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 flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individually.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMagicHash</option>:
137 <para> Allow "#" as a <link linkend="magic-hash">postfix modifier on identifiers</link>.
144 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
147 <para> These two flags control how generalisation is done.
148 See <xref linkend="monomorphism"/>.
155 <option>-XExtendedDefaultRules</option>:
156 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
159 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
160 Independent of the <option>-fglasgow-exts</option>
167 <option>-XOverlappingInstances</option>
168 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
171 <option>-XUndecidableInstances</option>
172 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
175 <option>-XIncoherentInstances</option>
176 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
179 <option>-fcontext-stack=N</option>
180 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
183 <para> See <xref linkend="instance-decls"/>. Only relevant
184 if you also use <option>-fglasgow-exts</option>.</para>
190 <option>-finline-phase</option>
191 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
194 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
195 you also use <option>-fglasgow-exts</option>.</para>
201 <option>-XArrows</option>
202 <indexterm><primary><option>-XArrows</option></primary></indexterm>
205 <para>See <xref linkend="arrow-notation"/>. Independent of
206 <option>-fglasgow-exts</option>.</para>
208 <para>New reserved words/symbols: <literal>rec</literal>,
209 <literal>proc</literal>, <literal>-<</literal>,
210 <literal>>-</literal>, <literal>-<<</literal>,
211 <literal>>>-</literal>.</para>
213 <para>Other syntax stolen: <literal>(|</literal>,
214 <literal>|)</literal>.</para>
220 <option>-XGenerics</option>
221 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
224 <para>See <xref linkend="generic-classes"/>. Independent of
225 <option>-fglasgow-exts</option>.</para>
230 <term><option>-XNoImplicitPrelude</option></term>
232 <para><indexterm><primary>-XNoImplicitPrelude
233 option</primary></indexterm> GHC normally imports
234 <filename>Prelude.hi</filename> files for you. If you'd
235 rather it didn't, then give it a
236 <option>-XNoImplicitPrelude</option> option. The idea is
237 that you can then import a Prelude of your own. (But don't
238 call it <literal>Prelude</literal>; the Haskell module
239 namespace is flat, and you must not conflict with any
240 Prelude module.)</para>
242 <para>Even though you have not imported the Prelude, most of
243 the built-in syntax still refers to the built-in Haskell
244 Prelude types and values, as specified by the Haskell
245 Report. For example, the type <literal>[Int]</literal>
246 still means <literal>Prelude.[] Int</literal>; tuples
247 continue to refer to the standard Prelude tuples; the
248 translation for list comprehensions continues to use
249 <literal>Prelude.map</literal> etc.</para>
251 <para>However, <option>-XNoImplicitPrelude</option> does
252 change the handling of certain built-in syntax: see <xref
253 linkend="rebindable-syntax"/>.</para>
258 <term><option>-XImplicitParams</option></term>
260 <para>Enables implicit parameters (see <xref
261 linkend="implicit-parameters"/>). Currently also implied by
262 <option>-fglasgow-exts</option>.</para>
265 <literal>?<replaceable>varid</replaceable></literal>,
266 <literal>%<replaceable>varid</replaceable></literal>.</para>
271 <term><option>-XOverloadedStrings</option></term>
273 <para>Enables overloaded string literals (see <xref
274 linkend="overloaded-strings"/>).</para>
279 <term><option>-XScopedTypeVariables</option></term>
281 <para>Enables lexically-scoped type variables (see <xref
282 linkend="scoped-type-variables"/>). Implied by
283 <option>-fglasgow-exts</option>.</para>
288 <term><option>-XTemplateHaskell</option></term>
290 <para>Enables Template Haskell (see <xref
291 linkend="template-haskell"/>). This flag must
292 be given explicitly; it is no longer implied by
293 <option>-fglasgow-exts</option>.</para>
295 <para>Syntax stolen: <literal>[|</literal>,
296 <literal>[e|</literal>, <literal>[p|</literal>,
297 <literal>[d|</literal>, <literal>[t|</literal>,
298 <literal>$(</literal>,
299 <literal>$<replaceable>varid</replaceable></literal>.</para>
304 <term><option>-XQuasiQuotes</option></term>
306 <para>Enables quasiquotation (see <xref
307 linkend="th-quasiquotation"/>).</para>
310 <literal>[:<replaceable>varid</replaceable>|</literal>.</para>
317 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
318 <sect1 id="primitives">
319 <title>Unboxed types and primitive operations</title>
321 <para>GHC is built on a raft of primitive data types and operations;
322 "primitive" in the sense that they cannot be defined in Haskell itself.
323 While you really can use this stuff to write fast code,
324 we generally find it a lot less painful, and more satisfying in the
325 long run, to use higher-level language features and libraries. With
326 any luck, the code you write will be optimised to the efficient
327 unboxed version in any case. And if it isn't, we'd like to know
330 <para>All these primitive data types and operations are exported by the
331 library <literal>GHC.Prim</literal>, for which there is
332 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
333 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
336 If you want to mention any of the primitive data types or operations in your
337 program, you must first import <literal>GHC.Prim</literal> to bring them
338 into scope. Many of them have names ending in "#", and to mention such
339 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
342 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
343 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
344 we briefly summarise here. </para>
346 <sect2 id="glasgow-unboxed">
351 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
354 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
355 that values of that type are represented by a pointer to a heap
356 object. The representation of a Haskell <literal>Int</literal>, for
357 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
358 type, however, is represented by the value itself, no pointers or heap
359 allocation are involved.
363 Unboxed types correspond to the “raw machine” types you
364 would use in C: <literal>Int#</literal> (long int),
365 <literal>Double#</literal> (double), <literal>Addr#</literal>
366 (void *), etc. The <emphasis>primitive operations</emphasis>
367 (PrimOps) on these types are what you might expect; e.g.,
368 <literal>(+#)</literal> is addition on
369 <literal>Int#</literal>s, and is the machine-addition that we all
370 know and love—usually one instruction.
374 Primitive (unboxed) types cannot be defined in Haskell, and are
375 therefore built into the language and compiler. Primitive types are
376 always unlifted; that is, a value of a primitive type cannot be
377 bottom. We use the convention (but it is only a convention)
378 that primitive types, values, and
379 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
380 For some primitive types we have special syntax for literals, also
381 described in the <link linkend="magic-hash">same section</link>.
385 Primitive values are often represented by a simple bit-pattern, such
386 as <literal>Int#</literal>, <literal>Float#</literal>,
387 <literal>Double#</literal>. But this is not necessarily the case:
388 a primitive value might be represented by a pointer to a
389 heap-allocated object. Examples include
390 <literal>Array#</literal>, the type of primitive arrays. A
391 primitive array is heap-allocated because it is too big a value to fit
392 in a register, and would be too expensive to copy around; in a sense,
393 it is accidental that it is represented by a pointer. If a pointer
394 represents a primitive value, then it really does point to that value:
395 no unevaluated thunks, no indirections…nothing can be at the
396 other end of the pointer than the primitive value.
397 A numerically-intensive program using unboxed types can
398 go a <emphasis>lot</emphasis> faster than its “standard”
399 counterpart—we saw a threefold speedup on one example.
403 There are some restrictions on the use of primitive types:
405 <listitem><para>The main restriction
406 is that you can't pass a primitive value to a polymorphic
407 function or store one in a polymorphic data type. This rules out
408 things like <literal>[Int#]</literal> (i.e. lists of primitive
409 integers). The reason for this restriction is that polymorphic
410 arguments and constructor fields are assumed to be pointers: if an
411 unboxed integer is stored in one of these, the garbage collector would
412 attempt to follow it, leading to unpredictable space leaks. Or a
413 <function>seq</function> operation on the polymorphic component may
414 attempt to dereference the pointer, with disastrous results. Even
415 worse, the unboxed value might be larger than a pointer
416 (<literal>Double#</literal> for instance).
419 <listitem><para> You cannot define a newtype whose representation type
420 (the argument type of the data constructor) is an unboxed type. Thus,
426 <listitem><para> You cannot bind a variable with an unboxed type
427 in a <emphasis>top-level</emphasis> binding.
429 <listitem><para> You cannot bind a variable with an unboxed type
430 in a <emphasis>recursive</emphasis> binding.
432 <listitem><para> You may bind unboxed variables in a (non-recursive,
433 non-top-level) pattern binding, but any such variable causes the entire
435 to become strict. For example:
437 data Foo = Foo Int Int#
439 f x = let (Foo a b, w) = ..rhs.. in ..body..
441 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
443 is strict, and the program behaves as if you had written
445 data Foo = Foo Int Int#
447 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
456 <sect2 id="unboxed-tuples">
457 <title>Unboxed Tuples
461 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
462 they're available by default with <option>-fglasgow-exts</option>. An
463 unboxed tuple looks like this:
475 where <literal>e_1..e_n</literal> are expressions of any
476 type (primitive or non-primitive). The type of an unboxed tuple looks
481 Unboxed tuples are used for functions that need to return multiple
482 values, but they avoid the heap allocation normally associated with
483 using fully-fledged tuples. When an unboxed tuple is returned, the
484 components are put directly into registers or on the stack; the
485 unboxed tuple itself does not have a composite representation. Many
486 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
488 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
489 tuples to avoid unnecessary allocation during sequences of operations.
493 There are some pretty stringent restrictions on the use of unboxed tuples:
498 Values of unboxed tuple types are subject to the same restrictions as
499 other unboxed types; i.e. they may not be stored in polymorphic data
500 structures or passed to polymorphic functions.
507 No variable can have an unboxed tuple type, nor may a constructor or function
508 argument have an unboxed tuple type. The following are all illegal:
512 data Foo = Foo (# Int, Int #)
514 f :: (# Int, Int #) -> (# Int, Int #)
517 g :: (# Int, Int #) -> Int
520 h x = let y = (# x,x #) in ...
527 The typical use of unboxed tuples is simply to return multiple values,
528 binding those multiple results with a <literal>case</literal> expression, thus:
530 f x y = (# x+1, y-1 #)
531 g x = case f x x of { (# a, b #) -> a + b }
533 You can have an unboxed tuple in a pattern binding, thus
535 f x = let (# p,q #) = h x in ..body..
537 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
538 the resulting binding is lazy like any other Haskell pattern binding. The
539 above example desugars like this:
541 f x = let t = case h x o f{ (# p,q #) -> (p,q)
546 Indeed, the bindings can even be recursive.
553 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
555 <sect1 id="syntax-extns">
556 <title>Syntactic extensions</title>
558 <sect2 id="magic-hash">
559 <title>The magic hash</title>
560 <para>The language extension <option>-XMagicHash</option> allows "#" as a
561 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
562 a valid type constructor or data constructor.</para>
564 <para>The hash sign does not change sematics at all. We tend to use variable
565 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
566 but there is no requirement to do so; they are just plain ordinary variables.
567 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
568 For example, to bring <literal>Int#</literal> into scope you must
569 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
570 the <option>-XMagicHash</option> extension
571 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
572 that is now in scope.</para>
573 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
575 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
576 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
577 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
578 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
579 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
580 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
581 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
582 is a <literal>Word#</literal>. </para> </listitem>
583 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
584 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
589 <!-- ====================== HIERARCHICAL MODULES ======================= -->
592 <sect2 id="hierarchical-modules">
593 <title>Hierarchical Modules</title>
595 <para>GHC supports a small extension to the syntax of module
596 names: a module name is allowed to contain a dot
597 <literal>‘.’</literal>. This is also known as the
598 “hierarchical module namespace” extension, because
599 it extends the normally flat Haskell module namespace into a
600 more flexible hierarchy of modules.</para>
602 <para>This extension has very little impact on the language
603 itself; modules names are <emphasis>always</emphasis> fully
604 qualified, so you can just think of the fully qualified module
605 name as <quote>the module name</quote>. In particular, this
606 means that the full module name must be given after the
607 <literal>module</literal> keyword at the beginning of the
608 module; for example, the module <literal>A.B.C</literal> must
611 <programlisting>module A.B.C</programlisting>
614 <para>It is a common strategy to use the <literal>as</literal>
615 keyword to save some typing when using qualified names with
616 hierarchical modules. For example:</para>
619 import qualified Control.Monad.ST.Strict as ST
622 <para>For details on how GHC searches for source and interface
623 files in the presence of hierarchical modules, see <xref
624 linkend="search-path"/>.</para>
626 <para>GHC comes with a large collection of libraries arranged
627 hierarchically; see the accompanying <ulink
628 url="../libraries/index.html">library
629 documentation</ulink>. More libraries to install are available
631 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
634 <!-- ====================== PATTERN GUARDS ======================= -->
636 <sect2 id="pattern-guards">
637 <title>Pattern guards</title>
640 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
641 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.)
645 Suppose we have an abstract data type of finite maps, with a
649 lookup :: FiniteMap -> Int -> Maybe Int
652 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
653 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
657 clunky env var1 var2 | ok1 && ok2 = val1 + val2
658 | otherwise = var1 + var2
669 The auxiliary functions are
673 maybeToBool :: Maybe a -> Bool
674 maybeToBool (Just x) = True
675 maybeToBool Nothing = False
677 expectJust :: Maybe a -> a
678 expectJust (Just x) = x
679 expectJust Nothing = error "Unexpected Nothing"
683 What is <function>clunky</function> doing? The guard <literal>ok1 &&
684 ok2</literal> checks that both lookups succeed, using
685 <function>maybeToBool</function> to convert the <function>Maybe</function>
686 types to booleans. The (lazily evaluated) <function>expectJust</function>
687 calls extract the values from the results of the lookups, and binds the
688 returned values to <varname>val1</varname> and <varname>val2</varname>
689 respectively. If either lookup fails, then clunky takes the
690 <literal>otherwise</literal> case and returns the sum of its arguments.
694 This is certainly legal Haskell, but it is a tremendously verbose and
695 un-obvious way to achieve the desired effect. Arguably, a more direct way
696 to write clunky would be to use case expressions:
700 clunky env var1 var2 = case lookup env var1 of
702 Just val1 -> case lookup env var2 of
704 Just val2 -> val1 + val2
710 This is a bit shorter, but hardly better. Of course, we can rewrite any set
711 of pattern-matching, guarded equations as case expressions; that is
712 precisely what the compiler does when compiling equations! The reason that
713 Haskell provides guarded equations is because they allow us to write down
714 the cases we want to consider, one at a time, independently of each other.
715 This structure is hidden in the case version. Two of the right-hand sides
716 are really the same (<function>fail</function>), and the whole expression
717 tends to become more and more indented.
721 Here is how I would write clunky:
726 | Just val1 <- lookup env var1
727 , Just val2 <- lookup env var2
729 ...other equations for clunky...
733 The semantics should be clear enough. The qualifiers are matched in order.
734 For a <literal><-</literal> qualifier, which I call a pattern guard, the
735 right hand side is evaluated and matched against the pattern on the left.
736 If the match fails then the whole guard fails and the next equation is
737 tried. If it succeeds, then the appropriate binding takes place, and the
738 next qualifier is matched, in the augmented environment. Unlike list
739 comprehensions, however, the type of the expression to the right of the
740 <literal><-</literal> is the same as the type of the pattern to its
741 left. The bindings introduced by pattern guards scope over all the
742 remaining guard qualifiers, and over the right hand side of the equation.
746 Just as with list comprehensions, boolean expressions can be freely mixed
747 with among the pattern guards. For example:
758 Haskell's current guards therefore emerge as a special case, in which the
759 qualifier list has just one element, a boolean expression.
763 <!-- ===================== View patterns =================== -->
765 <sect2 id="view-patterns">
770 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
771 More information and examples of view patterns can be found on the
772 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
777 View patterns are somewhat like pattern guards that can be nested inside
778 of other patterns. They are a convenient way of pattern-matching
779 against values of abstract types. For example, in a programming language
780 implementation, we might represent the syntax of the types of the
789 view :: Type -> TypeView
791 -- additional operations for constructing Typ's ...
794 The representation of Typ is held abstract, permitting implementations
795 to use a fancy representation (e.g., hash-consing to manage sharing).
797 Without view patterns, using this signature a little inconvenient:
799 size :: Typ -> Integer
800 size t = case view t of
802 Arrow t1 t2 -> size t1 + size t2
805 It is necessary to iterate the case, rather than using an equational
806 function definition. And the situation is even worse when the matching
807 against <literal>t</literal> is buried deep inside another pattern.
811 View patterns permit calling the view function inside the pattern and
812 matching against the result:
814 size (view -> Unit) = 1
815 size (view -> Arrow t1 t2) = size t1 + size t2
818 That is, we add a new form of pattern, written
819 <replaceable>expression</replaceable> <literal>-></literal>
820 <replaceable>pattern</replaceable> that means "apply the expression to
821 whatever we're trying to match against, and then match the result of
822 that application against the pattern". The expression can be any Haskell
823 expression of function type, and view patterns can be used wherever
828 The semantics of a pattern <literal>(</literal>
829 <replaceable>exp</replaceable> <literal>-></literal>
830 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
836 <para>The variables bound by the view pattern are the variables bound by
837 <replaceable>pat</replaceable>.
841 Any variables in <replaceable>exp</replaceable> are bound occurrences,
842 but variables bound "to the left" in a pattern are in scope. This
843 feature permits, for example, one argument to a function to be used in
844 the view of another argument. For example, the function
845 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
846 written using view patterns as follows:
849 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
850 ...other equations for clunky...
855 More precisely, the scoping rules are:
859 In a single pattern, variables bound by patterns to the left of a view
860 pattern expression are in scope. For example:
862 example :: Maybe ((String -> Integer,Integer), String) -> Bool
863 example Just ((f,_), f -> 4) = True
866 Additionally, in function definitions, variables bound by matching earlier curried
867 arguments may be used in view pattern expressions in later arguments:
869 example :: (String -> Integer) -> String -> Bool
870 example f (f -> 4) = True
872 That is, the scoping is the same as it would be if the curried arguments
873 were collected into a tuple.
879 In mutually recursive bindings, such as <literal>let</literal>,
880 <literal>where</literal>, or the top level, view patterns in one
881 declaration may not mention variables bound by other declarations. That
882 is, each declaration must be self-contained. For example, the following
883 program is not allowed:
890 restriction in the future; the only cost is that type checking patterns
891 would get a little more complicated.)
901 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
902 <replaceable>T1</replaceable> <literal>-></literal>
903 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
904 a <replaceable>T2</replaceable>, then the whole view pattern matches a
905 <replaceable>T1</replaceable>.
908 <listitem><para> Matching: To the equations in Section 3.17.3 of the
909 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
910 Report</ulink>, add the following:
912 case v of { (e -> p) -> e1 ; _ -> e2 }
914 case (e v) of { p -> e1 ; _ -> e2 }
916 That is, to match a variable <replaceable>v</replaceable> against a pattern
917 <literal>(</literal> <replaceable>exp</replaceable>
918 <literal>-></literal> <replaceable>pat</replaceable>
919 <literal>)</literal>, evaluate <literal>(</literal>
920 <replaceable>exp</replaceable> <replaceable> v</replaceable>
921 <literal>)</literal> and match the result against
922 <replaceable>pat</replaceable>.
925 <listitem><para> Efficiency: When the same view function is applied in
926 multiple branches of a function definition or a case expression (e.g.,
927 in <literal>size</literal> above), GHC makes an attempt to collect these
928 applications into a single nested case expression, so that the view
929 function is only applied once. Pattern compilation in GHC follows the
930 matrix algorithm described in Chapter 4 of <ulink
931 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
932 Implementation of Functional Programming Languages</ulink>. When the
933 top rows of the first column of a matrix are all view patterns with the
934 "same" expression, these patterns are transformed into a single nested
935 case. This includes, for example, adjacent view patterns that line up
938 f ((view -> A, p1), p2) = e1
939 f ((view -> B, p3), p4) = e2
943 <para> The current notion of when two view pattern expressions are "the
944 same" is very restricted: it is not even full syntactic equality.
945 However, it does include variables, literals, applications, and tuples;
946 e.g., two instances of <literal>view ("hi", "there")</literal> will be
947 collected. However, the current implementation does not compare up to
948 alpha-equivalence, so two instances of <literal>(x, view x ->
949 y)</literal> will not be coalesced.
959 <!-- ===================== Recursive do-notation =================== -->
961 <sect2 id="mdo-notation">
962 <title>The recursive do-notation
965 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
966 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
967 by Levent Erkok, John Launchbury,
968 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
969 This paper is essential reading for anyone making non-trivial use of mdo-notation,
970 and we do not repeat it here.
973 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
974 that is, the variables bound in a do-expression are visible only in the textually following
975 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
976 group. It turns out that several applications can benefit from recursive bindings in
977 the do-notation, and this extension provides the necessary syntactic support.
980 Here is a simple (yet contrived) example:
983 import Control.Monad.Fix
985 justOnes = mdo xs <- Just (1:xs)
989 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
993 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
996 class Monad m => MonadFix m where
997 mfix :: (a -> m a) -> m a
1000 The function <literal>mfix</literal>
1001 dictates how the required recursion operation should be performed. For example,
1002 <literal>justOnes</literal> desugars as follows:
1004 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
1006 For full details of the way in which mdo is typechecked and desugared, see
1007 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
1008 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
1011 If recursive bindings are required for a monad,
1012 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
1013 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1014 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
1015 for Haskell's internal state monad (strict and lazy, respectively).
1018 Here are some important points in using the recursive-do notation:
1021 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
1022 than <literal>do</literal>).
1026 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
1027 <literal>-fglasgow-exts</literal>.
1031 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
1032 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
1033 be distinct (Section 3.3 of the paper).
1037 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
1038 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
1039 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
1040 and improve termination (Section 3.2 of the paper).
1046 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb/">http://www.cse.ogi.edu/PacSoft/projects/rmb/</ulink>
1047 contains up to date information on recursive monadic bindings.
1051 Historical note: The old implementation of the mdo-notation (and most
1052 of the existing documents) used the name
1053 <literal>MonadRec</literal> for the class and the corresponding library.
1054 This name is not supported by GHC.
1060 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1062 <sect2 id="parallel-list-comprehensions">
1063 <title>Parallel List Comprehensions</title>
1064 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1066 <indexterm><primary>parallel list comprehensions</primary>
1069 <para>Parallel list comprehensions are a natural extension to list
1070 comprehensions. List comprehensions can be thought of as a nice
1071 syntax for writing maps and filters. Parallel comprehensions
1072 extend this to include the zipWith family.</para>
1074 <para>A parallel list comprehension has multiple independent
1075 branches of qualifier lists, each separated by a `|' symbol. For
1076 example, the following zips together two lists:</para>
1079 [ (x, y) | x <- xs | y <- ys ]
1082 <para>The behavior of parallel list comprehensions follows that of
1083 zip, in that the resulting list will have the same length as the
1084 shortest branch.</para>
1086 <para>We can define parallel list comprehensions by translation to
1087 regular comprehensions. Here's the basic idea:</para>
1089 <para>Given a parallel comprehension of the form: </para>
1092 [ e | p1 <- e11, p2 <- e12, ...
1093 | q1 <- e21, q2 <- e22, ...
1098 <para>This will be translated to: </para>
1101 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1102 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1107 <para>where `zipN' is the appropriate zip for the given number of
1112 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1114 <sect2 id="generalised-list-comprehensions">
1115 <title>Generalised (SQL-Like) List Comprehensions</title>
1116 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1118 <indexterm><primary>extended list comprehensions</primary>
1120 <indexterm><primary>group</primary></indexterm>
1121 <indexterm><primary>sql</primary></indexterm>
1124 <para>Generalised list comprehensions are a further enhancement to the
1125 list comprehension syntatic sugar to allow operations such as sorting
1126 and grouping which are familiar from SQL. They are fully described in the
1127 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1128 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1129 except that the syntax we use differs slightly from the paper.</para>
1130 <para>Here is an example:
1132 employees = [ ("Simon", "MS", 80)
1133 , ("Erik", "MS", 100)
1134 , ("Phil", "Ed", 40)
1135 , ("Gordon", "Ed", 45)
1136 , ("Paul", "Yale", 60)]
1138 output = [ (the dept, sum salary)
1139 | (name, dept, salary) <- employees
1140 , then group by dept
1141 , then sortWith by (sum salary)
1144 In this example, the list <literal>output</literal> would take on
1148 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1151 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1152 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1153 function that is exported by <literal>GHC.Exts</literal>.)</para>
1155 <para>There are five new forms of comprehension qualifier,
1156 all introduced by the (existing) keyword <literal>then</literal>:
1164 This statement requires that <literal>f</literal> have the type <literal>
1165 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1166 motivating example, as this form is used to apply <literal>take 5</literal>.
1177 This form is similar to the previous one, but allows you to create a function
1178 which will be passed as the first argument to f. As a consequence f must have
1179 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1180 from the type, this function lets f "project out" some information
1181 from the elements of the list it is transforming.</para>
1183 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1184 is supplied with a function that lets it find out the <literal>sum salary</literal>
1185 for any item in the list comprehension it transforms.</para>
1193 then group by e using f
1196 <para>This is the most general of the grouping-type statements. In this form,
1197 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1198 As with the <literal>then f by e</literal> case above, the first argument
1199 is a function supplied to f by the compiler which lets it compute e on every
1200 element of the list being transformed. However, unlike the non-grouping case,
1201 f additionally partitions the list into a number of sublists: this means that
1202 at every point after this statement, binders occurring before it in the comprehension
1203 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1204 this, let's look at an example:</para>
1207 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1208 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1209 groupRuns f = groupBy (\x y -> f x == f y)
1211 output = [ (the x, y)
1212 | x <- ([1..3] ++ [1..2])
1214 , then group by x using groupRuns ]
1217 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1220 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1223 <para>Note that we have used the <literal>the</literal> function to change the type
1224 of x from a list to its original numeric type. The variable y, in contrast, is left
1225 unchanged from the list form introduced by the grouping.</para>
1235 <para>This form of grouping is essentially the same as the one described above. However,
1236 since no function to use for the grouping has been supplied it will fall back on the
1237 <literal>groupWith</literal> function defined in
1238 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1239 is the form of the group statement that we made use of in the opening example.</para>
1250 <para>With this form of the group statement, f is required to simply have the type
1251 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1252 comprehension so far directly. An example of this form is as follows:</para>
1258 , then group using inits]
1261 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1264 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1272 <!-- ===================== REBINDABLE SYNTAX =================== -->
1274 <sect2 id="rebindable-syntax">
1275 <title>Rebindable syntax</title>
1277 <para>GHC allows most kinds of built-in syntax to be rebound by
1278 the user, to facilitate replacing the <literal>Prelude</literal>
1279 with a home-grown version, for example.</para>
1281 <para>You may want to define your own numeric class
1282 hierarchy. It completely defeats that purpose if the
1283 literal "1" means "<literal>Prelude.fromInteger
1284 1</literal>", which is what the Haskell Report specifies.
1285 So the <option>-XNoImplicitPrelude</option> flag causes
1286 the following pieces of built-in syntax to refer to
1287 <emphasis>whatever is in scope</emphasis>, not the Prelude
1292 <para>An integer literal <literal>368</literal> means
1293 "<literal>fromInteger (368::Integer)</literal>", rather than
1294 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1297 <listitem><para>Fractional literals are handed in just the same way,
1298 except that the translation is
1299 <literal>fromRational (3.68::Rational)</literal>.
1302 <listitem><para>The equality test in an overloaded numeric pattern
1303 uses whatever <literal>(==)</literal> is in scope.
1306 <listitem><para>The subtraction operation, and the
1307 greater-than-or-equal test, in <literal>n+k</literal> patterns
1308 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1312 <para>Negation (e.g. "<literal>- (f x)</literal>")
1313 means "<literal>negate (f x)</literal>", both in numeric
1314 patterns, and expressions.
1318 <para>"Do" notation is translated using whatever
1319 functions <literal>(>>=)</literal>,
1320 <literal>(>>)</literal>, and <literal>fail</literal>,
1321 are in scope (not the Prelude
1322 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1323 comprehensions, are unaffected. </para></listitem>
1327 notation (see <xref linkend="arrow-notation"/>)
1328 uses whatever <literal>arr</literal>,
1329 <literal>(>>>)</literal>, <literal>first</literal>,
1330 <literal>app</literal>, <literal>(|||)</literal> and
1331 <literal>loop</literal> functions are in scope. But unlike the
1332 other constructs, the types of these functions must match the
1333 Prelude types very closely. Details are in flux; if you want
1337 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1338 even if that is a little unexpected. For example, the
1339 static semantics of the literal <literal>368</literal>
1340 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1341 <literal>fromInteger</literal> to have any of the types:
1343 fromInteger :: Integer -> Integer
1344 fromInteger :: forall a. Foo a => Integer -> a
1345 fromInteger :: Num a => a -> Integer
1346 fromInteger :: Integer -> Bool -> Bool
1350 <para>Be warned: this is an experimental facility, with
1351 fewer checks than usual. Use <literal>-dcore-lint</literal>
1352 to typecheck the desugared program. If Core Lint is happy
1353 you should be all right.</para>
1357 <sect2 id="postfix-operators">
1358 <title>Postfix operators</title>
1361 GHC allows a small extension to the syntax of left operator sections, which
1362 allows you to define postfix operators. The extension is this: the left section
1366 is equivalent (from the point of view of both type checking and execution) to the expression
1370 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1371 The strict Haskell 98 interpretation is that the section is equivalent to
1375 That is, the operator must be a function of two arguments. GHC allows it to
1376 take only one argument, and that in turn allows you to write the function
1379 <para>Since this extension goes beyond Haskell 98, it should really be enabled
1380 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
1381 change their behaviour, of course.)
1383 <para>The extension does not extend to the left-hand side of function
1384 definitions; you must define such a function in prefix form.</para>
1388 <sect2 id="disambiguate-fields">
1389 <title>Record field disambiguation</title>
1391 In record construction and record pattern matching
1392 it is entirely unambiguous which field is referred to, even if there are two different
1393 data types in scope with a common field name. For example:
1396 data S = MkS { x :: Int, y :: Bool }
1401 data T = MkT { x :: Int }
1403 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1405 ok2 n = MkT { x = n+1 } -- Unambiguous
1407 bad1 k = k { x = 3 } -- Ambiguous
1408 bad2 k = x k -- Ambiguous
1410 Even though there are two <literal>x</literal>'s in scope,
1411 it is clear that the <literal>x</literal> in the pattern in the
1412 definition of <literal>ok1</literal> can only mean the field
1413 <literal>x</literal> from type <literal>S</literal>. Similarly for
1414 the function <literal>ok2</literal>. However, in the record update
1415 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1416 it is not clear which of the two types is intended.
1419 Haskell 98 regards all four as ambiguous, but with the
1420 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1421 the former two. The rules are precisely the same as those for instance
1422 declarations in Haskell 98, where the method names on the left-hand side
1423 of the method bindings in an instance declaration refer unambiguously
1424 to the method of that class (provided they are in scope at all), even
1425 if there are other variables in scope with the same name.
1426 This reduces the clutter of qualified names when you import two
1427 records from different modules that use the same field name.
1431 <!-- ===================== Record puns =================== -->
1433 <sect2 id="record-puns">
1438 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1442 When using records, it is common to write a pattern that binds a
1443 variable with the same name as a record field, such as:
1446 data C = C {a :: Int}
1452 Record punning permits the variable name to be elided, so one can simply
1459 to mean the same pattern as above. That is, in a record pattern, the
1460 pattern <literal>a</literal> expands into the pattern <literal>a =
1461 a</literal> for the same name <literal>a</literal>.
1465 Note that puns and other patterns can be mixed in the same record:
1467 data C = C {a :: Int, b :: Int}
1468 f (C {a, b = 4}) = a
1470 and that puns can be used wherever record patterns occur (e.g. in
1471 <literal>let</literal> bindings or at the top-level).
1475 Record punning can also be used in an expression, writing, for example,
1481 let a = 1 in C {a = a}
1484 Note that this expansion is purely syntactic, so the record pun
1485 expression refers to the nearest enclosing variable that is spelled the
1486 same as the field name.
1491 <!-- ===================== Record wildcards =================== -->
1493 <sect2 id="record-wildcards">
1494 <title>Record wildcards
1498 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1502 For records with many fields, it can be tiresome to write out each field
1503 individually in a record pattern, as in
1505 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1506 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1511 Record wildcard syntax permits a (<literal>..</literal>) in a record
1512 pattern, where each elided field <literal>f</literal> is replaced by the
1513 pattern <literal>f = f</literal>. For example, the above pattern can be
1516 f (C {a = 1, ..}) = b + c + d
1521 Note that wildcards can be mixed with other patterns, including puns
1522 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1523 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1524 wherever record patterns occur, including in <literal>let</literal>
1525 bindings and at the top-level. For example, the top-level binding
1529 defines <literal>b</literal>, <literal>c</literal>, and
1530 <literal>d</literal>.
1534 Record wildcards can also be used in expressions, writing, for example,
1537 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1543 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1546 Note that this expansion is purely syntactic, so the record wildcard
1547 expression refers to the nearest enclosing variables that are spelled
1548 the same as the omitted field names.
1553 <!-- ===================== Local fixity declarations =================== -->
1555 <sect2 id="local-fixity-declarations">
1556 <title>Local Fixity Declarations
1559 <para>A careful reading of the Haskell 98 Report reveals that fixity
1560 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1561 <literal>infixr</literal>) are permitted to appear inside local bindings
1562 such those introduced by <literal>let</literal> and
1563 <literal>where</literal>. However, the Haskell Report does not specify
1564 the semantics of such bindings very precisely.
1567 <para>In GHC, a fixity declaration may accompany a local binding:
1574 and the fixity declaration applies wherever the binding is in scope.
1575 For example, in a <literal>let</literal>, it applies in the right-hand
1576 sides of other <literal>let</literal>-bindings and the body of the
1577 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1578 expressions (<xref linkend="mdo-notation"/>), the local fixity
1579 declarations of a <literal>let</literal> statement scope over other
1580 statements in the group, just as the bound name does.
1584 Moreover, a local fixity declaration *must* accompany a local binding of
1585 that name: it is not possible to revise the fixity of name bound
1588 let infixr 9 $ in ...
1591 Because local fixity declarations are technically Haskell 98, no flag is
1592 necessary to enable them.
1596 <sect2 id="package-imports">
1597 <title>Package-qualified imports</title>
1599 <para>With the <option>-XPackageImports</option> flag, GHC allows
1600 import declarations to be qualified by the package name that the
1601 module is intended to be imported from. For example:</para>
1604 import "network" Network.Socket
1607 <para>would import the module <literal>Network.Socket</literal> from
1608 the package <literal>network</literal> (any version). This may
1609 be used to disambiguate an import when the same module is
1610 available from multiple packages, or is present in both the
1611 current package being built and an external package.</para>
1613 <para>Note: you probably don't need to use this feature, it was
1614 added mainly so that we can build backwards-compatible versions of
1615 packages when APIs change. It can lead to fragile dependencies in
1616 the common case: modules occasionally move from one package to
1617 another, rendering any package-qualified imports broken.</para>
1622 <!-- TYPE SYSTEM EXTENSIONS -->
1623 <sect1 id="data-type-extensions">
1624 <title>Extensions to data types and type synonyms</title>
1626 <sect2 id="nullary-types">
1627 <title>Data types with no constructors</title>
1629 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1630 a data type with no constructors. For example:</para>
1634 data T a -- T :: * -> *
1637 <para>Syntactically, the declaration lacks the "= constrs" part. The
1638 type can be parameterised over types of any kind, but if the kind is
1639 not <literal>*</literal> then an explicit kind annotation must be used
1640 (see <xref linkend="kinding"/>).</para>
1642 <para>Such data types have only one value, namely bottom.
1643 Nevertheless, they can be useful when defining "phantom types".</para>
1646 <sect2 id="infix-tycons">
1647 <title>Infix type constructors, classes, and type variables</title>
1650 GHC allows type constructors, classes, and type variables to be operators, and
1651 to be written infix, very much like expressions. More specifically:
1654 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1655 The lexical syntax is the same as that for data constructors.
1658 Data type and type-synonym declarations can be written infix, parenthesised
1659 if you want further arguments. E.g.
1661 data a :*: b = Foo a b
1662 type a :+: b = Either a b
1663 class a :=: b where ...
1665 data (a :**: b) x = Baz a b x
1666 type (a :++: b) y = Either (a,b) y
1670 Types, and class constraints, can be written infix. For example
1673 f :: (a :=: b) => a -> b
1677 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1678 The lexical syntax is the same as that for variable operators, excluding "(.)",
1679 "(!)", and "(*)". In a binding position, the operator must be
1680 parenthesised. For example:
1682 type T (+) = Int + Int
1686 liftA2 :: Arrow (~>)
1687 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1693 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1694 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1697 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1698 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1699 sets the fixity for a data constructor and the corresponding type constructor. For example:
1703 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1704 and similarly for <literal>:*:</literal>.
1705 <literal>Int `a` Bool</literal>.
1708 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1715 <sect2 id="type-synonyms">
1716 <title>Liberalised type synonyms</title>
1719 Type synonyms are like macros at the type level, and
1720 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1721 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1723 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1724 in a type synonym, thus:
1726 type Discard a = forall b. Show b => a -> b -> (a, String)
1731 g :: Discard Int -> (Int,String) -- A rank-2 type
1738 You can write an unboxed tuple in a type synonym:
1740 type Pr = (# Int, Int #)
1748 You can apply a type synonym to a forall type:
1750 type Foo a = a -> a -> Bool
1752 f :: Foo (forall b. b->b)
1754 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1756 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1761 You can apply a type synonym to a partially applied type synonym:
1763 type Generic i o = forall x. i x -> o x
1766 foo :: Generic Id []
1768 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1770 foo :: forall x. x -> [x]
1778 GHC currently does kind checking before expanding synonyms (though even that
1782 After expanding type synonyms, GHC does validity checking on types, looking for
1783 the following mal-formedness which isn't detected simply by kind checking:
1786 Type constructor applied to a type involving for-alls.
1789 Unboxed tuple on left of an arrow.
1792 Partially-applied type synonym.
1796 this will be rejected:
1798 type Pr = (# Int, Int #)
1803 because GHC does not allow unboxed tuples on the left of a function arrow.
1808 <sect2 id="existential-quantification">
1809 <title>Existentially quantified data constructors
1813 The idea of using existential quantification in data type declarations
1814 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1815 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1816 London, 1991). It was later formalised by Laufer and Odersky
1817 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1818 TOPLAS, 16(5), pp1411-1430, 1994).
1819 It's been in Lennart
1820 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1821 proved very useful. Here's the idea. Consider the declaration:
1827 data Foo = forall a. MkFoo a (a -> Bool)
1834 The data type <literal>Foo</literal> has two constructors with types:
1840 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1847 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1848 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1849 For example, the following expression is fine:
1855 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1861 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1862 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1863 isUpper</function> packages a character with a compatible function. These
1864 two things are each of type <literal>Foo</literal> and can be put in a list.
1868 What can we do with a value of type <literal>Foo</literal>?. In particular,
1869 what happens when we pattern-match on <function>MkFoo</function>?
1875 f (MkFoo val fn) = ???
1881 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1882 are compatible, the only (useful) thing we can do with them is to
1883 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1890 f (MkFoo val fn) = fn val
1896 What this allows us to do is to package heterogeneous values
1897 together with a bunch of functions that manipulate them, and then treat
1898 that collection of packages in a uniform manner. You can express
1899 quite a bit of object-oriented-like programming this way.
1902 <sect3 id="existential">
1903 <title>Why existential?
1907 What has this to do with <emphasis>existential</emphasis> quantification?
1908 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1914 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1920 But Haskell programmers can safely think of the ordinary
1921 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1922 adding a new existential quantification construct.
1927 <sect3 id="existential-with-context">
1928 <title>Existentials and type classes</title>
1931 An easy extension is to allow
1932 arbitrary contexts before the constructor. For example:
1938 data Baz = forall a. Eq a => Baz1 a a
1939 | forall b. Show b => Baz2 b (b -> b)
1945 The two constructors have the types you'd expect:
1951 Baz1 :: forall a. Eq a => a -> a -> Baz
1952 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1958 But when pattern matching on <function>Baz1</function> the matched values can be compared
1959 for equality, and when pattern matching on <function>Baz2</function> the first matched
1960 value can be converted to a string (as well as applying the function to it).
1961 So this program is legal:
1968 f (Baz1 p q) | p == q = "Yes"
1970 f (Baz2 v fn) = show (fn v)
1976 Operationally, in a dictionary-passing implementation, the
1977 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1978 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1979 extract it on pattern matching.
1984 <sect3 id="existential-records">
1985 <title>Record Constructors</title>
1988 GHC allows existentials to be used with records syntax as well. For example:
1991 data Counter a = forall self. NewCounter
1993 , _inc :: self -> self
1994 , _display :: self -> IO ()
1998 Here <literal>tag</literal> is a public field, with a well-typed selector
1999 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2000 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2001 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2002 compile-time error. In other words, <emphasis>GHC defines a record selector function
2003 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2004 (This example used an underscore in the fields for which record selectors
2005 will not be defined, but that is only programming style; GHC ignores them.)
2009 To make use of these hidden fields, we need to create some helper functions:
2012 inc :: Counter a -> Counter a
2013 inc (NewCounter x i d t) = NewCounter
2014 { _this = i x, _inc = i, _display = d, tag = t }
2016 display :: Counter a -> IO ()
2017 display NewCounter{ _this = x, _display = d } = d x
2020 Now we can define counters with different underlying implementations:
2023 counterA :: Counter String
2024 counterA = NewCounter
2025 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2027 counterB :: Counter String
2028 counterB = NewCounter
2029 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2032 display (inc counterA) -- prints "1"
2033 display (inc (inc counterB)) -- prints "##"
2036 At the moment, record update syntax is only supported for Haskell 98 data types,
2037 so the following function does <emphasis>not</emphasis> work:
2040 -- This is invalid; use explicit NewCounter instead for now
2041 setTag :: Counter a -> a -> Counter a
2042 setTag obj t = obj{ tag = t }
2051 <title>Restrictions</title>
2054 There are several restrictions on the ways in which existentially-quantified
2055 constructors can be use.
2064 When pattern matching, each pattern match introduces a new,
2065 distinct, type for each existential type variable. These types cannot
2066 be unified with any other type, nor can they escape from the scope of
2067 the pattern match. For example, these fragments are incorrect:
2075 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2076 is the result of <function>f1</function>. One way to see why this is wrong is to
2077 ask what type <function>f1</function> has:
2081 f1 :: Foo -> a -- Weird!
2085 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2090 f1 :: forall a. Foo -> a -- Wrong!
2094 The original program is just plain wrong. Here's another sort of error
2098 f2 (Baz1 a b) (Baz1 p q) = a==q
2102 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2103 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2104 from the two <function>Baz1</function> constructors.
2112 You can't pattern-match on an existentially quantified
2113 constructor in a <literal>let</literal> or <literal>where</literal> group of
2114 bindings. So this is illegal:
2118 f3 x = a==b where { Baz1 a b = x }
2121 Instead, use a <literal>case</literal> expression:
2124 f3 x = case x of Baz1 a b -> a==b
2127 In general, you can only pattern-match
2128 on an existentially-quantified constructor in a <literal>case</literal> expression or
2129 in the patterns of a function definition.
2131 The reason for this restriction is really an implementation one.
2132 Type-checking binding groups is already a nightmare without
2133 existentials complicating the picture. Also an existential pattern
2134 binding at the top level of a module doesn't make sense, because it's
2135 not clear how to prevent the existentially-quantified type "escaping".
2136 So for now, there's a simple-to-state restriction. We'll see how
2144 You can't use existential quantification for <literal>newtype</literal>
2145 declarations. So this is illegal:
2149 newtype T = forall a. Ord a => MkT a
2153 Reason: a value of type <literal>T</literal> must be represented as a
2154 pair of a dictionary for <literal>Ord t</literal> and a value of type
2155 <literal>t</literal>. That contradicts the idea that
2156 <literal>newtype</literal> should have no concrete representation.
2157 You can get just the same efficiency and effect by using
2158 <literal>data</literal> instead of <literal>newtype</literal>. If
2159 there is no overloading involved, then there is more of a case for
2160 allowing an existentially-quantified <literal>newtype</literal>,
2161 because the <literal>data</literal> version does carry an
2162 implementation cost, but single-field existentially quantified
2163 constructors aren't much use. So the simple restriction (no
2164 existential stuff on <literal>newtype</literal>) stands, unless there
2165 are convincing reasons to change it.
2173 You can't use <literal>deriving</literal> to define instances of a
2174 data type with existentially quantified data constructors.
2176 Reason: in most cases it would not make sense. For example:;
2179 data T = forall a. MkT [a] deriving( Eq )
2182 To derive <literal>Eq</literal> in the standard way we would need to have equality
2183 between the single component of two <function>MkT</function> constructors:
2187 (MkT a) == (MkT b) = ???
2190 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2191 It's just about possible to imagine examples in which the derived instance
2192 would make sense, but it seems altogether simpler simply to prohibit such
2193 declarations. Define your own instances!
2204 <!-- ====================== Generalised algebraic data types ======================= -->
2206 <sect2 id="gadt-style">
2207 <title>Declaring data types with explicit constructor signatures</title>
2209 <para>GHC allows you to declare an algebraic data type by
2210 giving the type signatures of constructors explicitly. For example:
2214 Just :: a -> Maybe a
2216 The form is called a "GADT-style declaration"
2217 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2218 can only be declared using this form.</para>
2219 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2220 For example, these two declarations are equivalent:
2222 data Foo = forall a. MkFoo a (a -> Bool)
2223 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2226 <para>Any data type that can be declared in standard Haskell-98 syntax
2227 can also be declared using GADT-style syntax.
2228 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2229 they treat class constraints on the data constructors differently.
2230 Specifically, if the constructor is given a type-class context, that
2231 context is made available by pattern matching. For example:
2234 MkSet :: Eq a => [a] -> Set a
2236 makeSet :: Eq a => [a] -> Set a
2237 makeSet xs = MkSet (nub xs)
2239 insert :: a -> Set a -> Set a
2240 insert a (MkSet as) | a `elem` as = MkSet as
2241 | otherwise = MkSet (a:as)
2243 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2244 gives rise to a <literal>(Eq a)</literal>
2245 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2246 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2247 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2248 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2249 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2250 In the example, the equality dictionary is used to satisfy the equality constraint
2251 generated by the call to <literal>elem</literal>, so that the type of
2252 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2255 For example, one possible application is to reify dictionaries:
2257 data NumInst a where
2258 MkNumInst :: Num a => NumInst a
2260 intInst :: NumInst Int
2263 plus :: NumInst a -> a -> a -> a
2264 plus MkNumInst p q = p + q
2266 Here, a value of type <literal>NumInst a</literal> is equivalent
2267 to an explicit <literal>(Num a)</literal> dictionary.
2270 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2271 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2275 = Num a => MkNumInst (NumInst a)
2277 Notice that, unlike the situation when declaring an existential, there is
2278 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2279 data type's universally quantified type variable <literal>a</literal>.
2280 A constructor may have both universal and existential type variables: for example,
2281 the following two declarations are equivalent:
2284 = forall b. (Num a, Eq b) => MkT1 a b
2286 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2289 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2290 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2291 In Haskell 98 the definition
2293 data Eq a => Set' a = MkSet' [a]
2295 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2296 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2297 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2298 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2299 GHC's behaviour is much more useful, as well as much more intuitive.
2303 The rest of this section gives further details about GADT-style data
2308 The result type of each data constructor must begin with the type constructor being defined.
2309 If the result type of all constructors
2310 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2311 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2312 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2316 The type signature of
2317 each constructor is independent, and is implicitly universally quantified as usual.
2318 Different constructors may have different universally-quantified type variables
2319 and different type-class constraints.
2320 For example, this is fine:
2323 T1 :: Eq b => b -> T b
2324 T2 :: (Show c, Ix c) => c -> [c] -> T c
2329 Unlike a Haskell-98-style
2330 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2331 have no scope. Indeed, one can write a kind signature instead:
2333 data Set :: * -> * where ...
2335 or even a mixture of the two:
2337 data Foo a :: (* -> *) -> * where ...
2339 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2342 data Foo a (b :: * -> *) where ...
2348 You can use strictness annotations, in the obvious places
2349 in the constructor type:
2352 Lit :: !Int -> Term Int
2353 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2354 Pair :: Term a -> Term b -> Term (a,b)
2359 You can use a <literal>deriving</literal> clause on a GADT-style data type
2360 declaration. For example, these two declarations are equivalent
2362 data Maybe1 a where {
2363 Nothing1 :: Maybe1 a ;
2364 Just1 :: a -> Maybe1 a
2365 } deriving( Eq, Ord )
2367 data Maybe2 a = Nothing2 | Just2 a
2373 You can use record syntax on a GADT-style data type declaration:
2377 Adult { name :: String, children :: [Person] } :: Person
2378 Child { name :: String } :: Person
2380 As usual, for every constructor that has a field <literal>f</literal>, the type of
2381 field <literal>f</literal> must be the same (modulo alpha conversion).
2384 At the moment, record updates are not yet possible with GADT-style declarations,
2385 so support is limited to record construction, selection and pattern matching.
2388 aPerson = Adult { name = "Fred", children = [] }
2390 shortName :: Person -> Bool
2391 hasChildren (Adult { children = kids }) = not (null kids)
2392 hasChildren (Child {}) = False
2397 As in the case of existentials declared using the Haskell-98-like record syntax
2398 (<xref linkend="existential-records"/>),
2399 record-selector functions are generated only for those fields that have well-typed
2401 Here is the example of that section, in GADT-style syntax:
2403 data Counter a where
2404 NewCounter { _this :: self
2405 , _inc :: self -> self
2406 , _display :: self -> IO ()
2411 As before, only one selector function is generated here, that for <literal>tag</literal>.
2412 Nevertheless, you can still use all the field names in pattern matching and record construction.
2414 </itemizedlist></para>
2418 <title>Generalised Algebraic Data Types (GADTs)</title>
2420 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2421 by allowing constructors to have richer return types. Here is an example:
2424 Lit :: Int -> Term Int
2425 Succ :: Term Int -> Term Int
2426 IsZero :: Term Int -> Term Bool
2427 If :: Term Bool -> Term a -> Term a -> Term a
2428 Pair :: Term a -> Term b -> Term (a,b)
2430 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2431 case with ordinary data types. This generality allows us to
2432 write a well-typed <literal>eval</literal> function
2433 for these <literal>Terms</literal>:
2437 eval (Succ t) = 1 + eval t
2438 eval (IsZero t) = eval t == 0
2439 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2440 eval (Pair e1 e2) = (eval e1, eval e2)
2442 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2443 For example, in the right hand side of the equation
2448 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2449 A precise specification of the type rules is beyond what this user manual aspires to,
2450 but the design closely follows that described in
2452 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2453 unification-based type inference for GADTs</ulink>,
2455 The general principle is this: <emphasis>type refinement is only carried out
2456 based on user-supplied type annotations</emphasis>.
2457 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2458 and lots of obscure error messages will
2459 occur. However, the refinement is quite general. For example, if we had:
2461 eval :: Term a -> a -> a
2462 eval (Lit i) j = i+j
2464 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2465 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2466 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2469 These and many other examples are given in papers by Hongwei Xi, and
2470 Tim Sheard. There is a longer introduction
2471 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2473 <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
2474 may use different notation to that implemented in GHC.
2477 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2478 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2481 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2482 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2483 The result type of each constructor must begin with the type constructor being defined,
2484 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2485 For example, in the <literal>Term</literal> data
2486 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2487 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2492 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2493 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2494 whose result type is not just <literal>T a b</literal>.
2498 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2499 an ordinary data type.
2503 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2507 Lit { val :: Int } :: Term Int
2508 Succ { num :: Term Int } :: Term Int
2509 Pred { num :: Term Int } :: Term Int
2510 IsZero { arg :: Term Int } :: Term Bool
2511 Pair { arg1 :: Term a
2514 If { cnd :: Term Bool
2519 However, for GADTs there is the following additional constraint:
2520 every constructor that has a field <literal>f</literal> must have
2521 the same result type (modulo alpha conversion)
2522 Hence, in the above example, we cannot merge the <literal>num</literal>
2523 and <literal>arg</literal> fields above into a
2524 single name. Although their field types are both <literal>Term Int</literal>,
2525 their selector functions actually have different types:
2528 num :: Term Int -> Term Int
2529 arg :: Term Bool -> Term Int
2534 When pattern-matching against data constructors drawn from a GADT,
2535 for example in a <literal>case</literal> expression, the following rules apply:
2537 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2538 <listitem><para>The type of the result of the <literal>case</literal> expression must be rigid.</para></listitem>
2539 <listitem><para>The type of any free variable mentioned in any of
2540 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2542 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2543 way to ensure that a variable a rigid type is to give it a type signature.
2552 <!-- ====================== End of Generalised algebraic data types ======================= -->
2554 <sect1 id="deriving">
2555 <title>Extensions to the "deriving" mechanism</title>
2557 <sect2 id="deriving-inferred">
2558 <title>Inferred context for deriving clauses</title>
2561 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2564 data T0 f a = MkT0 a deriving( Eq )
2565 data T1 f a = MkT1 (f a) deriving( Eq )
2566 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2568 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2570 instance Eq a => Eq (T0 f a) where ...
2571 instance Eq (f a) => Eq (T1 f a) where ...
2572 instance Eq (f (f a)) => Eq (T2 f a) where ...
2574 The first of these is obviously fine. The second is still fine, although less obviously.
2575 The third is not Haskell 98, and risks losing termination of instances.
2578 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2579 each constraint in the inferred instance context must consist only of type variables,
2580 with no repetitions.
2583 This rule is applied regardless of flags. If you want a more exotic context, you can write
2584 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2588 <sect2 id="stand-alone-deriving">
2589 <title>Stand-alone deriving declarations</title>
2592 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2594 data Foo a = Bar a | Baz String
2596 deriving instance Eq a => Eq (Foo a)
2598 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2599 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2600 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2601 exactly as you would in an ordinary instance declaration.
2602 (In contrast the context is inferred in a <literal>deriving</literal> clause
2603 attached to a data type declaration.)
2605 A <literal>deriving instance</literal> declaration
2606 must obey the same rules concerning form and termination as ordinary instance declarations,
2607 controlled by the same flags; see <xref linkend="instance-decls"/>.
2610 Unlike a <literal>deriving</literal>
2611 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2612 than the data type (assuming you also use
2613 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2616 data Foo a = Bar a | Baz String
2618 deriving instance Eq a => Eq (Foo [a])
2619 deriving instance Eq a => Eq (Foo (Maybe a))
2621 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2622 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2625 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2626 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2629 newtype Foo a = MkFoo (State Int a)
2631 deriving instance MonadState Int Foo
2633 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2634 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2640 <sect2 id="deriving-typeable">
2641 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2644 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2645 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2646 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2647 classes <literal>Eq</literal>, <literal>Ord</literal>,
2648 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2651 GHC extends this list with two more classes that may be automatically derived
2652 (provided the <option>-XDeriveDataTypeable</option> flag is specified):
2653 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2654 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
2655 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2657 <para>An instance of <literal>Typeable</literal> can only be derived if the
2658 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2659 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2661 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2662 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2664 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2665 are used, and only <literal>Typeable1</literal> up to
2666 <literal>Typeable7</literal> are provided in the library.)
2667 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2668 class, whose kind suits that of the data type constructor, and
2669 then writing the data type instance by hand.
2673 <sect2 id="newtype-deriving">
2674 <title>Generalised derived instances for newtypes</title>
2677 When you define an abstract type using <literal>newtype</literal>, you may want
2678 the new type to inherit some instances from its representation. In
2679 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2680 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2681 other classes you have to write an explicit instance declaration. For
2682 example, if you define
2685 newtype Dollars = Dollars Int
2688 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2689 explicitly define an instance of <literal>Num</literal>:
2692 instance Num Dollars where
2693 Dollars a + Dollars b = Dollars (a+b)
2696 All the instance does is apply and remove the <literal>newtype</literal>
2697 constructor. It is particularly galling that, since the constructor
2698 doesn't appear at run-time, this instance declaration defines a
2699 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2700 dictionary, only slower!
2704 <sect3> <title> Generalising the deriving clause </title>
2706 GHC now permits such instances to be derived instead,
2707 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2710 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2713 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2714 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2715 derives an instance declaration of the form
2718 instance Num Int => Num Dollars
2721 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2725 We can also derive instances of constructor classes in a similar
2726 way. For example, suppose we have implemented state and failure monad
2727 transformers, such that
2730 instance Monad m => Monad (State s m)
2731 instance Monad m => Monad (Failure m)
2733 In Haskell 98, we can define a parsing monad by
2735 type Parser tok m a = State [tok] (Failure m) a
2738 which is automatically a monad thanks to the instance declarations
2739 above. With the extension, we can make the parser type abstract,
2740 without needing to write an instance of class <literal>Monad</literal>, via
2743 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2746 In this case the derived instance declaration is of the form
2748 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2751 Notice that, since <literal>Monad</literal> is a constructor class, the
2752 instance is a <emphasis>partial application</emphasis> of the new type, not the
2753 entire left hand side. We can imagine that the type declaration is
2754 "eta-converted" to generate the context of the instance
2759 We can even derive instances of multi-parameter classes, provided the
2760 newtype is the last class parameter. In this case, a ``partial
2761 application'' of the class appears in the <literal>deriving</literal>
2762 clause. For example, given the class
2765 class StateMonad s m | m -> s where ...
2766 instance Monad m => StateMonad s (State s m) where ...
2768 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2770 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2771 deriving (Monad, StateMonad [tok])
2774 The derived instance is obtained by completing the application of the
2775 class to the new type:
2778 instance StateMonad [tok] (State [tok] (Failure m)) =>
2779 StateMonad [tok] (Parser tok m)
2784 As a result of this extension, all derived instances in newtype
2785 declarations are treated uniformly (and implemented just by reusing
2786 the dictionary for the representation type), <emphasis>except</emphasis>
2787 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2788 the newtype and its representation.
2792 <sect3> <title> A more precise specification </title>
2794 Derived instance declarations are constructed as follows. Consider the
2795 declaration (after expansion of any type synonyms)
2798 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2804 The <literal>ci</literal> are partial applications of
2805 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2806 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2809 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2812 The type <literal>t</literal> is an arbitrary type.
2815 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2816 nor in the <literal>ci</literal>, and
2819 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2820 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2821 should not "look through" the type or its constructor. You can still
2822 derive these classes for a newtype, but it happens in the usual way, not
2823 via this new mechanism.
2826 Then, for each <literal>ci</literal>, the derived instance
2829 instance ci t => ci (T v1...vk)
2831 As an example which does <emphasis>not</emphasis> work, consider
2833 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2835 Here we cannot derive the instance
2837 instance Monad (State s m) => Monad (NonMonad m)
2840 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2841 and so cannot be "eta-converted" away. It is a good thing that this
2842 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2843 not, in fact, a monad --- for the same reason. Try defining
2844 <literal>>>=</literal> with the correct type: you won't be able to.
2848 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2849 important, since we can only derive instances for the last one. If the
2850 <literal>StateMonad</literal> class above were instead defined as
2853 class StateMonad m s | m -> s where ...
2856 then we would not have been able to derive an instance for the
2857 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2858 classes usually have one "main" parameter for which deriving new
2859 instances is most interesting.
2861 <para>Lastly, all of this applies only for classes other than
2862 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2863 and <literal>Data</literal>, for which the built-in derivation applies (section
2864 4.3.3. of the Haskell Report).
2865 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2866 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2867 the standard method is used or the one described here.)
2874 <!-- TYPE SYSTEM EXTENSIONS -->
2875 <sect1 id="type-class-extensions">
2876 <title>Class and instances declarations</title>
2878 <sect2 id="multi-param-type-classes">
2879 <title>Class declarations</title>
2882 This section, and the next one, documents GHC's type-class extensions.
2883 There's lots of background in the paper <ulink
2884 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2885 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2886 Jones, Erik Meijer).
2889 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2893 <title>Multi-parameter type classes</title>
2895 Multi-parameter type classes are permitted. For example:
2899 class Collection c a where
2900 union :: c a -> c a -> c a
2908 <title>The superclasses of a class declaration</title>
2911 There are no restrictions on the context in a class declaration
2912 (which introduces superclasses), except that the class hierarchy must
2913 be acyclic. So these class declarations are OK:
2917 class Functor (m k) => FiniteMap m k where
2920 class (Monad m, Monad (t m)) => Transform t m where
2921 lift :: m a -> (t m) a
2927 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2928 of "acyclic" involves only the superclass relationships. For example,
2934 op :: D b => a -> b -> b
2937 class C a => D a where { ... }
2941 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2942 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2943 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2950 <sect3 id="class-method-types">
2951 <title>Class method types</title>
2954 Haskell 98 prohibits class method types to mention constraints on the
2955 class type variable, thus:
2958 fromList :: [a] -> s a
2959 elem :: Eq a => a -> s a -> Bool
2961 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2962 contains the constraint <literal>Eq a</literal>, constrains only the
2963 class type variable (in this case <literal>a</literal>).
2964 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
2971 <sect2 id="functional-dependencies">
2972 <title>Functional dependencies
2975 <para> Functional dependencies are implemented as described by Mark Jones
2976 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2977 In Proceedings of the 9th European Symposium on Programming,
2978 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2982 Functional dependencies are introduced by a vertical bar in the syntax of a
2983 class declaration; e.g.
2985 class (Monad m) => MonadState s m | m -> s where ...
2987 class Foo a b c | a b -> c where ...
2989 There should be more documentation, but there isn't (yet). Yell if you need it.
2992 <sect3><title>Rules for functional dependencies </title>
2994 In a class declaration, all of the class type variables must be reachable (in the sense
2995 mentioned in <xref linkend="type-restrictions"/>)
2996 from the free variables of each method type.
3000 class Coll s a where
3002 insert :: s -> a -> s
3005 is not OK, because the type of <literal>empty</literal> doesn't mention
3006 <literal>a</literal>. Functional dependencies can make the type variable
3009 class Coll s a | s -> a where
3011 insert :: s -> a -> s
3014 Alternatively <literal>Coll</literal> might be rewritten
3017 class Coll s a where
3019 insert :: s a -> a -> s a
3023 which makes the connection between the type of a collection of
3024 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3025 Occasionally this really doesn't work, in which case you can split the
3033 class CollE s => Coll s a where
3034 insert :: s -> a -> s
3041 <title>Background on functional dependencies</title>
3043 <para>The following description of the motivation and use of functional dependencies is taken
3044 from the Hugs user manual, reproduced here (with minor changes) by kind
3045 permission of Mark Jones.
3048 Consider the following class, intended as part of a
3049 library for collection types:
3051 class Collects e ce where
3053 insert :: e -> ce -> ce
3054 member :: e -> ce -> Bool
3056 The type variable e used here represents the element type, while ce is the type
3057 of the container itself. Within this framework, we might want to define
3058 instances of this class for lists or characteristic functions (both of which
3059 can be used to represent collections of any equality type), bit sets (which can
3060 be used to represent collections of characters), or hash tables (which can be
3061 used to represent any collection whose elements have a hash function). Omitting
3062 standard implementation details, this would lead to the following declarations:
3064 instance Eq e => Collects e [e] where ...
3065 instance Eq e => Collects e (e -> Bool) where ...
3066 instance Collects Char BitSet where ...
3067 instance (Hashable e, Collects a ce)
3068 => Collects e (Array Int ce) where ...
3070 All this looks quite promising; we have a class and a range of interesting
3071 implementations. Unfortunately, there are some serious problems with the class
3072 declaration. First, the empty function has an ambiguous type:
3074 empty :: Collects e ce => ce
3076 By "ambiguous" we mean that there is a type variable e that appears on the left
3077 of the <literal>=></literal> symbol, but not on the right. The problem with
3078 this is that, according to the theoretical foundations of Haskell overloading,
3079 we cannot guarantee a well-defined semantics for any term with an ambiguous
3083 We can sidestep this specific problem by removing the empty member from the
3084 class declaration. However, although the remaining members, insert and member,
3085 do not have ambiguous types, we still run into problems when we try to use
3086 them. For example, consider the following two functions:
3088 f x y = insert x . insert y
3091 for which GHC infers the following types:
3093 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3094 g :: (Collects Bool c, Collects Char c) => c -> c
3096 Notice that the type for f allows the two parameters x and y to be assigned
3097 different types, even though it attempts to insert each of the two values, one
3098 after the other, into the same collection. If we're trying to model collections
3099 that contain only one type of value, then this is clearly an inaccurate
3100 type. Worse still, the definition for g is accepted, without causing a type
3101 error. As a result, the error in this code will not be flagged at the point
3102 where it appears. Instead, it will show up only when we try to use g, which
3103 might even be in a different module.
3106 <sect4><title>An attempt to use constructor classes</title>
3109 Faced with the problems described above, some Haskell programmers might be
3110 tempted to use something like the following version of the class declaration:
3112 class Collects e c where
3114 insert :: e -> c e -> c e
3115 member :: e -> c e -> Bool
3117 The key difference here is that we abstract over the type constructor c that is
3118 used to form the collection type c e, and not over that collection type itself,
3119 represented by ce in the original class declaration. This avoids the immediate
3120 problems that we mentioned above: empty has type <literal>Collects e c => c
3121 e</literal>, which is not ambiguous.
3124 The function f from the previous section has a more accurate type:
3126 f :: (Collects e c) => e -> e -> c e -> c e
3128 The function g from the previous section is now rejected with a type error as
3129 we would hope because the type of f does not allow the two arguments to have
3131 This, then, is an example of a multiple parameter class that does actually work
3132 quite well in practice, without ambiguity problems.
3133 There is, however, a catch. This version of the Collects class is nowhere near
3134 as general as the original class seemed to be: only one of the four instances
3135 for <literal>Collects</literal>
3136 given above can be used with this version of Collects because only one of
3137 them---the instance for lists---has a collection type that can be written in
3138 the form c e, for some type constructor c, and element type e.
3142 <sect4><title>Adding functional dependencies</title>
3145 To get a more useful version of the Collects class, Hugs provides a mechanism
3146 that allows programmers to specify dependencies between the parameters of a
3147 multiple parameter class (For readers with an interest in theoretical
3148 foundations and previous work: The use of dependency information can be seen
3149 both as a generalization of the proposal for `parametric type classes' that was
3150 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3151 later framework for "improvement" of qualified types. The
3152 underlying ideas are also discussed in a more theoretical and abstract setting
3153 in a manuscript [implparam], where they are identified as one point in a
3154 general design space for systems of implicit parameterization.).
3156 To start with an abstract example, consider a declaration such as:
3158 class C a b where ...
3160 which tells us simply that C can be thought of as a binary relation on types
3161 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3162 included in the definition of classes to add information about dependencies
3163 between parameters, as in the following examples:
3165 class D a b | a -> b where ...
3166 class E a b | a -> b, b -> a where ...
3168 The notation <literal>a -> b</literal> used here between the | and where
3169 symbols --- not to be
3170 confused with a function type --- indicates that the a parameter uniquely
3171 determines the b parameter, and might be read as "a determines b." Thus D is
3172 not just a relation, but actually a (partial) function. Similarly, from the two
3173 dependencies that are included in the definition of E, we can see that E
3174 represents a (partial) one-one mapping between types.
3177 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3178 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3179 m>=0, meaning that the y parameters are uniquely determined by the x
3180 parameters. Spaces can be used as separators if more than one variable appears
3181 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3182 annotated with multiple dependencies using commas as separators, as in the
3183 definition of E above. Some dependencies that we can write in this notation are
3184 redundant, and will be rejected because they don't serve any useful
3185 purpose, and may instead indicate an error in the program. Examples of
3186 dependencies like this include <literal>a -> a </literal>,
3187 <literal>a -> a a </literal>,
3188 <literal>a -> </literal>, etc. There can also be
3189 some redundancy if multiple dependencies are given, as in
3190 <literal>a->b</literal>,
3191 <literal>b->c </literal>, <literal>a->c </literal>, and
3192 in which some subset implies the remaining dependencies. Examples like this are
3193 not treated as errors. Note that dependencies appear only in class
3194 declarations, and not in any other part of the language. In particular, the
3195 syntax for instance declarations, class constraints, and types is completely
3199 By including dependencies in a class declaration, we provide a mechanism for
3200 the programmer to specify each multiple parameter class more precisely. The
3201 compiler, on the other hand, is responsible for ensuring that the set of
3202 instances that are in scope at any given point in the program is consistent
3203 with any declared dependencies. For example, the following pair of instance
3204 declarations cannot appear together in the same scope because they violate the
3205 dependency for D, even though either one on its own would be acceptable:
3207 instance D Bool Int where ...
3208 instance D Bool Char where ...
3210 Note also that the following declaration is not allowed, even by itself:
3212 instance D [a] b where ...
3214 The problem here is that this instance would allow one particular choice of [a]
3215 to be associated with more than one choice for b, which contradicts the
3216 dependency specified in the definition of D. More generally, this means that,
3217 in any instance of the form:
3219 instance D t s where ...
3221 for some particular types t and s, the only variables that can appear in s are
3222 the ones that appear in t, and hence, if the type t is known, then s will be
3223 uniquely determined.
3226 The benefit of including dependency information is that it allows us to define
3227 more general multiple parameter classes, without ambiguity problems, and with
3228 the benefit of more accurate types. To illustrate this, we return to the
3229 collection class example, and annotate the original definition of <literal>Collects</literal>
3230 with a simple dependency:
3232 class Collects e ce | ce -> e where
3234 insert :: e -> ce -> ce
3235 member :: e -> ce -> Bool
3237 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3238 determined by the type of the collection ce. Note that both parameters of
3239 Collects are of kind *; there are no constructor classes here. Note too that
3240 all of the instances of Collects that we gave earlier can be used
3241 together with this new definition.
3244 What about the ambiguity problems that we encountered with the original
3245 definition? The empty function still has type Collects e ce => ce, but it is no
3246 longer necessary to regard that as an ambiguous type: Although the variable e
3247 does not appear on the right of the => symbol, the dependency for class
3248 Collects tells us that it is uniquely determined by ce, which does appear on
3249 the right of the => symbol. Hence the context in which empty is used can still
3250 give enough information to determine types for both ce and e, without
3251 ambiguity. More generally, we need only regard a type as ambiguous if it
3252 contains a variable on the left of the => that is not uniquely determined
3253 (either directly or indirectly) by the variables on the right.
3256 Dependencies also help to produce more accurate types for user defined
3257 functions, and hence to provide earlier detection of errors, and less cluttered
3258 types for programmers to work with. Recall the previous definition for a
3261 f x y = insert x y = insert x . insert y
3263 for which we originally obtained a type:
3265 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3267 Given the dependency information that we have for Collects, however, we can
3268 deduce that a and b must be equal because they both appear as the second
3269 parameter in a Collects constraint with the same first parameter c. Hence we
3270 can infer a shorter and more accurate type for f:
3272 f :: (Collects a c) => a -> a -> c -> c
3274 In a similar way, the earlier definition of g will now be flagged as a type error.
3277 Although we have given only a few examples here, it should be clear that the
3278 addition of dependency information can help to make multiple parameter classes
3279 more useful in practice, avoiding ambiguity problems, and allowing more general
3280 sets of instance declarations.
3286 <sect2 id="instance-decls">
3287 <title>Instance declarations</title>
3289 <sect3 id="instance-rules">
3290 <title>Relaxed rules for instance declarations</title>
3292 <para>An instance declaration has the form
3294 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 ...
3296 The part before the "<literal>=></literal>" is the
3297 <emphasis>context</emphasis>, while the part after the
3298 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3302 In Haskell 98 the head of an instance declaration
3303 must be of the form <literal>C (T a1 ... an)</literal>, where
3304 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
3305 and the <literal>a1 ... an</literal> are distinct type variables.
3306 Furthermore, the assertions in the context of the instance declaration
3307 must be of the form <literal>C a</literal> where <literal>a</literal>
3308 is a type variable that occurs in the head.
3311 The <option>-XFlexibleInstances</option> flag loosens these restrictions
3312 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
3313 the context and head of the instance declaration can each consist of arbitrary
3314 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3318 The Paterson Conditions: for each assertion in the context
3320 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3321 <listitem><para>The assertion has fewer constructors and variables (taken together
3322 and counting repetitions) than the head</para></listitem>
3326 <listitem><para>The Coverage Condition. For each functional dependency,
3327 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3328 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3329 every type variable in
3330 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3331 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3332 substitution mapping each type variable in the class declaration to the
3333 corresponding type in the instance declaration.
3336 These restrictions ensure that context reduction terminates: each reduction
3337 step makes the problem smaller by at least one
3338 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3339 if you give the <option>-XUndecidableInstances</option>
3340 flag (<xref linkend="undecidable-instances"/>).
3341 You can find lots of background material about the reason for these
3342 restrictions in the paper <ulink
3343 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3344 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3347 For example, these are OK:
3349 instance C Int [a] -- Multiple parameters
3350 instance Eq (S [a]) -- Structured type in head
3352 -- Repeated type variable in head
3353 instance C4 a a => C4 [a] [a]
3354 instance Stateful (ST s) (MutVar s)
3356 -- Head can consist of type variables only
3358 instance (Eq a, Show b) => C2 a b
3360 -- Non-type variables in context
3361 instance Show (s a) => Show (Sized s a)
3362 instance C2 Int a => C3 Bool [a]
3363 instance C2 Int a => C3 [a] b
3367 -- Context assertion no smaller than head
3368 instance C a => C a where ...
3369 -- (C b b) has more more occurrences of b than the head
3370 instance C b b => Foo [b] where ...
3375 The same restrictions apply to instances generated by
3376 <literal>deriving</literal> clauses. Thus the following is accepted:
3378 data MinHeap h a = H a (h a)
3381 because the derived instance
3383 instance (Show a, Show (h a)) => Show (MinHeap h a)
3385 conforms to the above rules.
3389 A useful idiom permitted by the above rules is as follows.
3390 If one allows overlapping instance declarations then it's quite
3391 convenient to have a "default instance" declaration that applies if
3392 something more specific does not:
3400 <sect3 id="undecidable-instances">
3401 <title>Undecidable instances</title>
3404 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3405 For example, sometimes you might want to use the following to get the
3406 effect of a "class synonym":
3408 class (C1 a, C2 a, C3 a) => C a where { }
3410 instance (C1 a, C2 a, C3 a) => C a where { }
3412 This allows you to write shorter signatures:
3418 f :: (C1 a, C2 a, C3 a) => ...
3420 The restrictions on functional dependencies (<xref
3421 linkend="functional-dependencies"/>) are particularly troublesome.
3422 It is tempting to introduce type variables in the context that do not appear in
3423 the head, something that is excluded by the normal rules. For example:
3425 class HasConverter a b | a -> b where
3428 data Foo a = MkFoo a
3430 instance (HasConverter a b,Show b) => Show (Foo a) where
3431 show (MkFoo value) = show (convert value)
3433 This is dangerous territory, however. Here, for example, is a program that would make the
3438 instance F [a] [[a]]
3439 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3441 Similarly, it can be tempting to lift the coverage condition:
3443 class Mul a b c | a b -> c where
3444 (.*.) :: a -> b -> c
3446 instance Mul Int Int Int where (.*.) = (*)
3447 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3448 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3450 The third instance declaration does not obey the coverage condition;
3451 and indeed the (somewhat strange) definition:
3453 f = \ b x y -> if b then x .*. [y] else y
3455 makes instance inference go into a loop, because it requires the constraint
3456 <literal>(Mul a [b] b)</literal>.
3459 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3460 the experimental flag <option>-XUndecidableInstances</option>
3461 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3462 both the Paterson Conditions and the Coverage Condition
3463 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3464 fixed-depth recursion stack. If you exceed the stack depth you get a
3465 sort of backtrace, and the opportunity to increase the stack depth
3466 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3472 <sect3 id="instance-overlap">
3473 <title>Overlapping instances</title>
3475 In general, <emphasis>GHC requires that that it be unambiguous which instance
3477 should be used to resolve a type-class constraint</emphasis>. This behaviour
3478 can be modified by two flags: <option>-XOverlappingInstances</option>
3479 <indexterm><primary>-XOverlappingInstances
3480 </primary></indexterm>
3481 and <option>-XIncoherentInstances</option>
3482 <indexterm><primary>-XIncoherentInstances
3483 </primary></indexterm>, as this section discusses. Both these
3484 flags are dynamic flags, and can be set on a per-module basis, using
3485 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3487 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3488 it tries to match every instance declaration against the
3490 by instantiating the head of the instance declaration. For example, consider
3493 instance context1 => C Int a where ... -- (A)
3494 instance context2 => C a Bool where ... -- (B)
3495 instance context3 => C Int [a] where ... -- (C)
3496 instance context4 => C Int [Int] where ... -- (D)
3498 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3499 but (C) and (D) do not. When matching, GHC takes
3500 no account of the context of the instance declaration
3501 (<literal>context1</literal> etc).
3502 GHC's default behaviour is that <emphasis>exactly one instance must match the
3503 constraint it is trying to resolve</emphasis>.
3504 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3505 including both declarations (A) and (B), say); an error is only reported if a
3506 particular constraint matches more than one.
3510 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3511 more than one instance to match, provided there is a most specific one. For
3512 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3513 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3514 most-specific match, the program is rejected.
3517 However, GHC is conservative about committing to an overlapping instance. For example:
3522 Suppose that from the RHS of <literal>f</literal> we get the constraint
3523 <literal>C Int [b]</literal>. But
3524 GHC does not commit to instance (C), because in a particular
3525 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3526 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3527 So GHC rejects the program.
3528 (If you add the flag <option>-XIncoherentInstances</option>,
3529 GHC will instead pick (C), without complaining about
3530 the problem of subsequent instantiations.)
3533 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3534 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3535 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3536 it instead. In this case, GHC will refrain from
3537 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
3538 as before) but, rather than rejecting the program, it will infer the type
3540 f :: C Int b => [b] -> [b]
3542 That postpones the question of which instance to pick to the
3543 call site for <literal>f</literal>
3544 by which time more is known about the type <literal>b</literal>.
3547 The willingness to be overlapped or incoherent is a property of
3548 the <emphasis>instance declaration</emphasis> itself, controlled by the
3549 presence or otherwise of the <option>-XOverlappingInstances</option>
3550 and <option>-XIncoherentInstances</option> flags when that module is
3551 being defined. Neither flag is required in a module that imports and uses the
3552 instance declaration. Specifically, during the lookup process:
3555 An instance declaration is ignored during the lookup process if (a) a more specific
3556 match is found, and (b) the instance declaration was compiled with
3557 <option>-XOverlappingInstances</option>. The flag setting for the
3558 more-specific instance does not matter.
3561 Suppose an instance declaration does not match the constraint being looked up, but
3562 does unify with it, so that it might match when the constraint is further
3563 instantiated. Usually GHC will regard this as a reason for not committing to
3564 some other constraint. But if the instance declaration was compiled with
3565 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3566 check for that declaration.
3569 These rules make it possible for a library author to design a library that relies on
3570 overlapping instances without the library client having to know.
3573 If an instance declaration is compiled without
3574 <option>-XOverlappingInstances</option>,
3575 then that instance can never be overlapped. This could perhaps be
3576 inconvenient. Perhaps the rule should instead say that the
3577 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3578 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3579 at a usage site should be permitted regardless of how the instance declarations
3580 are compiled, if the <option>-XOverlappingInstances</option> flag is
3581 used at the usage site. (Mind you, the exact usage site can occasionally be
3582 hard to pin down.) We are interested to receive feedback on these points.
3584 <para>The <option>-XIncoherentInstances</option> flag implies the
3585 <option>-XOverlappingInstances</option> flag, but not vice versa.
3590 <title>Type synonyms in the instance head</title>
3593 <emphasis>Unlike Haskell 98, instance heads may use type
3594 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
3595 As always, using a type synonym is just shorthand for
3596 writing the RHS of the type synonym definition. For example:
3600 type Point = (Int,Int)
3601 instance C Point where ...
3602 instance C [Point] where ...
3606 is legal. However, if you added
3610 instance C (Int,Int) where ...
3614 as well, then the compiler will complain about the overlapping
3615 (actually, identical) instance declarations. As always, type synonyms
3616 must be fully applied. You cannot, for example, write:
3621 instance Monad P where ...
3625 This design decision is independent of all the others, and easily
3626 reversed, but it makes sense to me.
3634 <sect2 id="overloaded-strings">
3635 <title>Overloaded string literals
3639 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3640 string literal has type <literal>String</literal>, but with overloaded string
3641 literals enabled (with <literal>-XOverloadedStrings</literal>)
3642 a string literal has type <literal>(IsString a) => a</literal>.
3645 This means that the usual string syntax can be used, e.g., for packed strings
3646 and other variations of string like types. String literals behave very much
3647 like integer literals, i.e., they can be used in both expressions and patterns.
3648 If used in a pattern the literal with be replaced by an equality test, in the same
3649 way as an integer literal is.
3652 The class <literal>IsString</literal> is defined as:
3654 class IsString a where
3655 fromString :: String -> a
3657 The only predefined instance is the obvious one to make strings work as usual:
3659 instance IsString [Char] where
3662 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3663 it explicitly (for example, to give an instance declaration for it), you can import it
3664 from module <literal>GHC.Exts</literal>.
3667 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3671 Each type in a default declaration must be an
3672 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3676 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3677 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3678 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3679 <emphasis>or</emphasis> <literal>IsString</literal>.
3688 import GHC.Exts( IsString(..) )
3690 newtype MyString = MyString String deriving (Eq, Show)
3691 instance IsString MyString where
3692 fromString = MyString
3694 greet :: MyString -> MyString
3695 greet "hello" = "world"
3699 print $ greet "hello"
3700 print $ greet "fool"
3704 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3705 to work since it gets translated into an equality comparison.
3711 <sect1 id="other-type-extensions">
3712 <title>Other type system extensions</title>
3714 <sect2 id="type-restrictions">
3715 <title>Type signatures</title>
3717 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
3719 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
3720 the form <emphasis>(class type-variable)</emphasis> or
3721 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
3722 these type signatures are perfectly OK
3725 g :: Ord (T a ()) => ...
3729 GHC imposes the following restrictions on the constraints in a type signature.
3733 forall tv1..tvn (c1, ...,cn) => type
3736 (Here, we write the "foralls" explicitly, although the Haskell source
3737 language omits them; in Haskell 98, all the free type variables of an
3738 explicit source-language type signature are universally quantified,
3739 except for the class type variables in a class declaration. However,
3740 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
3749 <emphasis>Each universally quantified type variable
3750 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
3752 A type variable <literal>a</literal> is "reachable" if it appears
3753 in the same constraint as either a type variable free in
3754 <literal>type</literal>, or another reachable type variable.
3755 A value with a type that does not obey
3756 this reachability restriction cannot be used without introducing
3757 ambiguity; that is why the type is rejected.
3758 Here, for example, is an illegal type:
3762 forall a. Eq a => Int
3766 When a value with this type was used, the constraint <literal>Eq tv</literal>
3767 would be introduced where <literal>tv</literal> is a fresh type variable, and
3768 (in the dictionary-translation implementation) the value would be
3769 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
3770 can never know which instance of <literal>Eq</literal> to use because we never
3771 get any more information about <literal>tv</literal>.
3775 that the reachability condition is weaker than saying that <literal>a</literal> is
3776 functionally dependent on a type variable free in
3777 <literal>type</literal> (see <xref
3778 linkend="functional-dependencies"/>). The reason for this is there
3779 might be a "hidden" dependency, in a superclass perhaps. So
3780 "reachable" is a conservative approximation to "functionally dependent".
3781 For example, consider:
3783 class C a b | a -> b where ...
3784 class C a b => D a b where ...
3785 f :: forall a b. D a b => a -> a
3787 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3788 but that is not immediately apparent from <literal>f</literal>'s type.
3794 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3795 universally quantified type variables <literal>tvi</literal></emphasis>.
3797 For example, this type is OK because <literal>C a b</literal> mentions the
3798 universally quantified type variable <literal>b</literal>:
3802 forall a. C a b => burble
3806 The next type is illegal because the constraint <literal>Eq b</literal> does not
3807 mention <literal>a</literal>:
3811 forall a. Eq b => burble
3815 The reason for this restriction is milder than the other one. The
3816 excluded types are never useful or necessary (because the offending
3817 context doesn't need to be witnessed at this point; it can be floated
3818 out). Furthermore, floating them out increases sharing. Lastly,
3819 excluding them is a conservative choice; it leaves a patch of
3820 territory free in case we need it later.
3834 <sect2 id="implicit-parameters">
3835 <title>Implicit parameters</title>
3837 <para> Implicit parameters are implemented as described in
3838 "Implicit parameters: dynamic scoping with static types",
3839 J Lewis, MB Shields, E Meijer, J Launchbury,
3840 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3844 <para>(Most of the following, still rather incomplete, documentation is
3845 due to Jeff Lewis.)</para>
3847 <para>Implicit parameter support is enabled with the option
3848 <option>-XImplicitParams</option>.</para>
3851 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3852 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3853 context. In Haskell, all variables are statically bound. Dynamic
3854 binding of variables is a notion that goes back to Lisp, but was later
3855 discarded in more modern incarnations, such as Scheme. Dynamic binding
3856 can be very confusing in an untyped language, and unfortunately, typed
3857 languages, in particular Hindley-Milner typed languages like Haskell,
3858 only support static scoping of variables.
3861 However, by a simple extension to the type class system of Haskell, we
3862 can support dynamic binding. Basically, we express the use of a
3863 dynamically bound variable as a constraint on the type. These
3864 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3865 function uses a dynamically-bound variable <literal>?x</literal>
3866 of type <literal>t'</literal>". For
3867 example, the following expresses the type of a sort function,
3868 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3870 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3872 The dynamic binding constraints are just a new form of predicate in the type class system.
3875 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3876 where <literal>x</literal> is
3877 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3878 Use of this construct also introduces a new
3879 dynamic-binding constraint in the type of the expression.
3880 For example, the following definition
3881 shows how we can define an implicitly parameterized sort function in
3882 terms of an explicitly parameterized <literal>sortBy</literal> function:
3884 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3886 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3892 <title>Implicit-parameter type constraints</title>
3894 Dynamic binding constraints behave just like other type class
3895 constraints in that they are automatically propagated. Thus, when a
3896 function is used, its implicit parameters are inherited by the
3897 function that called it. For example, our <literal>sort</literal> function might be used
3898 to pick out the least value in a list:
3900 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3901 least xs = head (sort xs)
3903 Without lifting a finger, the <literal>?cmp</literal> parameter is
3904 propagated to become a parameter of <literal>least</literal> as well. With explicit
3905 parameters, the default is that parameters must always be explicit
3906 propagated. With implicit parameters, the default is to always
3910 An implicit-parameter type constraint differs from other type class constraints in the
3911 following way: All uses of a particular implicit parameter must have
3912 the same type. This means that the type of <literal>(?x, ?x)</literal>
3913 is <literal>(?x::a) => (a,a)</literal>, and not
3914 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3918 <para> You can't have an implicit parameter in the context of a class or instance
3919 declaration. For example, both these declarations are illegal:
3921 class (?x::Int) => C a where ...
3922 instance (?x::a) => Foo [a] where ...
3924 Reason: exactly which implicit parameter you pick up depends on exactly where
3925 you invoke a function. But the ``invocation'' of instance declarations is done
3926 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3927 Easiest thing is to outlaw the offending types.</para>
3929 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3931 f :: (?x :: [a]) => Int -> Int
3934 g :: (Read a, Show a) => String -> String
3937 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3938 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3939 quite unambiguous, and fixes the type <literal>a</literal>.
3944 <title>Implicit-parameter bindings</title>
3947 An implicit parameter is <emphasis>bound</emphasis> using the standard
3948 <literal>let</literal> or <literal>where</literal> binding forms.
3949 For example, we define the <literal>min</literal> function by binding
3950 <literal>cmp</literal>.
3953 min = let ?cmp = (<=) in least
3957 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3958 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3959 (including in a list comprehension, or do-notation, or pattern guards),
3960 or a <literal>where</literal> clause.
3961 Note the following points:
3964 An implicit-parameter binding group must be a
3965 collection of simple bindings to implicit-style variables (no
3966 function-style bindings, and no type signatures); these bindings are
3967 neither polymorphic or recursive.
3970 You may not mix implicit-parameter bindings with ordinary bindings in a
3971 single <literal>let</literal>
3972 expression; use two nested <literal>let</literal>s instead.
3973 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3977 You may put multiple implicit-parameter bindings in a
3978 single binding group; but they are <emphasis>not</emphasis> treated
3979 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3980 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3981 parameter. The bindings are not nested, and may be re-ordered without changing
3982 the meaning of the program.
3983 For example, consider:
3985 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3987 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3988 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3990 f :: (?x::Int) => Int -> Int
3998 <sect3><title>Implicit parameters and polymorphic recursion</title>
4001 Consider these two definitions:
4004 len1 xs = let ?acc = 0 in len_acc1 xs
4007 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4012 len2 xs = let ?acc = 0 in len_acc2 xs
4014 len_acc2 :: (?acc :: Int) => [a] -> Int
4016 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4018 The only difference between the two groups is that in the second group
4019 <literal>len_acc</literal> is given a type signature.
4020 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4021 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4022 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4023 has a type signature, the recursive call is made to the
4024 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4025 as an implicit parameter. So we get the following results in GHCi:
4032 Adding a type signature dramatically changes the result! This is a rather
4033 counter-intuitive phenomenon, worth watching out for.
4037 <sect3><title>Implicit parameters and monomorphism</title>
4039 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4040 Haskell Report) to implicit parameters. For example, consider:
4048 Since the binding for <literal>y</literal> falls under the Monomorphism
4049 Restriction it is not generalised, so the type of <literal>y</literal> is
4050 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4051 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4052 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4053 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4054 <literal>y</literal> in the body of the <literal>let</literal> will see the
4055 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4056 <literal>14</literal>.
4061 <!-- ======================= COMMENTED OUT ========================
4063 We intend to remove linear implicit parameters, so I'm at least removing
4064 them from the 6.6 user manual
4066 <sect2 id="linear-implicit-parameters">
4067 <title>Linear implicit parameters</title>
4069 Linear implicit parameters are an idea developed by Koen Claessen,
4070 Mark Shields, and Simon PJ. They address the long-standing
4071 problem that monads seem over-kill for certain sorts of problem, notably:
4074 <listitem> <para> distributing a supply of unique names </para> </listitem>
4075 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4076 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4080 Linear implicit parameters are just like ordinary implicit parameters,
4081 except that they are "linear"; that is, they cannot be copied, and
4082 must be explicitly "split" instead. Linear implicit parameters are
4083 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4084 (The '/' in the '%' suggests the split!)
4089 import GHC.Exts( Splittable )
4091 data NameSupply = ...
4093 splitNS :: NameSupply -> (NameSupply, NameSupply)
4094 newName :: NameSupply -> Name
4096 instance Splittable NameSupply where
4100 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4101 f env (Lam x e) = Lam x' (f env e)
4104 env' = extend env x x'
4105 ...more equations for f...
4107 Notice that the implicit parameter %ns is consumed
4109 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4110 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4114 So the translation done by the type checker makes
4115 the parameter explicit:
4117 f :: NameSupply -> Env -> Expr -> Expr
4118 f ns env (Lam x e) = Lam x' (f ns1 env e)
4120 (ns1,ns2) = splitNS ns
4122 env = extend env x x'
4124 Notice the call to 'split' introduced by the type checker.
4125 How did it know to use 'splitNS'? Because what it really did
4126 was to introduce a call to the overloaded function 'split',
4127 defined by the class <literal>Splittable</literal>:
4129 class Splittable a where
4132 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4133 split for name supplies. But we can simply write
4139 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4141 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4142 <literal>GHC.Exts</literal>.
4147 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4148 are entirely distinct implicit parameters: you
4149 can use them together and they won't interfere with each other. </para>
4152 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4154 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4155 in the context of a class or instance declaration. </para></listitem>
4159 <sect3><title>Warnings</title>
4162 The monomorphism restriction is even more important than usual.
4163 Consider the example above:
4165 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4166 f env (Lam x e) = Lam x' (f env e)
4169 env' = extend env x x'
4171 If we replaced the two occurrences of x' by (newName %ns), which is
4172 usually a harmless thing to do, we get:
4174 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4175 f env (Lam x e) = Lam (newName %ns) (f env e)
4177 env' = extend env x (newName %ns)
4179 But now the name supply is consumed in <emphasis>three</emphasis> places
4180 (the two calls to newName,and the recursive call to f), so
4181 the result is utterly different. Urk! We don't even have
4185 Well, this is an experimental change. With implicit
4186 parameters we have already lost beta reduction anyway, and
4187 (as John Launchbury puts it) we can't sensibly reason about
4188 Haskell programs without knowing their typing.
4193 <sect3><title>Recursive functions</title>
4194 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
4197 foo :: %x::T => Int -> [Int]
4199 foo n = %x : foo (n-1)
4201 where T is some type in class Splittable.</para>
4203 Do you get a list of all the same T's or all different T's
4204 (assuming that split gives two distinct T's back)?
4206 If you supply the type signature, taking advantage of polymorphic
4207 recursion, you get what you'd probably expect. Here's the
4208 translated term, where the implicit param is made explicit:
4211 foo x n = let (x1,x2) = split x
4212 in x1 : foo x2 (n-1)
4214 But if you don't supply a type signature, GHC uses the Hindley
4215 Milner trick of using a single monomorphic instance of the function
4216 for the recursive calls. That is what makes Hindley Milner type inference
4217 work. So the translation becomes
4221 foom n = x : foom (n-1)
4225 Result: 'x' is not split, and you get a list of identical T's. So the
4226 semantics of the program depends on whether or not foo has a type signature.
4229 You may say that this is a good reason to dislike linear implicit parameters
4230 and you'd be right. That is why they are an experimental feature.
4236 ================ END OF Linear Implicit Parameters commented out -->
4238 <sect2 id="kinding">
4239 <title>Explicitly-kinded quantification</title>
4242 Haskell infers the kind of each type variable. Sometimes it is nice to be able
4243 to give the kind explicitly as (machine-checked) documentation,
4244 just as it is nice to give a type signature for a function. On some occasions,
4245 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
4246 John Hughes had to define the data type:
4248 data Set cxt a = Set [a]
4249 | Unused (cxt a -> ())
4251 The only use for the <literal>Unused</literal> constructor was to force the correct
4252 kind for the type variable <literal>cxt</literal>.
4255 GHC now instead allows you to specify the kind of a type variable directly, wherever
4256 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
4259 This flag enables kind signatures in the following places:
4261 <listitem><para><literal>data</literal> declarations:
4263 data Set (cxt :: * -> *) a = Set [a]
4264 </screen></para></listitem>
4265 <listitem><para><literal>type</literal> declarations:
4267 type T (f :: * -> *) = f Int
4268 </screen></para></listitem>
4269 <listitem><para><literal>class</literal> declarations:
4271 class (Eq a) => C (f :: * -> *) a where ...
4272 </screen></para></listitem>
4273 <listitem><para><literal>forall</literal>'s in type signatures:
4275 f :: forall (cxt :: * -> *). Set cxt Int
4276 </screen></para></listitem>
4281 The parentheses are required. Some of the spaces are required too, to
4282 separate the lexemes. If you write <literal>(f::*->*)</literal> you
4283 will get a parse error, because "<literal>::*->*</literal>" is a
4284 single lexeme in Haskell.
4288 As part of the same extension, you can put kind annotations in types
4291 f :: (Int :: *) -> Int
4292 g :: forall a. a -> (a :: *)
4296 atype ::= '(' ctype '::' kind ')
4298 The parentheses are required.
4303 <sect2 id="universal-quantification">
4304 <title>Arbitrary-rank polymorphism
4308 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
4309 allows us to say exactly what this means. For example:
4317 g :: forall b. (b -> b)
4319 The two are treated identically.
4323 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
4324 explicit universal quantification in
4326 For example, all the following types are legal:
4328 f1 :: forall a b. a -> b -> a
4329 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
4331 f2 :: (forall a. a->a) -> Int -> Int
4332 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
4334 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
4336 f4 :: Int -> (forall a. a -> a)
4338 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
4339 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
4340 The <literal>forall</literal> makes explicit the universal quantification that
4341 is implicitly added by Haskell.
4344 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
4345 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
4346 shows, the polymorphic type on the left of the function arrow can be overloaded.
4349 The function <literal>f3</literal> has a rank-3 type;
4350 it has rank-2 types on the left of a function arrow.
4353 GHC has three flags to control higher-rank types:
4356 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
4359 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
4362 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
4363 That is, you can nest <literal>forall</literal>s
4364 arbitrarily deep in function arrows.
4365 In particular, a forall-type (also called a "type scheme"),
4366 including an operational type class context, is legal:
4368 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
4369 of a function arrow </para> </listitem>
4370 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
4371 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
4372 field type signatures.</para> </listitem>
4373 <listitem> <para> As the type of an implicit parameter </para> </listitem>
4374 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
4378 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4379 a type variable any more!
4388 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
4389 the types of the constructor arguments. Here are several examples:
4395 data T a = T1 (forall b. b -> b -> b) a
4397 data MonadT m = MkMonad { return :: forall a. a -> m a,
4398 bind :: forall a b. m a -> (a -> m b) -> m b
4401 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
4407 The constructors have rank-2 types:
4413 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
4414 MkMonad :: forall m. (forall a. a -> m a)
4415 -> (forall a b. m a -> (a -> m b) -> m b)
4417 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
4423 Notice that you don't need to use a <literal>forall</literal> if there's an
4424 explicit context. For example in the first argument of the
4425 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
4426 prefixed to the argument type. The implicit <literal>forall</literal>
4427 quantifies all type variables that are not already in scope, and are
4428 mentioned in the type quantified over.
4432 As for type signatures, implicit quantification happens for non-overloaded
4433 types too. So if you write this:
4436 data T a = MkT (Either a b) (b -> b)
4439 it's just as if you had written this:
4442 data T a = MkT (forall b. Either a b) (forall b. b -> b)
4445 That is, since the type variable <literal>b</literal> isn't in scope, it's
4446 implicitly universally quantified. (Arguably, it would be better
4447 to <emphasis>require</emphasis> explicit quantification on constructor arguments
4448 where that is what is wanted. Feedback welcomed.)
4452 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
4453 the constructor to suitable values, just as usual. For example,
4464 a3 = MkSwizzle reverse
4467 a4 = let r x = Just x
4474 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
4475 mkTs f x y = [T1 f x, T1 f y]
4481 The type of the argument can, as usual, be more general than the type
4482 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
4483 does not need the <literal>Ord</literal> constraint.)
4487 When you use pattern matching, the bound variables may now have
4488 polymorphic types. For example:
4494 f :: T a -> a -> (a, Char)
4495 f (T1 w k) x = (w k x, w 'c' 'd')
4497 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
4498 g (MkSwizzle s) xs f = s (map f (s xs))
4500 h :: MonadT m -> [m a] -> m [a]
4501 h m [] = return m []
4502 h m (x:xs) = bind m x $ \y ->
4503 bind m (h m xs) $ \ys ->
4510 In the function <function>h</function> we use the record selectors <literal>return</literal>
4511 and <literal>bind</literal> to extract the polymorphic bind and return functions
4512 from the <literal>MonadT</literal> data structure, rather than using pattern
4518 <title>Type inference</title>
4521 In general, type inference for arbitrary-rank types is undecidable.
4522 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
4523 to get a decidable algorithm by requiring some help from the programmer.
4524 We do not yet have a formal specification of "some help" but the rule is this:
4527 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
4528 provides an explicit polymorphic type for x, or GHC's type inference will assume
4529 that x's type has no foralls in it</emphasis>.
4532 What does it mean to "provide" an explicit type for x? You can do that by
4533 giving a type signature for x directly, using a pattern type signature
4534 (<xref linkend="scoped-type-variables"/>), thus:
4536 \ f :: (forall a. a->a) -> (f True, f 'c')
4538 Alternatively, you can give a type signature to the enclosing
4539 context, which GHC can "push down" to find the type for the variable:
4541 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
4543 Here the type signature on the expression can be pushed inwards
4544 to give a type signature for f. Similarly, and more commonly,
4545 one can give a type signature for the function itself:
4547 h :: (forall a. a->a) -> (Bool,Char)
4548 h f = (f True, f 'c')
4550 You don't need to give a type signature if the lambda bound variable
4551 is a constructor argument. Here is an example we saw earlier:
4553 f :: T a -> a -> (a, Char)
4554 f (T1 w k) x = (w k x, w 'c' 'd')
4556 Here we do not need to give a type signature to <literal>w</literal>, because
4557 it is an argument of constructor <literal>T1</literal> and that tells GHC all
4564 <sect3 id="implicit-quant">
4565 <title>Implicit quantification</title>
4568 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
4569 user-written types, if and only if there is no explicit <literal>forall</literal>,
4570 GHC finds all the type variables mentioned in the type that are not already
4571 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
4575 f :: forall a. a -> a
4582 h :: forall b. a -> b -> b
4588 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
4591 f :: (a -> a) -> Int
4593 f :: forall a. (a -> a) -> Int
4595 f :: (forall a. a -> a) -> Int
4598 g :: (Ord a => a -> a) -> Int
4599 -- MEANS the illegal type
4600 g :: forall a. (Ord a => a -> a) -> Int
4602 g :: (forall a. Ord a => a -> a) -> Int
4604 The latter produces an illegal type, which you might think is silly,
4605 but at least the rule is simple. If you want the latter type, you
4606 can write your for-alls explicitly. Indeed, doing so is strongly advised
4613 <sect2 id="impredicative-polymorphism">
4614 <title>Impredicative polymorphism
4616 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
4617 enabled with <option>-XImpredicativeTypes</option>.
4619 that you can call a polymorphic function at a polymorphic type, and
4620 parameterise data structures over polymorphic types. For example:
4622 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
4623 f (Just g) = Just (g [3], g "hello")
4626 Notice here that the <literal>Maybe</literal> type is parameterised by the
4627 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
4630 <para>The technical details of this extension are described in the paper
4631 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
4632 type inference for higher-rank types and impredicativity</ulink>,
4633 which appeared at ICFP 2006.
4637 <sect2 id="scoped-type-variables">
4638 <title>Lexically scoped type variables
4642 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
4643 which some type signatures are simply impossible to write. For example:
4645 f :: forall a. [a] -> [a]
4651 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
4652 the entire definition of <literal>f</literal>.
4653 In particular, it is in scope at the type signature for <varname>ys</varname>.
4654 In Haskell 98 it is not possible to declare
4655 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
4656 it becomes possible to do so.
4658 <para>Lexically-scoped type variables are enabled by
4659 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
4661 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
4662 variables work, compared to earlier releases. Read this section
4666 <title>Overview</title>
4668 <para>The design follows the following principles
4670 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
4671 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
4672 design.)</para></listitem>
4673 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
4674 type variables. This means that every programmer-written type signature
4675 (including one that contains free scoped type variables) denotes a
4676 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
4677 checker, and no inference is involved.</para></listitem>
4678 <listitem><para>Lexical type variables may be alpha-renamed freely, without
4679 changing the program.</para></listitem>
4683 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
4685 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
4686 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
4687 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
4688 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
4692 In Haskell, a programmer-written type signature is implicitly quantified over
4693 its free type variables (<ulink
4694 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4696 of the Haskell Report).
4697 Lexically scoped type variables affect this implicit quantification rules
4698 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
4699 quantified. For example, if type variable <literal>a</literal> is in scope,
4702 (e :: a -> a) means (e :: a -> a)
4703 (e :: b -> b) means (e :: forall b. b->b)
4704 (e :: a -> b) means (e :: forall b. a->b)
4712 <sect3 id="decl-type-sigs">
4713 <title>Declaration type signatures</title>
4714 <para>A declaration type signature that has <emphasis>explicit</emphasis>
4715 quantification (using <literal>forall</literal>) brings into scope the
4716 explicitly-quantified
4717 type variables, in the definition of the named function. For example:
4719 f :: forall a. [a] -> [a]
4720 f (x:xs) = xs ++ [ x :: a ]
4722 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
4723 the definition of "<literal>f</literal>".
4725 <para>This only happens if:
4727 <listitem><para> The quantification in <literal>f</literal>'s type
4728 signature is explicit. For example:
4731 g (x:xs) = xs ++ [ x :: a ]
4733 This program will be rejected, because "<literal>a</literal>" does not scope
4734 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
4735 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
4736 quantification rules.
4738 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
4739 not a pattern binding.
4742 f1 :: forall a. [a] -> [a]
4743 f1 (x:xs) = xs ++ [ x :: a ] -- OK
4745 f2 :: forall a. [a] -> [a]
4746 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
4748 f3 :: forall a. [a] -> [a]
4749 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
4751 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
4752 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
4753 function binding, and <literal>f2</literal> binds a bare variable; in both cases
4754 the type signature brings <literal>a</literal> into scope.
4760 <sect3 id="exp-type-sigs">
4761 <title>Expression type signatures</title>
4763 <para>An expression type signature that has <emphasis>explicit</emphasis>
4764 quantification (using <literal>forall</literal>) brings into scope the
4765 explicitly-quantified
4766 type variables, in the annotated expression. For example:
4768 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
4770 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
4771 type variable <literal>s</literal> into scope, in the annotated expression
4772 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
4777 <sect3 id="pattern-type-sigs">
4778 <title>Pattern type signatures</title>
4780 A type signature may occur in any pattern; this is a <emphasis>pattern type
4781 signature</emphasis>.
4784 -- f and g assume that 'a' is already in scope
4785 f = \(x::Int, y::a) -> x
4787 h ((x,y) :: (Int,Bool)) = (y,x)
4789 In the case where all the type variables in the pattern type signature are
4790 already in scope (i.e. bound by the enclosing context), matters are simple: the
4791 signature simply constrains the type of the pattern in the obvious way.
4794 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
4795 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
4796 that are already in scope. For example:
4798 f :: forall a. [a] -> (Int, [a])
4801 (ys::[a], n) = (reverse xs, length xs) -- OK
4802 zs::[a] = xs ++ ys -- OK
4804 Just (v::b) = ... -- Not OK; b is not in scope
4806 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
4807 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
4811 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
4812 type signature may mention a type variable that is not in scope; in this case,
4813 <emphasis>the signature brings that type variable into scope</emphasis>.
4814 This is particularly important for existential data constructors. For example:
4816 data T = forall a. MkT [a]
4819 k (MkT [t::a]) = MkT t3
4823 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
4824 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
4825 because it is bound by the pattern match. GHC's rule is that in this situation
4826 (and only then), a pattern type signature can mention a type variable that is
4827 not already in scope; the effect is to bring it into scope, standing for the
4828 existentially-bound type variable.
4831 When a pattern type signature binds a type variable in this way, GHC insists that the
4832 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
4833 This means that any user-written type signature always stands for a completely known type.
4836 If all this seems a little odd, we think so too. But we must have
4837 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4838 could not name existentially-bound type variables in subsequent type signatures.
4841 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4842 signature is allowed to mention a lexical variable that is not already in
4844 For example, both <literal>f</literal> and <literal>g</literal> would be
4845 illegal if <literal>a</literal> was not already in scope.
4851 <!-- ==================== Commented out part about result type signatures
4853 <sect3 id="result-type-sigs">
4854 <title>Result type signatures</title>
4857 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4860 {- f assumes that 'a' is already in scope -}
4861 f x y :: [a] = [x,y,x]
4863 g = \ x :: [Int] -> [3,4]
4865 h :: forall a. [a] -> a
4869 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4870 the result of the function. Similarly, the body of the lambda in the RHS of
4871 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4872 alternative in <literal>h</literal> is <literal>a</literal>.
4874 <para> A result type signature never brings new type variables into scope.</para>
4876 There are a couple of syntactic wrinkles. First, notice that all three
4877 examples would parse quite differently with parentheses:
4879 {- f assumes that 'a' is already in scope -}
4880 f x (y :: [a]) = [x,y,x]
4882 g = \ (x :: [Int]) -> [3,4]
4884 h :: forall a. [a] -> a
4888 Now the signature is on the <emphasis>pattern</emphasis>; and
4889 <literal>h</literal> would certainly be ill-typed (since the pattern
4890 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4892 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4893 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4894 token or a parenthesised type of some sort). To see why,
4895 consider how one would parse this:
4904 <sect3 id="cls-inst-scoped-tyvars">
4905 <title>Class and instance declarations</title>
4908 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4909 scope over the methods defined in the <literal>where</literal> part. For example:
4927 <sect2 id="typing-binds">
4928 <title>Generalised typing of mutually recursive bindings</title>
4931 The Haskell Report specifies that a group of bindings (at top level, or in a
4932 <literal>let</literal> or <literal>where</literal>) should be sorted into
4933 strongly-connected components, and then type-checked in dependency order
4934 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4935 Report, Section 4.5.1</ulink>).
4936 As each group is type-checked, any binders of the group that
4938 an explicit type signature are put in the type environment with the specified
4940 and all others are monomorphic until the group is generalised
4941 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4944 <para>Following a suggestion of Mark Jones, in his paper
4945 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
4947 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4949 <emphasis>the dependency analysis ignores references to variables that have an explicit
4950 type signature</emphasis>.
4951 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4952 typecheck. For example, consider:
4954 f :: Eq a => a -> Bool
4955 f x = (x == x) || g True || g "Yes"
4957 g y = (y <= y) || f True
4959 This is rejected by Haskell 98, but under Jones's scheme the definition for
4960 <literal>g</literal> is typechecked first, separately from that for
4961 <literal>f</literal>,
4962 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4963 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
4964 type is generalised, to get
4966 g :: Ord a => a -> Bool
4968 Now, the definition for <literal>f</literal> is typechecked, with this type for
4969 <literal>g</literal> in the type environment.
4973 The same refined dependency analysis also allows the type signatures of
4974 mutually-recursive functions to have different contexts, something that is illegal in
4975 Haskell 98 (Section 4.5.2, last sentence). With
4976 <option>-XRelaxedPolyRec</option>
4977 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4978 type signatures; in practice this means that only variables bound by the same
4979 pattern binding must have the same context. For example, this is fine:
4981 f :: Eq a => a -> Bool
4982 f x = (x == x) || g True
4984 g :: Ord a => a -> Bool
4985 g y = (y <= y) || f True
4990 <sect2 id="type-families">
4991 <title>Type families
4995 GHC supports the definition of type families indexed by types. They may be
4996 seen as an extension of Haskell 98's class-based overloading of values to
4997 types. When type families are declared in classes, they are also known as
5001 There are two forms of type families: data families and type synonym families.
5002 Currently, only the former are fully implemented, while we are still working
5003 on the latter. As a result, the specification of the language extension is
5004 also still to some degree in flux. Hence, a more detailed description of
5005 the language extension and its use is currently available
5006 from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
5007 wiki page on type families</ulink>. The material will be moved to this user's
5008 guide when it has stabilised.
5011 Type families are enabled by the flag <option>-XTypeFamilies</option>.
5018 <!-- ==================== End of type system extensions ================= -->
5020 <!-- ====================== TEMPLATE HASKELL ======================= -->
5022 <sect1 id="template-haskell">
5023 <title>Template Haskell</title>
5025 <para>Template Haskell allows you to do compile-time meta-programming in
5028 the main technical innovations is discussed in "<ulink
5029 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5030 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5033 There is a Wiki page about
5034 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5035 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5039 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5040 Haskell library reference material</ulink>
5041 (look for module <literal>Language.Haskell.TH</literal>).
5042 Many changes to the original design are described in
5043 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5044 Notes on Template Haskell version 2</ulink>.
5045 Not all of these changes are in GHC, however.
5048 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5049 as a worked example to help get you started.
5053 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5054 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5059 <title>Syntax</title>
5061 <para> Template Haskell has the following new syntactic
5062 constructions. You need to use the flag
5063 <option>-XTemplateHaskell</option>
5064 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5065 </indexterm>to switch these syntactic extensions on
5066 (<option>-XTemplateHaskell</option> is no longer implied by
5067 <option>-fglasgow-exts</option>).</para>
5071 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5072 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5073 There must be no space between the "$" and the identifier or parenthesis. This use
5074 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5075 of "." as an infix operator. If you want the infix operator, put spaces around it.
5077 <para> A splice can occur in place of
5079 <listitem><para> an expression; the spliced expression must
5080 have type <literal>Q Exp</literal></para></listitem>
5081 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5084 Inside a splice you can can only call functions defined in imported modules,
5085 not functions defined elsewhere in the same module.</listitem>
5089 A expression quotation is written in Oxford brackets, thus:
5091 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5092 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5093 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5094 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5095 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5096 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5097 </itemizedlist></para></listitem>
5100 A quasi-quotation can appear in either a pattern context or an
5101 expression context and is also written in Oxford brackets:
5103 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5104 where the "..." is an arbitrary string; a full description of the
5105 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5106 </itemizedlist></para></listitem>
5109 A name can be quoted with either one or two prefix single quotes:
5111 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5112 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5113 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5115 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5116 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5119 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5120 may also be given as an argument to the <literal>reify</literal> function.
5126 (Compared to the original paper, there are many differences of detail.
5127 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5128 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5129 Type splices are not implemented, and neither are pattern splices or quotations.
5133 <sect2> <title> Using Template Haskell </title>
5137 The data types and monadic constructor functions for Template Haskell are in the library
5138 <literal>Language.Haskell.THSyntax</literal>.
5142 You can only run a function at compile time if it is imported from another module. That is,
5143 you can't define a function in a module, and call it from within a splice in the same module.
5144 (It would make sense to do so, but it's hard to implement.)
5148 You can only run a function at compile time if it is imported
5149 from another module <emphasis>that is not part of a mutually-recursive group of modules
5150 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5151 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5152 splice is to be run.</para>
5154 For example, when compiling module A,
5155 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5156 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5160 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5163 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5164 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5165 compiles and runs a program, and then looks at the result. So it's important that
5166 the program it compiles produces results whose representations are identical to
5167 those of the compiler itself.
5171 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5172 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5177 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5178 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5179 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5186 -- Import our template "pr"
5187 import Printf ( pr )
5189 -- The splice operator $ takes the Haskell source code
5190 -- generated at compile time by "pr" and splices it into
5191 -- the argument of "putStrLn".
5192 main = putStrLn ( $(pr "Hello") )
5198 -- Skeletal printf from the paper.
5199 -- It needs to be in a separate module to the one where
5200 -- you intend to use it.
5202 -- Import some Template Haskell syntax
5203 import Language.Haskell.TH
5205 -- Describe a format string
5206 data Format = D | S | L String
5208 -- Parse a format string. This is left largely to you
5209 -- as we are here interested in building our first ever
5210 -- Template Haskell program and not in building printf.
5211 parse :: String -> [Format]
5214 -- Generate Haskell source code from a parsed representation
5215 -- of the format string. This code will be spliced into
5216 -- the module which calls "pr", at compile time.
5217 gen :: [Format] -> Q Exp
5218 gen [D] = [| \n -> show n |]
5219 gen [S] = [| \s -> s |]
5220 gen [L s] = stringE s
5222 -- Here we generate the Haskell code for the splice
5223 -- from an input format string.
5224 pr :: String -> Q Exp
5225 pr s = gen (parse s)
5228 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
5231 $ ghc --make -XTemplateHaskell main.hs -o main.exe
5234 <para>Run "main.exe" and here is your output:</para>
5244 <title>Using Template Haskell with Profiling</title>
5245 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
5247 <para>Template Haskell relies on GHC's built-in bytecode compiler and
5248 interpreter to run the splice expressions. The bytecode interpreter
5249 runs the compiled expression on top of the same runtime on which GHC
5250 itself is running; this means that the compiled code referred to by
5251 the interpreted expression must be compatible with this runtime, and
5252 in particular this means that object code that is compiled for
5253 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
5254 expression, because profiled object code is only compatible with the
5255 profiling version of the runtime.</para>
5257 <para>This causes difficulties if you have a multi-module program
5258 containing Template Haskell code and you need to compile it for
5259 profiling, because GHC cannot load the profiled object code and use it
5260 when executing the splices. Fortunately GHC provides a workaround.
5261 The basic idea is to compile the program twice:</para>
5265 <para>Compile the program or library first the normal way, without
5266 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
5269 <para>Then compile it again with <option>-prof</option>, and
5270 additionally use <option>-osuf
5271 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
5272 to name the object files differently (you can choose any suffix
5273 that isn't the normal object suffix here). GHC will automatically
5274 load the object files built in the first step when executing splice
5275 expressions. If you omit the <option>-osuf</option> flag when
5276 building with <option>-prof</option> and Template Haskell is used,
5277 GHC will emit an error message. </para>
5282 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
5283 <para>Quasi-quotation allows patterns and expressions to be written using
5284 programmer-defined concrete syntax; the motivation behind the extension and
5285 several examples are documented in
5286 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
5287 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
5288 2007). The example below shows how to write a quasiquoter for a simple
5289 expression language.</para>
5292 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
5293 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
5294 functions for quoting expressions and patterns, respectively. The first argument
5295 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
5296 context of the quasi-quotation statement determines which of the two parsers is
5297 called: if the quasi-quotation occurs in an expression context, the expression
5298 parser is called, and if it occurs in a pattern context, the pattern parser is
5302 Note that in the example we make use of an antiquoted
5303 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
5304 (this syntax for anti-quotation was defined by the parser's
5305 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
5306 integer value argument of the constructor <literal>IntExpr</literal> when
5307 pattern matching. Please see the referenced paper for further details regarding
5308 anti-quotation as well as the description of a technique that uses SYB to
5309 leverage a single parser of type <literal>String -> a</literal> to generate both
5310 an expression parser that returns a value of type <literal>Q Exp</literal> and a
5311 pattern parser that returns a value of type <literal>Q Pat</literal>.
5314 <para>In general, a quasi-quote has the form
5315 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
5316 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
5317 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
5318 can be arbitrary, and may contain newlines.
5321 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
5322 the example, <literal>expr</literal> cannot be defined
5323 in <literal>Main.hs</literal> where it is used, but must be imported.
5334 main = do { print $ eval [$expr|1 + 2|]
5336 { [$expr|'int:n|] -> print n
5345 import qualified Language.Haskell.TH as TH
5346 import Language.Haskell.TH.Quasi
5348 data Expr = IntExpr Integer
5349 | AntiIntExpr String
5350 | BinopExpr BinOp Expr Expr
5352 deriving(Show, Typeable, Data)
5358 deriving(Show, Typeable, Data)
5360 eval :: Expr -> Integer
5361 eval (IntExpr n) = n
5362 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
5369 expr = QuasiQuoter parseExprExp parseExprPat
5371 -- Parse an Expr, returning its representation as
5372 -- either a Q Exp or a Q Pat. See the referenced paper
5373 -- for how to use SYB to do this by writing a single
5374 -- parser of type String -> Expr instead of two
5375 -- separate parsers.
5377 parseExprExp :: String -> Q Exp
5380 parseExprPat :: String -> Q Pat
5384 <para>Now run the compiler:
5387 $ ghc --make -XQuasiQuotes Main.hs -o main
5390 <para>Run "main" and here is your output:</para>
5402 <!-- ===================== Arrow notation =================== -->
5404 <sect1 id="arrow-notation">
5405 <title>Arrow notation
5408 <para>Arrows are a generalization of monads introduced by John Hughes.
5409 For more details, see
5414 “Generalising Monads to Arrows”,
5415 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
5416 pp67–111, May 2000.
5422 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
5423 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
5429 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
5430 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
5436 and the arrows web page at
5437 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
5438 With the <option>-XArrows</option> flag, GHC supports the arrow
5439 notation described in the second of these papers.
5440 What follows is a brief introduction to the notation;
5441 it won't make much sense unless you've read Hughes's paper.
5442 This notation is translated to ordinary Haskell,
5443 using combinators from the
5444 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5448 <para>The extension adds a new kind of expression for defining arrows:
5450 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
5451 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5453 where <literal>proc</literal> is a new keyword.
5454 The variables of the pattern are bound in the body of the
5455 <literal>proc</literal>-expression,
5456 which is a new sort of thing called a <firstterm>command</firstterm>.
5457 The syntax of commands is as follows:
5459 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
5460 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
5461 | <replaceable>cmd</replaceable><superscript>0</superscript>
5463 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
5464 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
5465 infix operators as for expressions, and
5467 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
5468 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
5469 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
5470 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
5471 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
5472 | <replaceable>fcmd</replaceable>
5474 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
5475 | ( <replaceable>cmd</replaceable> )
5476 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
5478 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
5479 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
5480 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
5481 | <replaceable>cmd</replaceable>
5483 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
5484 except that the bodies are commands instead of expressions.
5488 Commands produce values, but (like monadic computations)
5489 may yield more than one value,
5490 or none, and may do other things as well.
5491 For the most part, familiarity with monadic notation is a good guide to
5493 However the values of expressions, even monadic ones,
5494 are determined by the values of the variables they contain;
5495 this is not necessarily the case for commands.
5499 A simple example of the new notation is the expression
5501 proc x -> f -< x+1
5503 We call this a <firstterm>procedure</firstterm> or
5504 <firstterm>arrow abstraction</firstterm>.
5505 As with a lambda expression, the variable <literal>x</literal>
5506 is a new variable bound within the <literal>proc</literal>-expression.
5507 It refers to the input to the arrow.
5508 In the above example, <literal>-<</literal> is not an identifier but an
5509 new reserved symbol used for building commands from an expression of arrow
5510 type and an expression to be fed as input to that arrow.
5511 (The weird look will make more sense later.)
5512 It may be read as analogue of application for arrows.
5513 The above example is equivalent to the Haskell expression
5515 arr (\ x -> x+1) >>> f
5517 That would make no sense if the expression to the left of
5518 <literal>-<</literal> involves the bound variable <literal>x</literal>.
5519 More generally, the expression to the left of <literal>-<</literal>
5520 may not involve any <firstterm>local variable</firstterm>,
5521 i.e. a variable bound in the current arrow abstraction.
5522 For such a situation there is a variant <literal>-<<</literal>, as in
5524 proc x -> f x -<< x+1
5526 which is equivalent to
5528 arr (\ x -> (f x, x+1)) >>> app
5530 so in this case the arrow must belong to the <literal>ArrowApply</literal>
5532 Such an arrow is equivalent to a monad, so if you're using this form
5533 you may find a monadic formulation more convenient.
5537 <title>do-notation for commands</title>
5540 Another form of command is a form of <literal>do</literal>-notation.
5541 For example, you can write
5550 You can read this much like ordinary <literal>do</literal>-notation,
5551 but with commands in place of monadic expressions.
5552 The first line sends the value of <literal>x+1</literal> as an input to
5553 the arrow <literal>f</literal>, and matches its output against
5554 <literal>y</literal>.
5555 In the next line, the output is discarded.
5556 The arrow <function>returnA</function> is defined in the
5557 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5558 module as <literal>arr id</literal>.
5559 The above example is treated as an abbreviation for
5561 arr (\ x -> (x, x)) >>>
5562 first (arr (\ x -> x+1) >>> f) >>>
5563 arr (\ (y, x) -> (y, (x, y))) >>>
5564 first (arr (\ y -> 2*y) >>> g) >>>
5566 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
5567 first (arr (\ (x, z) -> x*z) >>> h) >>>
5568 arr (\ (t, z) -> t+z) >>>
5571 Note that variables not used later in the composition are projected out.
5572 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
5574 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
5575 module, this reduces to
5577 arr (\ x -> (x+1, x)) >>>
5579 arr (\ (y, x) -> (2*y, (x, y))) >>>
5581 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
5583 arr (\ (t, z) -> t+z)
5585 which is what you might have written by hand.
5586 With arrow notation, GHC keeps track of all those tuples of variables for you.
5590 Note that although the above translation suggests that
5591 <literal>let</literal>-bound variables like <literal>z</literal> must be
5592 monomorphic, the actual translation produces Core,
5593 so polymorphic variables are allowed.
5597 It's also possible to have mutually recursive bindings,
5598 using the new <literal>rec</literal> keyword, as in the following example:
5600 counter :: ArrowCircuit a => a Bool Int
5601 counter = proc reset -> do
5602 rec output <- returnA -< if reset then 0 else next
5603 next <- delay 0 -< output+1
5604 returnA -< output
5606 The translation of such forms uses the <function>loop</function> combinator,
5607 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
5613 <title>Conditional commands</title>
5616 In the previous example, we used a conditional expression to construct the
5618 Sometimes we want to conditionally execute different commands, as in
5625 which is translated to
5627 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
5628 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
5630 Since the translation uses <function>|||</function>,
5631 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
5635 There are also <literal>case</literal> commands, like
5641 y <- h -< (x1, x2)
5645 The syntax is the same as for <literal>case</literal> expressions,
5646 except that the bodies of the alternatives are commands rather than expressions.
5647 The translation is similar to that of <literal>if</literal> commands.
5653 <title>Defining your own control structures</title>
5656 As we're seen, arrow notation provides constructs,
5657 modelled on those for expressions,
5658 for sequencing, value recursion and conditionals.
5659 But suitable combinators,
5660 which you can define in ordinary Haskell,
5661 may also be used to build new commands out of existing ones.
5662 The basic idea is that a command defines an arrow from environments to values.
5663 These environments assign values to the free local variables of the command.
5664 Thus combinators that produce arrows from arrows
5665 may also be used to build commands from commands.
5666 For example, the <literal>ArrowChoice</literal> class includes a combinator
5668 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
5670 so we can use it to build commands:
5672 expr' = proc x -> do
5675 symbol Plus -< ()
5676 y <- term -< ()
5679 symbol Minus -< ()
5680 y <- term -< ()
5683 (The <literal>do</literal> on the first line is needed to prevent the first
5684 <literal><+> ...</literal> from being interpreted as part of the
5685 expression on the previous line.)
5686 This is equivalent to
5688 expr' = (proc x -> returnA -< x)
5689 <+> (proc x -> do
5690 symbol Plus -< ()
5691 y <- term -< ()
5693 <+> (proc x -> do
5694 symbol Minus -< ()
5695 y <- term -< ()
5698 It is essential that this operator be polymorphic in <literal>e</literal>
5699 (representing the environment input to the command
5700 and thence to its subcommands)
5701 and satisfy the corresponding naturality property
5703 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
5705 at least for strict <literal>k</literal>.
5706 (This should be automatic if you're not using <function>seq</function>.)
5707 This ensures that environments seen by the subcommands are environments
5708 of the whole command,
5709 and also allows the translation to safely trim these environments.
5710 The operator must also not use any variable defined within the current
5715 We could define our own operator
5717 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
5718 untilA body cond = proc x ->
5719 if cond x then returnA -< ()
5722 untilA body cond -< x
5724 and use it in the same way.
5725 Of course this infix syntax only makes sense for binary operators;
5726 there is also a more general syntax involving special brackets:
5730 (|untilA (increment -< x+y) (within 0.5 -< x)|)
5737 <title>Primitive constructs</title>
5740 Some operators will need to pass additional inputs to their subcommands.
5741 For example, in an arrow type supporting exceptions,
5742 the operator that attaches an exception handler will wish to pass the
5743 exception that occurred to the handler.
5744 Such an operator might have a type
5746 handleA :: ... => a e c -> a (e,Ex) c -> a e c
5748 where <literal>Ex</literal> is the type of exceptions handled.
5749 You could then use this with arrow notation by writing a command
5751 body `handleA` \ ex -> handler
5753 so that if an exception is raised in the command <literal>body</literal>,
5754 the variable <literal>ex</literal> is bound to the value of the exception
5755 and the command <literal>handler</literal>,
5756 which typically refers to <literal>ex</literal>, is entered.
5757 Though the syntax here looks like a functional lambda,
5758 we are talking about commands, and something different is going on.
5759 The input to the arrow represented by a command consists of values for
5760 the free local variables in the command, plus a stack of anonymous values.
5761 In all the prior examples, this stack was empty.
5762 In the second argument to <function>handleA</function>,
5763 this stack consists of one value, the value of the exception.
5764 The command form of lambda merely gives this value a name.
5769 the values on the stack are paired to the right of the environment.
5770 So operators like <function>handleA</function> that pass
5771 extra inputs to their subcommands can be designed for use with the notation
5772 by pairing the values with the environment in this way.
5773 More precisely, the type of each argument of the operator (and its result)
5774 should have the form
5776 a (...(e,t1), ... tn) t
5778 where <replaceable>e</replaceable> is a polymorphic variable
5779 (representing the environment)
5780 and <replaceable>ti</replaceable> are the types of the values on the stack,
5781 with <replaceable>t1</replaceable> being the <quote>top</quote>.
5782 The polymorphic variable <replaceable>e</replaceable> must not occur in
5783 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
5784 <replaceable>t</replaceable>.
5785 However the arrows involved need not be the same.
5786 Here are some more examples of suitable operators:
5788 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
5789 runReader :: ... => a e c -> a' (e,State) c
5790 runState :: ... => a e c -> a' (e,State) (c,State)
5792 We can supply the extra input required by commands built with the last two
5793 by applying them to ordinary expressions, as in
5797 (|runReader (do { ... })|) s
5799 which adds <literal>s</literal> to the stack of inputs to the command
5800 built using <function>runReader</function>.
5804 The command versions of lambda abstraction and application are analogous to
5805 the expression versions.
5806 In particular, the beta and eta rules describe equivalences of commands.
5807 These three features (operators, lambda abstraction and application)
5808 are the core of the notation; everything else can be built using them,
5809 though the results would be somewhat clumsy.
5810 For example, we could simulate <literal>do</literal>-notation by defining
5812 bind :: Arrow a => a e b -> a (e,b) c -> a e c
5813 u `bind` f = returnA &&& u >>> f
5815 bind_ :: Arrow a => a e b -> a e c -> a e c
5816 u `bind_` f = u `bind` (arr fst >>> f)
5818 We could simulate <literal>if</literal> by defining
5820 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
5821 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
5828 <title>Differences with the paper</title>
5833 <para>Instead of a single form of arrow application (arrow tail) with two
5834 translations, the implementation provides two forms
5835 <quote><literal>-<</literal></quote> (first-order)
5836 and <quote><literal>-<<</literal></quote> (higher-order).
5841 <para>User-defined operators are flagged with banana brackets instead of
5842 a new <literal>form</literal> keyword.
5851 <title>Portability</title>
5854 Although only GHC implements arrow notation directly,
5855 there is also a preprocessor
5857 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
5858 that translates arrow notation into Haskell 98
5859 for use with other Haskell systems.
5860 You would still want to check arrow programs with GHC;
5861 tracing type errors in the preprocessor output is not easy.
5862 Modules intended for both GHC and the preprocessor must observe some
5863 additional restrictions:
5868 The module must import
5869 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
5875 The preprocessor cannot cope with other Haskell extensions.
5876 These would have to go in separate modules.
5882 Because the preprocessor targets Haskell (rather than Core),
5883 <literal>let</literal>-bound variables are monomorphic.
5894 <!-- ==================== BANG PATTERNS ================= -->
5896 <sect1 id="bang-patterns">
5897 <title>Bang patterns
5898 <indexterm><primary>Bang patterns</primary></indexterm>
5900 <para>GHC supports an extension of pattern matching called <emphasis>bang
5901 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5903 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5904 prime feature description</ulink> contains more discussion and examples
5905 than the material below.
5908 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5911 <sect2 id="bang-patterns-informal">
5912 <title>Informal description of bang patterns
5915 The main idea is to add a single new production to the syntax of patterns:
5919 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5920 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5925 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5926 whereas without the bang it would be lazy.
5927 Bang patterns can be nested of course:
5931 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5932 <literal>y</literal>.
5933 A bang only really has an effect if it precedes a variable or wild-card pattern:
5938 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5939 forces evaluation anyway does nothing.
5941 Bang patterns work in <literal>case</literal> expressions too, of course:
5943 g5 x = let y = f x in body
5944 g6 x = case f x of { y -> body }
5945 g7 x = case f x of { !y -> body }
5947 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5948 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
5949 result, and then evaluates <literal>body</literal>.
5951 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5952 definitions too. For example:
5956 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5957 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5958 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5959 in a function argument <literal>![x,y]</literal> means the
5960 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5961 is part of the syntax of <literal>let</literal> bindings.
5966 <sect2 id="bang-patterns-sem">
5967 <title>Syntax and semantics
5971 We add a single new production to the syntax of patterns:
5975 There is one problem with syntactic ambiguity. Consider:
5979 Is this a definition of the infix function "<literal>(!)</literal>",
5980 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5981 ambiguity in favour of the latter. If you want to define
5982 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5987 The semantics of Haskell pattern matching is described in <ulink
5988 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
5989 Section 3.17.2</ulink> of the Haskell Report. To this description add
5990 one extra item 10, saying:
5991 <itemizedlist><listitem><para>Matching
5992 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5993 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5994 <listitem><para>otherwise, <literal>pat</literal> is matched against
5995 <literal>v</literal></para></listitem>
5997 </para></listitem></itemizedlist>
5998 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
5999 Section 3.17.3</ulink>, add a new case (t):
6001 case v of { !pat -> e; _ -> e' }
6002 = v `seq` case v of { pat -> e; _ -> e' }
6005 That leaves let expressions, whose translation is given in
6006 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6008 of the Haskell Report.
6009 In the translation box, first apply
6010 the following transformation: for each pattern <literal>pi</literal> that is of
6011 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6012 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6013 have a bang at the top, apply the rules in the existing box.
6015 <para>The effect of the let rule is to force complete matching of the pattern
6016 <literal>qi</literal> before evaluation of the body is begun. The bang is
6017 retained in the translated form in case <literal>qi</literal> is a variable,
6025 The let-binding can be recursive. However, it is much more common for
6026 the let-binding to be non-recursive, in which case the following law holds:
6027 <literal>(let !p = rhs in body)</literal>
6029 <literal>(case rhs of !p -> body)</literal>
6032 A pattern with a bang at the outermost level is not allowed at the top level of
6038 <!-- ==================== ASSERTIONS ================= -->
6040 <sect1 id="assertions">
6042 <indexterm><primary>Assertions</primary></indexterm>
6046 If you want to make use of assertions in your standard Haskell code, you
6047 could define a function like the following:
6053 assert :: Bool -> a -> a
6054 assert False x = error "assertion failed!"
6061 which works, but gives you back a less than useful error message --
6062 an assertion failed, but which and where?
6066 One way out is to define an extended <function>assert</function> function which also
6067 takes a descriptive string to include in the error message and
6068 perhaps combine this with the use of a pre-processor which inserts
6069 the source location where <function>assert</function> was used.
6073 Ghc offers a helping hand here, doing all of this for you. For every
6074 use of <function>assert</function> in the user's source:
6080 kelvinToC :: Double -> Double
6081 kelvinToC k = assert (k >= 0.0) (k+273.15)
6087 Ghc will rewrite this to also include the source location where the
6094 assert pred val ==> assertError "Main.hs|15" pred val
6100 The rewrite is only performed by the compiler when it spots
6101 applications of <function>Control.Exception.assert</function>, so you
6102 can still define and use your own versions of
6103 <function>assert</function>, should you so wish. If not, import
6104 <literal>Control.Exception</literal> to make use
6105 <function>assert</function> in your code.
6109 GHC ignores assertions when optimisation is turned on with the
6110 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6111 <literal>assert pred e</literal> will be rewritten to
6112 <literal>e</literal>. You can also disable assertions using the
6113 <option>-fignore-asserts</option>
6114 option<indexterm><primary><option>-fignore-asserts</option></primary>
6115 </indexterm>.</para>
6118 Assertion failures can be caught, see the documentation for the
6119 <literal>Control.Exception</literal> library for the details.
6125 <!-- =============================== PRAGMAS =========================== -->
6127 <sect1 id="pragmas">
6128 <title>Pragmas</title>
6130 <indexterm><primary>pragma</primary></indexterm>
6132 <para>GHC supports several pragmas, or instructions to the
6133 compiler placed in the source code. Pragmas don't normally affect
6134 the meaning of the program, but they might affect the efficiency
6135 of the generated code.</para>
6137 <para>Pragmas all take the form
6139 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6141 where <replaceable>word</replaceable> indicates the type of
6142 pragma, and is followed optionally by information specific to that
6143 type of pragma. Case is ignored in
6144 <replaceable>word</replaceable>. The various values for
6145 <replaceable>word</replaceable> that GHC understands are described
6146 in the following sections; any pragma encountered with an
6147 unrecognised <replaceable>word</replaceable> is (silently)
6148 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6149 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6151 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>. A file-header
6152 pragma must precede the <literal>module</literal> keyword in the file.
6153 There can be as many file-header pragmas as you please, and they can be
6154 preceded or followed by comments.</para>
6156 <sect2 id="language-pragma">
6157 <title>LANGUAGE pragma</title>
6159 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
6160 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
6162 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
6164 It is the intention that all Haskell compilers support the
6165 <literal>LANGUAGE</literal> pragma with the same syntax, although not
6166 all extensions are supported by all compilers, of
6167 course. The <literal>LANGUAGE</literal> pragma should be used instead
6168 of <literal>OPTIONS_GHC</literal>, if possible.</para>
6170 <para>For example, to enable the FFI and preprocessing with CPP:</para>
6172 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
6174 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6176 <para>Every language extension can also be turned into a command-line flag
6177 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
6178 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
6181 <para>A list of all supported language extensions can be obtained by invoking
6182 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
6184 <para>Any extension from the <literal>Extension</literal> type defined in
6186 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
6187 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
6191 <sect2 id="options-pragma">
6192 <title>OPTIONS_GHC pragma</title>
6193 <indexterm><primary>OPTIONS_GHC</primary>
6195 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
6198 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
6199 additional options that are given to the compiler when compiling
6200 this source file. See <xref linkend="source-file-options"/> for
6203 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
6204 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
6207 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6209 <sect2 id="include-pragma">
6210 <title>INCLUDE pragma</title>
6212 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
6213 of C header files that should be <literal>#include</literal>'d into
6214 the C source code generated by the compiler for the current module (if
6215 compiling via C). For example:</para>
6218 {-# INCLUDE "foo.h" #-}
6219 {-# INCLUDE <stdio.h> #-}</programlisting>
6221 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
6223 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
6224 to the <option>-#include</option> option (<xref
6225 linkend="options-C-compiler" />), because the
6226 <literal>INCLUDE</literal> pragma is understood by other
6227 compilers. Yet another alternative is to add the include file to each
6228 <literal>foreign import</literal> declaration in your code, but we
6229 don't recommend using this approach with GHC.</para>
6232 <sect2 id="warning-deprecated-pragma">
6233 <title>WARNING and DEPRECATED pragmas</title>
6234 <indexterm><primary>WARNING</primary></indexterm>
6235 <indexterm><primary>DEPRECATED</primary></indexterm>
6237 <para>The WARNING pragma allows you to attach an arbitrary warning
6238 to a particular function, class, or type.
6239 A DEPRECATED pragma lets you specify that
6240 a particular function, class, or type is deprecated.
6241 There are two ways of using these pragmas.
6245 <para>You can work on an entire module thus:</para>
6247 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
6252 module Wibble {-# WARNING "This is an unstable interface." #-} where
6255 <para>When you compile any module that import
6256 <literal>Wibble</literal>, GHC will print the specified
6261 <para>You can attach a warning to a function, class, type, or data constructor, with the
6262 following top-level declarations:</para>
6264 {-# DEPRECATED f, C, T "Don't use these" #-}
6265 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
6267 <para>When you compile any module that imports and uses any
6268 of the specified entities, GHC will print the specified
6270 <para> You can only attach to entities declared at top level in the module
6271 being compiled, and you can only use unqualified names in the list of
6272 entities. A capitalised name, such as <literal>T</literal>
6273 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
6274 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
6275 both are in scope. If both are in scope, there is currently no way to
6276 specify one without the other (c.f. fixities
6277 <xref linkend="infix-tycons"/>).</para>
6280 Warnings and deprecations are not reported for
6281 (a) uses within the defining module, and
6282 (b) uses in an export list.
6283 The latter reduces spurious complaints within a library
6284 in which one module gathers together and re-exports
6285 the exports of several others.
6287 <para>You can suppress the warnings with the flag
6288 <option>-fno-warn-warnings-deprecations</option>.</para>
6291 <sect2 id="inline-noinline-pragma">
6292 <title>INLINE and NOINLINE pragmas</title>
6294 <para>These pragmas control the inlining of function
6297 <sect3 id="inline-pragma">
6298 <title>INLINE pragma</title>
6299 <indexterm><primary>INLINE</primary></indexterm>
6301 <para>GHC (with <option>-O</option>, as always) tries to
6302 inline (or “unfold”) functions/values that are
6303 “small enough,” thus avoiding the call overhead
6304 and possibly exposing other more-wonderful optimisations.
6305 Normally, if GHC decides a function is “too
6306 expensive” to inline, it will not do so, nor will it
6307 export that unfolding for other modules to use.</para>
6309 <para>The sledgehammer you can bring to bear is the
6310 <literal>INLINE</literal><indexterm><primary>INLINE
6311 pragma</primary></indexterm> pragma, used thusly:</para>
6314 key_function :: Int -> String -> (Bool, Double)
6315 {-# INLINE key_function #-}
6318 <para>The major effect of an <literal>INLINE</literal> pragma
6319 is to declare a function's “cost” to be very low.
6320 The normal unfolding machinery will then be very keen to
6321 inline it. However, an <literal>INLINE</literal> pragma for a
6322 function "<literal>f</literal>" has a number of other effects:
6325 No functions are inlined into <literal>f</literal>. Otherwise
6326 GHC might inline a big function into <literal>f</literal>'s right hand side,
6327 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
6330 The float-in, float-out, and common-sub-expression transformations are not
6331 applied to the body of <literal>f</literal>.
6334 An INLINE function is not worker/wrappered by strictness analysis.
6335 It's going to be inlined wholesale instead.
6338 All of these effects are aimed at ensuring that what gets inlined is
6339 exactly what you asked for, no more and no less.
6341 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
6342 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
6343 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
6344 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
6345 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
6346 when there is no choice even an INLINE function can be selected, in which case
6347 the INLINE pragma is ignored.
6348 For example, for a self-recursive function, the loop breaker can only be the function
6349 itself, so an INLINE pragma is always ignored.</para>
6351 <para>Syntactically, an <literal>INLINE</literal> pragma for a
6352 function can be put anywhere its type signature could be
6355 <para><literal>INLINE</literal> pragmas are a particularly
6357 <literal>then</literal>/<literal>return</literal> (or
6358 <literal>bind</literal>/<literal>unit</literal>) functions in
6359 a monad. For example, in GHC's own
6360 <literal>UniqueSupply</literal> monad code, we have:</para>
6363 {-# INLINE thenUs #-}
6364 {-# INLINE returnUs #-}
6367 <para>See also the <literal>NOINLINE</literal> pragma (<xref
6368 linkend="noinline-pragma"/>).</para>
6370 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
6371 so if you want your code to be HBC-compatible you'll have to surround
6372 the pragma with C pre-processor directives
6373 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
6377 <sect3 id="noinline-pragma">
6378 <title>NOINLINE pragma</title>
6380 <indexterm><primary>NOINLINE</primary></indexterm>
6381 <indexterm><primary>NOTINLINE</primary></indexterm>
6383 <para>The <literal>NOINLINE</literal> pragma does exactly what
6384 you'd expect: it stops the named function from being inlined
6385 by the compiler. You shouldn't ever need to do this, unless
6386 you're very cautious about code size.</para>
6388 <para><literal>NOTINLINE</literal> is a synonym for
6389 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
6390 specified by Haskell 98 as the standard way to disable
6391 inlining, so it should be used if you want your code to be
6395 <sect3 id="phase-control">
6396 <title>Phase control</title>
6398 <para> Sometimes you want to control exactly when in GHC's
6399 pipeline the INLINE pragma is switched on. Inlining happens
6400 only during runs of the <emphasis>simplifier</emphasis>. Each
6401 run of the simplifier has a different <emphasis>phase
6402 number</emphasis>; the phase number decreases towards zero.
6403 If you use <option>-dverbose-core2core</option> you'll see the
6404 sequence of phase numbers for successive runs of the
6405 simplifier. In an INLINE pragma you can optionally specify a
6409 <para>"<literal>INLINE[k] f</literal>" means: do not inline
6410 <literal>f</literal>
6411 until phase <literal>k</literal>, but from phase
6412 <literal>k</literal> onwards be very keen to inline it.
6415 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
6416 <literal>f</literal>
6417 until phase <literal>k</literal>, but from phase
6418 <literal>k</literal> onwards do not inline it.
6421 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
6422 <literal>f</literal>
6423 until phase <literal>k</literal>, but from phase
6424 <literal>k</literal> onwards be willing to inline it (as if
6425 there was no pragma).
6428 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
6429 <literal>f</literal>
6430 until phase <literal>k</literal>, but from phase
6431 <literal>k</literal> onwards do not inline it.
6434 The same information is summarised here:
6436 -- Before phase 2 Phase 2 and later
6437 {-# INLINE [2] f #-} -- No Yes
6438 {-# INLINE [~2] f #-} -- Yes No
6439 {-# NOINLINE [2] f #-} -- No Maybe
6440 {-# NOINLINE [~2] f #-} -- Maybe No
6442 {-# INLINE f #-} -- Yes Yes
6443 {-# NOINLINE f #-} -- No No
6445 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
6446 function body is small, or it is applied to interesting-looking arguments etc).
6447 Another way to understand the semantics is this:
6449 <listitem><para>For both INLINE and NOINLINE, the phase number says
6450 when inlining is allowed at all.</para></listitem>
6451 <listitem><para>The INLINE pragma has the additional effect of making the
6452 function body look small, so that when inlining is allowed it is very likely to
6457 <para>The same phase-numbering control is available for RULES
6458 (<xref linkend="rewrite-rules"/>).</para>
6462 <sect2 id="line-pragma">
6463 <title>LINE pragma</title>
6465 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
6466 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
6467 <para>This pragma is similar to C's <literal>#line</literal>
6468 pragma, and is mainly for use in automatically generated Haskell
6469 code. It lets you specify the line number and filename of the
6470 original code; for example</para>
6472 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
6474 <para>if you'd generated the current file from something called
6475 <filename>Foo.vhs</filename> and this line corresponds to line
6476 42 in the original. GHC will adjust its error messages to refer
6477 to the line/file named in the <literal>LINE</literal>
6482 <title>RULES pragma</title>
6484 <para>The RULES pragma lets you specify rewrite rules. It is
6485 described in <xref linkend="rewrite-rules"/>.</para>
6488 <sect2 id="specialize-pragma">
6489 <title>SPECIALIZE pragma</title>
6491 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6492 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
6493 <indexterm><primary>overloading, death to</primary></indexterm>
6495 <para>(UK spelling also accepted.) For key overloaded
6496 functions, you can create extra versions (NB: more code space)
6497 specialised to particular types. Thus, if you have an
6498 overloaded function:</para>
6501 hammeredLookup :: Ord key => [(key, value)] -> key -> value
6504 <para>If it is heavily used on lists with
6505 <literal>Widget</literal> keys, you could specialise it as
6509 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
6512 <para>A <literal>SPECIALIZE</literal> pragma for a function can
6513 be put anywhere its type signature could be put.</para>
6515 <para>A <literal>SPECIALIZE</literal> has the effect of generating
6516 (a) a specialised version of the function and (b) a rewrite rule
6517 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
6518 un-specialised function into a call to the specialised one.</para>
6520 <para>The type in a SPECIALIZE pragma can be any type that is less
6521 polymorphic than the type of the original function. In concrete terms,
6522 if the original function is <literal>f</literal> then the pragma
6524 {-# SPECIALIZE f :: <type> #-}
6526 is valid if and only if the definition
6528 f_spec :: <type>
6531 is valid. Here are some examples (where we only give the type signature
6532 for the original function, not its code):
6534 f :: Eq a => a -> b -> b
6535 {-# SPECIALISE f :: Int -> b -> b #-}
6537 g :: (Eq a, Ix b) => a -> b -> b
6538 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
6540 h :: Eq a => a -> a -> a
6541 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
6543 The last of these examples will generate a
6544 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
6545 well. If you use this kind of specialisation, let us know how well it works.
6548 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
6549 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
6550 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
6551 The <literal>INLINE</literal> pragma affects the specialised version of the
6552 function (only), and applies even if the function is recursive. The motivating
6555 -- A GADT for arrays with type-indexed representation
6557 ArrInt :: !Int -> ByteArray# -> Arr Int
6558 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
6560 (!:) :: Arr e -> Int -> e
6561 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
6562 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
6563 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
6564 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
6566 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
6567 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
6568 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
6569 the specialised function will be inlined. It has two calls to
6570 <literal>(!:)</literal>,
6571 both at type <literal>Int</literal>. Both these calls fire the first
6572 specialisation, whose body is also inlined. The result is a type-based
6573 unrolling of the indexing function.</para>
6574 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
6575 on an ordinarily-recursive function.</para>
6577 <para>Note: In earlier versions of GHC, it was possible to provide your own
6578 specialised function for a given type:
6581 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
6584 This feature has been removed, as it is now subsumed by the
6585 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
6589 <sect2 id="specialize-instance-pragma">
6590 <title>SPECIALIZE instance pragma
6594 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
6595 <indexterm><primary>overloading, death to</primary></indexterm>
6596 Same idea, except for instance declarations. For example:
6599 instance (Eq a) => Eq (Foo a) where {
6600 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
6604 The pragma must occur inside the <literal>where</literal> part
6605 of the instance declaration.
6608 Compatible with HBC, by the way, except perhaps in the placement
6614 <sect2 id="unpack-pragma">
6615 <title>UNPACK pragma</title>
6617 <indexterm><primary>UNPACK</primary></indexterm>
6619 <para>The <literal>UNPACK</literal> indicates to the compiler
6620 that it should unpack the contents of a constructor field into
6621 the constructor itself, removing a level of indirection. For
6625 data T = T {-# UNPACK #-} !Float
6626 {-# UNPACK #-} !Float
6629 <para>will create a constructor <literal>T</literal> containing
6630 two unboxed floats. This may not always be an optimisation: if
6631 the <function>T</function> constructor is scrutinised and the
6632 floats passed to a non-strict function for example, they will
6633 have to be reboxed (this is done automatically by the
6636 <para>Unpacking constructor fields should only be used in
6637 conjunction with <option>-O</option>, in order to expose
6638 unfoldings to the compiler so the reboxing can be removed as
6639 often as possible. For example:</para>
6643 f (T f1 f2) = f1 + f2
6646 <para>The compiler will avoid reboxing <function>f1</function>
6647 and <function>f2</function> by inlining <function>+</function>
6648 on floats, but only when <option>-O</option> is on.</para>
6650 <para>Any single-constructor data is eligible for unpacking; for
6654 data T = T {-# UNPACK #-} !(Int,Int)
6657 <para>will store the two <literal>Int</literal>s directly in the
6658 <function>T</function> constructor, by flattening the pair.
6659 Multi-level unpacking is also supported:
6662 data T = T {-# UNPACK #-} !S
6663 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
6666 will store two unboxed <literal>Int#</literal>s
6667 directly in the <function>T</function> constructor. The
6668 unpacker can see through newtypes, too.</para>
6670 <para>If a field cannot be unpacked, you will not get a warning,
6671 so it might be an idea to check the generated code with
6672 <option>-ddump-simpl</option>.</para>
6674 <para>See also the <option>-funbox-strict-fields</option> flag,
6675 which essentially has the effect of adding
6676 <literal>{-# UNPACK #-}</literal> to every strict
6677 constructor field.</para>
6680 <sect2 id="source-pragma">
6681 <title>SOURCE pragma</title>
6683 <indexterm><primary>SOURCE</primary></indexterm>
6684 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
6685 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
6691 <!-- ======================= REWRITE RULES ======================== -->
6693 <sect1 id="rewrite-rules">
6694 <title>Rewrite rules
6696 <indexterm><primary>RULES pragma</primary></indexterm>
6697 <indexterm><primary>pragma, RULES</primary></indexterm>
6698 <indexterm><primary>rewrite rules</primary></indexterm></title>
6701 The programmer can specify rewrite rules as part of the source program
6707 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6712 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
6713 If you need more information, then <option>-ddump-rule-firings</option> shows you
6714 each individual rule firing in detail.
6718 <title>Syntax</title>
6721 From a syntactic point of view:
6727 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
6728 may be generated by the layout rule).
6734 The layout rule applies in a pragma.
6735 Currently no new indentation level
6736 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
6737 you must lay out the starting in the same column as the enclosing definitions.
6740 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
6741 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
6744 Furthermore, the closing <literal>#-}</literal>
6745 should start in a column to the right of the opening <literal>{-#</literal>.
6751 Each rule has a name, enclosed in double quotes. The name itself has
6752 no significance at all. It is only used when reporting how many times the rule fired.
6758 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
6759 immediately after the name of the rule. Thus:
6762 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
6765 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
6766 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
6775 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
6776 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
6777 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
6778 by spaces, just like in a type <literal>forall</literal>.
6784 A pattern variable may optionally have a type signature.
6785 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
6786 For example, here is the <literal>foldr/build</literal> rule:
6789 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
6790 foldr k z (build g) = g k z
6793 Since <function>g</function> has a polymorphic type, it must have a type signature.
6800 The left hand side of a rule must consist of a top-level variable applied
6801 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
6804 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
6805 "wrong2" forall f. f True = True
6808 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
6815 A rule does not need to be in the same module as (any of) the
6816 variables it mentions, though of course they need to be in scope.
6822 All rules are implicitly exported from the module, and are therefore
6823 in force in any module that imports the module that defined the rule, directly
6824 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6825 in force when compiling A.) The situation is very similar to that for instance
6833 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
6834 any other flag settings. Furthermore, inside a RULE, the language extension
6835 <option>-XScopedTypeVariables</option> is automatically enabled; see
6836 <xref linkend="scoped-type-variables"/>.
6842 Like other pragmas, RULE pragmas are always checked for scope errors, and
6843 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
6844 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
6845 if the <option>-fenable-rewrite-rules</option> flag is
6846 on (see <xref linkend="rule-semantics"/>).
6855 <sect2 id="rule-semantics">
6856 <title>Semantics</title>
6859 From a semantic point of view:
6864 Rules are enabled (that is, used during optimisation)
6865 by the <option>-fenable-rewrite-rules</option> flag.
6866 This flag is implied by <option>-O</option>, and may be switched
6867 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
6868 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
6869 may not do what you expect, though, because without <option>-O</option> GHC
6870 ignores all optimisation information in interface files;
6871 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
6872 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
6873 has no effect on parsing or typechecking.
6879 Rules are regarded as left-to-right rewrite rules.
6880 When GHC finds an expression that is a substitution instance of the LHS
6881 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
6882 By "a substitution instance" we mean that the LHS can be made equal to the
6883 expression by substituting for the pattern variables.
6890 GHC makes absolutely no attempt to verify that the LHS and RHS
6891 of a rule have the same meaning. That is undecidable in general, and
6892 infeasible in most interesting cases. The responsibility is entirely the programmer's!
6899 GHC makes no attempt to make sure that the rules are confluent or
6900 terminating. For example:
6903 "loop" forall x y. f x y = f y x
6906 This rule will cause the compiler to go into an infinite loop.
6913 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
6919 GHC currently uses a very simple, syntactic, matching algorithm
6920 for matching a rule LHS with an expression. It seeks a substitution
6921 which makes the LHS and expression syntactically equal modulo alpha
6922 conversion. The pattern (rule), but not the expression, is eta-expanded if
6923 necessary. (Eta-expanding the expression can lead to laziness bugs.)
6924 But not beta conversion (that's called higher-order matching).
6928 Matching is carried out on GHC's intermediate language, which includes
6929 type abstractions and applications. So a rule only matches if the
6930 types match too. See <xref linkend="rule-spec"/> below.
6936 GHC keeps trying to apply the rules as it optimises the program.
6937 For example, consider:
6946 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
6947 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
6948 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
6949 not be substituted, and the rule would not fire.
6956 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
6957 results. Consider this (artificial) example
6960 {-# RULES "f" f True = False #-}
6966 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
6971 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
6973 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
6974 would have been a better chance that <literal>f</literal>'s RULE might fire.
6977 The way to get predictable behaviour is to use a NOINLINE
6978 pragma on <literal>f</literal>, to ensure
6979 that it is not inlined until its RULEs have had a chance to fire.
6989 <title>List fusion</title>
6992 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6993 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6994 intermediate list should be eliminated entirely.
6998 The following are good producers:
7010 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7016 Explicit lists (e.g. <literal>[True, False]</literal>)
7022 The cons constructor (e.g <literal>3:4:[]</literal>)
7028 <function>++</function>
7034 <function>map</function>
7040 <function>take</function>, <function>filter</function>
7046 <function>iterate</function>, <function>repeat</function>
7052 <function>zip</function>, <function>zipWith</function>
7061 The following are good consumers:
7073 <function>array</function> (on its second argument)
7079 <function>++</function> (on its first argument)
7085 <function>foldr</function>
7091 <function>map</function>
7097 <function>take</function>, <function>filter</function>
7103 <function>concat</function>
7109 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
7115 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
7116 will fuse with one but not the other)
7122 <function>partition</function>
7128 <function>head</function>
7134 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
7140 <function>sequence_</function>
7146 <function>msum</function>
7152 <function>sortBy</function>
7161 So, for example, the following should generate no intermediate lists:
7164 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
7170 This list could readily be extended; if there are Prelude functions that you use
7171 a lot which are not included, please tell us.
7175 If you want to write your own good consumers or producers, look at the
7176 Prelude definitions of the above functions to see how to do so.
7181 <sect2 id="rule-spec">
7182 <title>Specialisation
7186 Rewrite rules can be used to get the same effect as a feature
7187 present in earlier versions of GHC.
7188 For example, suppose that:
7191 genericLookup :: Ord a => Table a b -> a -> b
7192 intLookup :: Table Int b -> Int -> b
7195 where <function>intLookup</function> is an implementation of
7196 <function>genericLookup</function> that works very fast for
7197 keys of type <literal>Int</literal>. You might wish
7198 to tell GHC to use <function>intLookup</function> instead of
7199 <function>genericLookup</function> whenever the latter was called with
7200 type <literal>Table Int b -> Int -> b</literal>.
7201 It used to be possible to write
7204 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
7207 This feature is no longer in GHC, but rewrite rules let you do the same thing:
7210 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
7213 This slightly odd-looking rule instructs GHC to replace
7214 <function>genericLookup</function> by <function>intLookup</function>
7215 <emphasis>whenever the types match</emphasis>.
7216 What is more, this rule does not need to be in the same
7217 file as <function>genericLookup</function>, unlike the
7218 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
7219 have an original definition available to specialise).
7222 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
7223 <function>intLookup</function> really behaves as a specialised version
7224 of <function>genericLookup</function>!!!</para>
7226 <para>An example in which using <literal>RULES</literal> for
7227 specialisation will Win Big:
7230 toDouble :: Real a => a -> Double
7231 toDouble = fromRational . toRational
7233 {-# RULES "toDouble/Int" toDouble = i2d #-}
7234 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
7237 The <function>i2d</function> function is virtually one machine
7238 instruction; the default conversion—via an intermediate
7239 <literal>Rational</literal>—is obscenely expensive by
7246 <title>Controlling what's going on</title>
7254 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
7260 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
7261 If you add <option>-dppr-debug</option> you get a more detailed listing.
7267 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
7270 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
7271 {-# INLINE build #-}
7275 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
7276 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
7277 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
7278 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
7285 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
7286 see how to write rules that will do fusion and yet give an efficient
7287 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
7297 <sect2 id="core-pragma">
7298 <title>CORE pragma</title>
7300 <indexterm><primary>CORE pragma</primary></indexterm>
7301 <indexterm><primary>pragma, CORE</primary></indexterm>
7302 <indexterm><primary>core, annotation</primary></indexterm>
7305 The external core format supports <quote>Note</quote> annotations;
7306 the <literal>CORE</literal> pragma gives a way to specify what these
7307 should be in your Haskell source code. Syntactically, core
7308 annotations are attached to expressions and take a Haskell string
7309 literal as an argument. The following function definition shows an
7313 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
7316 Semantically, this is equivalent to:
7324 However, when external core is generated (via
7325 <option>-fext-core</option>), there will be Notes attached to the
7326 expressions <function>show</function> and <varname>x</varname>.
7327 The core function declaration for <function>f</function> is:
7331 f :: %forall a . GHCziShow.ZCTShow a ->
7332 a -> GHCziBase.ZMZN GHCziBase.Char =
7333 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
7335 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
7337 (tpl1::GHCziBase.Int ->
7339 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7341 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
7342 (tpl3::GHCziBase.ZMZN a ->
7343 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
7351 Here, we can see that the function <function>show</function> (which
7352 has been expanded out to a case expression over the Show dictionary)
7353 has a <literal>%note</literal> attached to it, as does the
7354 expression <varname>eta</varname> (which used to be called
7355 <varname>x</varname>).
7362 <sect1 id="special-ids">
7363 <title>Special built-in functions</title>
7364 <para>GHC has a few built-in functions with special behaviour. These
7365 are now described in the module <ulink
7366 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
7367 in the library documentation.</para>
7371 <sect1 id="generic-classes">
7372 <title>Generic classes</title>
7375 The ideas behind this extension are described in detail in "Derivable type classes",
7376 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
7377 An example will give the idea:
7385 fromBin :: [Int] -> (a, [Int])
7387 toBin {| Unit |} Unit = []
7388 toBin {| a :+: b |} (Inl x) = 0 : toBin x
7389 toBin {| a :+: b |} (Inr y) = 1 : toBin y
7390 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
7392 fromBin {| Unit |} bs = (Unit, bs)
7393 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
7394 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
7395 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
7396 (y,bs'') = fromBin bs'
7399 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
7400 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
7401 which are defined thus in the library module <literal>Generics</literal>:
7405 data a :+: b = Inl a | Inr b
7406 data a :*: b = a :*: b
7409 Now you can make a data type into an instance of Bin like this:
7411 instance (Bin a, Bin b) => Bin (a,b)
7412 instance Bin a => Bin [a]
7414 That is, just leave off the "where" clause. Of course, you can put in the
7415 where clause and over-ride whichever methods you please.
7419 <title> Using generics </title>
7420 <para>To use generics you need to</para>
7423 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
7424 <option>-XGenerics</option> (to generate extra per-data-type code),
7425 and <option>-package lang</option> (to make the <literal>Generics</literal> library
7429 <para>Import the module <literal>Generics</literal> from the
7430 <literal>lang</literal> package. This import brings into
7431 scope the data types <literal>Unit</literal>,
7432 <literal>:*:</literal>, and <literal>:+:</literal>. (You
7433 don't need this import if you don't mention these types
7434 explicitly; for example, if you are simply giving instance
7435 declarations.)</para>
7440 <sect2> <title> Changes wrt the paper </title>
7442 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
7443 can be written infix (indeed, you can now use
7444 any operator starting in a colon as an infix type constructor). Also note that
7445 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
7446 Finally, note that the syntax of the type patterns in the class declaration
7447 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
7448 alone would ambiguous when they appear on right hand sides (an extension we
7449 anticipate wanting).
7453 <sect2> <title>Terminology and restrictions</title>
7455 Terminology. A "generic default method" in a class declaration
7456 is one that is defined using type patterns as above.
7457 A "polymorphic default method" is a default method defined as in Haskell 98.
7458 A "generic class declaration" is a class declaration with at least one
7459 generic default method.
7467 Alas, we do not yet implement the stuff about constructor names and
7474 A generic class can have only one parameter; you can't have a generic
7475 multi-parameter class.
7481 A default method must be defined entirely using type patterns, or entirely
7482 without. So this is illegal:
7485 op :: a -> (a, Bool)
7486 op {| Unit |} Unit = (Unit, True)
7489 However it is perfectly OK for some methods of a generic class to have
7490 generic default methods and others to have polymorphic default methods.
7496 The type variable(s) in the type pattern for a generic method declaration
7497 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:
7501 op {| p :*: q |} (x :*: y) = op (x :: p)
7509 The type patterns in a generic default method must take one of the forms:
7515 where "a" and "b" are type variables. Furthermore, all the type patterns for
7516 a single type constructor (<literal>:*:</literal>, say) must be identical; they
7517 must use the same type variables. So this is illegal:
7521 op {| a :+: b |} (Inl x) = True
7522 op {| p :+: q |} (Inr y) = False
7524 The type patterns must be identical, even in equations for different methods of the class.
7525 So this too is illegal:
7529 op1 {| a :*: b |} (x :*: y) = True
7532 op2 {| p :*: q |} (x :*: y) = False
7534 (The reason for this restriction is that we gather all the equations for a particular type constructor
7535 into a single generic instance declaration.)
7541 A generic method declaration must give a case for each of the three type constructors.
7547 The type for a generic method can be built only from:
7549 <listitem> <para> Function arrows </para> </listitem>
7550 <listitem> <para> Type variables </para> </listitem>
7551 <listitem> <para> Tuples </para> </listitem>
7552 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
7554 Here are some example type signatures for generic methods:
7557 op2 :: Bool -> (a,Bool)
7558 op3 :: [Int] -> a -> a
7561 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
7565 This restriction is an implementation restriction: we just haven't got around to
7566 implementing the necessary bidirectional maps over arbitrary type constructors.
7567 It would be relatively easy to add specific type constructors, such as Maybe and list,
7568 to the ones that are allowed.</para>
7573 In an instance declaration for a generic class, the idea is that the compiler
7574 will fill in the methods for you, based on the generic templates. However it can only
7579 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
7584 No constructor of the instance type has unboxed fields.
7588 (Of course, these things can only arise if you are already using GHC extensions.)
7589 However, you can still give an instance declarations for types which break these rules,
7590 provided you give explicit code to override any generic default methods.
7598 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
7599 what the compiler does with generic declarations.
7604 <sect2> <title> Another example </title>
7606 Just to finish with, here's another example I rather like:
7610 nCons {| Unit |} _ = 1
7611 nCons {| a :*: b |} _ = 1
7612 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
7615 tag {| Unit |} _ = 1
7616 tag {| a :*: b |} _ = 1
7617 tag {| a :+: b |} (Inl x) = tag x
7618 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
7624 <sect1 id="monomorphism">
7625 <title>Control over monomorphism</title>
7627 <para>GHC supports two flags that control the way in which generalisation is
7628 carried out at let and where bindings.
7632 <title>Switching off the dreaded Monomorphism Restriction</title>
7633 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
7635 <para>Haskell's monomorphism restriction (see
7636 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
7638 of the Haskell Report)
7639 can be completely switched off by
7640 <option>-XNoMonomorphismRestriction</option>.
7645 <title>Monomorphic pattern bindings</title>
7646 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
7647 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
7649 <para> As an experimental change, we are exploring the possibility of
7650 making pattern bindings monomorphic; that is, not generalised at all.
7651 A pattern binding is a binding whose LHS has no function arguments,
7652 and is not a simple variable. For example:
7654 f x = x -- Not a pattern binding
7655 f = \x -> x -- Not a pattern binding
7656 f :: Int -> Int = \x -> x -- Not a pattern binding
7658 (g,h) = e -- A pattern binding
7659 (f) = e -- A pattern binding
7660 [x] = e -- A pattern binding
7662 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
7663 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
7672 ;;; Local Variables: ***
7674 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
7675 ;;; ispell-local-dictionary: "british" ***
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