct
5181 kind for the type variable <literal>cxt</literal>.
5184 GHC now instead allows you to specify the kind of a type variable directly, wherever
5185 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5188 This flag enables kind signatures in the following places:
5190 <listitem><para><literal>data</literal> declarations:
5192 data Set (cxt :: * -> *) a = Set [a]
5193 </screen></para></listitem>
5194 <listitem><para><literal>type</literal> declarations:
5196 type T (f :: * -> *) = f Int
5197 </screen></para></listitem>
5198 <listitem><para><literal>class</literal> declarations:
5200 class (Eq a) => C (f :: * -> *) a where ...
5201 </screen></para></listitem>
5202 <listitem><para><literal>forall</literal>'s in type signatures:
5204 f :: forall (cxt :: * -> *). Set cxt Int
5205 </screen></para></listitem>
5210 The parentheses are required. Some of the spaces are required too, to
5211 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5212 will get a parse error, because "<literal>::*->*</literal>" is a
5213 single lexeme in Haskell.
5217 As part of the same extension, you can put kind annotations in types
5220 f :: (Int :: *) -> Int
5221 g :: forall a. a -> (a :: *)
5225 atype ::= '(' ctype '::' kind ')
5227 The parentheses are required.
5232 <sect2 id="universal-quantification">
5233 <title>Arbitrary-rank polymorphism
5237 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5238 allows us to say exactly what this means. For example:
5246 g :: forall b. (b -> b)
5248 The two are treated identically.
5252 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5253 explicit universal quantification in
5255 For example, all the following types are legal:
5257 f1 :: forall a b. a -> b -> a
5258 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5260 f2 :: (forall a. a->a) -> Int -> Int
5261 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5263 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5265 f4 :: Int -> (forall a. a -> a)
5267 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5268 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5269 The <literal>forall</literal> makes explicit the universal quantification that
5270 is implicitly added by Haskell.
5273 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5274 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5275 shows, the polymorphic type on the left of the function arrow can be overloaded.
5278 The function <literal>f3</literal> has a rank-3 type;
5279 it has rank-2 types on the left of a function arrow.
5282 GHC has three flags to control higher-rank types:
5285 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5288 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5291 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5292 That is, you can nest <literal>forall</literal>s
5293 arbitrarily deep in function arrows.
5294 In particular, a forall-type (also called a "type scheme"),
5295 including an operational type class context, is legal:
5297 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5298 of a function arrow </para> </listitem>
5299 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5300 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5301 field type signatures.</para> </listitem>
5302 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5303 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5307 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5308 a type variable any more!
5317 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5318 the types of the constructor arguments. Here are several examples:
5324 data T a = T1 (forall b. b -> b -> b) a
5326 data MonadT m = MkMonad { return :: forall a. a -> m a,
5327 bind :: forall a b. m a -> (a -> m b) -> m b
5330 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5336 The constructors have rank-2 types:
5342 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5343 MkMonad :: forall m. (forall a. a -> m a)
5344 -> (forall a b. m a -> (a -> m b) -> m b)
5346 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5352 Notice that you don't need to use a <literal>forall</literal> if there's an
5353 explicit context. For example in the first argument of the
5354 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5355 prefixed to the argument type. The implicit <literal>forall</literal>
5356 quantifies all type variables that are not already in scope, and are
5357 mentioned in the type quantified over.
5361 As for type signatures, implicit quantification happens for non-overloaded
5362 types too. So if you write this:
5365 data T a = MkT (Either a b) (b -> b)
5368 it's just as if you had written this:
5371 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5374 That is, since the type variable <literal>b</literal> isn't in scope, it's
5375 implicitly universally quantified. (Arguably, it would be better
5376 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5377 where that is what is wanted. Feedback welcomed.)
5381 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5382 the constructor to suitable values, just as usual. For example,
5393 a3 = MkSwizzle reverse
5396 a4 = let r x = Just x
5403 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5404 mkTs f x y = [T1 f x, T1 f y]
5410 The type of the argument can, as usual, be more general than the type
5411 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5412 does not need the <literal>Ord</literal> constraint.)
5416 When you use pattern matching, the bound variables may now have
5417 polymorphic types. For example:
5423 f :: T a -> a -> (a, Char)
5424 f (T1 w k) x = (w k x, w 'c' 'd')
5426 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5427 g (MkSwizzle s) xs f = s (map f (s xs))
5429 h :: MonadT m -> [m a] -> m [a]
5430 h m [] = return m []
5431 h m (x:xs) = bind m x $ \y ->
5432 bind m (h m xs) $ \ys ->
5439 In the function <function>h</function> we use the record selectors <literal>return</literal>
5440 and <literal>bind</literal> to extract the polymorphic bind and return functions
5441 from the <literal>MonadT</literal> data structure, rather than using pattern
5447 <title>Type inference</title>
5450 In general, type inference for arbitrary-rank types is undecidable.
5451 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5452 to get a decidable algorithm by requiring some help from the programmer.
5453 We do not yet have a formal specification of "some help" but the rule is this:
5456 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5457 provides an explicit polymorphic type for x, or GHC's type inference will assume
5458 that x's type has no foralls in it</emphasis>.
5461 What does it mean to "provide" an explicit type for x? You can do that by
5462 giving a type signature for x directly, using a pattern type signature
5463 (<xref linkend="scoped-type-variables"/>), thus:
5465 \ f :: (forall a. a->a) -> (f True, f 'c')
5467 Alternatively, you can give a type signature to the enclosing
5468 context, which GHC can "push down" to find the type for the variable:
5470 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5472 Here the type signature on the expression can be pushed inwards
5473 to give a type signature for f. Similarly, and more commonly,
5474 one can give a type signature for the function itself:
5476 h :: (forall a. a->a) -> (Bool,Char)
5477 h f = (f True, f 'c')
5479 You don't need to give a type signature if the lambda bound variable
5480 is a constructor argument. Here is an example we saw earlier:
5482 f :: T a -> a -> (a, Char)
5483 f (T1 w k) x = (w k x, w 'c' 'd')
5485 Here we do not need to give a type signature to <literal>w</literal>, because
5486 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5493 <sect3 id="implicit-quant">
5494 <title>Implicit quantification</title>
5497 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5498 user-written types, if and only if there is no explicit <literal>forall</literal>,
5499 GHC finds all the type variables mentioned in the type that are not already
5500 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5504 f :: forall a. a -> a
5511 h :: forall b. a -> b -> b
5517 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5520 f :: (a -> a) -> Int
5522 f :: forall a. (a -> a) -> Int
5524 f :: (forall a. a -> a) -> Int
5527 g :: (Ord a => a -> a) -> Int
5528 -- MEANS the illegal type
5529 g :: forall a. (Ord a => a -> a) -> Int
5531 g :: (forall a. Ord a => a -> a) -> Int
5533 The latter produces an illegal type, which you might think is silly,
5534 but at least the rule is simple. If you want the latter type, you
5535 can write your for-alls explicitly. Indeed, doing so is strongly advised
5542 <sect2 id="impredicative-polymorphism">
5543 <title>Impredicative polymorphism
5545 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5546 enabled with <option>-XImpredicativeTypes</option>.
5548 that you can call a polymorphic function at a polymorphic type, and
5549 parameterise data structures over polymorphic types. For example:
5551 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5552 f (Just g) = Just (g [3], g "hello")
5555 Notice here that the <literal>Maybe</literal> type is parameterised by the
5556 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5559 <para>The technical details of this extension are described in the paper
5560 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5561 type inference for higher-rank types and impredicativity</ulink>,
5562 which appeared at ICFP 2006.
5566 <sect2 id="scoped-type-variables">
5567 <title>Lexically scoped type variables
5571 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5572 which some type signatures are simply impossible to write. For example:
5574 f :: forall a. [a] -> [a]
5580 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5581 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5582 The type variables bound by a <literal>forall</literal> scope over
5583 the entire definition of the accompanying value declaration.
5584 In this example, the type variable <literal>a</literal> scopes over the whole
5585 definition of <literal>f</literal>, including over
5586 the type signature for <varname>ys</varname>.
5587 In Haskell 98 it is not possible to declare
5588 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5589 it becomes possible to do so.
5591 <para>Lexically-scoped type variables are enabled by
5592 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5594 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5595 variables work, compared to earlier releases. Read this section
5599 <title>Overview</title>
5601 <para>The design follows the following principles
5603 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5604 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5605 design.)</para></listitem>
5606 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5607 type variables. This means that every programmer-written type signature
5608 (including one that contains free scoped type variables) denotes a
5609 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5610 checker, and no inference is involved.</para></listitem>
5611 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5612 changing the program.</para></listitem>
5616 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5618 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5619 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5620 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5621 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5625 In Haskell, a programmer-written type signature is implicitly quantified over
5626 its free type variables (<ulink
5627 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5629 of the Haskell Report).
5630 Lexically scoped type variables affect this implicit quantification rules
5631 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5632 quantified. For example, if type variable <literal>a</literal> is in scope,
5635 (e :: a -> a) means (e :: a -> a)
5636 (e :: b -> b) means (e :: forall b. b->b)
5637 (e :: a -> b) means (e :: forall b. a->b)
5645 <sect3 id="decl-type-sigs">
5646 <title>Declaration type signatures</title>
5647 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5648 quantification (using <literal>forall</literal>) brings into scope the
5649 explicitly-quantified
5650 type variables, in the definition of the named function. For example:
5652 f :: forall a. [a] -> [a]
5653 f (x:xs) = xs ++ [ x :: a ]
5655 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5656 the definition of "<literal>f</literal>".
5658 <para>This only happens if:
5660 <listitem><para> The quantification in <literal>f</literal>'s type
5661 signature is explicit. For example:
5664 g (x:xs) = xs ++ [ x :: a ]
5666 This program will be rejected, because "<literal>a</literal>" does not scope
5667 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5668 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5669 quantification rules.
5671 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5672 not a pattern binding.
5675 f1 :: forall a. [a] -> [a]
5676 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5678 f2 :: forall a. [a] -> [a]
5679 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5681 f3 :: forall a. [a] -> [a]
5682 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5684 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5685 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5686 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5687 the type signature brings <literal>a</literal> into scope.
5693 <sect3 id="exp-type-sigs">
5694 <title>Expression type signatures</title>
5696 <para>An expression type signature that has <emphasis>explicit</emphasis>
5697 quantification (using <literal>forall</literal>) brings into scope the
5698 explicitly-quantified
5699 type variables, in the annotated expression. For example:
5701 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5703 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5704 type variable <literal>s</literal> into scope, in the annotated expression
5705 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5710 <sect3 id="pattern-type-sigs">
5711 <title>Pattern type signatures</title>
5713 A type signature may occur in any pattern; this is a <emphasis>pattern type
5714 signature</emphasis>.
5717 -- f and g assume that 'a' is already in scope
5718 f = \(x::Int, y::a) -> x
5720 h ((x,y) :: (Int,Bool)) = (y,x)
5722 In the case where all the type variables in the pattern type signature are
5723 already in scope (i.e. bound by the enclosing context), matters are simple: the
5724 signature simply constrains the type of the pattern in the obvious way.
5727 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5728 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5729 that are already in scope. For example:
5731 f :: forall a. [a] -> (Int, [a])
5734 (ys::[a], n) = (reverse xs, length xs) -- OK
5735 zs::[a] = xs ++ ys -- OK
5737 Just (v::b) = ... -- Not OK; b is not in scope
5739 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5740 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5744 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5745 type signature may mention a type variable that is not in scope; in this case,
5746 <emphasis>the signature brings that type variable into scope</emphasis>.
5747 This is particularly important for existential data constructors. For example:
5749 data T = forall a. MkT [a]
5752 k (MkT [t::a]) = MkT t3
5756 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5757 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5758 because it is bound by the pattern match. GHC's rule is that in this situation
5759 (and only then), a pattern type signature can mention a type variable that is
5760 not already in scope; the effect is to bring it into scope, standing for the
5761 existentially-bound type variable.
5764 When a pattern type signature binds a type variable in this way, GHC insists that the
5765 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5766 This means that any user-written type signature always stands for a completely known type.
5769 If all this seems a little odd, we think so too. But we must have
5770 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5771 could not name existentially-bound type variables in subsequent type signatures.
5774 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5775 signature is allowed to mention a lexical variable that is not already in
5777 For example, both <literal>f</literal> and <literal>g</literal> would be
5778 illegal if <literal>a</literal> was not already in scope.
5784 <!-- ==================== Commented out part about result type signatures
5786 <sect3 id="result-type-sigs">
5787 <title>Result type signatures</title>
5790 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5793 {- f assumes that 'a' is already in scope -}
5794 f x y :: [a] = [x,y,x]
5796 g = \ x :: [Int] -> [3,4]
5798 h :: forall a. [a] -> a
5802 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5803 the result of the function. Similarly, the body of the lambda in the RHS of
5804 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5805 alternative in <literal>h</literal> is <literal>a</literal>.
5807 <para> A result type signature never brings new type variables into scope.</para>
5809 There are a couple of syntactic wrinkles. First, notice that all three
5810 examples would parse quite differently with parentheses:
5812 {- f assumes that 'a' is already in scope -}
5813 f x (y :: [a]) = [x,y,x]
5815 g = \ (x :: [Int]) -> [3,4]
5817 h :: forall a. [a] -> a
5821 Now the signature is on the <emphasis>pattern</emphasis>; and
5822 <literal>h</literal> would certainly be ill-typed (since the pattern
5823 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5825 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5826 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5827 token or a parenthesised type of some sort). To see why,
5828 consider how one would parse this:
5837 <sect3 id="cls-inst-scoped-tyvars">
5838 <title>Class and instance declarations</title>
5841 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5842 scope over the methods defined in the <literal>where</literal> part. For example:
5860 <sect2 id="typing-binds">
5861 <title>Generalised typing of mutually recursive bindings</title>
5864 The Haskell Report specifies that a group of bindings (at top level, or in a
5865 <literal>let</literal> or <literal>where</literal>) should be sorted into
5866 strongly-connected components, and then type-checked in dependency order
5867 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5868 Report, Section 4.5.1</ulink>).
5869 As each group is type-checked, any binders of the group that
5871 an explicit type signature are put in the type environment with the specified
5873 and all others are monomorphic until the group is generalised
5874 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5877 <para>Following a suggestion of Mark Jones, in his paper
5878 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5880 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5882 <emphasis>the dependency analysis ignores references to variables that have an explicit
5883 type signature</emphasis>.
5884 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5885 typecheck. For example, consider:
5887 f :: Eq a => a -> Bool
5888 f x = (x == x) || g True || g "Yes"
5890 g y = (y <= y) || f True
5892 This is rejected by Haskell 98, but under Jones's scheme the definition for
5893 <literal>g</literal> is typechecked first, separately from that for
5894 <literal>f</literal>,
5895 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5896 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5897 type is generalised, to get
5899 g :: Ord a => a -> Bool
5901 Now, the definition for <literal>f</literal> is typechecked, with this type for
5902 <literal>g</literal> in the type environment.
5906 The same refined dependency analysis also allows the type signatures of
5907 mutually-recursive functions to have different contexts, something that is illegal in
5908 Haskell 98 (Section 4.5.2, last sentence). With
5909 <option>-XRelaxedPolyRec</option>
5910 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5911 type signatures; in practice this means that only variables bound by the same
5912 pattern binding must have the same context. For example, this is fine:
5914 f :: Eq a => a -> Bool
5915 f x = (x == x) || g True
5917 g :: Ord a => a -> Bool
5918 g y = (y <= y) || f True
5924 <!-- ==================== End of type system extensions ================= -->
5926 <!-- ====================== TEMPLATE HASKELL ======================= -->
5928 <sect1 id="template-haskell">
5929 <title>Template Haskell</title>
5931 <para>Template Haskell allows you to do compile-time meta-programming in
5934 the main technical innovations is discussed in "<ulink
5935 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5936 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5939 There is a Wiki page about
5940 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5941 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5945 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5946 Haskell library reference material</ulink>
5947 (look for module <literal>Language.Haskell.TH</literal>).
5948 Many changes to the original design are described in
5949 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5950 Notes on Template Haskell version 2</ulink>.
5951 Not all of these changes are in GHC, however.
5954 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5955 as a worked example to help get you started.
5959 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5960 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5965 <title>Syntax</title>
5967 <para> Template Haskell has the following new syntactic
5968 constructions. You need to use the flag
5969 <option>-XTemplateHaskell</option>
5970 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5971 </indexterm>to switch these syntactic extensions on
5972 (<option>-XTemplateHaskell</option> is no longer implied by
5973 <option>-fglasgow-exts</option>).</para>
5977 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5978 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5979 There must be no space between the "$" and the identifier or parenthesis. This use
5980 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5981 of "." as an infix operator. If you want the infix operator, put spaces around it.
5983 <para> A splice can occur in place of
5985 <listitem><para> an expression; the spliced expression must
5986 have type <literal>Q Exp</literal></para></listitem>
5987 <listitem><para> an type; the spliced expression must
5988 have type <literal>Q Typ</literal></para></listitem>
5989 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5992 Inside a splice you can can only call functions defined in imported modules,
5993 not functions defined elsewhere in the same module.</listitem>
5997 A expression quotation is written in Oxford brackets, thus:
5999 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6000 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6001 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6002 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6003 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6004 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6005 </itemizedlist></para></listitem>
6008 A quasi-quotation can appear in either a pattern context or an
6009 expression context and is also written in Oxford brackets:
6011 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
6012 where the "..." is an arbitrary string; a full description of the
6013 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6014 </itemizedlist></para></listitem>
6017 A name can be quoted with either one or two prefix single quotes:
6019 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6020 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6021 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6023 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6024 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6027 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6028 may also be given as an argument to the <literal>reify</literal> function.
6034 (Compared to the original paper, there are many differences of detail.
6035 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6036 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6037 Pattern splices and quotations are not implemented.)
6041 <sect2> <title> Using Template Haskell </title>
6045 The data types and monadic constructor functions for Template Haskell are in the library
6046 <literal>Language.Haskell.THSyntax</literal>.
6050 You can only run a function at compile time if it is imported from another module. That is,
6051 you can't define a function in a module, and call it from within a splice in the same module.
6052 (It would make sense to do so, but it's hard to implement.)
6056 You can only run a function at compile time if it is imported
6057 from another module <emphasis>that is not part of a mutually-recursive group of modules
6058 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6059 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6060 splice is to be run.</para>
6062 For example, when compiling module A,
6063 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6064 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6068 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6071 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6072 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6073 compiles and runs a program, and then looks at the result. So it's important that
6074 the program it compiles produces results whose representations are identical to
6075 those of the compiler itself.
6079 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6080 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6085 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6086 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6087 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6094 -- Import our template "pr"
6095 import Printf ( pr )
6097 -- The splice operator $ takes the Haskell source code
6098 -- generated at compile time by "pr" and splices it into
6099 -- the argument of "putStrLn".
6100 main = putStrLn ( $(pr "Hello") )
6106 -- Skeletal printf from the paper.
6107 -- It needs to be in a separate module to the one where
6108 -- you intend to use it.
6110 -- Import some Template Haskell syntax
6111 import Language.Haskell.TH
6113 -- Describe a format string
6114 data Format = D | S | L String
6116 -- Parse a format string. This is left largely to you
6117 -- as we are here interested in building our first ever
6118 -- Template Haskell program and not in building printf.
6119 parse :: String -> [Format]
6122 -- Generate Haskell source code from a parsed representation
6123 -- of the format string. This code will be spliced into
6124 -- the module which calls "pr", at compile time.
6125 gen :: [Format] -> Q Exp
6126 gen [D] = [| \n -> show n |]
6127 gen [S] = [| \s -> s |]
6128 gen [L s] = stringE s
6130 -- Here we generate the Haskell code for the splice
6131 -- from an input format string.
6132 pr :: String -> Q Exp
6133 pr s = gen (parse s)
6136 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6139 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6142 <para>Run "main.exe" and here is your output:</para>
6152 <title>Using Template Haskell with Profiling</title>
6153 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6155 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6156 interpreter to run the splice expressions. The bytecode interpreter
6157 runs the compiled expression on top of the same runtime on which GHC
6158 itself is running; this means that the compiled code referred to by
6159 the interpreted expression must be compatible with this runtime, and
6160 in particular this means that object code that is compiled for
6161 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6162 expression, because profiled object code is only compatible with the
6163 profiling version of the runtime.</para>
6165 <para>This causes difficulties if you have a multi-module program
6166 containing Template Haskell code and you need to compile it for
6167 profiling, because GHC cannot load the profiled object code and use it
6168 when executing the splices. Fortunately GHC provides a workaround.
6169 The basic idea is to compile the program twice:</para>
6173 <para>Compile the program or library first the normal way, without
6174 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6177 <para>Then compile it again with <option>-prof</option>, and
6178 additionally use <option>-osuf
6179 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6180 to name the object files differently (you can choose any suffix
6181 that isn't the normal object suffix here). GHC will automatically
6182 load the object files built in the first step when executing splice
6183 expressions. If you omit the <option>-osuf</option> flag when
6184 building with <option>-prof</option> and Template Haskell is used,
6185 GHC will emit an error message. </para>
6190 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6191 <para>Quasi-quotation allows patterns and expressions to be written using
6192 programmer-defined concrete syntax; the motivation behind the extension and
6193 several examples are documented in
6194 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6195 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6196 2007). The example below shows how to write a quasiquoter for a simple
6197 expression language.</para>
6200 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6201 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6202 functions for quoting expressions and patterns, respectively. The first argument
6203 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6204 context of the quasi-quotation statement determines which of the two parsers is
6205 called: if the quasi-quotation occurs in an expression context, the expression
6206 parser is called, and if it occurs in a pattern context, the pattern parser is
6210 Note that in the example we make use of an antiquoted
6211 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6212 (this syntax for anti-quotation was defined by the parser's
6213 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6214 integer value argument of the constructor <literal>IntExpr</literal> when
6215 pattern matching. Please see the referenced paper for further details regarding
6216 anti-quotation as well as the description of a technique that uses SYB to
6217 leverage a single parser of type <literal>String -> a</literal> to generate both
6218 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6219 pattern parser that returns a value of type <literal>Q Pat</literal>.
6222 <para>In general, a quasi-quote has the form
6223 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6224 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6225 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6226 can be arbitrary, and may contain newlines.
6229 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6230 the example, <literal>expr</literal> cannot be defined
6231 in <literal>Main.hs</literal> where it is used, but must be imported.
6242 main = do { print $ eval [$expr|1 + 2|]
6244 { [$expr|'int:n|] -> print n
6253 import qualified Language.Haskell.TH as TH
6254 import Language.Haskell.TH.Quote
6256 data Expr = IntExpr Integer
6257 | AntiIntExpr String
6258 | BinopExpr BinOp Expr Expr
6260 deriving(Show, Typeable, Data)
6266 deriving(Show, Typeable, Data)
6268 eval :: Expr -> Integer
6269 eval (IntExpr n) = n
6270 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6277 expr = QuasiQuoter parseExprExp parseExprPat
6279 -- Parse an Expr, returning its representation as
6280 -- either a Q Exp or a Q Pat. See the referenced paper
6281 -- for how to use SYB to do this by writing a single
6282 -- parser of type String -> Expr instead of two
6283 -- separate parsers.
6285 parseExprExp :: String -> Q Exp
6288 parseExprPat :: String -> Q Pat
6292 <para>Now run the compiler:
6295 $ ghc --make -XQuasiQuotes Main.hs -o main
6298 <para>Run "main" and here is your output:</para>
6310 <!-- ===================== Arrow notation =================== -->
6312 <sect1 id="arrow-notation">
6313 <title>Arrow notation
6316 <para>Arrows are a generalization of monads introduced by John Hughes.
6317 For more details, see
6322 “Generalising Monads to Arrows”,
6323 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6324 pp67–111, May 2000.
6325 The paper that introduced arrows: a friendly introduction, motivated with
6326 programming examples.
6332 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6333 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6334 Introduced the notation described here.
6340 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6341 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6348 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6349 John Hughes, in <citetitle>5th International Summer School on
6350 Advanced Functional Programming</citetitle>,
6351 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6353 This paper includes another introduction to the notation,
6354 with practical examples.
6360 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6361 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6362 A terse enumeration of the formal rules used
6363 (extracted from comments in the source code).
6369 The arrows web page at
6370 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6375 With the <option>-XArrows</option> flag, GHC supports the arrow
6376 notation described in the second of these papers,
6377 translating it using combinators from the
6378 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6380 What follows is a brief introduction to the notation;
6381 it won't make much sense unless you've read Hughes's paper.
6384 <para>The extension adds a new kind of expression for defining arrows:
6386 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6387 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6389 where <literal>proc</literal> is a new keyword.
6390 The variables of the pattern are bound in the body of the
6391 <literal>proc</literal>-expression,
6392 which is a new sort of thing called a <firstterm>command</firstterm>.
6393 The syntax of commands is as follows:
6395 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6396 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6397 | <replaceable>cmd</replaceable><superscript>0</superscript>
6399 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6400 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6401 infix operators as for expressions, and
6403 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6404 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6405 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6406 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6407 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6408 | <replaceable>fcmd</replaceable>
6410 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6411 | ( <replaceable>cmd</replaceable> )
6412 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6414 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6415 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6416 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6417 | <replaceable>cmd</replaceable>
6419 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6420 except that the bodies are commands instead of expressions.
6424 Commands produce values, but (like monadic computations)
6425 may yield more than one value,
6426 or none, and may do other things as well.
6427 For the most part, familiarity with monadic notation is a good guide to
6429 However the values of expressions, even monadic ones,
6430 are determined by the values of the variables they contain;
6431 this is not necessarily the case for commands.
6435 A simple example of the new notation is the expression
6437 proc x -> f -< x+1
6439 We call this a <firstterm>procedure</firstterm> or
6440 <firstterm>arrow abstraction</firstterm>.
6441 As with a lambda expression, the variable <literal>x</literal>
6442 is a new variable bound within the <literal>proc</literal>-expression.
6443 It refers to the input to the arrow.
6444 In the above example, <literal>-<</literal> is not an identifier but an
6445 new reserved symbol used for building commands from an expression of arrow
6446 type and an expression to be fed as input to that arrow.
6447 (The weird look will make more sense later.)
6448 It may be read as analogue of application for arrows.
6449 The above example is equivalent to the Haskell expression
6451 arr (\ x -> x+1) >>> f
6453 That would make no sense if the expression to the left of
6454 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6455 More generally, the expression to the left of <literal>-<</literal>
6456 may not involve any <firstterm>local variable</firstterm>,
6457 i.e. a variable bound in the current arrow abstraction.
6458 For such a situation there is a variant <literal>-<<</literal>, as in
6460 proc x -> f x -<< x+1
6462 which is equivalent to
6464 arr (\ x -> (f x, x+1)) >>> app
6466 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6468 Such an arrow is equivalent to a monad, so if you're using this form
6469 you may find a monadic formulation more convenient.
6473 <title>do-notation for commands</title>
6476 Another form of command is a form of <literal>do</literal>-notation.
6477 For example, you can write
6486 You can read this much like ordinary <literal>do</literal>-notation,
6487 but with commands in place of monadic expressions.
6488 The first line sends the value of <literal>x+1</literal> as an input to
6489 the arrow <literal>f</literal>, and matches its output against
6490 <literal>y</literal>.
6491 In the next line, the output is discarded.
6492 The arrow <function>returnA</function> is defined in the
6493 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6494 module as <literal>arr id</literal>.
6495 The above example is treated as an abbreviation for
6497 arr (\ x -> (x, x)) >>>
6498 first (arr (\ x -> x+1) >>> f) >>>
6499 arr (\ (y, x) -> (y, (x, y))) >>>
6500 first (arr (\ y -> 2*y) >>> g) >>>
6502 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6503 first (arr (\ (x, z) -> x*z) >>> h) >>>
6504 arr (\ (t, z) -> t+z) >>>
6507 Note that variables not used later in the composition are projected out.
6508 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6510 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6511 module, this reduces to
6513 arr (\ x -> (x+1, x)) >>>
6515 arr (\ (y, x) -> (2*y, (x, y))) >>>
6517 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6519 arr (\ (t, z) -> t+z)
6521 which is what you might have written by hand.
6522 With arrow notation, GHC keeps track of all those tuples of variables for you.
6526 Note that although the above translation suggests that
6527 <literal>let</literal>-bound variables like <literal>z</literal> must be
6528 monomorphic, the actual translation produces Core,
6529 so polymorphic variables are allowed.
6533 It's also possible to have mutually recursive bindings,
6534 using the new <literal>rec</literal> keyword, as in the following example:
6536 counter :: ArrowCircuit a => a Bool Int
6537 counter = proc reset -> do
6538 rec output <- returnA -< if reset then 0 else next
6539 next <- delay 0 -< output+1
6540 returnA -< output
6542 The translation of such forms uses the <function>loop</function> combinator,
6543 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6549 <title>Conditional commands</title>
6552 In the previous example, we used a conditional expression to construct the
6554 Sometimes we want to conditionally execute different commands, as in
6561 which is translated to
6563 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6564 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6566 Since the translation uses <function>|||</function>,
6567 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6571 There are also <literal>case</literal> commands, like
6577 y <- h -< (x1, x2)
6581 The syntax is the same as for <literal>case</literal> expressions,
6582 except that the bodies of the alternatives are commands rather than expressions.
6583 The translation is similar to that of <literal>if</literal> commands.
6589 <title>Defining your own control structures</title>
6592 As we're seen, arrow notation provides constructs,
6593 modelled on those for expressions,
6594 for sequencing, value recursion and conditionals.
6595 But suitable combinators,
6596 which you can define in ordinary Haskell,
6597 may also be used to build new commands out of existing ones.
6598 The basic idea is that a command defines an arrow from environments to values.
6599 These environments assign values to the free local variables of the command.
6600 Thus combinators that produce arrows from arrows
6601 may also be used to build commands from commands.
6602 For example, the <literal>ArrowChoice</literal> class includes a combinator
6604 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6606 so we can use it to build commands:
6608 expr' = proc x -> do
6611 symbol Plus -< ()
6612 y <- term -< ()
6615 symbol Minus -< ()
6616 y <- term -< ()
6619 (The <literal>do</literal> on the first line is needed to prevent the first
6620 <literal><+> ...</literal> from being interpreted as part of the
6621 expression on the previous line.)
6622 This is equivalent to
6624 expr' = (proc x -> returnA -< x)
6625 <+> (proc x -> do
6626 symbol Plus -< ()
6627 y <- term -< ()
6629 <+> (proc x -> do
6630 symbol Minus -< ()
6631 y <- term -< ()
6634 It is essential that this operator be polymorphic in <literal>e</literal>
6635 (representing the environment input to the command
6636 and thence to its subcommands)
6637 and satisfy the corresponding naturality property
6639 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6641 at least for strict <literal>k</literal>.
6642 (This should be automatic if you're not using <function>seq</function>.)
6643 This ensures that environments seen by the subcommands are environments
6644 of the whole command,
6645 and also allows the translation to safely trim these environments.
6646 The operator must also not use any variable defined within the current
6651 We could define our own operator
6653 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6654 untilA body cond = proc x ->
6655 b <- cond -< x
6656 if b then returnA -< ()
6659 untilA body cond -< x
6661 and use it in the same way.
6662 Of course this infix syntax only makes sense for binary operators;
6663 there is also a more general syntax involving special brackets:
6667 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6674 <title>Primitive constructs</title>
6677 Some operators will need to pass additional inputs to their subcommands.
6678 For example, in an arrow type supporting exceptions,
6679 the operator that attaches an exception handler will wish to pass the
6680 exception that occurred to the handler.
6681 Such an operator might have a type
6683 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6685 where <literal>Ex</literal> is the type of exceptions handled.
6686 You could then use this with arrow notation by writing a command
6688 body `handleA` \ ex -> handler
6690 so that if an exception is raised in the command <literal>body</literal>,
6691 the variable <literal>ex</literal> is bound to the value of the exception
6692 and the command <literal>handler</literal>,
6693 which typically refers to <literal>ex</literal>, is entered.
6694 Though the syntax here looks like a functional lambda,
6695 we are talking about commands, and something different is going on.
6696 The input to the arrow represented by a command consists of values for
6697 the free local variables in the command, plus a stack of anonymous values.
6698 In all the prior examples, this stack was empty.
6699 In the second argument to <function>handleA</function>,
6700 this stack consists of one value, the value of the exception.
6701 The command form of lambda merely gives this value a name.
6706 the values on the stack are paired to the right of the environment.
6707 So operators like <function>handleA</function> that pass
6708 extra inputs to their subcommands can be designed for use with the notation
6709 by pairing the values with the environment in this way.
6710 More precisely, the type of each argument of the operator (and its result)
6711 should have the form
6713 a (...(e,t1), ... tn) t
6715 where <replaceable>e</replaceable> is a polymorphic variable
6716 (representing the environment)
6717 and <replaceable>ti</replaceable> are the types of the values on the stack,
6718 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6719 The polymorphic variable <replaceable>e</replaceable> must not occur in
6720 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6721 <replaceable>t</replaceable>.
6722 However the arrows involved need not be the same.
6723 Here are some more examples of suitable operators:
6725 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6726 runReader :: ... => a e c -> a' (e,State) c
6727 runState :: ... => a e c -> a' (e,State) (c,State)
6729 We can supply the extra input required by commands built with the last two
6730 by applying them to ordinary expressions, as in
6734 (|runReader (do { ... })|) s
6736 which adds <literal>s</literal> to the stack of inputs to the command
6737 built using <function>runReader</function>.
6741 The command versions of lambda abstraction and application are analogous to
6742 the expression versions.
6743 In particular, the beta and eta rules describe equivalences of commands.
6744 These three features (operators, lambda abstraction and application)
6745 are the core of the notation; everything else can be built using them,
6746 though the results would be somewhat clumsy.
6747 For example, we could simulate <literal>do</literal>-notation by defining
6749 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6750 u `bind` f = returnA &&& u >>> f
6752 bind_ :: Arrow a => a e b -> a e c -> a e c
6753 u `bind_` f = u `bind` (arr fst >>> f)
6755 We could simulate <literal>if</literal> by defining
6757 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6758 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6765 <title>Differences with the paper</title>
6770 <para>Instead of a single form of arrow application (arrow tail) with two
6771 translations, the implementation provides two forms
6772 <quote><literal>-<</literal></quote> (first-order)
6773 and <quote><literal>-<<</literal></quote> (higher-order).
6778 <para>User-defined operators are flagged with banana brackets instead of
6779 a new <literal>form</literal> keyword.
6788 <title>Portability</title>
6791 Although only GHC implements arrow notation directly,
6792 there is also a preprocessor
6794 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6795 that translates arrow notation into Haskell 98
6796 for use with other Haskell systems.
6797 You would still want to check arrow programs with GHC;
6798 tracing type errors in the preprocessor output is not easy.
6799 Modules intended for both GHC and the preprocessor must observe some
6800 additional restrictions:
6805 The module must import
6806 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6812 The preprocessor cannot cope with other Haskell extensions.
6813 These would have to go in separate modules.
6819 Because the preprocessor targets Haskell (rather than Core),
6820 <literal>let</literal>-bound variables are monomorphic.
6831 <!-- ==================== BANG PATTERNS ================= -->
6833 <sect1 id="bang-patterns">
6834 <title>Bang patterns
6835 <indexterm><primary>Bang patterns</primary></indexterm>
6837 <para>GHC supports an extension of pattern matching called <emphasis>bang
6838 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6839 Bang patterns are under consideration for Haskell Prime.
6841 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6842 prime feature description</ulink> contains more discussion and examples
6843 than the material below.
6846 The key change is the addition of a new rule to the
6847 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6848 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6849 against a value <replaceable>v</replaceable> behaves as follows:
6851 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6852 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6856 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6859 <sect2 id="bang-patterns-informal">
6860 <title>Informal description of bang patterns
6863 The main idea is to add a single new production to the syntax of patterns:
6867 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6868 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6873 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6874 whereas without the bang it would be lazy.
6875 Bang patterns can be nested of course:
6879 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6880 <literal>y</literal>.
6881 A bang only really has an effect if it precedes a variable or wild-card pattern:
6886 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6887 putting a bang before a pattern that
6888 forces evaluation anyway does nothing.
6891 There is one (apparent) exception to this general rule that a bang only
6892 makes a difference when it precedes a variable or wild-card: a bang at the
6893 top level of a <literal>let</literal> or <literal>where</literal>
6894 binding makes the binding strict, regardless of the pattern. For example:
6898 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6899 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6900 (We say "apparent" exception because the Right Way to think of it is that the bang
6901 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6902 is part of the syntax of the <emphasis>binding</emphasis>.)
6903 Nested bangs in a pattern binding behave uniformly with all other forms of
6904 pattern matching. For example
6906 let (!x,[y]) = e in b
6908 is equivalent to this:
6910 let { t = case e of (x,[y]) -> x `seq` (x,y)
6915 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6916 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6917 evaluation of <literal>x</literal>.
6920 Bang patterns work in <literal>case</literal> expressions too, of course:
6922 g5 x = let y = f x in body
6923 g6 x = case f x of { y -> body }
6924 g7 x = case f x of { !y -> body }
6926 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6927 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6928 result, and then evaluates <literal>body</literal>.
6933 <sect2 id="bang-patterns-sem">
6934 <title>Syntax and semantics
6938 We add a single new production to the syntax of patterns:
6942 There is one problem with syntactic ambiguity. Consider:
6946 Is this a definition of the infix function "<literal>(!)</literal>",
6947 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6948 ambiguity in favour of the latter. If you want to define
6949 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6954 The semantics of Haskell pattern matching is described in <ulink
6955 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6956 Section 3.17.2</ulink> of the Haskell Report. To this description add
6957 one extra item 10, saying:
6958 <itemizedlist><listitem><para>Matching
6959 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6960 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6961 <listitem><para>otherwise, <literal>pat</literal> is matched against
6962 <literal>v</literal></para></listitem>
6964 </para></listitem></itemizedlist>
6965 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6966 Section 3.17.3</ulink>, add a new case (t):
6968 case v of { !pat -> e; _ -> e' }
6969 = v `seq` case v of { pat -> e; _ -> e' }
6972 That leaves let expressions, whose translation is given in
6973 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6975 of the Haskell Report.
6976 In the translation box, first apply
6977 the following transformation: for each pattern <literal>pi</literal> that is of
6978 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6979 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6980 have a bang at the top, apply the rules in the existing box.
6982 <para>The effect of the let rule is to force complete matching of the pattern
6983 <literal>qi</literal> before evaluation of the body is begun. The bang is
6984 retained in the translated form in case <literal>qi</literal> is a variable,
6992 The let-binding can be recursive. However, it is much more common for
6993 the let-binding to be non-recursive, in which case the following law holds:
6994 <literal>(let !p = rhs in body)</literal>
6996 <literal>(case rhs of !p -> body)</literal>
6999 A pattern with a bang at the outermost level is not allowed at the top level of
7005 <!-- ==================== ASSERTIONS ================= -->
7007 <sect1 id="assertions">
7009 <indexterm><primary>Assertions</primary></indexterm>
7013 If you want to make use of assertions in your standard Haskell code, you
7014 could define a function like the following:
7020 assert :: Bool -> a -> a
7021 assert False x = error "assertion failed!"
7028 which works, but gives you back a less than useful error message --
7029 an assertion failed, but which and where?
7033 One way out is to define an extended <function>assert</function> function which also
7034 takes a descriptive string to include in the error message and
7035 perhaps combine this with the use of a pre-processor which inserts
7036 the source location where <function>assert</function> was used.
7040 Ghc offers a helping hand here, doing all of this for you. For every
7041 use of <function>assert</function> in the user's source:
7047 kelvinToC :: Double -> Double
7048 kelvinToC k = assert (k >= 0.0) (k+273.15)
7054 Ghc will rewrite this to also include the source location where the
7061 assert pred val ==> assertError "Main.hs|15" pred val
7067 The rewrite is only performed by the compiler when it spots
7068 applications of <function>Control.Exception.assert</function>, so you
7069 can still define and use your own versions of
7070 <function>assert</function>, should you so wish. If not, import
7071 <literal>Control.Exception</literal> to make use
7072 <function>assert</function> in your code.
7076 GHC ignores assertions when optimisation is turned on with the
7077 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7078 <literal>assert pred e</literal> will be rewritten to
7079 <literal>e</literal>. You can also disable assertions using the
7080 <option>-fignore-asserts</option>
7081 option<indexterm><primary><option>-fignore-asserts</option></primary>
7082 </indexterm>.</para>
7085 Assertion failures can be caught, see the documentation for the
7086 <literal>Control.Exception</literal> library for the details.
7092 <!-- =============================== PRAGMAS =========================== -->
7094 <sect1 id="pragmas">
7095 <title>Pragmas</title>
7097 <indexterm><primary>pragma</primary></indexterm>
7099 <para>GHC supports several pragmas, or instructions to the
7100 compiler placed in the source code. Pragmas don't normally affect
7101 the meaning of the program, but they might affect the efficiency
7102 of the generated code.</para>
7104 <para>Pragmas all take the form
7106 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7108 where <replaceable>word</replaceable> indicates the type of
7109 pragma, and is followed optionally by information specific to that
7110 type of pragma. Case is ignored in
7111 <replaceable>word</replaceable>. The various values for
7112 <replaceable>word</replaceable> that GHC understands are described
7113 in the following sections; any pragma encountered with an
7114 unrecognised <replaceable>word</replaceable> is
7115 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7116 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7118 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7122 pragma must precede the <literal>module</literal> keyword in the file.
7125 There can be as many file-header pragmas as you please, and they can be
7126 preceded or followed by comments.
7129 File-header pragmas are read once only, before
7130 pre-processing the file (e.g. with cpp).
7133 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7134 <literal>{-# OPTIONS_GHC #-}</literal>, and
7135 <literal>{-# INCLUDE #-}</literal>.
7140 <sect2 id="language-pragma">
7141 <title>LANGUAGE pragma</title>
7143 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7144 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7146 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7148 It is the intention that all Haskell compilers support the
7149 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7150 all extensions are supported by all compilers, of
7151 course. The <literal>LANGUAGE</literal> pragma should be used instead
7152 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7154 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7156 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7158 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7160 <para>Every language extension can also be turned into a command-line flag
7161 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7162 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7165 <para>A list of all supported language extensions can be obtained by invoking
7166 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7168 <para>Any extension from the <literal>Extension</literal> type defined in
7170 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7171 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7175 <sect2 id="options-pragma">
7176 <title>OPTIONS_GHC pragma</title>
7177 <indexterm><primary>OPTIONS_GHC</primary>
7179 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7182 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7183 additional options that are given to the compiler when compiling
7184 this source file. See <xref linkend="source-file-options"/> for
7187 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7188 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7191 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7193 <sect2 id="include-pragma">
7194 <title>INCLUDE pragma</title>
7196 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
7197 of C header files that should be <literal>#include</literal>'d into
7198 the C source code generated by the compiler for the current module (if
7199 compiling via C). For example:</para>
7202 {-# INCLUDE "foo.h" #-}
7203 {-# INCLUDE <stdio.h> #-}</programlisting>
7205 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7207 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
7208 to the <option>-#include</option> option (<xref
7209 linkend="options-C-compiler" />), because the
7210 <literal>INCLUDE</literal> pragma is understood by other
7211 compilers. Yet another alternative is to add the include file to each
7212 <literal>foreign import</literal> declaration in your code, but we
7213 don't recommend using this approach with GHC.</para>
7216 <sect2 id="warning-deprecated-pragma">
7217 <title>WARNING and DEPRECATED pragmas</title>
7218 <indexterm><primary>WARNING</primary></indexterm>
7219 <indexterm><primary>DEPRECATED</primary></indexterm>
7221 <para>The WARNING pragma allows you to attach an arbitrary warning
7222 to a particular function, class, or type.
7223 A DEPRECATED pragma lets you specify that
7224 a particular function, class, or type is deprecated.
7225 There are two ways of using these pragmas.
7229 <para>You can work on an entire module thus:</para>
7231 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7236 module Wibble {-# WARNING "This is an unstable interface." #-} where
7239 <para>When you compile any module that import
7240 <literal>Wibble</literal>, GHC will print the specified
7245 <para>You can attach a warning to a function, class, type, or data constructor, with the
7246 following top-level declarations:</para>
7248 {-# DEPRECATED f, C, T "Don't use these" #-}
7249 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7251 <para>When you compile any module that imports and uses any
7252 of the specified entities, GHC will print the specified
7254 <para> You can only attach to entities declared at top level in the module
7255 being compiled, and you can only use unqualified names in the list of
7256 entities. A capitalised name, such as <literal>T</literal>
7257 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7258 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7259 both are in scope. If both are in scope, there is currently no way to
7260 specify one without the other (c.f. fixities
7261 <xref linkend="infix-tycons"/>).</para>
7264 Warnings and deprecations are not reported for
7265 (a) uses within the defining module, and
7266 (b) uses in an export list.
7267 The latter reduces spurious complaints within a library
7268 in which one module gathers together and re-exports
7269 the exports of several others.
7271 <para>You can suppress the warnings with the flag
7272 <option>-fno-warn-warnings-deprecations</option>.</para>
7275 <sect2 id="inline-noinline-pragma">
7276 <title>INLINE and NOINLINE pragmas</title>
7278 <para>These pragmas control the inlining of function
7281 <sect3 id="inline-pragma">
7282 <title>INLINE pragma</title>
7283 <indexterm><primary>INLINE</primary></indexterm>
7285 <para>GHC (with <option>-O</option>, as always) tries to
7286 inline (or “unfold”) functions/values that are
7287 “small enough,” thus avoiding the call overhead
7288 and possibly exposing other more-wonderful optimisations.
7289 Normally, if GHC decides a function is “too
7290 expensive” to inline, it will not do so, nor will it
7291 export that unfolding for other modules to use.</para>
7293 <para>The sledgehammer you can bring to bear is the
7294 <literal>INLINE</literal><indexterm><primary>INLINE
7295 pragma</primary></indexterm> pragma, used thusly:</para>
7298 key_function :: Int -> String -> (Bool, Double)
7299 {-# INLINE key_function #-}
7302 <para>The major effect of an <literal>INLINE</literal> pragma
7303 is to declare a function's “cost” to be very low.
7304 The normal unfolding machinery will then be very keen to
7305 inline it. However, an <literal>INLINE</literal> pragma for a
7306 function "<literal>f</literal>" has a number of other effects:
7309 No functions are inlined into <literal>f</literal>. Otherwise
7310 GHC might inline a big function into <literal>f</literal>'s right hand side,
7311 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7314 The float-in, float-out, and common-sub-expression transformations are not
7315 applied to the body of <literal>f</literal>.
7318 An INLINE function is not worker/wrappered by strictness analysis.
7319 It's going to be inlined wholesale instead.
7322 All of these effects are aimed at ensuring that what gets inlined is
7323 exactly what you asked for, no more and no less.
7325 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7326 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7327 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7328 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7329 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7330 when there is no choice even an INLINE function can be selected, in which case
7331 the INLINE pragma is ignored.
7332 For example, for a self-recursive function, the loop breaker can only be the function
7333 itself, so an INLINE pragma is always ignored.</para>
7335 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7336 function can be put anywhere its type signature could be
7339 <para><literal>INLINE</literal> pragmas are a particularly
7341 <literal>then</literal>/<literal>return</literal> (or
7342 <literal>bind</literal>/<literal>unit</literal>) functions in
7343 a monad. For example, in GHC's own
7344 <literal>UniqueSupply</literal> monad code, we have:</para>
7347 {-# INLINE thenUs #-}
7348 {-# INLINE returnUs #-}
7351 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7352 linkend="noinline-pragma"/>).</para>
7354 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7355 so if you want your code to be HBC-compatible you'll have to surround
7356 the pragma with C pre-processor directives
7357 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7361 <sect3 id="noinline-pragma">
7362 <title>NOINLINE pragma</title>
7364 <indexterm><primary>NOINLINE</primary></indexterm>
7365 <indexterm><primary>NOTINLINE</primary></indexterm>
7367 <para>The <literal>NOINLINE</literal> pragma does exactly what
7368 you'd expect: it stops the named function from being inlined
7369 by the compiler. You shouldn't ever need to do this, unless
7370 you're very cautious about code size.</para>
7372 <para><literal>NOTINLINE</literal> is a synonym for
7373 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7374 specified by Haskell 98 as the standard way to disable
7375 inlining, so it should be used if you want your code to be
7379 <sect3 id="phase-control">
7380 <title>Phase control</title>
7382 <para> Sometimes you want to control exactly when in GHC's
7383 pipeline the INLINE pragma is switched on. Inlining happens
7384 only during runs of the <emphasis>simplifier</emphasis>. Each
7385 run of the simplifier has a different <emphasis>phase
7386 number</emphasis>; the phase number decreases towards zero.
7387 If you use <option>-dverbose-core2core</option> you'll see the
7388 sequence of phase numbers for successive runs of the
7389 simplifier. In an INLINE pragma you can optionally specify a
7393 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7394 <literal>f</literal>
7395 until phase <literal>k</literal>, but from phase
7396 <literal>k</literal> onwards be very keen to inline it.
7399 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7400 <literal>f</literal>
7401 until phase <literal>k</literal>, but from phase
7402 <literal>k</literal> onwards do not inline it.
7405 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7406 <literal>f</literal>
7407 until phase <literal>k</literal>, but from phase
7408 <literal>k</literal> onwards be willing to inline it (as if
7409 there was no pragma).
7412 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7413 <literal>f</literal>
7414 until phase <literal>k</literal>, but from phase
7415 <literal>k</literal> onwards do not inline it.
7418 The same information is summarised here:
7420 -- Before phase 2 Phase 2 and later
7421 {-# INLINE [2] f #-} -- No Yes
7422 {-# INLINE [~2] f #-} -- Yes No
7423 {-# NOINLINE [2] f #-} -- No Maybe
7424 {-# NOINLINE [~2] f #-} -- Maybe No
7426 {-# INLINE f #-} -- Yes Yes
7427 {-# NOINLINE f #-} -- No No
7429 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7430 function body is small, or it is applied to interesting-looking arguments etc).
7431 Another way to understand the semantics is this:
7433 <listitem><para>For both INLINE and NOINLINE, the phase number says
7434 when inlining is allowed at all.</para></listitem>
7435 <listitem><para>The INLINE pragma has the additional effect of making the
7436 function body look small, so that when inlining is allowed it is very likely to
7441 <para>The same phase-numbering control is available for RULES
7442 (<xref linkend="rewrite-rules"/>).</para>
7446 <sect2 id="annotation-pragmas">
7447 <title>ANN pragmas</title>
7449 <para>GHC offers the ability to annotate various code constructs with additional
7450 data by using three pragmas. This data can then be inspected at a later date by
7451 using GHC-as-a-library.</para>
7453 <sect3 id="ann-pragma">
7454 <title>Annotating values</title>
7456 <indexterm><primary>ANN</primary></indexterm>
7458 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7459 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7460 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7461 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7462 you would do this:</para>
7465 {-# ANN foo (Just "Hello") #-}
7470 A number of restrictions apply to use of annotations:
7472 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7473 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7474 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7475 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7476 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7478 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7479 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7482 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7483 please give the GHC team a shout</ulink>.
7486 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7487 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7490 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7495 <sect3 id="typeann-pragma">
7496 <title>Annotating types</title>
7498 <indexterm><primary>ANN type</primary></indexterm>
7499 <indexterm><primary>ANN</primary></indexterm>
7501 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7504 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7509 <sect3 id="modann-pragma">
7510 <title>Annotating modules</title>
7512 <indexterm><primary>ANN module</primary></indexterm>
7513 <indexterm><primary>ANN</primary></indexterm>
7515 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7518 {-# ANN module (Just "A `Maybe String' annotation") #-}
7523 <sect2 id="line-pragma">
7524 <title>LINE pragma</title>
7526 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7527 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7528 <para>This pragma is similar to C's <literal>#line</literal>
7529 pragma, and is mainly for use in automatically generated Haskell
7530 code. It lets you specify the line number and filename of the
7531 original code; for example</para>
7533 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7535 <para>if you'd generated the current file from something called
7536 <filename>Foo.vhs</filename> and this line corresponds to line
7537 42 in the original. GHC will adjust its error messages to refer
7538 to the line/file named in the <literal>LINE</literal>
7543 <title>RULES pragma</title>
7545 <para>The RULES pragma lets you specify rewrite rules. It is
7546 described in <xref linkend="rewrite-rules"/>.</para>
7549 <sect2 id="specialize-pragma">
7550 <title>SPECIALIZE pragma</title>
7552 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7553 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7554 <indexterm><primary>overloading, death to</primary></indexterm>
7556 <para>(UK spelling also accepted.) For key overloaded
7557 functions, you can create extra versions (NB: more code space)
7558 specialised to particular types. Thus, if you have an
7559 overloaded function:</para>
7562 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7565 <para>If it is heavily used on lists with
7566 <literal>Widget</literal> keys, you could specialise it as
7570 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7573 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7574 be put anywhere its type signature could be put.</para>
7576 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7577 (a) a specialised version of the function and (b) a rewrite rule
7578 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7579 un-specialised function into a call to the specialised one.</para>
7581 <para>The type in a SPECIALIZE pragma can be any type that is less
7582 polymorphic than the type of the original function. In concrete terms,
7583 if the original function is <literal>f</literal> then the pragma
7585 {-# SPECIALIZE f :: <type> #-}
7587 is valid if and only if the definition
7589 f_spec :: <type>
7592 is valid. Here are some examples (where we only give the type signature
7593 for the original function, not its code):
7595 f :: Eq a => a -> b -> b
7596 {-# SPECIALISE f :: Int -> b -> b #-}
7598 g :: (Eq a, Ix b) => a -> b -> b
7599 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7601 h :: Eq a => a -> a -> a
7602 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7604 The last of these examples will generate a
7605 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7606 well. If you use this kind of specialisation, let us know how well it works.
7609 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7610 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7611 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7612 The <literal>INLINE</literal> pragma affects the specialised version of the
7613 function (only), and applies even if the function is recursive. The motivating
7616 -- A GADT for arrays with type-indexed representation
7618 ArrInt :: !Int -> ByteArray# -> Arr Int
7619 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7621 (!:) :: Arr e -> Int -> e
7622 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7623 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7624 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7625 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7627 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7628 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7629 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7630 the specialised function will be inlined. It has two calls to
7631 <literal>(!:)</literal>,
7632 both at type <literal>Int</literal>. Both these calls fire the first
7633 specialisation, whose body is also inlined. The result is a type-based
7634 unrolling of the indexing function.</para>
7635 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7636 on an ordinarily-recursive function.</para>
7638 <para>Note: In earlier versions of GHC, it was possible to provide your own
7639 specialised function for a given type:
7642 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7645 This feature has been removed, as it is now subsumed by the
7646 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7650 <sect2 id="specialize-instance-pragma">
7651 <title>SPECIALIZE instance pragma
7655 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7656 <indexterm><primary>overloading, death to</primary></indexterm>
7657 Same idea, except for instance declarations. For example:
7660 instance (Eq a) => Eq (Foo a) where {
7661 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7665 The pragma must occur inside the <literal>where</literal> part
7666 of the instance declaration.
7669 Compatible with HBC, by the way, except perhaps in the placement
7675 <sect2 id="unpack-pragma">
7676 <title>UNPACK pragma</title>
7678 <indexterm><primary>UNPACK</primary></indexterm>
7680 <para>The <literal>UNPACK</literal> indicates to the compiler
7681 that it should unpack the contents of a constructor field into
7682 the constructor itself, removing a level of indirection. For
7686 data T = T {-# UNPACK #-} !Float
7687 {-# UNPACK #-} !Float
7690 <para>will create a constructor <literal>T</literal> containing
7691 two unboxed floats. This may not always be an optimisation: if
7692 the <function>T</function> constructor is scrutinised and the
7693 floats passed to a non-strict function for example, they will
7694 have to be reboxed (this is done automatically by the
7697 <para>Unpacking constructor fields should only be used in
7698 conjunction with <option>-O</option>, in order to expose
7699 unfoldings to the compiler so the reboxing can be removed as
7700 often as possible. For example:</para>
7704 f (T f1 f2) = f1 + f2
7707 <para>The compiler will avoid reboxing <function>f1</function>
7708 and <function>f2</function> by inlining <function>+</function>
7709 on floats, but only when <option>-O</option> is on.</para>
7711 <para>Any single-constructor data is eligible for unpacking; for
7715 data T = T {-# UNPACK #-} !(Int,Int)
7718 <para>will store the two <literal>Int</literal>s directly in the
7719 <function>T</function> constructor, by flattening the pair.
7720 Multi-level unpacking is also supported:
7723 data T = T {-# UNPACK #-} !S
7724 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7727 will store two unboxed <literal>Int#</literal>s
7728 directly in the <function>T</function> constructor. The
7729 unpacker can see through newtypes, too.</para>
7731 <para>If a field cannot be unpacked, you will not get a warning,
7732 so it might be an idea to check the generated code with
7733 <option>-ddump-simpl</option>.</para>
7735 <para>See also the <option>-funbox-strict-fields</option> flag,
7736 which essentially has the effect of adding
7737 <literal>{-# UNPACK #-}</literal> to every strict
7738 constructor field.</para>
7741 <sect2 id="source-pragma">
7742 <title>SOURCE pragma</title>
7744 <indexterm><primary>SOURCE</primary></indexterm>
7745 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7746 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7752 <!-- ======================= REWRITE RULES ======================== -->
7754 <sect1 id="rewrite-rules">
7755 <title>Rewrite rules
7757 <indexterm><primary>RULES pragma</primary></indexterm>
7758 <indexterm><primary>pragma, RULES</primary></indexterm>
7759 <indexterm><primary>rewrite rules</primary></indexterm></title>
7762 The programmer can specify rewrite rules as part of the source program
7768 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7773 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7774 If you need more information, then <option>-ddump-rule-firings</option> shows you
7775 each individual rule firing in detail.
7779 <title>Syntax</title>
7782 From a syntactic point of view:
7788 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7789 may be generated by the layout rule).
7795 The layout rule applies in a pragma.
7796 Currently no new indentation level
7797 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7798 you must lay out the starting in the same column as the enclosing definitions.
7801 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7802 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7805 Furthermore, the closing <literal>#-}</literal>
7806 should start in a column to the right of the opening <literal>{-#</literal>.
7812 Each rule has a name, enclosed in double quotes. The name itself has
7813 no significance at all. It is only used when reporting how many times the rule fired.
7819 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7820 immediately after the name of the rule. Thus:
7823 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7826 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7827 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7836 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7837 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7838 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7839 by spaces, just like in a type <literal>forall</literal>.
7845 A pattern variable may optionally have a type signature.
7846 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7847 For example, here is the <literal>foldr/build</literal> rule:
7850 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7851 foldr k z (build g) = g k z
7854 Since <function>g</function> has a polymorphic type, it must have a type signature.
7861 The left hand side of a rule must consist of a top-level variable applied
7862 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7865 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7866 "wrong2" forall f. f True = True
7869 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7876 A rule does not need to be in the same module as (any of) the
7877 variables it mentions, though of course they need to be in scope.
7883 All rules are implicitly exported from the module, and are therefore
7884 in force in any module that imports the module that defined the rule, directly
7885 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7886 in force when compiling A.) The situation is very similar to that for instance
7894 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7895 any other flag settings. Furthermore, inside a RULE, the language extension
7896 <option>-XScopedTypeVariables</option> is automatically enabled; see
7897 <xref linkend="scoped-type-variables"/>.
7903 Like other pragmas, RULE pragmas are always checked for scope errors, and
7904 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7905 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7906 if the <option>-fenable-rewrite-rules</option> flag is
7907 on (see <xref linkend="rule-semantics"/>).
7916 <sect2 id="rule-semantics">
7917 <title>Semantics</title>
7920 From a semantic point of view:
7925 Rules are enabled (that is, used during optimisation)
7926 by the <option>-fenable-rewrite-rules</option> flag.
7927 This flag is implied by <option>-O</option>, and may be switched
7928 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7929 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7930 may not do what you expect, though, because without <option>-O</option> GHC
7931 ignores all optimisation information in interface files;
7932 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7933 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7934 has no effect on parsing or typechecking.
7940 Rules are regarded as left-to-right rewrite rules.
7941 When GHC finds an expression that is a substitution instance of the LHS
7942 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7943 By "a substitution instance" we mean that the LHS can be made equal to the
7944 expression by substituting for the pattern variables.
7951 GHC makes absolutely no attempt to verify that the LHS and RHS
7952 of a rule have the same meaning. That is undecidable in general, and
7953 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7960 GHC makes no attempt to make sure that the rules are confluent or
7961 terminating. For example:
7964 "loop" forall x y. f x y = f y x
7967 This rule will cause the compiler to go into an infinite loop.
7974 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7980 GHC currently uses a very simple, syntactic, matching algorithm
7981 for matching a rule LHS with an expression. It seeks a substitution
7982 which makes the LHS and expression syntactically equal modulo alpha
7983 conversion. The pattern (rule), but not the expression, is eta-expanded if
7984 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7985 But not beta conversion (that's called higher-order matching).
7989 Matching is carried out on GHC's intermediate language, which includes
7990 type abstractions and applications. So a rule only matches if the
7991 types match too. See <xref linkend="rule-spec"/> below.
7997 GHC keeps trying to apply the rules as it optimises the program.
7998 For example, consider:
8007 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8008 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8009 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8010 not be substituted, and the rule would not fire.
8017 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8018 results. Consider this (artificial) example
8021 {-# RULES "f" f True = False #-}
8027 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8032 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8034 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8035 would have been a better chance that <literal>f</literal>'s RULE might fire.
8038 The way to get predictable behaviour is to use a NOINLINE
8039 pragma on <literal>f</literal>, to ensure
8040 that it is not inlined until its RULEs have had a chance to fire.
8050 <title>List fusion</title>
8053 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8054 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8055 intermediate list should be eliminated entirely.
8059 The following are good producers:
8071 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8077 Explicit lists (e.g. <literal>[True, False]</literal>)
8083 The cons constructor (e.g <literal>3:4:[]</literal>)
8089 <function>++</function>
8095 <function>map</function>
8101 <function>take</function>, <function>filter</function>
8107 <function>iterate</function>, <function>repeat</function>
8113 <function>zip</function>, <function>zipWith</function>
8122 The following are good consumers:
8134 <function>array</function> (on its second argument)
8140 <function>++</function> (on its first argument)
8146 <function>foldr</function>
8152 <function>map</function>
8158 <function>take</function>, <function>filter</function>
8164 <function>concat</function>
8170 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8176 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8177 will fuse with one but not the other)
8183 <function>partition</function>
8189 <function>head</function>
8195 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8201 <function>sequence_</function>
8207 <function>msum</function>
8213 <function>sortBy</function>
8222 So, for example, the following should generate no intermediate lists:
8225 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8231 This list could readily be extended; if there are Prelude functions that you use
8232 a lot which are not included, please tell us.
8236 If you want to write your own good consumers or producers, look at the
8237 Prelude definitions of the above functions to see how to do so.
8242 <sect2 id="rule-spec">
8243 <title>Specialisation
8247 Rewrite rules can be used to get the same effect as a feature
8248 present in earlier versions of GHC.
8249 For example, suppose that:
8252 genericLookup :: Ord a => Table a b -> a -> b
8253 intLookup :: Table Int b -> Int -> b
8256 where <function>intLookup</function> is an implementation of
8257 <function>genericLookup</function> that works very fast for
8258 keys of type <literal>Int</literal>. You might wish
8259 to tell GHC to use <function>intLookup</function> instead of
8260 <function>genericLookup</function> whenever the latter was called with
8261 type <literal>Table Int b -> Int -> b</literal>.
8262 It used to be possible to write
8265 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8268 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8271 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8274 This slightly odd-looking rule instructs GHC to replace
8275 <function>genericLookup</function> by <function>intLookup</function>
8276 <emphasis>whenever the types match</emphasis>.
8277 What is more, this rule does not need to be in the same
8278 file as <function>genericLookup</function>, unlike the
8279 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8280 have an original definition available to specialise).
8283 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8284 <function>intLookup</function> really behaves as a specialised version
8285 of <function>genericLookup</function>!!!</para>
8287 <para>An example in which using <literal>RULES</literal> for
8288 specialisation will Win Big:
8291 toDouble :: Real a => a -> Double
8292 toDouble = fromRational . toRational
8294 {-# RULES "toDouble/Int" toDouble = i2d #-}
8295 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8298 The <function>i2d</function> function is virtually one machine
8299 instruction; the default conversion—via an intermediate
8300 <literal>Rational</literal>—is obscenely expensive by
8307 <title>Controlling what's going on</title>
8315 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8321 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8322 If you add <option>-dppr-debug</option> you get a more detailed listing.
8328 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8331 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8332 {-# INLINE build #-}
8336 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8337 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8338 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8339 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8346 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8347 see how to write rules that will do fusion and yet give an efficient
8348 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8358 <sect2 id="core-pragma">
8359 <title>CORE pragma</title>
8361 <indexterm><primary>CORE pragma</primary></indexterm>
8362 <indexterm><primary>pragma, CORE</primary></indexterm>
8363 <indexterm><primary>core, annotation</primary></indexterm>
8366 The external core format supports <quote>Note</quote> annotations;
8367 the <literal>CORE</literal> pragma gives a way to specify what these
8368 should be in your Haskell source code. Syntactically, core
8369 annotations are attached to expressions and take a Haskell string
8370 literal as an argument. The following function definition shows an
8374 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8377 Semantically, this is equivalent to:
8385 However, when external core is generated (via
8386 <option>-fext-core</option>), there will be Notes attached to the
8387 expressions <function>show</function> and <varname>x</varname>.
8388 The core function declaration for <function>f</function> is:
8392 f :: %forall a . GHCziShow.ZCTShow a ->
8393 a -> GHCziBase.ZMZN GHCziBase.Char =
8394 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8396 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8398 (tpl1::GHCziBase.Int ->
8400 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8402 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8403 (tpl3::GHCziBase.ZMZN a ->
8404 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8412 Here, we can see that the function <function>show</function> (which
8413 has been expanded out to a case expression over the Show dictionary)
8414 has a <literal>%note</literal> attached to it, as does the
8415 expression <varname>eta</varname> (which used to be called
8416 <varname>x</varname>).
8423 <sect1 id="special-ids">
8424 <title>Special built-in functions</title>
8425 <para>GHC has a few built-in functions with special behaviour. These
8426 are now described in the module <ulink
8427 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8428 in the library documentation.</para>
8432 <sect1 id="generic-classes">
8433 <title>Generic classes</title>
8436 The ideas behind this extension are described in detail in "Derivable type classes",
8437 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8438 An example will give the idea:
8446 fromBin :: [Int] -> (a, [Int])
8448 toBin {| Unit |} Unit = []
8449 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8450 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8451 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8453 fromBin {| Unit |} bs = (Unit, bs)
8454 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8455 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8456 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8457 (y,bs'') = fromBin bs'
8460 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8461 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8462 which are defined thus in the library module <literal>Generics</literal>:
8466 data a :+: b = Inl a | Inr b
8467 data a :*: b = a :*: b
8470 Now you can make a data type into an instance of Bin like this:
8472 instance (Bin a, Bin b) => Bin (a,b)
8473 instance Bin a => Bin [a]
8475 That is, just leave off the "where" clause. Of course, you can put in the
8476 where clause and over-ride whichever methods you please.
8480 <title> Using generics </title>
8481 <para>To use generics you need to</para>
8484 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8485 <option>-XGenerics</option> (to generate extra per-data-type code),
8486 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8490 <para>Import the module <literal>Generics</literal> from the
8491 <literal>lang</literal> package. This import brings into
8492 scope the data types <literal>Unit</literal>,
8493 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8494 don't need this import if you don't mention these types
8495 explicitly; for example, if you are simply giving instance
8496 declarations.)</para>
8501 <sect2> <title> Changes wrt the paper </title>
8503 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8504 can be written infix (indeed, you can now use
8505 any operator starting in a colon as an infix type constructor). Also note that
8506 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8507 Finally, note that the syntax of the type patterns in the class declaration
8508 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8509 alone would ambiguous when they appear on right hand sides (an extension we
8510 anticipate wanting).
8514 <sect2> <title>Terminology and restrictions</title>
8516 Terminology. A "generic default method" in a class declaration
8517 is one that is defined using type patterns as above.
8518 A "polymorphic default method" is a default method defined as in Haskell 98.
8519 A "generic class declaration" is a class declaration with at least one
8520 generic default method.
8528 Alas, we do not yet implement the stuff about constructor names and
8535 A generic class can have only one parameter; you can't have a generic
8536 multi-parameter class.
8542 A default method must be defined entirely using type patterns, or entirely
8543 without. So this is illegal:
8546 op :: a -> (a, Bool)
8547 op {| Unit |} Unit = (Unit, True)
8550 However it is perfectly OK for some methods of a generic class to have
8551 generic default methods and others to have polymorphic default methods.
8557 The type variable(s) in the type pattern for a generic method declaration
8558 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:
8562 op {| p :*: q |} (x :*: y) = op (x :: p)
8570 The type patterns in a generic default method must take one of the forms:
8576 where "a" and "b" are type variables. Furthermore, all the type patterns for
8577 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8578 must use the same type variables. So this is illegal:
8582 op {| a :+: b |} (Inl x) = True
8583 op {| p :+: q |} (Inr y) = False
8585 The type patterns must be identical, even in equations for different methods of the class.
8586 So this too is illegal:
8590 op1 {| a :*: b |} (x :*: y) = True
8593 op2 {| p :*: q |} (x :*: y) = False
8595 (The reason for this restriction is that we gather all the equations for a particular type constructor
8596 into a single generic instance declaration.)
8602 A generic method declaration must give a case for each of the three type constructors.
8608 The type for a generic method can be built only from:
8610 <listitem> <para> Function arrows </para> </listitem>
8611 <listitem> <para> Type variables </para> </listitem>
8612 <listitem> <para> Tuples </para> </listitem>
8613 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8615 Here are some example type signatures for generic methods:
8618 op2 :: Bool -> (a,Bool)
8619 op3 :: [Int] -> a -> a
8622 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8626 This restriction is an implementation restriction: we just haven't got around to
8627 implementing the necessary bidirectional maps over arbitrary type constructors.
8628 It would be relatively easy to add specific type constructors, such as Maybe and list,
8629 to the ones that are allowed.</para>
8634 In an instance declaration for a generic class, the idea is that the compiler
8635 will fill in the methods for you, based on the generic templates. However it can only
8640 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8645 No constructor of the instance type has unboxed fields.
8649 (Of course, these things can only arise if you are already using GHC extensions.)
8650 However, you can still give an instance declarations for types which break these rules,
8651 provided you give explicit code to override any generic default methods.
8659 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8660 what the compiler does with generic declarations.
8665 <sect2> <title> Another example </title>
8667 Just to finish with, here's another example I rather like:
8671 nCons {| Unit |} _ = 1
8672 nCons {| a :*: b |} _ = 1
8673 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8676 tag {| Unit |} _ = 1
8677 tag {| a :*: b |} _ = 1
8678 tag {| a :+: b |} (Inl x) = tag x
8679 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8685 <sect1 id="monomorphism">
8686 <title>Control over monomorphism</title>
8688 <para>GHC supports two flags that control the way in which generalisation is
8689 carried out at let and where bindings.
8693 <title>Switching off the dreaded Monomorphism Restriction</title>
8694 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8696 <para>Haskell's monomorphism restriction (see
8697 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8699 of the Haskell Report)
8700 can be completely switched off by
8701 <option>-XNoMonomorphismRestriction</option>.
8706 <title>Monomorphic pattern bindings</title>
8707 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8708 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8710 <para> As an experimental change, we are exploring the possibility of
8711 making pattern bindings monomorphic; that is, not generalised at all.
8712 A pattern binding is a binding whose LHS has no function arguments,
8713 and is not a simple variable. For example:
8715 f x = x -- Not a pattern binding
8716 f = \x -> x -- Not a pattern binding
8717 f :: Int -> Int = \x -> x -- Not a pattern binding
8719 (g,h) = e -- A pattern binding
8720 (f) = e -- A pattern binding
8721 [x] = e -- A pattern binding
8723 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8724 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
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