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>" or "<option>-X=</option>";
46 e.g. <option>-X=TemplateHaskell</option>. Before anything else is done, the string following
47 "<option>-X</option>" is normalised by removing hyphens and converting
48 to lower case. So <option>-X=TemplateHaskell</option>, <option>-XTemplateHaskell</option>, and
49 <option>-Xtemplate-haskell</option> are all equivalent.
52 <para> All the language options can be turned off by using the prefix "<option>No</option>";
53 e.g. "<option>-X=NoTemplateHaskell</option>".</para>
55 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
56 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
58 <para> All the language options can be introduced with "<option>-f</option>" as well as "<option>-X</option>",
59 but this is a deprecated feature for backward compatibility. Use the "<option>-X</option>"
60 or LANGUAGE-pragma form.</para>
62 <para>Turning on an option that enables special syntax
63 <emphasis>might</emphasis> cause working Haskell 98 code to fail
64 to compile, perhaps because it uses a variable name which has
65 become a reserved word. So, together with each option below, we
66 list the special syntax which is enabled by this option. We use
67 notation and nonterminal names from the Haskell 98 lexical syntax
68 (see the Haskell 98 Report). There are two classes of special
73 <para>New reserved words and symbols: character sequences
74 which are no longer available for use as identifiers in the
78 <para>Other special syntax: sequences of characters that have
79 a different meaning when this particular option is turned
84 <para>We are only listing syntax changes here that might affect
85 existing working programs (i.e. "stolen" syntax). Many of these
86 extensions will also enable new context-free syntax, but in all
87 cases programs written to use the new syntax would not be
88 compilable without the option enabled.</para>
94 <option>-fglasgow-exts</option>:
95 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
98 <para>This simultaneously enables all of the extensions to
99 Haskell 98 described in <xref
100 linkend="ghc-language-features"/>, except where otherwise
101 noted. We are trying to move away from this portmanteau flag,
102 and towards enabling features individaully.</para>
104 <para>New reserved words: <literal>forall</literal> (only in
105 types), <literal>mdo</literal>.</para>
107 <para>Other syntax stolen:
108 <replaceable>varid</replaceable>{<literal>#</literal>},
109 <replaceable>char</replaceable><literal>#</literal>,
110 <replaceable>string</replaceable><literal>#</literal>,
111 <replaceable>integer</replaceable><literal>#</literal>,
112 <replaceable>float</replaceable><literal>#</literal>,
113 <replaceable>float</replaceable><literal>##</literal>,
114 <literal>(#</literal>, <literal>#)</literal>,
115 <literal>|)</literal>, <literal>{|</literal>.</para>
117 <para>Implies these specific language options:
118 <option>-X=ForeignFunctionInterface</option>,
119 <option>-X=ImplicitParams</option>,
120 <option>-X=ScopedTypeVariables</option>,
121 <option>-X=GADTs</option>,
122 <option>-X=TypeFamilies</option>. </para>
128 <option>-X=ffi</option> and <option>-X=ForeignFunctionInterface</option>:
129 <indexterm><primary><option>-X=FFI</option></primary></indexterm>
132 <para>This option enables the language extension defined in the
133 Haskell 98 Foreign Function Interface Addendum.</para>
135 <para>New reserved words: <literal>foreign</literal>.</para>
141 <option>-X=MonomorphismRestriction</option>,<option>-X=MonoPatBinds</option>:
144 <para> These two flags control how generalisation is done.
145 See <xref linkend="monomorphism"/>.
152 <option>-X=ExtendedDefaultRules</option>:
153 <indexterm><primary><option>-X=ExtendedDefaultRules</option></primary></indexterm>
156 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
157 Independent of the <option>-fglasgow-exts</option>
164 <option>-X=AllowOverlappingInstances</option>
165 <indexterm><primary><option>-X=AllowOverlappingInstances</option></primary></indexterm>
168 <option>-X=AllowUndecidableInstances</option>
169 <indexterm><primary><option>-X=AllowUndecidableInstances</option></primary></indexterm>
172 <option>-X=AllowIncoherentInstances</option>
173 <indexterm><primary><option>-X=AllowIncoherentInstances</option></primary></indexterm>
176 <option>-fcontext-stack=N</option>
177 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
180 <para> See <xref linkend="instance-decls"/>. Only relevant
181 if you also use <option>-fglasgow-exts</option>.</para>
187 <option>-finline-phase</option>
188 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
191 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
192 you also use <option>-fglasgow-exts</option>.</para>
198 <option>-X=Arrows</option>
199 <indexterm><primary><option>-X=Arrows</option></primary></indexterm>
202 <para>See <xref linkend="arrow-notation"/>. Independent of
203 <option>-fglasgow-exts</option>.</para>
205 <para>New reserved words/symbols: <literal>rec</literal>,
206 <literal>proc</literal>, <literal>-<</literal>,
207 <literal>>-</literal>, <literal>-<<</literal>,
208 <literal>>>-</literal>.</para>
210 <para>Other syntax stolen: <literal>(|</literal>,
211 <literal>|)</literal>.</para>
217 <option>-X=Generics</option>
218 <indexterm><primary><option>-X=Generics</option></primary></indexterm>
221 <para>See <xref linkend="generic-classes"/>. Independent of
222 <option>-fglasgow-exts</option>.</para>
227 <term><option>-X=NoImplicitIrelude</option></term>
229 <para><indexterm><primary>-XnoImplicitPrelude
230 option</primary></indexterm> GHC normally imports
231 <filename>Prelude.hi</filename> files for you. If you'd
232 rather it didn't, then give it a
233 <option>-XnoImplicitPrelude</option> option. The idea is
234 that you can then import a Prelude of your own. (But don't
235 call it <literal>Prelude</literal>; the Haskell module
236 namespace is flat, and you must not conflict with any
237 Prelude module.)</para>
239 <para>Even though you have not imported the Prelude, most of
240 the built-in syntax still refers to the built-in Haskell
241 Prelude types and values, as specified by the Haskell
242 Report. For example, the type <literal>[Int]</literal>
243 still means <literal>Prelude.[] Int</literal>; tuples
244 continue to refer to the standard Prelude tuples; the
245 translation for list comprehensions continues to use
246 <literal>Prelude.map</literal> etc.</para>
248 <para>However, <option>-X=NoImplicitPrelude</option> does
249 change the handling of certain built-in syntax: see <xref
250 linkend="rebindable-syntax"/>.</para>
255 <term><option>-X=ImplicitParams</option></term>
257 <para>Enables implicit parameters (see <xref
258 linkend="implicit-parameters"/>). Currently also implied by
259 <option>-fglasgow-exts</option>.</para>
262 <literal>?<replaceable>varid</replaceable></literal>,
263 <literal>%<replaceable>varid</replaceable></literal>.</para>
268 <term><option>-X=OverloadedStrings</option></term>
270 <para>Enables overloaded string literals (see <xref
271 linkend="overloaded-strings"/>).</para>
276 <term><option>-X=ScopedTypeVariables</option></term>
278 <para>Enables lexically-scoped type variables (see <xref
279 linkend="scoped-type-variables"/>). Implied by
280 <option>-fglasgow-exts</option>.</para>
285 <term><option>-X=TH</option>, <option>-X=TemplateHaskell</option></term>
287 <para>Enables Template Haskell (see <xref
288 linkend="template-haskell"/>). This flag must
289 be given explicitly; it is no longer implied by
290 <option>-fglasgow-exts</option>.</para>
292 <para>Syntax stolen: <literal>[|</literal>,
293 <literal>[e|</literal>, <literal>[p|</literal>,
294 <literal>[d|</literal>, <literal>[t|</literal>,
295 <literal>$(</literal>,
296 <literal>$<replaceable>varid</replaceable></literal>.</para>
303 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
304 <sect1 id="primitives">
305 <title>Unboxed types and primitive operations</title>
307 <para>GHC is built on a raft of primitive data types and operations.
308 While you really can use this stuff to write fast code,
309 we generally find it a lot less painful, and more satisfying in the
310 long run, to use higher-level language features and libraries. With
311 any luck, the code you write will be optimised to the efficient
312 unboxed version in any case. And if it isn't, we'd like to know
315 <para>We do not currently have good, up-to-date documentation about the
316 primitives, perhaps because they are mainly intended for internal use.
317 There used to be a long section about them here in the User Guide, but it
318 became out of date, and wrong information is worse than none.</para>
320 <para>The Real Truth about what primitive types there are, and what operations
321 work over those types, is held in the file
322 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
323 This file is used directly to generate GHC's primitive-operation definitions, so
324 it is always correct! It is also intended for processing into text.</para>
327 the result of such processing is part of the description of the
329 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
330 Core language</ulink>.
331 So that document is a good place to look for a type-set version.
332 We would be very happy if someone wanted to volunteer to produce an SGML
333 back end to the program that processes <filename>primops.txt</filename> so that
334 we could include the results here in the User Guide.</para>
336 <para>What follows here is a brief summary of some main points.</para>
338 <sect2 id="glasgow-unboxed">
343 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
346 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
347 that values of that type are represented by a pointer to a heap
348 object. The representation of a Haskell <literal>Int</literal>, for
349 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
350 type, however, is represented by the value itself, no pointers or heap
351 allocation are involved.
355 Unboxed types correspond to the “raw machine” types you
356 would use in C: <literal>Int#</literal> (long int),
357 <literal>Double#</literal> (double), <literal>Addr#</literal>
358 (void *), etc. The <emphasis>primitive operations</emphasis>
359 (PrimOps) on these types are what you might expect; e.g.,
360 <literal>(+#)</literal> is addition on
361 <literal>Int#</literal>s, and is the machine-addition that we all
362 know and love—usually one instruction.
366 Primitive (unboxed) types cannot be defined in Haskell, and are
367 therefore built into the language and compiler. Primitive types are
368 always unlifted; that is, a value of a primitive type cannot be
369 bottom. We use the convention that primitive types, values, and
370 operations have a <literal>#</literal> suffix.
374 Primitive values are often represented by a simple bit-pattern, such
375 as <literal>Int#</literal>, <literal>Float#</literal>,
376 <literal>Double#</literal>. But this is not necessarily the case:
377 a primitive value might be represented by a pointer to a
378 heap-allocated object. Examples include
379 <literal>Array#</literal>, the type of primitive arrays. A
380 primitive array is heap-allocated because it is too big a value to fit
381 in a register, and would be too expensive to copy around; in a sense,
382 it is accidental that it is represented by a pointer. If a pointer
383 represents a primitive value, then it really does point to that value:
384 no unevaluated thunks, no indirections…nothing can be at the
385 other end of the pointer than the primitive value.
386 A numerically-intensive program using unboxed types can
387 go a <emphasis>lot</emphasis> faster than its “standard”
388 counterpart—we saw a threefold speedup on one example.
392 There are some restrictions on the use of primitive types:
394 <listitem><para>The main restriction
395 is that you can't pass a primitive value to a polymorphic
396 function or store one in a polymorphic data type. This rules out
397 things like <literal>[Int#]</literal> (i.e. lists of primitive
398 integers). The reason for this restriction is that polymorphic
399 arguments and constructor fields are assumed to be pointers: if an
400 unboxed integer is stored in one of these, the garbage collector would
401 attempt to follow it, leading to unpredictable space leaks. Or a
402 <function>seq</function> operation on the polymorphic component may
403 attempt to dereference the pointer, with disastrous results. Even
404 worse, the unboxed value might be larger than a pointer
405 (<literal>Double#</literal> for instance).
408 <listitem><para> You cannot define a newtype whose representation type
409 (the argument type of the data constructor) is an unboxed type. Thus,
415 <listitem><para> You cannot bind a variable with an unboxed type
416 in a <emphasis>top-level</emphasis> binding.
418 <listitem><para> You cannot bind a variable with an unboxed type
419 in a <emphasis>recursive</emphasis> binding.
421 <listitem><para> You may bind unboxed variables in a (non-recursive,
422 non-top-level) pattern binding, but any such variable causes the entire
424 to become strict. For example:
426 data Foo = Foo Int Int#
428 f x = let (Foo a b, w) = ..rhs.. in ..body..
430 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
432 is strict, and the program behaves as if you had written
434 data Foo = Foo Int Int#
436 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
445 <sect2 id="unboxed-tuples">
446 <title>Unboxed Tuples
450 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
451 they're available by default with <option>-fglasgow-exts</option>. An
452 unboxed tuple looks like this:
464 where <literal>e_1..e_n</literal> are expressions of any
465 type (primitive or non-primitive). The type of an unboxed tuple looks
470 Unboxed tuples are used for functions that need to return multiple
471 values, but they avoid the heap allocation normally associated with
472 using fully-fledged tuples. When an unboxed tuple is returned, the
473 components are put directly into registers or on the stack; the
474 unboxed tuple itself does not have a composite representation. Many
475 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
477 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
478 tuples to avoid unnecessary allocation during sequences of operations.
482 There are some pretty stringent restrictions on the use of unboxed tuples:
487 Values of unboxed tuple types are subject to the same restrictions as
488 other unboxed types; i.e. they may not be stored in polymorphic data
489 structures or passed to polymorphic functions.
496 No variable can have an unboxed tuple type, nor may a constructor or function
497 argument have an unboxed tuple type. The following are all illegal:
501 data Foo = Foo (# Int, Int #)
503 f :: (# Int, Int #) -> (# Int, Int #)
506 g :: (# Int, Int #) -> Int
509 h x = let y = (# x,x #) in ...
516 The typical use of unboxed tuples is simply to return multiple values,
517 binding those multiple results with a <literal>case</literal> expression, thus:
519 f x y = (# x+1, y-1 #)
520 g x = case f x x of { (# a, b #) -> a + b }
522 You can have an unboxed tuple in a pattern binding, thus
524 f x = let (# p,q #) = h x in ..body..
526 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
527 the resulting binding is lazy like any other Haskell pattern binding. The
528 above example desugars like this:
530 f x = let t = case h x o f{ (# p,q #) -> (p,q)
535 Indeed, the bindings can even be recursive.
542 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
544 <sect1 id="syntax-extns">
545 <title>Syntactic extensions</title>
547 <!-- ====================== HIERARCHICAL MODULES ======================= -->
549 <sect2 id="hierarchical-modules">
550 <title>Hierarchical Modules</title>
552 <para>GHC supports a small extension to the syntax of module
553 names: a module name is allowed to contain a dot
554 <literal>‘.’</literal>. This is also known as the
555 “hierarchical module namespace” extension, because
556 it extends the normally flat Haskell module namespace into a
557 more flexible hierarchy of modules.</para>
559 <para>This extension has very little impact on the language
560 itself; modules names are <emphasis>always</emphasis> fully
561 qualified, so you can just think of the fully qualified module
562 name as <quote>the module name</quote>. In particular, this
563 means that the full module name must be given after the
564 <literal>module</literal> keyword at the beginning of the
565 module; for example, the module <literal>A.B.C</literal> must
568 <programlisting>module A.B.C</programlisting>
571 <para>It is a common strategy to use the <literal>as</literal>
572 keyword to save some typing when using qualified names with
573 hierarchical modules. For example:</para>
576 import qualified Control.Monad.ST.Strict as ST
579 <para>For details on how GHC searches for source and interface
580 files in the presence of hierarchical modules, see <xref
581 linkend="search-path"/>.</para>
583 <para>GHC comes with a large collection of libraries arranged
584 hierarchically; see the accompanying <ulink
585 url="../libraries/index.html">library
586 documentation</ulink>. More libraries to install are available
588 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
591 <!-- ====================== PATTERN GUARDS ======================= -->
593 <sect2 id="pattern-guards">
594 <title>Pattern guards</title>
597 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
598 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.)
602 Suppose we have an abstract data type of finite maps, with a
606 lookup :: FiniteMap -> Int -> Maybe Int
609 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
610 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
614 clunky env var1 var2 | ok1 && ok2 = val1 + val2
615 | otherwise = var1 + var2
626 The auxiliary functions are
630 maybeToBool :: Maybe a -> Bool
631 maybeToBool (Just x) = True
632 maybeToBool Nothing = False
634 expectJust :: Maybe a -> a
635 expectJust (Just x) = x
636 expectJust Nothing = error "Unexpected Nothing"
640 What is <function>clunky</function> doing? The guard <literal>ok1 &&
641 ok2</literal> checks that both lookups succeed, using
642 <function>maybeToBool</function> to convert the <function>Maybe</function>
643 types to booleans. The (lazily evaluated) <function>expectJust</function>
644 calls extract the values from the results of the lookups, and binds the
645 returned values to <varname>val1</varname> and <varname>val2</varname>
646 respectively. If either lookup fails, then clunky takes the
647 <literal>otherwise</literal> case and returns the sum of its arguments.
651 This is certainly legal Haskell, but it is a tremendously verbose and
652 un-obvious way to achieve the desired effect. Arguably, a more direct way
653 to write clunky would be to use case expressions:
657 clunky env var1 var2 = case lookup env var1 of
659 Just val1 -> case lookup env var2 of
661 Just val2 -> val1 + val2
667 This is a bit shorter, but hardly better. Of course, we can rewrite any set
668 of pattern-matching, guarded equations as case expressions; that is
669 precisely what the compiler does when compiling equations! The reason that
670 Haskell provides guarded equations is because they allow us to write down
671 the cases we want to consider, one at a time, independently of each other.
672 This structure is hidden in the case version. Two of the right-hand sides
673 are really the same (<function>fail</function>), and the whole expression
674 tends to become more and more indented.
678 Here is how I would write clunky:
683 | Just val1 <- lookup env var1
684 , Just val2 <- lookup env var2
686 ...other equations for clunky...
690 The semantics should be clear enough. The qualifiers are matched in order.
691 For a <literal><-</literal> qualifier, which I call a pattern guard, the
692 right hand side is evaluated and matched against the pattern on the left.
693 If the match fails then the whole guard fails and the next equation is
694 tried. If it succeeds, then the appropriate binding takes place, and the
695 next qualifier is matched, in the augmented environment. Unlike list
696 comprehensions, however, the type of the expression to the right of the
697 <literal><-</literal> is the same as the type of the pattern to its
698 left. The bindings introduced by pattern guards scope over all the
699 remaining guard qualifiers, and over the right hand side of the equation.
703 Just as with list comprehensions, boolean expressions can be freely mixed
704 with among the pattern guards. For example:
715 Haskell's current guards therefore emerge as a special case, in which the
716 qualifier list has just one element, a boolean expression.
720 <!-- ===================== Recursive do-notation =================== -->
722 <sect2 id="mdo-notation">
723 <title>The recursive do-notation
726 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
727 "A recursive do for Haskell",
728 Levent Erkok, John Launchbury",
729 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
732 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
733 that is, the variables bound in a do-expression are visible only in the textually following
734 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
735 group. It turns out that several applications can benefit from recursive bindings in
736 the do-notation, and this extension provides the necessary syntactic support.
739 Here is a simple (yet contrived) example:
742 import Control.Monad.Fix
744 justOnes = mdo xs <- Just (1:xs)
748 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
752 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
755 class Monad m => MonadFix m where
756 mfix :: (a -> m a) -> m a
759 The function <literal>mfix</literal>
760 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
761 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
762 For details, see the above mentioned reference.
765 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
766 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
767 for Haskell's internal state monad (strict and lazy, respectively).
770 There are three important points in using the recursive-do notation:
773 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
774 than <literal>do</literal>).
778 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
784 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
785 contains up to date information on recursive monadic bindings.
789 Historical note: The old implementation of the mdo-notation (and most
790 of the existing documents) used the name
791 <literal>MonadRec</literal> for the class and the corresponding library.
792 This name is not supported by GHC.
798 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
800 <sect2 id="parallel-list-comprehensions">
801 <title>Parallel List Comprehensions</title>
802 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
804 <indexterm><primary>parallel list comprehensions</primary>
807 <para>Parallel list comprehensions are a natural extension to list
808 comprehensions. List comprehensions can be thought of as a nice
809 syntax for writing maps and filters. Parallel comprehensions
810 extend this to include the zipWith family.</para>
812 <para>A parallel list comprehension has multiple independent
813 branches of qualifier lists, each separated by a `|' symbol. For
814 example, the following zips together two lists:</para>
817 [ (x, y) | x <- xs | y <- ys ]
820 <para>The behavior of parallel list comprehensions follows that of
821 zip, in that the resulting list will have the same length as the
822 shortest branch.</para>
824 <para>We can define parallel list comprehensions by translation to
825 regular comprehensions. Here's the basic idea:</para>
827 <para>Given a parallel comprehension of the form: </para>
830 [ e | p1 <- e11, p2 <- e12, ...
831 | q1 <- e21, q2 <- e22, ...
836 <para>This will be translated to: </para>
839 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
840 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
845 <para>where `zipN' is the appropriate zip for the given number of
850 <sect2 id="rebindable-syntax">
851 <title>Rebindable syntax</title>
854 <para>GHC allows most kinds of built-in syntax to be rebound by
855 the user, to facilitate replacing the <literal>Prelude</literal>
856 with a home-grown version, for example.</para>
858 <para>You may want to define your own numeric class
859 hierarchy. It completely defeats that purpose if the
860 literal "1" means "<literal>Prelude.fromInteger
861 1</literal>", which is what the Haskell Report specifies.
862 So the <option>-X=NoImplicitPrelude</option> flag causes
863 the following pieces of built-in syntax to refer to
864 <emphasis>whatever is in scope</emphasis>, not the Prelude
869 <para>An integer literal <literal>368</literal> means
870 "<literal>fromInteger (368::Integer)</literal>", rather than
871 "<literal>Prelude.fromInteger (368::Integer)</literal>".
874 <listitem><para>Fractional literals are handed in just the same way,
875 except that the translation is
876 <literal>fromRational (3.68::Rational)</literal>.
879 <listitem><para>The equality test in an overloaded numeric pattern
880 uses whatever <literal>(==)</literal> is in scope.
883 <listitem><para>The subtraction operation, and the
884 greater-than-or-equal test, in <literal>n+k</literal> patterns
885 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
889 <para>Negation (e.g. "<literal>- (f x)</literal>")
890 means "<literal>negate (f x)</literal>", both in numeric
891 patterns, and expressions.
895 <para>"Do" notation is translated using whatever
896 functions <literal>(>>=)</literal>,
897 <literal>(>>)</literal>, and <literal>fail</literal>,
898 are in scope (not the Prelude
899 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
900 comprehensions, are unaffected. </para></listitem>
904 notation (see <xref linkend="arrow-notation"/>)
905 uses whatever <literal>arr</literal>,
906 <literal>(>>>)</literal>, <literal>first</literal>,
907 <literal>app</literal>, <literal>(|||)</literal> and
908 <literal>loop</literal> functions are in scope. But unlike the
909 other constructs, the types of these functions must match the
910 Prelude types very closely. Details are in flux; if you want
914 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
915 even if that is a little unexpected. For emample, the
916 static semantics of the literal <literal>368</literal>
917 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
918 <literal>fromInteger</literal> to have any of the types:
920 fromInteger :: Integer -> Integer
921 fromInteger :: forall a. Foo a => Integer -> a
922 fromInteger :: Num a => a -> Integer
923 fromInteger :: Integer -> Bool -> Bool
927 <para>Be warned: this is an experimental facility, with
928 fewer checks than usual. Use <literal>-dcore-lint</literal>
929 to typecheck the desugared program. If Core Lint is happy
930 you should be all right.</para>
934 <sect2 id="postfix-operators">
935 <title>Postfix operators</title>
938 GHC allows a small extension to the syntax of left operator sections, which
939 allows you to define postfix operators. The extension is this: the left section
943 is equivalent (from the point of view of both type checking and execution) to the expression
947 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
948 The strict Haskell 98 interpretation is that the section is equivalent to
952 That is, the operator must be a function of two arguments. GHC allows it to
953 take only one argument, and that in turn allows you to write the function
956 <para>Since this extension goes beyond Haskell 98, it should really be enabled
957 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
958 change their behaviour, of course.)
960 <para>The extension does not extend to the left-hand side of function
961 definitions; you must define such a function in prefix form.</para>
965 <sect2 id="disambiguate-fields">
966 <title>Record field disambiguation</title>
968 In record construction and record pattern matching
969 it is entirely unambiguous which field is referred to, even if there are two different
970 data types in scope with a common field name. For example:
973 data S = MkS { x :: Int, y :: Bool }
978 data T = MkT { x :: Int }
980 ok1 (MkS { x = n }) = n+1 -- Unambiguous
982 ok2 n = MkT { x = n+1 } -- Unambiguous
984 bad1 k = k { x = 3 } -- Ambiguous
985 bad2 k = x k -- Ambiguous
987 Even though there are two <literal>x</literal>'s in scope,
988 it is clear that the <literal>x</literal> in the pattern in the
989 definition of <literal>ok1</literal> can only mean the field
990 <literal>x</literal> from type <literal>S</literal>. Similarly for
991 the function <literal>ok2</literal>. However, in the record update
992 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
993 it is not clear which of the two types is intended.
996 Haskell 98 regards all four as ambiguous, but with the
997 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
998 the former two. The rules are precisely the same as those for instance
999 declarations in Haskell 98, where the method names on the left-hand side
1000 of the method bindings in an instance declaration refer unambiguously
1001 to the method of that class (provided they are in scope at all), even
1002 if there are other variables in scope with the same name.
1003 This reduces the clutter of qualified names when you import two
1004 records from different modules that use the same field name.
1010 <!-- TYPE SYSTEM EXTENSIONS -->
1011 <sect1 id="data-type-extensions">
1012 <title>Extensions to data types and type synonyms</title>
1014 <sect2 id="nullary-types">
1015 <title>Data types with no constructors</title>
1017 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1018 a data type with no constructors. For example:</para>
1022 data T a -- T :: * -> *
1025 <para>Syntactically, the declaration lacks the "= constrs" part. The
1026 type can be parameterised over types of any kind, but if the kind is
1027 not <literal>*</literal> then an explicit kind annotation must be used
1028 (see <xref linkend="kinding"/>).</para>
1030 <para>Such data types have only one value, namely bottom.
1031 Nevertheless, they can be useful when defining "phantom types".</para>
1034 <sect2 id="infix-tycons">
1035 <title>Infix type constructors, classes, and type variables</title>
1038 GHC allows type constructors, classes, and type variables to be operators, and
1039 to be written infix, very much like expressions. More specifically:
1042 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1043 The lexical syntax is the same as that for data constructors.
1046 Data type and type-synonym declarations can be written infix, parenthesised
1047 if you want further arguments. E.g.
1049 data a :*: b = Foo a b
1050 type a :+: b = Either a b
1051 class a :=: b where ...
1053 data (a :**: b) x = Baz a b x
1054 type (a :++: b) y = Either (a,b) y
1058 Types, and class constraints, can be written infix. For example
1061 f :: (a :=: b) => a -> b
1065 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1066 The lexical syntax is the same as that for variable operators, excluding "(.)",
1067 "(!)", and "(*)". In a binding position, the operator must be
1068 parenthesised. For example:
1070 type T (+) = Int + Int
1074 liftA2 :: Arrow (~>)
1075 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1081 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1082 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1085 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1086 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1087 sets the fixity for a data constructor and the corresponding type constructor. For example:
1091 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1092 and similarly for <literal>:*:</literal>.
1093 <literal>Int `a` Bool</literal>.
1096 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1103 <sect2 id="type-synonyms">
1104 <title>Liberalised type synonyms</title>
1107 Type synonyms are like macros at the type level, and
1108 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1109 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1111 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1112 in a type synonym, thus:
1114 type Discard a = forall b. Show b => a -> b -> (a, String)
1119 g :: Discard Int -> (Int,String) -- A rank-2 type
1126 You can write an unboxed tuple in a type synonym:
1128 type Pr = (# Int, Int #)
1136 You can apply a type synonym to a forall type:
1138 type Foo a = a -> a -> Bool
1140 f :: Foo (forall b. b->b)
1142 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1144 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1149 You can apply a type synonym to a partially applied type synonym:
1151 type Generic i o = forall x. i x -> o x
1154 foo :: Generic Id []
1156 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1158 foo :: forall x. x -> [x]
1166 GHC currently does kind checking before expanding synonyms (though even that
1170 After expanding type synonyms, GHC does validity checking on types, looking for
1171 the following mal-formedness which isn't detected simply by kind checking:
1174 Type constructor applied to a type involving for-alls.
1177 Unboxed tuple on left of an arrow.
1180 Partially-applied type synonym.
1184 this will be rejected:
1186 type Pr = (# Int, Int #)
1191 because GHC does not allow unboxed tuples on the left of a function arrow.
1196 <sect2 id="existential-quantification">
1197 <title>Existentially quantified data constructors
1201 The idea of using existential quantification in data type declarations
1202 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1203 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1204 London, 1991). It was later formalised by Laufer and Odersky
1205 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1206 TOPLAS, 16(5), pp1411-1430, 1994).
1207 It's been in Lennart
1208 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1209 proved very useful. Here's the idea. Consider the declaration:
1215 data Foo = forall a. MkFoo a (a -> Bool)
1222 The data type <literal>Foo</literal> has two constructors with types:
1228 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1235 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1236 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1237 For example, the following expression is fine:
1243 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1249 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1250 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1251 isUpper</function> packages a character with a compatible function. These
1252 two things are each of type <literal>Foo</literal> and can be put in a list.
1256 What can we do with a value of type <literal>Foo</literal>?. In particular,
1257 what happens when we pattern-match on <function>MkFoo</function>?
1263 f (MkFoo val fn) = ???
1269 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1270 are compatible, the only (useful) thing we can do with them is to
1271 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1278 f (MkFoo val fn) = fn val
1284 What this allows us to do is to package heterogenous values
1285 together with a bunch of functions that manipulate them, and then treat
1286 that collection of packages in a uniform manner. You can express
1287 quite a bit of object-oriented-like programming this way.
1290 <sect3 id="existential">
1291 <title>Why existential?
1295 What has this to do with <emphasis>existential</emphasis> quantification?
1296 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1302 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1308 But Haskell programmers can safely think of the ordinary
1309 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1310 adding a new existential quantification construct.
1316 <title>Type classes</title>
1319 An easy extension is to allow
1320 arbitrary contexts before the constructor. For example:
1326 data Baz = forall a. Eq a => Baz1 a a
1327 | forall b. Show b => Baz2 b (b -> b)
1333 The two constructors have the types you'd expect:
1339 Baz1 :: forall a. Eq a => a -> a -> Baz
1340 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1346 But when pattern matching on <function>Baz1</function> the matched values can be compared
1347 for equality, and when pattern matching on <function>Baz2</function> the first matched
1348 value can be converted to a string (as well as applying the function to it).
1349 So this program is legal:
1356 f (Baz1 p q) | p == q = "Yes"
1358 f (Baz2 v fn) = show (fn v)
1364 Operationally, in a dictionary-passing implementation, the
1365 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1366 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1367 extract it on pattern matching.
1371 Notice the way that the syntax fits smoothly with that used for
1372 universal quantification earlier.
1377 <sect3 id="existential-records">
1378 <title>Record Constructors</title>
1381 GHC allows existentials to be used with records syntax as well. For example:
1384 data Counter a = forall self. NewCounter
1386 , _inc :: self -> self
1387 , _display :: self -> IO ()
1391 Here <literal>tag</literal> is a public field, with a well-typed selector
1392 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1393 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1394 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1395 compile-time error. In other words, <emphasis>GHC defines a record selector function
1396 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1397 (This example used an underscore in the fields for which record selectors
1398 will not be defined, but that is only programming style; GHC ignores them.)
1402 To make use of these hidden fields, we need to create some helper functions:
1405 inc :: Counter a -> Counter a
1406 inc (NewCounter x i d t) = NewCounter
1407 { _this = i x, _inc = i, _display = d, tag = t }
1409 display :: Counter a -> IO ()
1410 display NewCounter{ _this = x, _display = d } = d x
1413 Now we can define counters with different underlying implementations:
1416 counterA :: Counter String
1417 counterA = NewCounter
1418 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1420 counterB :: Counter String
1421 counterB = NewCounter
1422 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1425 display (inc counterA) -- prints "1"
1426 display (inc (inc counterB)) -- prints "##"
1429 At the moment, record update syntax is only supported for Haskell 98 data types,
1430 so the following function does <emphasis>not</emphasis> work:
1433 -- This is invalid; use explicit NewCounter instead for now
1434 setTag :: Counter a -> a -> Counter a
1435 setTag obj t = obj{ tag = t }
1444 <title>Restrictions</title>
1447 There are several restrictions on the ways in which existentially-quantified
1448 constructors can be use.
1457 When pattern matching, each pattern match introduces a new,
1458 distinct, type for each existential type variable. These types cannot
1459 be unified with any other type, nor can they escape from the scope of
1460 the pattern match. For example, these fragments are incorrect:
1468 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1469 is the result of <function>f1</function>. One way to see why this is wrong is to
1470 ask what type <function>f1</function> has:
1474 f1 :: Foo -> a -- Weird!
1478 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1483 f1 :: forall a. Foo -> a -- Wrong!
1487 The original program is just plain wrong. Here's another sort of error
1491 f2 (Baz1 a b) (Baz1 p q) = a==q
1495 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1496 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1497 from the two <function>Baz1</function> constructors.
1505 You can't pattern-match on an existentially quantified
1506 constructor in a <literal>let</literal> or <literal>where</literal> group of
1507 bindings. So this is illegal:
1511 f3 x = a==b where { Baz1 a b = x }
1514 Instead, use a <literal>case</literal> expression:
1517 f3 x = case x of Baz1 a b -> a==b
1520 In general, you can only pattern-match
1521 on an existentially-quantified constructor in a <literal>case</literal> expression or
1522 in the patterns of a function definition.
1524 The reason for this restriction is really an implementation one.
1525 Type-checking binding groups is already a nightmare without
1526 existentials complicating the picture. Also an existential pattern
1527 binding at the top level of a module doesn't make sense, because it's
1528 not clear how to prevent the existentially-quantified type "escaping".
1529 So for now, there's a simple-to-state restriction. We'll see how
1537 You can't use existential quantification for <literal>newtype</literal>
1538 declarations. So this is illegal:
1542 newtype T = forall a. Ord a => MkT a
1546 Reason: a value of type <literal>T</literal> must be represented as a
1547 pair of a dictionary for <literal>Ord t</literal> and a value of type
1548 <literal>t</literal>. That contradicts the idea that
1549 <literal>newtype</literal> should have no concrete representation.
1550 You can get just the same efficiency and effect by using
1551 <literal>data</literal> instead of <literal>newtype</literal>. If
1552 there is no overloading involved, then there is more of a case for
1553 allowing an existentially-quantified <literal>newtype</literal>,
1554 because the <literal>data</literal> version does carry an
1555 implementation cost, but single-field existentially quantified
1556 constructors aren't much use. So the simple restriction (no
1557 existential stuff on <literal>newtype</literal>) stands, unless there
1558 are convincing reasons to change it.
1566 You can't use <literal>deriving</literal> to define instances of a
1567 data type with existentially quantified data constructors.
1569 Reason: in most cases it would not make sense. For example:;
1572 data T = forall a. MkT [a] deriving( Eq )
1575 To derive <literal>Eq</literal> in the standard way we would need to have equality
1576 between the single component of two <function>MkT</function> constructors:
1580 (MkT a) == (MkT b) = ???
1583 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1584 It's just about possible to imagine examples in which the derived instance
1585 would make sense, but it seems altogether simpler simply to prohibit such
1586 declarations. Define your own instances!
1597 <!-- ====================== Generalised algebraic data types ======================= -->
1599 <sect2 id="gadt-style">
1600 <title>Declaring data types with explicit constructor signatures</title>
1602 <para>GHC allows you to declare an algebraic data type by
1603 giving the type signatures of constructors explicitly. For example:
1607 Just :: a -> Maybe a
1609 The form is called a "GADT-style declaration"
1610 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1611 can only be declared using this form.</para>
1612 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1613 For example, these two declarations are equivalent:
1615 data Foo = forall a. MkFoo a (a -> Bool)
1616 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1619 <para>Any data type that can be declared in standard Haskell-98 syntax
1620 can also be declared using GADT-style syntax.
1621 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1622 they treat class constraints on the data constructors differently.
1623 Specifically, if the constructor is given a type-class context, that
1624 context is made available by pattern matching. For example:
1627 MkSet :: Eq a => [a] -> Set a
1629 makeSet :: Eq a => [a] -> Set a
1630 makeSet xs = MkSet (nub xs)
1632 insert :: a -> Set a -> Set a
1633 insert a (MkSet as) | a `elem` as = MkSet as
1634 | otherwise = MkSet (a:as)
1636 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1637 gives rise to a <literal>(Eq a)</literal>
1638 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1639 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1640 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1641 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1642 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1643 In the example, the equality dictionary is used to satisfy the equality constraint
1644 generated by the call to <literal>elem</literal>, so that the type of
1645 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1647 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1648 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1649 In Haskell 98 the defintion
1651 data Eq a => Set' a = MkSet' [a]
1653 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1654 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1655 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1656 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1657 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1659 For example, a possible application of GHC's behaviour is to reify dictionaries:
1661 data NumInst a where
1662 MkNumInst :: Num a => NumInst a
1664 intInst :: NumInst Int
1667 plus :: NumInst a -> a -> a -> a
1668 plus MkNumInst p q = p + q
1670 Here, a value of type <literal>NumInst a</literal> is equivalent
1671 to an explicit <literal>(Num a)</literal> dictionary.
1675 The rest of this section gives further details about GADT-style data
1680 The result type of each data constructor must begin with the type constructor being defined.
1681 If the result type of all constructors
1682 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1683 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1684 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1688 The type signature of
1689 each constructor is independent, and is implicitly universally quantified as usual.
1690 Different constructors may have different universally-quantified type variables
1691 and different type-class constraints.
1692 For example, this is fine:
1695 T1 :: Eq b => b -> T b
1696 T2 :: (Show c, Ix c) => c -> [c] -> T c
1701 Unlike a Haskell-98-style
1702 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1703 have no scope. Indeed, one can write a kind signature instead:
1705 data Set :: * -> * where ...
1707 or even a mixture of the two:
1709 data Foo a :: (* -> *) -> * where ...
1711 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1714 data Foo a (b :: * -> *) where ...
1720 You can use strictness annotations, in the obvious places
1721 in the constructor type:
1724 Lit :: !Int -> Term Int
1725 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1726 Pair :: Term a -> Term b -> Term (a,b)
1731 You can use a <literal>deriving</literal> clause on a GADT-style data type
1732 declaration. For example, these two declarations are equivalent
1734 data Maybe1 a where {
1735 Nothing1 :: Maybe1 a ;
1736 Just1 :: a -> Maybe1 a
1737 } deriving( Eq, Ord )
1739 data Maybe2 a = Nothing2 | Just2 a
1745 You can use record syntax on a GADT-style data type declaration:
1749 Adult { name :: String, children :: [Person] } :: Person
1750 Child { name :: String } :: Person
1752 As usual, for every constructor that has a field <literal>f</literal>, the type of
1753 field <literal>f</literal> must be the same (modulo alpha conversion).
1756 At the moment, record updates are not yet possible with GADT-style declarations,
1757 so support is limited to record construction, selection and pattern matching.
1760 aPerson = Adult { name = "Fred", children = [] }
1762 shortName :: Person -> Bool
1763 hasChildren (Adult { children = kids }) = not (null kids)
1764 hasChildren (Child {}) = False
1769 As in the case of existentials declared using the Haskell-98-like record syntax
1770 (<xref linkend="existential-records"/>),
1771 record-selector functions are generated only for those fields that have well-typed
1773 Here is the example of that section, in GADT-style syntax:
1775 data Counter a where
1776 NewCounter { _this :: self
1777 , _inc :: self -> self
1778 , _display :: self -> IO ()
1783 As before, only one selector function is generated here, that for <literal>tag</literal>.
1784 Nevertheless, you can still use all the field names in pattern matching and record construction.
1786 </itemizedlist></para>
1790 <title>Generalised Algebraic Data Types (GADTs)</title>
1792 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1793 by allowing constructors to have richer return types. Here is an example:
1796 Lit :: Int -> Term Int
1797 Succ :: Term Int -> Term Int
1798 IsZero :: Term Int -> Term Bool
1799 If :: Term Bool -> Term a -> Term a -> Term a
1800 Pair :: Term a -> Term b -> Term (a,b)
1802 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1803 case with ordinary data types. This generality allows us to
1804 write a well-typed <literal>eval</literal> function
1805 for these <literal>Terms</literal>:
1809 eval (Succ t) = 1 + eval t
1810 eval (IsZero t) = eval t == 0
1811 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1812 eval (Pair e1 e2) = (eval e1, eval e2)
1814 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1815 For example, in the right hand side of the equation
1820 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1821 A precise specification of the type rules is beyond what this user manual aspires to,
1822 but the design closely follows that described in
1824 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1825 unification-based type inference for GADTs</ulink>,
1827 The general principle is this: <emphasis>type refinement is only carried out
1828 based on user-supplied type annotations</emphasis>.
1829 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1830 and lots of obscure error messages will
1831 occur. However, the refinement is quite general. For example, if we had:
1833 eval :: Term a -> a -> a
1834 eval (Lit i) j = i+j
1836 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1837 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1838 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1841 These and many other examples are given in papers by Hongwei Xi, and
1842 Tim Sheard. There is a longer introduction
1843 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1845 <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
1846 may use different notation to that implemented in GHC.
1849 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
1850 <option>-X=GADTs</option>.
1853 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1854 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1855 The result type of each constructor must begin with the type constructor being defined,
1856 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1857 For example, in the <literal>Term</literal> data
1858 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1859 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1864 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1865 an ordianary data type.
1869 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1873 Lit { val :: Int } :: Term Int
1874 Succ { num :: Term Int } :: Term Int
1875 Pred { num :: Term Int } :: Term Int
1876 IsZero { arg :: Term Int } :: Term Bool
1877 Pair { arg1 :: Term a
1880 If { cnd :: Term Bool
1885 However, for GADTs there is the following additional constraint:
1886 every constructor that has a field <literal>f</literal> must have
1887 the same result type (modulo alpha conversion)
1888 Hence, in the above example, we cannot merge the <literal>num</literal>
1889 and <literal>arg</literal> fields above into a
1890 single name. Although their field types are both <literal>Term Int</literal>,
1891 their selector functions actually have different types:
1894 num :: Term Int -> Term Int
1895 arg :: Term Bool -> Term Int
1904 <!-- ====================== End of Generalised algebraic data types ======================= -->
1907 <sect2 id="deriving-typeable">
1908 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1911 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1912 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1913 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1914 classes <literal>Eq</literal>, <literal>Ord</literal>,
1915 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1918 GHC extends this list with two more classes that may be automatically derived
1919 (provided the <option>-fglasgow-exts</option> flag is specified):
1920 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1921 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1922 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1924 <para>An instance of <literal>Typeable</literal> can only be derived if the
1925 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1926 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1928 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1929 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1931 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1932 are used, and only <literal>Typeable1</literal> up to
1933 <literal>Typeable7</literal> are provided in the library.)
1934 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1935 class, whose kind suits that of the data type constructor, and
1936 then writing the data type instance by hand.
1940 <sect2 id="newtype-deriving">
1941 <title>Generalised derived instances for newtypes</title>
1944 When you define an abstract type using <literal>newtype</literal>, you may want
1945 the new type to inherit some instances from its representation. In
1946 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1947 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1948 other classes you have to write an explicit instance declaration. For
1949 example, if you define
1952 newtype Dollars = Dollars Int
1955 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1956 explicitly define an instance of <literal>Num</literal>:
1959 instance Num Dollars where
1960 Dollars a + Dollars b = Dollars (a+b)
1963 All the instance does is apply and remove the <literal>newtype</literal>
1964 constructor. It is particularly galling that, since the constructor
1965 doesn't appear at run-time, this instance declaration defines a
1966 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1967 dictionary, only slower!
1971 <sect3> <title> Generalising the deriving clause </title>
1973 GHC now permits such instances to be derived instead, so one can write
1975 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1978 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1979 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1980 derives an instance declaration of the form
1983 instance Num Int => Num Dollars
1986 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1990 We can also derive instances of constructor classes in a similar
1991 way. For example, suppose we have implemented state and failure monad
1992 transformers, such that
1995 instance Monad m => Monad (State s m)
1996 instance Monad m => Monad (Failure m)
1998 In Haskell 98, we can define a parsing monad by
2000 type Parser tok m a = State [tok] (Failure m) a
2003 which is automatically a monad thanks to the instance declarations
2004 above. With the extension, we can make the parser type abstract,
2005 without needing to write an instance of class <literal>Monad</literal>, via
2008 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2011 In this case the derived instance declaration is of the form
2013 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2016 Notice that, since <literal>Monad</literal> is a constructor class, the
2017 instance is a <emphasis>partial application</emphasis> of the new type, not the
2018 entire left hand side. We can imagine that the type declaration is
2019 ``eta-converted'' to generate the context of the instance
2024 We can even derive instances of multi-parameter classes, provided the
2025 newtype is the last class parameter. In this case, a ``partial
2026 application'' of the class appears in the <literal>deriving</literal>
2027 clause. For example, given the class
2030 class StateMonad s m | m -> s where ...
2031 instance Monad m => StateMonad s (State s m) where ...
2033 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2035 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2036 deriving (Monad, StateMonad [tok])
2039 The derived instance is obtained by completing the application of the
2040 class to the new type:
2043 instance StateMonad [tok] (State [tok] (Failure m)) =>
2044 StateMonad [tok] (Parser tok m)
2049 As a result of this extension, all derived instances in newtype
2050 declarations are treated uniformly (and implemented just by reusing
2051 the dictionary for the representation type), <emphasis>except</emphasis>
2052 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2053 the newtype and its representation.
2057 <sect3> <title> A more precise specification </title>
2059 Derived instance declarations are constructed as follows. Consider the
2060 declaration (after expansion of any type synonyms)
2063 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2069 The <literal>ci</literal> are partial applications of
2070 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2071 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2074 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2077 The type <literal>t</literal> is an arbitrary type.
2080 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2081 nor in the <literal>ci</literal>, and
2084 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2085 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2086 should not "look through" the type or its constructor. You can still
2087 derive these classes for a newtype, but it happens in the usual way, not
2088 via this new mechanism.
2091 Then, for each <literal>ci</literal>, the derived instance
2094 instance ci t => ci (T v1...vk)
2096 As an example which does <emphasis>not</emphasis> work, consider
2098 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2100 Here we cannot derive the instance
2102 instance Monad (State s m) => Monad (NonMonad m)
2105 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2106 and so cannot be "eta-converted" away. It is a good thing that this
2107 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2108 not, in fact, a monad --- for the same reason. Try defining
2109 <literal>>>=</literal> with the correct type: you won't be able to.
2113 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2114 important, since we can only derive instances for the last one. If the
2115 <literal>StateMonad</literal> class above were instead defined as
2118 class StateMonad m s | m -> s where ...
2121 then we would not have been able to derive an instance for the
2122 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2123 classes usually have one "main" parameter for which deriving new
2124 instances is most interesting.
2126 <para>Lastly, all of this applies only for classes other than
2127 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2128 and <literal>Data</literal>, for which the built-in derivation applies (section
2129 4.3.3. of the Haskell Report).
2130 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2131 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2132 the standard method is used or the one described here.)
2138 <sect2 id="stand-alone-deriving">
2139 <title>Stand-alone deriving declarations</title>
2142 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2144 data Foo a = Bar a | Baz String
2146 derive instance Eq (Foo a)
2148 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2149 you can use it as a variable name elsewhere.</para>
2150 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2151 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2154 newtype Foo a = MkFoo (State Int a)
2156 derive instance MonadState Int Foo
2158 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2159 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2167 <!-- TYPE SYSTEM EXTENSIONS -->
2168 <sect1 id="other-type-extensions">
2169 <title>Other type system extensions</title>
2171 <sect2 id="multi-param-type-classes">
2172 <title>Class declarations</title>
2175 This section, and the next one, documents GHC's type-class extensions.
2176 There's lots of background in the paper <ulink
2177 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2178 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2179 Jones, Erik Meijer).
2182 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2186 <title>Multi-parameter type classes</title>
2188 Multi-parameter type classes are permitted. For example:
2192 class Collection c a where
2193 union :: c a -> c a -> c a
2201 <title>The superclasses of a class declaration</title>
2204 There are no restrictions on the context in a class declaration
2205 (which introduces superclasses), except that the class hierarchy must
2206 be acyclic. So these class declarations are OK:
2210 class Functor (m k) => FiniteMap m k where
2213 class (Monad m, Monad (t m)) => Transform t m where
2214 lift :: m a -> (t m) a
2220 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2221 of "acyclic" involves only the superclass relationships. For example,
2227 op :: D b => a -> b -> b
2230 class C a => D a where { ... }
2234 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2235 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2236 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2243 <sect3 id="class-method-types">
2244 <title>Class method types</title>
2247 Haskell 98 prohibits class method types to mention constraints on the
2248 class type variable, thus:
2251 fromList :: [a] -> s a
2252 elem :: Eq a => a -> s a -> Bool
2254 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2255 contains the constraint <literal>Eq a</literal>, constrains only the
2256 class type variable (in this case <literal>a</literal>).
2257 GHC lifts this restriction.
2264 <sect2 id="functional-dependencies">
2265 <title>Functional dependencies
2268 <para> Functional dependencies are implemented as described by Mark Jones
2269 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2270 In Proceedings of the 9th European Symposium on Programming,
2271 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2275 Functional dependencies are introduced by a vertical bar in the syntax of a
2276 class declaration; e.g.
2278 class (Monad m) => MonadState s m | m -> s where ...
2280 class Foo a b c | a b -> c where ...
2282 There should be more documentation, but there isn't (yet). Yell if you need it.
2285 <sect3><title>Rules for functional dependencies </title>
2287 In a class declaration, all of the class type variables must be reachable (in the sense
2288 mentioned in <xref linkend="type-restrictions"/>)
2289 from the free variables of each method type.
2293 class Coll s a where
2295 insert :: s -> a -> s
2298 is not OK, because the type of <literal>empty</literal> doesn't mention
2299 <literal>a</literal>. Functional dependencies can make the type variable
2302 class Coll s a | s -> a where
2304 insert :: s -> a -> s
2307 Alternatively <literal>Coll</literal> might be rewritten
2310 class Coll s a where
2312 insert :: s a -> a -> s a
2316 which makes the connection between the type of a collection of
2317 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2318 Occasionally this really doesn't work, in which case you can split the
2326 class CollE s => Coll s a where
2327 insert :: s -> a -> s
2334 <title>Background on functional dependencies</title>
2336 <para>The following description of the motivation and use of functional dependencies is taken
2337 from the Hugs user manual, reproduced here (with minor changes) by kind
2338 permission of Mark Jones.
2341 Consider the following class, intended as part of a
2342 library for collection types:
2344 class Collects e ce where
2346 insert :: e -> ce -> ce
2347 member :: e -> ce -> Bool
2349 The type variable e used here represents the element type, while ce is the type
2350 of the container itself. Within this framework, we might want to define
2351 instances of this class for lists or characteristic functions (both of which
2352 can be used to represent collections of any equality type), bit sets (which can
2353 be used to represent collections of characters), or hash tables (which can be
2354 used to represent any collection whose elements have a hash function). Omitting
2355 standard implementation details, this would lead to the following declarations:
2357 instance Eq e => Collects e [e] where ...
2358 instance Eq e => Collects e (e -> Bool) where ...
2359 instance Collects Char BitSet where ...
2360 instance (Hashable e, Collects a ce)
2361 => Collects e (Array Int ce) where ...
2363 All this looks quite promising; we have a class and a range of interesting
2364 implementations. Unfortunately, there are some serious problems with the class
2365 declaration. First, the empty function has an ambiguous type:
2367 empty :: Collects e ce => ce
2369 By "ambiguous" we mean that there is a type variable e that appears on the left
2370 of the <literal>=></literal> symbol, but not on the right. The problem with
2371 this is that, according to the theoretical foundations of Haskell overloading,
2372 we cannot guarantee a well-defined semantics for any term with an ambiguous
2376 We can sidestep this specific problem by removing the empty member from the
2377 class declaration. However, although the remaining members, insert and member,
2378 do not have ambiguous types, we still run into problems when we try to use
2379 them. For example, consider the following two functions:
2381 f x y = insert x . insert y
2384 for which GHC infers the following types:
2386 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2387 g :: (Collects Bool c, Collects Char c) => c -> c
2389 Notice that the type for f allows the two parameters x and y to be assigned
2390 different types, even though it attempts to insert each of the two values, one
2391 after the other, into the same collection. If we're trying to model collections
2392 that contain only one type of value, then this is clearly an inaccurate
2393 type. Worse still, the definition for g is accepted, without causing a type
2394 error. As a result, the error in this code will not be flagged at the point
2395 where it appears. Instead, it will show up only when we try to use g, which
2396 might even be in a different module.
2399 <sect4><title>An attempt to use constructor classes</title>
2402 Faced with the problems described above, some Haskell programmers might be
2403 tempted to use something like the following version of the class declaration:
2405 class Collects e c where
2407 insert :: e -> c e -> c e
2408 member :: e -> c e -> Bool
2410 The key difference here is that we abstract over the type constructor c that is
2411 used to form the collection type c e, and not over that collection type itself,
2412 represented by ce in the original class declaration. This avoids the immediate
2413 problems that we mentioned above: empty has type <literal>Collects e c => c
2414 e</literal>, which is not ambiguous.
2417 The function f from the previous section has a more accurate type:
2419 f :: (Collects e c) => e -> e -> c e -> c e
2421 The function g from the previous section is now rejected with a type error as
2422 we would hope because the type of f does not allow the two arguments to have
2424 This, then, is an example of a multiple parameter class that does actually work
2425 quite well in practice, without ambiguity problems.
2426 There is, however, a catch. This version of the Collects class is nowhere near
2427 as general as the original class seemed to be: only one of the four instances
2428 for <literal>Collects</literal>
2429 given above can be used with this version of Collects because only one of
2430 them---the instance for lists---has a collection type that can be written in
2431 the form c e, for some type constructor c, and element type e.
2435 <sect4><title>Adding functional dependencies</title>
2438 To get a more useful version of the Collects class, Hugs provides a mechanism
2439 that allows programmers to specify dependencies between the parameters of a
2440 multiple parameter class (For readers with an interest in theoretical
2441 foundations and previous work: The use of dependency information can be seen
2442 both as a generalization of the proposal for `parametric type classes' that was
2443 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2444 later framework for "improvement" of qualified types. The
2445 underlying ideas are also discussed in a more theoretical and abstract setting
2446 in a manuscript [implparam], where they are identified as one point in a
2447 general design space for systems of implicit parameterization.).
2449 To start with an abstract example, consider a declaration such as:
2451 class C a b where ...
2453 which tells us simply that C can be thought of as a binary relation on types
2454 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2455 included in the definition of classes to add information about dependencies
2456 between parameters, as in the following examples:
2458 class D a b | a -> b where ...
2459 class E a b | a -> b, b -> a where ...
2461 The notation <literal>a -> b</literal> used here between the | and where
2462 symbols --- not to be
2463 confused with a function type --- indicates that the a parameter uniquely
2464 determines the b parameter, and might be read as "a determines b." Thus D is
2465 not just a relation, but actually a (partial) function. Similarly, from the two
2466 dependencies that are included in the definition of E, we can see that E
2467 represents a (partial) one-one mapping between types.
2470 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2471 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2472 m>=0, meaning that the y parameters are uniquely determined by the x
2473 parameters. Spaces can be used as separators if more than one variable appears
2474 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2475 annotated with multiple dependencies using commas as separators, as in the
2476 definition of E above. Some dependencies that we can write in this notation are
2477 redundant, and will be rejected because they don't serve any useful
2478 purpose, and may instead indicate an error in the program. Examples of
2479 dependencies like this include <literal>a -> a </literal>,
2480 <literal>a -> a a </literal>,
2481 <literal>a -> </literal>, etc. There can also be
2482 some redundancy if multiple dependencies are given, as in
2483 <literal>a->b</literal>,
2484 <literal>b->c </literal>, <literal>a->c </literal>, and
2485 in which some subset implies the remaining dependencies. Examples like this are
2486 not treated as errors. Note that dependencies appear only in class
2487 declarations, and not in any other part of the language. In particular, the
2488 syntax for instance declarations, class constraints, and types is completely
2492 By including dependencies in a class declaration, we provide a mechanism for
2493 the programmer to specify each multiple parameter class more precisely. The
2494 compiler, on the other hand, is responsible for ensuring that the set of
2495 instances that are in scope at any given point in the program is consistent
2496 with any declared dependencies. For example, the following pair of instance
2497 declarations cannot appear together in the same scope because they violate the
2498 dependency for D, even though either one on its own would be acceptable:
2500 instance D Bool Int where ...
2501 instance D Bool Char where ...
2503 Note also that the following declaration is not allowed, even by itself:
2505 instance D [a] b where ...
2507 The problem here is that this instance would allow one particular choice of [a]
2508 to be associated with more than one choice for b, which contradicts the
2509 dependency specified in the definition of D. More generally, this means that,
2510 in any instance of the form:
2512 instance D t s where ...
2514 for some particular types t and s, the only variables that can appear in s are
2515 the ones that appear in t, and hence, if the type t is known, then s will be
2516 uniquely determined.
2519 The benefit of including dependency information is that it allows us to define
2520 more general multiple parameter classes, without ambiguity problems, and with
2521 the benefit of more accurate types. To illustrate this, we return to the
2522 collection class example, and annotate the original definition of <literal>Collects</literal>
2523 with a simple dependency:
2525 class Collects e ce | ce -> e where
2527 insert :: e -> ce -> ce
2528 member :: e -> ce -> Bool
2530 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2531 determined by the type of the collection ce. Note that both parameters of
2532 Collects are of kind *; there are no constructor classes here. Note too that
2533 all of the instances of Collects that we gave earlier can be used
2534 together with this new definition.
2537 What about the ambiguity problems that we encountered with the original
2538 definition? The empty function still has type Collects e ce => ce, but it is no
2539 longer necessary to regard that as an ambiguous type: Although the variable e
2540 does not appear on the right of the => symbol, the dependency for class
2541 Collects tells us that it is uniquely determined by ce, which does appear on
2542 the right of the => symbol. Hence the context in which empty is used can still
2543 give enough information to determine types for both ce and e, without
2544 ambiguity. More generally, we need only regard a type as ambiguous if it
2545 contains a variable on the left of the => that is not uniquely determined
2546 (either directly or indirectly) by the variables on the right.
2549 Dependencies also help to produce more accurate types for user defined
2550 functions, and hence to provide earlier detection of errors, and less cluttered
2551 types for programmers to work with. Recall the previous definition for a
2554 f x y = insert x y = insert x . insert y
2556 for which we originally obtained a type:
2558 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2560 Given the dependency information that we have for Collects, however, we can
2561 deduce that a and b must be equal because they both appear as the second
2562 parameter in a Collects constraint with the same first parameter c. Hence we
2563 can infer a shorter and more accurate type for f:
2565 f :: (Collects a c) => a -> a -> c -> c
2567 In a similar way, the earlier definition of g will now be flagged as a type error.
2570 Although we have given only a few examples here, it should be clear that the
2571 addition of dependency information can help to make multiple parameter classes
2572 more useful in practice, avoiding ambiguity problems, and allowing more general
2573 sets of instance declarations.
2579 <sect2 id="instance-decls">
2580 <title>Instance declarations</title>
2582 <sect3 id="instance-rules">
2583 <title>Relaxed rules for instance declarations</title>
2585 <para>An instance declaration has the form
2587 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 ...
2589 The part before the "<literal>=></literal>" is the
2590 <emphasis>context</emphasis>, while the part after the
2591 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2595 In Haskell 98 the head of an instance declaration
2596 must be of the form <literal>C (T a1 ... an)</literal>, where
2597 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2598 and the <literal>a1 ... an</literal> are distinct type variables.
2599 Furthermore, the assertions in the context of the instance declaration
2600 must be of the form <literal>C a</literal> where <literal>a</literal>
2601 is a type variable that occurs in the head.
2604 The <option>-fglasgow-exts</option> flag loosens these restrictions
2605 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2606 the context and head of the instance declaration can each consist of arbitrary
2607 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2611 The Paterson Conditions: for each assertion in the context
2613 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2614 <listitem><para>The assertion has fewer constructors and variables (taken together
2615 and counting repetitions) than the head</para></listitem>
2619 <listitem><para>The Coverage Condition. For each functional dependency,
2620 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2621 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2622 every type variable in
2623 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2624 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2625 substitution mapping each type variable in the class declaration to the
2626 corresponding type in the instance declaration.
2629 These restrictions ensure that context reduction terminates: each reduction
2630 step makes the problem smaller by at least one
2631 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2632 if you give the <option>-fallow-undecidable-instances</option>
2633 flag (<xref linkend="undecidable-instances"/>).
2634 You can find lots of background material about the reason for these
2635 restrictions in the paper <ulink
2636 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2637 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2640 For example, these are OK:
2642 instance C Int [a] -- Multiple parameters
2643 instance Eq (S [a]) -- Structured type in head
2645 -- Repeated type variable in head
2646 instance C4 a a => C4 [a] [a]
2647 instance Stateful (ST s) (MutVar s)
2649 -- Head can consist of type variables only
2651 instance (Eq a, Show b) => C2 a b
2653 -- Non-type variables in context
2654 instance Show (s a) => Show (Sized s a)
2655 instance C2 Int a => C3 Bool [a]
2656 instance C2 Int a => C3 [a] b
2660 -- Context assertion no smaller than head
2661 instance C a => C a where ...
2662 -- (C b b) has more more occurrences of b than the head
2663 instance C b b => Foo [b] where ...
2668 The same restrictions apply to instances generated by
2669 <literal>deriving</literal> clauses. Thus the following is accepted:
2671 data MinHeap h a = H a (h a)
2674 because the derived instance
2676 instance (Show a, Show (h a)) => Show (MinHeap h a)
2678 conforms to the above rules.
2682 A useful idiom permitted by the above rules is as follows.
2683 If one allows overlapping instance declarations then it's quite
2684 convenient to have a "default instance" declaration that applies if
2685 something more specific does not:
2693 <sect3 id="undecidable-instances">
2694 <title>Undecidable instances</title>
2697 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2698 For example, sometimes you might want to use the following to get the
2699 effect of a "class synonym":
2701 class (C1 a, C2 a, C3 a) => C a where { }
2703 instance (C1 a, C2 a, C3 a) => C a where { }
2705 This allows you to write shorter signatures:
2711 f :: (C1 a, C2 a, C3 a) => ...
2713 The restrictions on functional dependencies (<xref
2714 linkend="functional-dependencies"/>) are particularly troublesome.
2715 It is tempting to introduce type variables in the context that do not appear in
2716 the head, something that is excluded by the normal rules. For example:
2718 class HasConverter a b | a -> b where
2721 data Foo a = MkFoo a
2723 instance (HasConverter a b,Show b) => Show (Foo a) where
2724 show (MkFoo value) = show (convert value)
2726 This is dangerous territory, however. Here, for example, is a program that would make the
2731 instance F [a] [[a]]
2732 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2734 Similarly, it can be tempting to lift the coverage condition:
2736 class Mul a b c | a b -> c where
2737 (.*.) :: a -> b -> c
2739 instance Mul Int Int Int where (.*.) = (*)
2740 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2741 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2743 The third instance declaration does not obey the coverage condition;
2744 and indeed the (somewhat strange) definition:
2746 f = \ b x y -> if b then x .*. [y] else y
2748 makes instance inference go into a loop, because it requires the constraint
2749 <literal>(Mul a [b] b)</literal>.
2752 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2753 the experimental flag <option>-X=AllowUndecidableInstances</option>
2754 <indexterm><primary>-X=AllowUndecidableInstances</primary></indexterm>,
2755 both the Paterson Conditions and the Coverage Condition
2756 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2757 fixed-depth recursion stack. If you exceed the stack depth you get a
2758 sort of backtrace, and the opportunity to increase the stack depth
2759 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2765 <sect3 id="instance-overlap">
2766 <title>Overlapping instances</title>
2768 In general, <emphasis>GHC requires that that it be unambiguous which instance
2770 should be used to resolve a type-class constraint</emphasis>. This behaviour
2771 can be modified by two flags: <option>-X=AllowOverlappingInstances</option>
2772 <indexterm><primary>-X=AllowOverlappingInstances
2773 </primary></indexterm>
2774 and <option>-X=AllowIncoherentInstances</option>
2775 <indexterm><primary>-X=AllowIncoherentInstances
2776 </primary></indexterm>, as this section discusses. Both these
2777 flags are dynamic flags, and can be set on a per-module basis, using
2778 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2780 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2781 it tries to match every instance declaration against the
2783 by instantiating the head of the instance declaration. For example, consider
2786 instance context1 => C Int a where ... -- (A)
2787 instance context2 => C a Bool where ... -- (B)
2788 instance context3 => C Int [a] where ... -- (C)
2789 instance context4 => C Int [Int] where ... -- (D)
2791 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2792 but (C) and (D) do not. When matching, GHC takes
2793 no account of the context of the instance declaration
2794 (<literal>context1</literal> etc).
2795 GHC's default behaviour is that <emphasis>exactly one instance must match the
2796 constraint it is trying to resolve</emphasis>.
2797 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2798 including both declarations (A) and (B), say); an error is only reported if a
2799 particular constraint matches more than one.
2803 The <option>-X=AllowOverlappingInstances</option> flag instructs GHC to allow
2804 more than one instance to match, provided there is a most specific one. For
2805 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2806 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2807 most-specific match, the program is rejected.
2810 However, GHC is conservative about committing to an overlapping instance. For example:
2815 Suppose that from the RHS of <literal>f</literal> we get the constraint
2816 <literal>C Int [b]</literal>. But
2817 GHC does not commit to instance (C), because in a particular
2818 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2819 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2820 So GHC rejects the program. If you add the flag <option>-X=AllowIncoherentInstances</option>,
2821 GHC will instead pick (C), without complaining about
2822 the problem of subsequent instantiations.
2825 The willingness to be overlapped or incoherent is a property of
2826 the <emphasis>instance declaration</emphasis> itself, controlled by the
2827 presence or otherwise of the <option>-X=AllowOverlappingInstances</option>
2828 and <option>-X=AllowIncoherentInstances</option> flags when that mdodule is
2829 being defined. Neither flag is required in a module that imports and uses the
2830 instance declaration. Specifically, during the lookup process:
2833 An instance declaration is ignored during the lookup process if (a) a more specific
2834 match is found, and (b) the instance declaration was compiled with
2835 <option>-X=AllowOverlappingInstances</option>. The flag setting for the
2836 more-specific instance does not matter.
2839 Suppose an instance declaration does not match the constraint being looked up, but
2840 does unify with it, so that it might match when the constraint is further
2841 instantiated. Usually GHC will regard this as a reason for not committing to
2842 some other constraint. But if the instance declaration was compiled with
2843 <option>-X=AllowIncoherentInstances</option>, GHC will skip the "does-it-unify?"
2844 check for that declaration.
2847 These rules make it possible for a library author to design a library that relies on
2848 overlapping instances without the library client having to know.
2851 If an instance declaration is compiled without
2852 <option>-X=AllowOverlappingInstances</option>,
2853 then that instance can never be overlapped. This could perhaps be
2854 inconvenient. Perhaps the rule should instead say that the
2855 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2856 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2857 at a usage site should be permitted regardless of how the instance declarations
2858 are compiled, if the <option>-X=AllowOverlappingInstances</option> flag is
2859 used at the usage site. (Mind you, the exact usage site can occasionally be
2860 hard to pin down.) We are interested to receive feedback on these points.
2862 <para>The <option>-X=AllowIncoherentInstances</option> flag implies the
2863 <option>-X=AllowOverlappingInstances</option> flag, but not vice versa.
2868 <title>Type synonyms in the instance head</title>
2871 <emphasis>Unlike Haskell 98, instance heads may use type
2872 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2873 As always, using a type synonym is just shorthand for
2874 writing the RHS of the type synonym definition. For example:
2878 type Point = (Int,Int)
2879 instance C Point where ...
2880 instance C [Point] where ...
2884 is legal. However, if you added
2888 instance C (Int,Int) where ...
2892 as well, then the compiler will complain about the overlapping
2893 (actually, identical) instance declarations. As always, type synonyms
2894 must be fully applied. You cannot, for example, write:
2899 instance Monad P where ...
2903 This design decision is independent of all the others, and easily
2904 reversed, but it makes sense to me.
2912 <sect2 id="type-restrictions">
2913 <title>Type signatures</title>
2915 <sect3><title>The context of a type signature</title>
2917 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2918 the form <emphasis>(class type-variable)</emphasis> or
2919 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2920 these type signatures are perfectly OK
2923 g :: Ord (T a ()) => ...
2927 GHC imposes the following restrictions on the constraints in a type signature.
2931 forall tv1..tvn (c1, ...,cn) => type
2934 (Here, we write the "foralls" explicitly, although the Haskell source
2935 language omits them; in Haskell 98, all the free type variables of an
2936 explicit source-language type signature are universally quantified,
2937 except for the class type variables in a class declaration. However,
2938 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2947 <emphasis>Each universally quantified type variable
2948 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2950 A type variable <literal>a</literal> is "reachable" if it it appears
2951 in the same constraint as either a type variable free in in
2952 <literal>type</literal>, or another reachable type variable.
2953 A value with a type that does not obey
2954 this reachability restriction cannot be used without introducing
2955 ambiguity; that is why the type is rejected.
2956 Here, for example, is an illegal type:
2960 forall a. Eq a => Int
2964 When a value with this type was used, the constraint <literal>Eq tv</literal>
2965 would be introduced where <literal>tv</literal> is a fresh type variable, and
2966 (in the dictionary-translation implementation) the value would be
2967 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2968 can never know which instance of <literal>Eq</literal> to use because we never
2969 get any more information about <literal>tv</literal>.
2973 that the reachability condition is weaker than saying that <literal>a</literal> is
2974 functionally dependent on a type variable free in
2975 <literal>type</literal> (see <xref
2976 linkend="functional-dependencies"/>). The reason for this is there
2977 might be a "hidden" dependency, in a superclass perhaps. So
2978 "reachable" is a conservative approximation to "functionally dependent".
2979 For example, consider:
2981 class C a b | a -> b where ...
2982 class C a b => D a b where ...
2983 f :: forall a b. D a b => a -> a
2985 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2986 but that is not immediately apparent from <literal>f</literal>'s type.
2992 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2993 universally quantified type variables <literal>tvi</literal></emphasis>.
2995 For example, this type is OK because <literal>C a b</literal> mentions the
2996 universally quantified type variable <literal>b</literal>:
3000 forall a. C a b => burble
3004 The next type is illegal because the constraint <literal>Eq b</literal> does not
3005 mention <literal>a</literal>:
3009 forall a. Eq b => burble
3013 The reason for this restriction is milder than the other one. The
3014 excluded types are never useful or necessary (because the offending
3015 context doesn't need to be witnessed at this point; it can be floated
3016 out). Furthermore, floating them out increases sharing. Lastly,
3017 excluding them is a conservative choice; it leaves a patch of
3018 territory free in case we need it later.
3032 <sect2 id="implicit-parameters">
3033 <title>Implicit parameters</title>
3035 <para> Implicit parameters are implemented as described in
3036 "Implicit parameters: dynamic scoping with static types",
3037 J Lewis, MB Shields, E Meijer, J Launchbury,
3038 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3042 <para>(Most of the following, stil rather incomplete, documentation is
3043 due to Jeff Lewis.)</para>
3045 <para>Implicit parameter support is enabled with the option
3046 <option>-X=ImplicitParams</option>.</para>
3049 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3050 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3051 context. In Haskell, all variables are statically bound. Dynamic
3052 binding of variables is a notion that goes back to Lisp, but was later
3053 discarded in more modern incarnations, such as Scheme. Dynamic binding
3054 can be very confusing in an untyped language, and unfortunately, typed
3055 languages, in particular Hindley-Milner typed languages like Haskell,
3056 only support static scoping of variables.
3059 However, by a simple extension to the type class system of Haskell, we
3060 can support dynamic binding. Basically, we express the use of a
3061 dynamically bound variable as a constraint on the type. These
3062 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3063 function uses a dynamically-bound variable <literal>?x</literal>
3064 of type <literal>t'</literal>". For
3065 example, the following expresses the type of a sort function,
3066 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3068 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3070 The dynamic binding constraints are just a new form of predicate in the type class system.
3073 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3074 where <literal>x</literal> is
3075 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3076 Use of this construct also introduces a new
3077 dynamic-binding constraint in the type of the expression.
3078 For example, the following definition
3079 shows how we can define an implicitly parameterized sort function in
3080 terms of an explicitly parameterized <literal>sortBy</literal> function:
3082 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3084 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3090 <title>Implicit-parameter type constraints</title>
3092 Dynamic binding constraints behave just like other type class
3093 constraints in that they are automatically propagated. Thus, when a
3094 function is used, its implicit parameters are inherited by the
3095 function that called it. For example, our <literal>sort</literal> function might be used
3096 to pick out the least value in a list:
3098 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3099 least xs = head (sort xs)
3101 Without lifting a finger, the <literal>?cmp</literal> parameter is
3102 propagated to become a parameter of <literal>least</literal> as well. With explicit
3103 parameters, the default is that parameters must always be explicit
3104 propagated. With implicit parameters, the default is to always
3108 An implicit-parameter type constraint differs from other type class constraints in the
3109 following way: All uses of a particular implicit parameter must have
3110 the same type. This means that the type of <literal>(?x, ?x)</literal>
3111 is <literal>(?x::a) => (a,a)</literal>, and not
3112 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3116 <para> You can't have an implicit parameter in the context of a class or instance
3117 declaration. For example, both these declarations are illegal:
3119 class (?x::Int) => C a where ...
3120 instance (?x::a) => Foo [a] where ...
3122 Reason: exactly which implicit parameter you pick up depends on exactly where
3123 you invoke a function. But the ``invocation'' of instance declarations is done
3124 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3125 Easiest thing is to outlaw the offending types.</para>
3127 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3129 f :: (?x :: [a]) => Int -> Int
3132 g :: (Read a, Show a) => String -> String
3135 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3136 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3137 quite unambiguous, and fixes the type <literal>a</literal>.
3142 <title>Implicit-parameter bindings</title>
3145 An implicit parameter is <emphasis>bound</emphasis> using the standard
3146 <literal>let</literal> or <literal>where</literal> binding forms.
3147 For example, we define the <literal>min</literal> function by binding
3148 <literal>cmp</literal>.
3151 min = let ?cmp = (<=) in least
3155 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3156 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3157 (including in a list comprehension, or do-notation, or pattern guards),
3158 or a <literal>where</literal> clause.
3159 Note the following points:
3162 An implicit-parameter binding group must be a
3163 collection of simple bindings to implicit-style variables (no
3164 function-style bindings, and no type signatures); these bindings are
3165 neither polymorphic or recursive.
3168 You may not mix implicit-parameter bindings with ordinary bindings in a
3169 single <literal>let</literal>
3170 expression; use two nested <literal>let</literal>s instead.
3171 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3175 You may put multiple implicit-parameter bindings in a
3176 single binding group; but they are <emphasis>not</emphasis> treated
3177 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3178 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3179 parameter. The bindings are not nested, and may be re-ordered without changing
3180 the meaning of the program.
3181 For example, consider:
3183 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3185 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3186 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3188 f :: (?x::Int) => Int -> Int
3196 <sect3><title>Implicit parameters and polymorphic recursion</title>
3199 Consider these two definitions:
3202 len1 xs = let ?acc = 0 in len_acc1 xs
3205 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3210 len2 xs = let ?acc = 0 in len_acc2 xs
3212 len_acc2 :: (?acc :: Int) => [a] -> Int
3214 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3216 The only difference between the two groups is that in the second group
3217 <literal>len_acc</literal> is given a type signature.
3218 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3219 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3220 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3221 has a type signature, the recursive call is made to the
3222 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3223 as an implicit parameter. So we get the following results in GHCi:
3230 Adding a type signature dramatically changes the result! This is a rather
3231 counter-intuitive phenomenon, worth watching out for.
3235 <sect3><title>Implicit parameters and monomorphism</title>
3237 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3238 Haskell Report) to implicit parameters. For example, consider:
3246 Since the binding for <literal>y</literal> falls under the Monomorphism
3247 Restriction it is not generalised, so the type of <literal>y</literal> is
3248 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3249 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3250 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3251 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3252 <literal>y</literal> in the body of the <literal>let</literal> will see the
3253 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3254 <literal>14</literal>.
3259 <!-- ======================= COMMENTED OUT ========================
3261 We intend to remove linear implicit parameters, so I'm at least removing
3262 them from the 6.6 user manual
3264 <sect2 id="linear-implicit-parameters">
3265 <title>Linear implicit parameters</title>
3267 Linear implicit parameters are an idea developed by Koen Claessen,
3268 Mark Shields, and Simon PJ. They address the long-standing
3269 problem that monads seem over-kill for certain sorts of problem, notably:
3272 <listitem> <para> distributing a supply of unique names </para> </listitem>
3273 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3274 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3278 Linear implicit parameters are just like ordinary implicit parameters,
3279 except that they are "linear"; that is, they cannot be copied, and
3280 must be explicitly "split" instead. Linear implicit parameters are
3281 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3282 (The '/' in the '%' suggests the split!)
3287 import GHC.Exts( Splittable )
3289 data NameSupply = ...
3291 splitNS :: NameSupply -> (NameSupply, NameSupply)
3292 newName :: NameSupply -> Name
3294 instance Splittable NameSupply where
3298 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3299 f env (Lam x e) = Lam x' (f env e)
3302 env' = extend env x x'
3303 ...more equations for f...
3305 Notice that the implicit parameter %ns is consumed
3307 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3308 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3312 So the translation done by the type checker makes
3313 the parameter explicit:
3315 f :: NameSupply -> Env -> Expr -> Expr
3316 f ns env (Lam x e) = Lam x' (f ns1 env e)
3318 (ns1,ns2) = splitNS ns
3320 env = extend env x x'
3322 Notice the call to 'split' introduced by the type checker.
3323 How did it know to use 'splitNS'? Because what it really did
3324 was to introduce a call to the overloaded function 'split',
3325 defined by the class <literal>Splittable</literal>:
3327 class Splittable a where
3330 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3331 split for name supplies. But we can simply write
3337 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3339 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3340 <literal>GHC.Exts</literal>.
3345 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3346 are entirely distinct implicit parameters: you
3347 can use them together and they won't intefere with each other. </para>
3350 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3352 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3353 in the context of a class or instance declaration. </para></listitem>
3357 <sect3><title>Warnings</title>
3360 The monomorphism restriction is even more important than usual.
3361 Consider the example above:
3363 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3364 f env (Lam x e) = Lam x' (f env e)
3367 env' = extend env x x'
3369 If we replaced the two occurrences of x' by (newName %ns), which is
3370 usually a harmless thing to do, we get:
3372 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3373 f env (Lam x e) = Lam (newName %ns) (f env e)
3375 env' = extend env x (newName %ns)
3377 But now the name supply is consumed in <emphasis>three</emphasis> places
3378 (the two calls to newName,and the recursive call to f), so
3379 the result is utterly different. Urk! We don't even have
3383 Well, this is an experimental change. With implicit
3384 parameters we have already lost beta reduction anyway, and
3385 (as John Launchbury puts it) we can't sensibly reason about
3386 Haskell programs without knowing their typing.
3391 <sect3><title>Recursive functions</title>
3392 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3395 foo :: %x::T => Int -> [Int]
3397 foo n = %x : foo (n-1)
3399 where T is some type in class Splittable.</para>
3401 Do you get a list of all the same T's or all different T's
3402 (assuming that split gives two distinct T's back)?
3404 If you supply the type signature, taking advantage of polymorphic
3405 recursion, you get what you'd probably expect. Here's the
3406 translated term, where the implicit param is made explicit:
3409 foo x n = let (x1,x2) = split x
3410 in x1 : foo x2 (n-1)
3412 But if you don't supply a type signature, GHC uses the Hindley
3413 Milner trick of using a single monomorphic instance of the function
3414 for the recursive calls. That is what makes Hindley Milner type inference
3415 work. So the translation becomes
3419 foom n = x : foom (n-1)
3423 Result: 'x' is not split, and you get a list of identical T's. So the
3424 semantics of the program depends on whether or not foo has a type signature.
3427 You may say that this is a good reason to dislike linear implicit parameters
3428 and you'd be right. That is why they are an experimental feature.
3434 ================ END OF Linear Implicit Parameters commented out -->
3436 <sect2 id="kinding">
3437 <title>Explicitly-kinded quantification</title>
3440 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3441 to give the kind explicitly as (machine-checked) documentation,
3442 just as it is nice to give a type signature for a function. On some occasions,
3443 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3444 John Hughes had to define the data type:
3446 data Set cxt a = Set [a]
3447 | Unused (cxt a -> ())
3449 The only use for the <literal>Unused</literal> constructor was to force the correct
3450 kind for the type variable <literal>cxt</literal>.
3453 GHC now instead allows you to specify the kind of a type variable directly, wherever
3454 a type variable is explicitly bound. Namely:
3456 <listitem><para><literal>data</literal> declarations:
3458 data Set (cxt :: * -> *) a = Set [a]
3459 </screen></para></listitem>
3460 <listitem><para><literal>type</literal> declarations:
3462 type T (f :: * -> *) = f Int
3463 </screen></para></listitem>
3464 <listitem><para><literal>class</literal> declarations:
3466 class (Eq a) => C (f :: * -> *) a where ...
3467 </screen></para></listitem>
3468 <listitem><para><literal>forall</literal>'s in type signatures:
3470 f :: forall (cxt :: * -> *). Set cxt Int
3471 </screen></para></listitem>
3476 The parentheses are required. Some of the spaces are required too, to
3477 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3478 will get a parse error, because "<literal>::*->*</literal>" is a
3479 single lexeme in Haskell.
3483 As part of the same extension, you can put kind annotations in types
3486 f :: (Int :: *) -> Int
3487 g :: forall a. a -> (a :: *)
3491 atype ::= '(' ctype '::' kind ')
3493 The parentheses are required.
3498 <sect2 id="universal-quantification">
3499 <title>Arbitrary-rank polymorphism
3503 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3504 allows us to say exactly what this means. For example:
3512 g :: forall b. (b -> b)
3514 The two are treated identically.
3518 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3519 explicit universal quantification in
3521 For example, all the following types are legal:
3523 f1 :: forall a b. a -> b -> a
3524 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3526 f2 :: (forall a. a->a) -> Int -> Int
3527 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3529 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3531 f4 :: Int -> (forall a. a -> a)
3533 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3534 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3535 The <literal>forall</literal> makes explicit the universal quantification that
3536 is implicitly added by Haskell.
3539 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3540 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3541 shows, the polymorphic type on the left of the function arrow can be overloaded.
3544 The function <literal>f3</literal> has a rank-3 type;
3545 it has rank-2 types on the left of a function arrow.
3548 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3549 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3550 that restriction has now been lifted.)
3551 In particular, a forall-type (also called a "type scheme"),
3552 including an operational type class context, is legal:
3554 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3555 of a function arrow </para> </listitem>
3556 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3557 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3558 field type signatures.</para> </listitem>
3559 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3560 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3562 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3563 a type variable any more!
3572 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3573 the types of the constructor arguments. Here are several examples:
3579 data T a = T1 (forall b. b -> b -> b) a
3581 data MonadT m = MkMonad { return :: forall a. a -> m a,
3582 bind :: forall a b. m a -> (a -> m b) -> m b
3585 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3591 The constructors have rank-2 types:
3597 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3598 MkMonad :: forall m. (forall a. a -> m a)
3599 -> (forall a b. m a -> (a -> m b) -> m b)
3601 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3607 Notice that you don't need to use a <literal>forall</literal> if there's an
3608 explicit context. For example in the first argument of the
3609 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3610 prefixed to the argument type. The implicit <literal>forall</literal>
3611 quantifies all type variables that are not already in scope, and are
3612 mentioned in the type quantified over.
3616 As for type signatures, implicit quantification happens for non-overloaded
3617 types too. So if you write this:
3620 data T a = MkT (Either a b) (b -> b)
3623 it's just as if you had written this:
3626 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3629 That is, since the type variable <literal>b</literal> isn't in scope, it's
3630 implicitly universally quantified. (Arguably, it would be better
3631 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3632 where that is what is wanted. Feedback welcomed.)
3636 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3637 the constructor to suitable values, just as usual. For example,
3648 a3 = MkSwizzle reverse
3651 a4 = let r x = Just x
3658 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3659 mkTs f x y = [T1 f x, T1 f y]
3665 The type of the argument can, as usual, be more general than the type
3666 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3667 does not need the <literal>Ord</literal> constraint.)
3671 When you use pattern matching, the bound variables may now have
3672 polymorphic types. For example:
3678 f :: T a -> a -> (a, Char)
3679 f (T1 w k) x = (w k x, w 'c' 'd')
3681 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3682 g (MkSwizzle s) xs f = s (map f (s xs))
3684 h :: MonadT m -> [m a] -> m [a]
3685 h m [] = return m []
3686 h m (x:xs) = bind m x $ \y ->
3687 bind m (h m xs) $ \ys ->
3694 In the function <function>h</function> we use the record selectors <literal>return</literal>
3695 and <literal>bind</literal> to extract the polymorphic bind and return functions
3696 from the <literal>MonadT</literal> data structure, rather than using pattern
3702 <title>Type inference</title>
3705 In general, type inference for arbitrary-rank types is undecidable.
3706 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3707 to get a decidable algorithm by requiring some help from the programmer.
3708 We do not yet have a formal specification of "some help" but the rule is this:
3711 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3712 provides an explicit polymorphic type for x, or GHC's type inference will assume
3713 that x's type has no foralls in it</emphasis>.
3716 What does it mean to "provide" an explicit type for x? You can do that by
3717 giving a type signature for x directly, using a pattern type signature
3718 (<xref linkend="scoped-type-variables"/>), thus:
3720 \ f :: (forall a. a->a) -> (f True, f 'c')
3722 Alternatively, you can give a type signature to the enclosing
3723 context, which GHC can "push down" to find the type for the variable:
3725 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3727 Here the type signature on the expression can be pushed inwards
3728 to give a type signature for f. Similarly, and more commonly,
3729 one can give a type signature for the function itself:
3731 h :: (forall a. a->a) -> (Bool,Char)
3732 h f = (f True, f 'c')
3734 You don't need to give a type signature if the lambda bound variable
3735 is a constructor argument. Here is an example we saw earlier:
3737 f :: T a -> a -> (a, Char)
3738 f (T1 w k) x = (w k x, w 'c' 'd')
3740 Here we do not need to give a type signature to <literal>w</literal>, because
3741 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3748 <sect3 id="implicit-quant">
3749 <title>Implicit quantification</title>
3752 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3753 user-written types, if and only if there is no explicit <literal>forall</literal>,
3754 GHC finds all the type variables mentioned in the type that are not already
3755 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3759 f :: forall a. a -> a
3766 h :: forall b. a -> b -> b
3772 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3775 f :: (a -> a) -> Int
3777 f :: forall a. (a -> a) -> Int
3779 f :: (forall a. a -> a) -> Int
3782 g :: (Ord a => a -> a) -> Int
3783 -- MEANS the illegal type
3784 g :: forall a. (Ord a => a -> a) -> Int
3786 g :: (forall a. Ord a => a -> a) -> Int
3788 The latter produces an illegal type, which you might think is silly,
3789 but at least the rule is simple. If you want the latter type, you
3790 can write your for-alls explicitly. Indeed, doing so is strongly advised
3797 <sect2 id="impredicative-polymorphism">
3798 <title>Impredicative polymorphism
3800 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3801 that you can call a polymorphic function at a polymorphic type, and
3802 parameterise data structures over polymorphic types. For example:
3804 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3805 f (Just g) = Just (g [3], g "hello")
3808 Notice here that the <literal>Maybe</literal> type is parameterised by the
3809 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3812 <para>The technical details of this extension are described in the paper
3813 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3814 type inference for higher-rank types and impredicativity</ulink>,
3815 which appeared at ICFP 2006.
3819 <sect2 id="scoped-type-variables">
3820 <title>Lexically scoped type variables
3824 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3825 which some type signatures are simply impossible to write. For example:
3827 f :: forall a. [a] -> [a]
3833 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3834 the entire definition of <literal>f</literal>.
3835 In particular, it is in scope at the type signature for <varname>ys</varname>.
3836 In Haskell 98 it is not possible to declare
3837 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3838 it becomes possible to do so.
3840 <para>Lexically-scoped type variables are enabled by
3841 <option>-fglasgow-exts</option>.
3843 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3844 variables work, compared to earlier releases. Read this section
3848 <title>Overview</title>
3850 <para>The design follows the following principles
3852 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3853 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3854 design.)</para></listitem>
3855 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3856 type variables. This means that every programmer-written type signature
3857 (includin one that contains free scoped type variables) denotes a
3858 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3859 checker, and no inference is involved.</para></listitem>
3860 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3861 changing the program.</para></listitem>
3865 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3867 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3868 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3869 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3870 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3874 In Haskell, a programmer-written type signature is implicitly quantifed over
3875 its free type variables (<ulink
3876 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3878 of the Haskel Report).
3879 Lexically scoped type variables affect this implicit quantification rules
3880 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3881 quantified. For example, if type variable <literal>a</literal> is in scope,
3884 (e :: a -> a) means (e :: a -> a)
3885 (e :: b -> b) means (e :: forall b. b->b)
3886 (e :: a -> b) means (e :: forall b. a->b)
3894 <sect3 id="decl-type-sigs">
3895 <title>Declaration type signatures</title>
3896 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3897 quantification (using <literal>forall</literal>) brings into scope the
3898 explicitly-quantified
3899 type variables, in the definition of the named function(s). For example:
3901 f :: forall a. [a] -> [a]
3902 f (x:xs) = xs ++ [ x :: a ]
3904 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3905 the definition of "<literal>f</literal>".
3907 <para>This only happens if the quantification in <literal>f</literal>'s type
3908 signature is explicit. For example:
3911 g (x:xs) = xs ++ [ x :: a ]
3913 This program will be rejected, because "<literal>a</literal>" does not scope
3914 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3915 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3916 quantification rules.
3920 <sect3 id="exp-type-sigs">
3921 <title>Expression type signatures</title>
3923 <para>An expression type signature that has <emphasis>explicit</emphasis>
3924 quantification (using <literal>forall</literal>) brings into scope the
3925 explicitly-quantified
3926 type variables, in the annotated expression. For example:
3928 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3930 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3931 type variable <literal>s</literal> into scope, in the annotated expression
3932 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3937 <sect3 id="pattern-type-sigs">
3938 <title>Pattern type signatures</title>
3940 A type signature may occur in any pattern; this is a <emphasis>pattern type
3941 signature</emphasis>.
3944 -- f and g assume that 'a' is already in scope
3945 f = \(x::Int, y::a) -> x
3947 h ((x,y) :: (Int,Bool)) = (y,x)
3949 In the case where all the type variables in the pattern type sigature are
3950 already in scope (i.e. bound by the enclosing context), matters are simple: the
3951 signature simply constrains the type of the pattern in the obvious way.
3954 There is only one situation in which you can write a pattern type signature that
3955 mentions a type variable that is not already in scope, namely in pattern match
3956 of an existential data constructor. For example:
3958 data T = forall a. MkT [a]
3961 k (MkT [t::a]) = MkT t3
3965 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3966 variable that is not already in scope. Indeed, it cannot already be in scope,
3967 because it is bound by the pattern match. GHC's rule is that in this situation
3968 (and only then), a pattern type signature can mention a type variable that is
3969 not already in scope; the effect is to bring it into scope, standing for the
3970 existentially-bound type variable.
3973 If this seems a little odd, we think so too. But we must have
3974 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3975 could not name existentially-bound type variables in subequent type signatures.
3978 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3979 signature is allowed to mention a lexical variable that is not already in
3981 For example, both <literal>f</literal> and <literal>g</literal> would be
3982 illegal if <literal>a</literal> was not already in scope.
3988 <!-- ==================== Commented out part about result type signatures
3990 <sect3 id="result-type-sigs">
3991 <title>Result type signatures</title>
3994 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3997 {- f assumes that 'a' is already in scope -}
3998 f x y :: [a] = [x,y,x]
4000 g = \ x :: [Int] -> [3,4]
4002 h :: forall a. [a] -> a
4006 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4007 the result of the function. Similarly, the body of the lambda in the RHS of
4008 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4009 alternative in <literal>h</literal> is <literal>a</literal>.
4011 <para> A result type signature never brings new type variables into scope.</para>
4013 There are a couple of syntactic wrinkles. First, notice that all three
4014 examples would parse quite differently with parentheses:
4016 {- f assumes that 'a' is already in scope -}
4017 f x (y :: [a]) = [x,y,x]
4019 g = \ (x :: [Int]) -> [3,4]
4021 h :: forall a. [a] -> a
4025 Now the signature is on the <emphasis>pattern</emphasis>; and
4026 <literal>h</literal> would certainly be ill-typed (since the pattern
4027 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4029 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4030 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4031 token or a parenthesised type of some sort). To see why,
4032 consider how one would parse this:
4041 <sect3 id="cls-inst-scoped-tyvars">
4042 <title>Class and instance declarations</title>
4045 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4046 scope over the methods defined in the <literal>where</literal> part. For example:
4064 <sect2 id="typing-binds">
4065 <title>Generalised typing of mutually recursive bindings</title>
4068 The Haskell Report specifies that a group of bindings (at top level, or in a
4069 <literal>let</literal> or <literal>where</literal>) should be sorted into
4070 strongly-connected components, and then type-checked in dependency order
4071 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4072 Report, Section 4.5.1</ulink>).
4073 As each group is type-checked, any binders of the group that
4075 an explicit type signature are put in the type environment with the specified
4077 and all others are monomorphic until the group is generalised
4078 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4081 <para>Following a suggestion of Mark Jones, in his paper
4082 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4084 GHC implements a more general scheme. If <option>-X=RelaxedPolyRec</option> is
4086 <emphasis>the dependency analysis ignores references to variables that have an explicit
4087 type signature</emphasis>.
4088 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4089 typecheck. For example, consider:
4091 f :: Eq a => a -> Bool
4092 f x = (x == x) || g True || g "Yes"
4094 g y = (y <= y) || f True
4096 This is rejected by Haskell 98, but under Jones's scheme the definition for
4097 <literal>g</literal> is typechecked first, separately from that for
4098 <literal>f</literal>,
4099 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4100 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4101 type is generalised, to get
4103 g :: Ord a => a -> Bool
4105 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4106 <literal>g</literal> in the type environment.
4110 The same refined dependency analysis also allows the type signatures of
4111 mutually-recursive functions to have different contexts, something that is illegal in
4112 Haskell 98 (Section 4.5.2, last sentence). With
4113 <option>-X=RelaxedPolyRec</option>
4114 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4115 type signatures; in practice this means that only variables bound by the same
4116 pattern binding must have the same context. For example, this is fine:
4118 f :: Eq a => a -> Bool
4119 f x = (x == x) || g True
4121 g :: Ord a => a -> Bool
4122 g y = (y <= y) || f True
4127 <sect2 id="overloaded-strings">
4128 <title>Overloaded string literals
4132 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4133 string literal has type <literal>String</literal>, but with overloaded string
4134 literals enabled (with <literal>-X=OverloadedStrings</literal>)
4135 a string literal has type <literal>(IsString a) => a</literal>.
4138 This means that the usual string syntax can be used, e.g., for packed strings
4139 and other variations of string like types. String literals behave very much
4140 like integer literals, i.e., they can be used in both expressions and patterns.
4141 If used in a pattern the literal with be replaced by an equality test, in the same
4142 way as an integer literal is.
4145 The class <literal>IsString</literal> is defined as:
4147 class IsString a where
4148 fromString :: String -> a
4150 The only predefined instance is the obvious one to make strings work as usual:
4152 instance IsString [Char] where
4155 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4156 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4157 from module <literal>GHC.Exts</literal>.
4160 Haskell's defaulting mechanism is extended to cover string literals, when <option>-X-OverloadedStrings</option> is specified.
4164 Each type in a default declaration must be an
4165 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4169 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4170 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4171 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4172 <emphasis>or</emphasis> <literal>IsString</literal>.
4181 import GHC.Exts( IsString(..) )
4183 newtype MyString = MyString String deriving (Eq, Show)
4184 instance IsString MyString where
4185 fromString = MyString
4187 greet :: MyString -> MyString
4188 greet "hello" = "world"
4192 print $ greet "hello"
4193 print $ greet "fool"
4197 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4198 to work since it gets translated into an equality comparison.
4202 <sect2 id="type-families">
4203 <title>Type families
4207 GHC supports the definition of type families indexed by types. They may be
4208 seen as an extension of Haskell 98's class-based overloading of values to
4209 types. When type families are declared in classes, they are also known as
4213 There are two forms of type families: data families and type synonym families.
4214 Currently, only the former are fully implemented, while we are still working
4215 on the latter. As a result, the specification of the language extension is
4216 also still to some degree in flux. Hence, a more detailed description of
4217 the language extension and its use is currently available
4218 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4219 wiki page on type families</ulink>. The material will be moved to this user's
4220 guide when it has stabilised.
4223 Type families are enabled by the flag <option>-X=TypeFamilies</option>.
4230 <!-- ==================== End of type system extensions ================= -->
4232 <!-- ====================== TEMPLATE HASKELL ======================= -->
4234 <sect1 id="template-haskell">
4235 <title>Template Haskell</title>
4237 <para>Template Haskell allows you to do compile-time meta-programming in
4240 the main technical innovations is discussed in "<ulink
4241 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4242 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4245 There is a Wiki page about
4246 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4247 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4251 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4252 Haskell library reference material</ulink>
4253 (search for the type ExpQ).
4254 [Temporary: many changes to the original design are described in
4255 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4256 Not all of these changes are in GHC 6.6.]
4259 <para> The first example from that paper is set out below as a worked example to help get you started.
4263 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4264 Tim Sheard is going to expand it.)
4268 <title>Syntax</title>
4270 <para> Template Haskell has the following new syntactic
4271 constructions. You need to use the flag
4272 <option>-X=TemplateHaskell</option> or <option>-X=TH</option>
4273 <indexterm><primary><option>-X=TemplateHaskell</option></primary>
4274 </indexterm>to switch these syntactic extensions on
4275 (<option>-X=TemplateHaskell</option> is no longer implied by
4276 <option>-fglasgow-exts</option>).</para>
4280 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4281 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4282 There must be no space between the "$" and the identifier or parenthesis. This use
4283 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4284 of "." as an infix operator. If you want the infix operator, put spaces around it.
4286 <para> A splice can occur in place of
4288 <listitem><para> an expression; the spliced expression must
4289 have type <literal>Q Exp</literal></para></listitem>
4290 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4291 <listitem><para> [Planned, but not implemented yet.] a
4292 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4294 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4295 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4301 A expression quotation is written in Oxford brackets, thus:
4303 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4304 the quotation has type <literal>Expr</literal>.</para></listitem>
4305 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4306 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4307 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4308 the quotation has type <literal>Type</literal>.</para></listitem>
4309 </itemizedlist></para></listitem>
4312 Reification is written thus:
4314 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4315 has type <literal>Dec</literal>. </para></listitem>
4316 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4317 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4318 <listitem><para> Still to come: fixities </para></listitem>
4320 </itemizedlist></para>
4327 <sect2> <title> Using Template Haskell </title>
4331 The data types and monadic constructor functions for Template Haskell are in the library
4332 <literal>Language.Haskell.THSyntax</literal>.
4336 You can only run a function at compile time if it is imported from another module. That is,
4337 you can't define a function in a module, and call it from within a splice in the same module.
4338 (It would make sense to do so, but it's hard to implement.)
4342 Furthermore, you can only run a function at compile time if it is imported
4343 from another module <emphasis>that is not part of a mutually-recursive group of modules
4344 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4345 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4346 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4350 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4353 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4354 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4355 compiles and runs a program, and then looks at the result. So it's important that
4356 the program it compiles produces results whose representations are identical to
4357 those of the compiler itself.
4361 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4362 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4367 <sect2> <title> A Template Haskell Worked Example </title>
4368 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4369 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4376 -- Import our template "pr"
4377 import Printf ( pr )
4379 -- The splice operator $ takes the Haskell source code
4380 -- generated at compile time by "pr" and splices it into
4381 -- the argument of "putStrLn".
4382 main = putStrLn ( $(pr "Hello") )
4388 -- Skeletal printf from the paper.
4389 -- It needs to be in a separate module to the one where
4390 -- you intend to use it.
4392 -- Import some Template Haskell syntax
4393 import Language.Haskell.TH
4395 -- Describe a format string
4396 data Format = D | S | L String
4398 -- Parse a format string. This is left largely to you
4399 -- as we are here interested in building our first ever
4400 -- Template Haskell program and not in building printf.
4401 parse :: String -> [Format]
4404 -- Generate Haskell source code from a parsed representation
4405 -- of the format string. This code will be spliced into
4406 -- the module which calls "pr", at compile time.
4407 gen :: [Format] -> ExpQ
4408 gen [D] = [| \n -> show n |]
4409 gen [S] = [| \s -> s |]
4410 gen [L s] = stringE s
4412 -- Here we generate the Haskell code for the splice
4413 -- from an input format string.
4414 pr :: String -> ExpQ
4415 pr s = gen (parse s)
4418 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4421 $ ghc --make -X=TemplateHaskell main.hs -o main.exe
4424 <para>Run "main.exe" and here is your output:</para>
4434 <title>Using Template Haskell with Profiling</title>
4435 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4437 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4438 interpreter to run the splice expressions. The bytecode interpreter
4439 runs the compiled expression on top of the same runtime on which GHC
4440 itself is running; this means that the compiled code referred to by
4441 the interpreted expression must be compatible with this runtime, and
4442 in particular this means that object code that is compiled for
4443 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4444 expression, because profiled object code is only compatible with the
4445 profiling version of the runtime.</para>
4447 <para>This causes difficulties if you have a multi-module program
4448 containing Template Haskell code and you need to compile it for
4449 profiling, because GHC cannot load the profiled object code and use it
4450 when executing the splices. Fortunately GHC provides a workaround.
4451 The basic idea is to compile the program twice:</para>
4455 <para>Compile the program or library first the normal way, without
4456 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4459 <para>Then compile it again with <option>-prof</option>, and
4460 additionally use <option>-osuf
4461 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4462 to name the object files differentliy (you can choose any suffix
4463 that isn't the normal object suffix here). GHC will automatically
4464 load the object files built in the first step when executing splice
4465 expressions. If you omit the <option>-osuf</option> flag when
4466 building with <option>-prof</option> and Template Haskell is used,
4467 GHC will emit an error message. </para>
4474 <!-- ===================== Arrow notation =================== -->
4476 <sect1 id="arrow-notation">
4477 <title>Arrow notation
4480 <para>Arrows are a generalization of monads introduced by John Hughes.
4481 For more details, see
4486 “Generalising Monads to Arrows”,
4487 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4488 pp67–111, May 2000.
4494 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4495 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4501 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4502 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4508 and the arrows web page at
4509 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4510 With the <option>-X=Arrows</option> flag, GHC supports the arrow
4511 notation described in the second of these papers.
4512 What follows is a brief introduction to the notation;
4513 it won't make much sense unless you've read Hughes's paper.
4514 This notation is translated to ordinary Haskell,
4515 using combinators from the
4516 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4520 <para>The extension adds a new kind of expression for defining arrows:
4522 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4523 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4525 where <literal>proc</literal> is a new keyword.
4526 The variables of the pattern are bound in the body of the
4527 <literal>proc</literal>-expression,
4528 which is a new sort of thing called a <firstterm>command</firstterm>.
4529 The syntax of commands is as follows:
4531 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4532 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4533 | <replaceable>cmd</replaceable><superscript>0</superscript>
4535 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4536 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4537 infix operators as for expressions, and
4539 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4540 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4541 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4542 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4543 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4544 | <replaceable>fcmd</replaceable>
4546 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4547 | ( <replaceable>cmd</replaceable> )
4548 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4550 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4551 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4552 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4553 | <replaceable>cmd</replaceable>
4555 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4556 except that the bodies are commands instead of expressions.
4560 Commands produce values, but (like monadic computations)
4561 may yield more than one value,
4562 or none, and may do other things as well.
4563 For the most part, familiarity with monadic notation is a good guide to
4565 However the values of expressions, even monadic ones,
4566 are determined by the values of the variables they contain;
4567 this is not necessarily the case for commands.
4571 A simple example of the new notation is the expression
4573 proc x -> f -< x+1
4575 We call this a <firstterm>procedure</firstterm> or
4576 <firstterm>arrow abstraction</firstterm>.
4577 As with a lambda expression, the variable <literal>x</literal>
4578 is a new variable bound within the <literal>proc</literal>-expression.
4579 It refers to the input to the arrow.
4580 In the above example, <literal>-<</literal> is not an identifier but an
4581 new reserved symbol used for building commands from an expression of arrow
4582 type and an expression to be fed as input to that arrow.
4583 (The weird look will make more sense later.)
4584 It may be read as analogue of application for arrows.
4585 The above example is equivalent to the Haskell expression
4587 arr (\ x -> x+1) >>> f
4589 That would make no sense if the expression to the left of
4590 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4591 More generally, the expression to the left of <literal>-<</literal>
4592 may not involve any <firstterm>local variable</firstterm>,
4593 i.e. a variable bound in the current arrow abstraction.
4594 For such a situation there is a variant <literal>-<<</literal>, as in
4596 proc x -> f x -<< x+1
4598 which is equivalent to
4600 arr (\ x -> (f x, x+1)) >>> app
4602 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4604 Such an arrow is equivalent to a monad, so if you're using this form
4605 you may find a monadic formulation more convenient.
4609 <title>do-notation for commands</title>
4612 Another form of command is a form of <literal>do</literal>-notation.
4613 For example, you can write
4622 You can read this much like ordinary <literal>do</literal>-notation,
4623 but with commands in place of monadic expressions.
4624 The first line sends the value of <literal>x+1</literal> as an input to
4625 the arrow <literal>f</literal>, and matches its output against
4626 <literal>y</literal>.
4627 In the next line, the output is discarded.
4628 The arrow <function>returnA</function> is defined in the
4629 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4630 module as <literal>arr id</literal>.
4631 The above example is treated as an abbreviation for
4633 arr (\ x -> (x, x)) >>>
4634 first (arr (\ x -> x+1) >>> f) >>>
4635 arr (\ (y, x) -> (y, (x, y))) >>>
4636 first (arr (\ y -> 2*y) >>> g) >>>
4638 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4639 first (arr (\ (x, z) -> x*z) >>> h) >>>
4640 arr (\ (t, z) -> t+z) >>>
4643 Note that variables not used later in the composition are projected out.
4644 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4646 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4647 module, this reduces to
4649 arr (\ x -> (x+1, x)) >>>
4651 arr (\ (y, x) -> (2*y, (x, y))) >>>
4653 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4655 arr (\ (t, z) -> t+z)
4657 which is what you might have written by hand.
4658 With arrow notation, GHC keeps track of all those tuples of variables for you.
4662 Note that although the above translation suggests that
4663 <literal>let</literal>-bound variables like <literal>z</literal> must be
4664 monomorphic, the actual translation produces Core,
4665 so polymorphic variables are allowed.
4669 It's also possible to have mutually recursive bindings,
4670 using the new <literal>rec</literal> keyword, as in the following example:
4672 counter :: ArrowCircuit a => a Bool Int
4673 counter = proc reset -> do
4674 rec output <- returnA -< if reset then 0 else next
4675 next <- delay 0 -< output+1
4676 returnA -< output
4678 The translation of such forms uses the <function>loop</function> combinator,
4679 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4685 <title>Conditional commands</title>
4688 In the previous example, we used a conditional expression to construct the
4690 Sometimes we want to conditionally execute different commands, as in
4697 which is translated to
4699 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4700 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4702 Since the translation uses <function>|||</function>,
4703 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4707 There are also <literal>case</literal> commands, like
4713 y <- h -< (x1, x2)
4717 The syntax is the same as for <literal>case</literal> expressions,
4718 except that the bodies of the alternatives are commands rather than expressions.
4719 The translation is similar to that of <literal>if</literal> commands.
4725 <title>Defining your own control structures</title>
4728 As we're seen, arrow notation provides constructs,
4729 modelled on those for expressions,
4730 for sequencing, value recursion and conditionals.
4731 But suitable combinators,
4732 which you can define in ordinary Haskell,
4733 may also be used to build new commands out of existing ones.
4734 The basic idea is that a command defines an arrow from environments to values.
4735 These environments assign values to the free local variables of the command.
4736 Thus combinators that produce arrows from arrows
4737 may also be used to build commands from commands.
4738 For example, the <literal>ArrowChoice</literal> class includes a combinator
4740 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4742 so we can use it to build commands:
4744 expr' = proc x -> do
4747 symbol Plus -< ()
4748 y <- term -< ()
4751 symbol Minus -< ()
4752 y <- term -< ()
4755 (The <literal>do</literal> on the first line is needed to prevent the first
4756 <literal><+> ...</literal> from being interpreted as part of the
4757 expression on the previous line.)
4758 This is equivalent to
4760 expr' = (proc x -> returnA -< x)
4761 <+> (proc x -> do
4762 symbol Plus -< ()
4763 y <- term -< ()
4765 <+> (proc x -> do
4766 symbol Minus -< ()
4767 y <- term -< ()
4770 It is essential that this operator be polymorphic in <literal>e</literal>
4771 (representing the environment input to the command
4772 and thence to its subcommands)
4773 and satisfy the corresponding naturality property
4775 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4777 at least for strict <literal>k</literal>.
4778 (This should be automatic if you're not using <function>seq</function>.)
4779 This ensures that environments seen by the subcommands are environments
4780 of the whole command,
4781 and also allows the translation to safely trim these environments.
4782 The operator must also not use any variable defined within the current
4787 We could define our own operator
4789 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4790 untilA body cond = proc x ->
4791 if cond x then returnA -< ()
4794 untilA body cond -< x
4796 and use it in the same way.
4797 Of course this infix syntax only makes sense for binary operators;
4798 there is also a more general syntax involving special brackets:
4802 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4809 <title>Primitive constructs</title>
4812 Some operators will need to pass additional inputs to their subcommands.
4813 For example, in an arrow type supporting exceptions,
4814 the operator that attaches an exception handler will wish to pass the
4815 exception that occurred to the handler.
4816 Such an operator might have a type
4818 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4820 where <literal>Ex</literal> is the type of exceptions handled.
4821 You could then use this with arrow notation by writing a command
4823 body `handleA` \ ex -> handler
4825 so that if an exception is raised in the command <literal>body</literal>,
4826 the variable <literal>ex</literal> is bound to the value of the exception
4827 and the command <literal>handler</literal>,
4828 which typically refers to <literal>ex</literal>, is entered.
4829 Though the syntax here looks like a functional lambda,
4830 we are talking about commands, and something different is going on.
4831 The input to the arrow represented by a command consists of values for
4832 the free local variables in the command, plus a stack of anonymous values.
4833 In all the prior examples, this stack was empty.
4834 In the second argument to <function>handleA</function>,
4835 this stack consists of one value, the value of the exception.
4836 The command form of lambda merely gives this value a name.
4841 the values on the stack are paired to the right of the environment.
4842 So operators like <function>handleA</function> that pass
4843 extra inputs to their subcommands can be designed for use with the notation
4844 by pairing the values with the environment in this way.
4845 More precisely, the type of each argument of the operator (and its result)
4846 should have the form
4848 a (...(e,t1), ... tn) t
4850 where <replaceable>e</replaceable> is a polymorphic variable
4851 (representing the environment)
4852 and <replaceable>ti</replaceable> are the types of the values on the stack,
4853 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4854 The polymorphic variable <replaceable>e</replaceable> must not occur in
4855 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4856 <replaceable>t</replaceable>.
4857 However the arrows involved need not be the same.
4858 Here are some more examples of suitable operators:
4860 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4861 runReader :: ... => a e c -> a' (e,State) c
4862 runState :: ... => a e c -> a' (e,State) (c,State)
4864 We can supply the extra input required by commands built with the last two
4865 by applying them to ordinary expressions, as in
4869 (|runReader (do { ... })|) s
4871 which adds <literal>s</literal> to the stack of inputs to the command
4872 built using <function>runReader</function>.
4876 The command versions of lambda abstraction and application are analogous to
4877 the expression versions.
4878 In particular, the beta and eta rules describe equivalences of commands.
4879 These three features (operators, lambda abstraction and application)
4880 are the core of the notation; everything else can be built using them,
4881 though the results would be somewhat clumsy.
4882 For example, we could simulate <literal>do</literal>-notation by defining
4884 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4885 u `bind` f = returnA &&& u >>> f
4887 bind_ :: Arrow a => a e b -> a e c -> a e c
4888 u `bind_` f = u `bind` (arr fst >>> f)
4890 We could simulate <literal>if</literal> by defining
4892 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4893 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4900 <title>Differences with the paper</title>
4905 <para>Instead of a single form of arrow application (arrow tail) with two
4906 translations, the implementation provides two forms
4907 <quote><literal>-<</literal></quote> (first-order)
4908 and <quote><literal>-<<</literal></quote> (higher-order).
4913 <para>User-defined operators are flagged with banana brackets instead of
4914 a new <literal>form</literal> keyword.
4923 <title>Portability</title>
4926 Although only GHC implements arrow notation directly,
4927 there is also a preprocessor
4929 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4930 that translates arrow notation into Haskell 98
4931 for use with other Haskell systems.
4932 You would still want to check arrow programs with GHC;
4933 tracing type errors in the preprocessor output is not easy.
4934 Modules intended for both GHC and the preprocessor must observe some
4935 additional restrictions:
4940 The module must import
4941 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4947 The preprocessor cannot cope with other Haskell extensions.
4948 These would have to go in separate modules.
4954 Because the preprocessor targets Haskell (rather than Core),
4955 <literal>let</literal>-bound variables are monomorphic.
4966 <!-- ==================== BANG PATTERNS ================= -->
4968 <sect1 id="bang-patterns">
4969 <title>Bang patterns
4970 <indexterm><primary>Bang patterns</primary></indexterm>
4972 <para>GHC supports an extension of pattern matching called <emphasis>bang
4973 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4975 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4976 prime feature description</ulink> contains more discussion and examples
4977 than the material below.
4980 Bang patterns are enabled by the flag <option>-X=BangPatterns</option>.
4983 <sect2 id="bang-patterns-informal">
4984 <title>Informal description of bang patterns
4987 The main idea is to add a single new production to the syntax of patterns:
4991 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4992 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4997 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4998 whereas without the bang it would be lazy.
4999 Bang patterns can be nested of course:
5003 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5004 <literal>y</literal>.
5005 A bang only really has an effect if it precedes a variable or wild-card pattern:
5010 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5011 forces evaluation anyway does nothing.
5013 Bang patterns work in <literal>case</literal> expressions too, of course:
5015 g5 x = let y = f x in body
5016 g6 x = case f x of { y -> body }
5017 g7 x = case f x of { !y -> body }
5019 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5020 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
5021 result, and then evaluates <literal>body</literal>.
5023 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5024 definitions too. For example:
5028 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5029 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5030 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5031 in a function argument <literal>![x,y]</literal> means the
5032 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5033 is part of the syntax of <literal>let</literal> bindings.
5038 <sect2 id="bang-patterns-sem">
5039 <title>Syntax and semantics
5043 We add a single new production to the syntax of patterns:
5047 There is one problem with syntactic ambiguity. Consider:
5051 Is this a definition of the infix function "<literal>(!)</literal>",
5052 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5053 ambiguity in favour of the latter. If you want to define
5054 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5059 The semantics of Haskell pattern matching is described in <ulink
5060 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5061 Section 3.17.2</ulink> of the Haskell Report. To this description add
5062 one extra item 10, saying:
5063 <itemizedlist><listitem><para>Matching
5064 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5065 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5066 <listitem><para>otherwise, <literal>pat</literal> is matched against
5067 <literal>v</literal></para></listitem>
5069 </para></listitem></itemizedlist>
5070 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5071 Section 3.17.3</ulink>, add a new case (t):
5073 case v of { !pat -> e; _ -> e' }
5074 = v `seq` case v of { pat -> e; _ -> e' }
5077 That leaves let expressions, whose translation is given in
5078 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5080 of the Haskell Report.
5081 In the translation box, first apply
5082 the following transformation: for each pattern <literal>pi</literal> that is of
5083 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5084 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5085 have a bang at the top, apply the rules in the existing box.
5087 <para>The effect of the let rule is to force complete matching of the pattern
5088 <literal>qi</literal> before evaluation of the body is begun. The bang is
5089 retained in the translated form in case <literal>qi</literal> is a variable,
5097 The let-binding can be recursive. However, it is much more common for
5098 the let-binding to be non-recursive, in which case the following law holds:
5099 <literal>(let !p = rhs in body)</literal>
5101 <literal>(case rhs of !p -> body)</literal>
5104 A pattern with a bang at the outermost level is not allowed at the top level of
5110 <!-- ==================== ASSERTIONS ================= -->
5112 <sect1 id="assertions">
5114 <indexterm><primary>Assertions</primary></indexterm>
5118 If you want to make use of assertions in your standard Haskell code, you
5119 could define a function like the following:
5125 assert :: Bool -> a -> a
5126 assert False x = error "assertion failed!"
5133 which works, but gives you back a less than useful error message --
5134 an assertion failed, but which and where?
5138 One way out is to define an extended <function>assert</function> function which also
5139 takes a descriptive string to include in the error message and
5140 perhaps combine this with the use of a pre-processor which inserts
5141 the source location where <function>assert</function> was used.
5145 Ghc offers a helping hand here, doing all of this for you. For every
5146 use of <function>assert</function> in the user's source:
5152 kelvinToC :: Double -> Double
5153 kelvinToC k = assert (k >= 0.0) (k+273.15)
5159 Ghc will rewrite this to also include the source location where the
5166 assert pred val ==> assertError "Main.hs|15" pred val
5172 The rewrite is only performed by the compiler when it spots
5173 applications of <function>Control.Exception.assert</function>, so you
5174 can still define and use your own versions of
5175 <function>assert</function>, should you so wish. If not, import
5176 <literal>Control.Exception</literal> to make use
5177 <function>assert</function> in your code.
5181 GHC ignores assertions when optimisation is turned on with the
5182 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5183 <literal>assert pred e</literal> will be rewritten to
5184 <literal>e</literal>. You can also disable assertions using the
5185 <option>-fignore-asserts</option>
5186 option<indexterm><primary><option>-fignore-asserts</option></primary>
5187 </indexterm>.</para>
5190 Assertion failures can be caught, see the documentation for the
5191 <literal>Control.Exception</literal> library for the details.
5197 <!-- =============================== PRAGMAS =========================== -->
5199 <sect1 id="pragmas">
5200 <title>Pragmas</title>
5202 <indexterm><primary>pragma</primary></indexterm>
5204 <para>GHC supports several pragmas, or instructions to the
5205 compiler placed in the source code. Pragmas don't normally affect
5206 the meaning of the program, but they might affect the efficiency
5207 of the generated code.</para>
5209 <para>Pragmas all take the form
5211 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5213 where <replaceable>word</replaceable> indicates the type of
5214 pragma, and is followed optionally by information specific to that
5215 type of pragma. Case is ignored in
5216 <replaceable>word</replaceable>. The various values for
5217 <replaceable>word</replaceable> that GHC understands are described
5218 in the following sections; any pragma encountered with an
5219 unrecognised <replaceable>word</replaceable> is (silently)
5222 <sect2 id="deprecated-pragma">
5223 <title>DEPRECATED pragma</title>
5224 <indexterm><primary>DEPRECATED</primary>
5227 <para>The DEPRECATED pragma lets you specify that a particular
5228 function, class, or type, is deprecated. There are two
5233 <para>You can deprecate an entire module thus:</para>
5235 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5238 <para>When you compile any module that import
5239 <literal>Wibble</literal>, GHC will print the specified
5244 <para>You can deprecate a function, class, type, or data constructor, with the
5245 following top-level declaration:</para>
5247 {-# DEPRECATED f, C, T "Don't use these" #-}
5249 <para>When you compile any module that imports and uses any
5250 of the specified entities, GHC will print the specified
5252 <para> You can only depecate entities declared at top level in the module
5253 being compiled, and you can only use unqualified names in the list of
5254 entities being deprecated. A capitalised name, such as <literal>T</literal>
5255 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5256 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5257 both are in scope. If both are in scope, there is currently no way to deprecate
5258 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5261 Any use of the deprecated item, or of anything from a deprecated
5262 module, will be flagged with an appropriate message. However,
5263 deprecations are not reported for
5264 (a) uses of a deprecated function within its defining module, and
5265 (b) uses of a deprecated function in an export list.
5266 The latter reduces spurious complaints within a library
5267 in which one module gathers together and re-exports
5268 the exports of several others.
5270 <para>You can suppress the warnings with the flag
5271 <option>-fno-warn-deprecations</option>.</para>
5274 <sect2 id="include-pragma">
5275 <title>INCLUDE pragma</title>
5277 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5278 of C header files that should be <literal>#include</literal>'d into
5279 the C source code generated by the compiler for the current module (if
5280 compiling via C). For example:</para>
5283 {-# INCLUDE "foo.h" #-}
5284 {-# INCLUDE <stdio.h> #-}</programlisting>
5286 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5287 your source file with any <literal>OPTIONS_GHC</literal>
5290 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5291 to the <option>-#include</option> option (<xref
5292 linkend="options-C-compiler" />), because the
5293 <literal>INCLUDE</literal> pragma is understood by other
5294 compilers. Yet another alternative is to add the include file to each
5295 <literal>foreign import</literal> declaration in your code, but we
5296 don't recommend using this approach with GHC.</para>
5299 <sect2 id="inline-noinline-pragma">
5300 <title>INLINE and NOINLINE pragmas</title>
5302 <para>These pragmas control the inlining of function
5305 <sect3 id="inline-pragma">
5306 <title>INLINE pragma</title>
5307 <indexterm><primary>INLINE</primary></indexterm>
5309 <para>GHC (with <option>-O</option>, as always) tries to
5310 inline (or “unfold”) functions/values that are
5311 “small enough,” thus avoiding the call overhead
5312 and possibly exposing other more-wonderful optimisations.
5313 Normally, if GHC decides a function is “too
5314 expensive” to inline, it will not do so, nor will it
5315 export that unfolding for other modules to use.</para>
5317 <para>The sledgehammer you can bring to bear is the
5318 <literal>INLINE</literal><indexterm><primary>INLINE
5319 pragma</primary></indexterm> pragma, used thusly:</para>
5322 key_function :: Int -> String -> (Bool, Double)
5324 #ifdef __GLASGOW_HASKELL__
5325 {-# INLINE key_function #-}
5329 <para>(You don't need to do the C pre-processor carry-on
5330 unless you're going to stick the code through HBC—it
5331 doesn't like <literal>INLINE</literal> pragmas.)</para>
5333 <para>The major effect of an <literal>INLINE</literal> pragma
5334 is to declare a function's “cost” to be very low.
5335 The normal unfolding machinery will then be very keen to
5338 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5339 function can be put anywhere its type signature could be
5342 <para><literal>INLINE</literal> pragmas are a particularly
5344 <literal>then</literal>/<literal>return</literal> (or
5345 <literal>bind</literal>/<literal>unit</literal>) functions in
5346 a monad. For example, in GHC's own
5347 <literal>UniqueSupply</literal> monad code, we have:</para>
5350 #ifdef __GLASGOW_HASKELL__
5351 {-# INLINE thenUs #-}
5352 {-# INLINE returnUs #-}
5356 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5357 linkend="noinline-pragma"/>).</para>
5360 <sect3 id="noinline-pragma">
5361 <title>NOINLINE pragma</title>
5363 <indexterm><primary>NOINLINE</primary></indexterm>
5364 <indexterm><primary>NOTINLINE</primary></indexterm>
5366 <para>The <literal>NOINLINE</literal> pragma does exactly what
5367 you'd expect: it stops the named function from being inlined
5368 by the compiler. You shouldn't ever need to do this, unless
5369 you're very cautious about code size.</para>
5371 <para><literal>NOTINLINE</literal> is a synonym for
5372 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5373 specified by Haskell 98 as the standard way to disable
5374 inlining, so it should be used if you want your code to be
5378 <sect3 id="phase-control">
5379 <title>Phase control</title>
5381 <para> Sometimes you want to control exactly when in GHC's
5382 pipeline the INLINE pragma is switched on. Inlining happens
5383 only during runs of the <emphasis>simplifier</emphasis>. Each
5384 run of the simplifier has a different <emphasis>phase
5385 number</emphasis>; the phase number decreases towards zero.
5386 If you use <option>-dverbose-core2core</option> you'll see the
5387 sequence of phase numbers for successive runs of the
5388 simplifier. In an INLINE pragma you can optionally specify a
5392 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5393 <literal>f</literal>
5394 until phase <literal>k</literal>, but from phase
5395 <literal>k</literal> onwards be very keen to inline it.
5398 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5399 <literal>f</literal>
5400 until phase <literal>k</literal>, but from phase
5401 <literal>k</literal> onwards do not inline it.
5404 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5405 <literal>f</literal>
5406 until phase <literal>k</literal>, but from phase
5407 <literal>k</literal> onwards be willing to inline it (as if
5408 there was no pragma).
5411 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5412 <literal>f</literal>
5413 until phase <literal>k</literal>, but from phase
5414 <literal>k</literal> onwards do not inline it.
5417 The same information is summarised here:
5419 -- Before phase 2 Phase 2 and later
5420 {-# INLINE [2] f #-} -- No Yes
5421 {-# INLINE [~2] f #-} -- Yes No
5422 {-# NOINLINE [2] f #-} -- No Maybe
5423 {-# NOINLINE [~2] f #-} -- Maybe No
5425 {-# INLINE f #-} -- Yes Yes
5426 {-# NOINLINE f #-} -- No No
5428 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5429 function body is small, or it is applied to interesting-looking arguments etc).
5430 Another way to understand the semantics is this:
5432 <listitem><para>For both INLINE and NOINLINE, the phase number says
5433 when inlining is allowed at all.</para></listitem>
5434 <listitem><para>The INLINE pragma has the additional effect of making the
5435 function body look small, so that when inlining is allowed it is very likely to
5440 <para>The same phase-numbering control is available for RULES
5441 (<xref linkend="rewrite-rules"/>).</para>
5445 <sect2 id="language-pragma">
5446 <title>LANGUAGE pragma</title>
5448 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5449 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5451 <para>This allows language extensions to be enabled in a portable way.
5452 It is the intention that all Haskell compilers support the
5453 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5454 all extensions are supported by all compilers, of
5455 course. The <literal>LANGUAGE</literal> pragma should be used instead
5456 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5458 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5460 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5462 <para>Any extension from the <literal>Extension</literal> type defined in
5464 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink> may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5468 <sect2 id="line-pragma">
5469 <title>LINE pragma</title>
5471 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5472 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5473 <para>This pragma is similar to C's <literal>#line</literal>
5474 pragma, and is mainly for use in automatically generated Haskell
5475 code. It lets you specify the line number and filename of the
5476 original code; for example</para>
5478 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5480 <para>if you'd generated the current file from something called
5481 <filename>Foo.vhs</filename> and this line corresponds to line
5482 42 in the original. GHC will adjust its error messages to refer
5483 to the line/file named in the <literal>LINE</literal>
5487 <sect2 id="options-pragma">
5488 <title>OPTIONS_GHC pragma</title>
5489 <indexterm><primary>OPTIONS_GHC</primary>
5491 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5494 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5495 additional options that are given to the compiler when compiling
5496 this source file. See <xref linkend="source-file-options"/> for
5499 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5500 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5504 <title>RULES pragma</title>
5506 <para>The RULES pragma lets you specify rewrite rules. It is
5507 described in <xref linkend="rewrite-rules"/>.</para>
5510 <sect2 id="specialize-pragma">
5511 <title>SPECIALIZE pragma</title>
5513 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5514 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5515 <indexterm><primary>overloading, death to</primary></indexterm>
5517 <para>(UK spelling also accepted.) For key overloaded
5518 functions, you can create extra versions (NB: more code space)
5519 specialised to particular types. Thus, if you have an
5520 overloaded function:</para>
5523 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5526 <para>If it is heavily used on lists with
5527 <literal>Widget</literal> keys, you could specialise it as
5531 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5534 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5535 be put anywhere its type signature could be put.</para>
5537 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5538 (a) a specialised version of the function and (b) a rewrite rule
5539 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5540 un-specialised function into a call to the specialised one.</para>
5542 <para>The type in a SPECIALIZE pragma can be any type that is less
5543 polymorphic than the type of the original function. In concrete terms,
5544 if the original function is <literal>f</literal> then the pragma
5546 {-# SPECIALIZE f :: <type> #-}
5548 is valid if and only if the defintion
5550 f_spec :: <type>
5553 is valid. Here are some examples (where we only give the type signature
5554 for the original function, not its code):
5556 f :: Eq a => a -> b -> b
5557 {-# SPECIALISE f :: Int -> b -> b #-}
5559 g :: (Eq a, Ix b) => a -> b -> b
5560 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5562 h :: Eq a => a -> a -> a
5563 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5565 The last of these examples will generate a
5566 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5567 well. If you use this kind of specialisation, let us know how well it works.
5570 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5571 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5572 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5573 The <literal>INLINE</literal> pragma affects the specialised verison of the
5574 function (only), and applies even if the function is recursive. The motivating
5577 -- A GADT for arrays with type-indexed representation
5579 ArrInt :: !Int -> ByteArray# -> Arr Int
5580 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5582 (!:) :: Arr e -> Int -> e
5583 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5584 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5585 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5586 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5588 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5589 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5590 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5591 the specialised function will be inlined. It has two calls to
5592 <literal>(!:)</literal>,
5593 both at type <literal>Int</literal>. Both these calls fire the first
5594 specialisation, whose body is also inlined. The result is a type-based
5595 unrolling of the indexing function.</para>
5596 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5597 on an ordinarily-recursive function.</para>
5599 <para>Note: In earlier versions of GHC, it was possible to provide your own
5600 specialised function for a given type:
5603 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5606 This feature has been removed, as it is now subsumed by the
5607 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5611 <sect2 id="specialize-instance-pragma">
5612 <title>SPECIALIZE instance pragma
5616 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5617 <indexterm><primary>overloading, death to</primary></indexterm>
5618 Same idea, except for instance declarations. For example:
5621 instance (Eq a) => Eq (Foo a) where {
5622 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5626 The pragma must occur inside the <literal>where</literal> part
5627 of the instance declaration.
5630 Compatible with HBC, by the way, except perhaps in the placement
5636 <sect2 id="unpack-pragma">
5637 <title>UNPACK pragma</title>
5639 <indexterm><primary>UNPACK</primary></indexterm>
5641 <para>The <literal>UNPACK</literal> indicates to the compiler
5642 that it should unpack the contents of a constructor field into
5643 the constructor itself, removing a level of indirection. For
5647 data T = T {-# UNPACK #-} !Float
5648 {-# UNPACK #-} !Float
5651 <para>will create a constructor <literal>T</literal> containing
5652 two unboxed floats. This may not always be an optimisation: if
5653 the <function>T</function> constructor is scrutinised and the
5654 floats passed to a non-strict function for example, they will
5655 have to be reboxed (this is done automatically by the
5658 <para>Unpacking constructor fields should only be used in
5659 conjunction with <option>-O</option>, in order to expose
5660 unfoldings to the compiler so the reboxing can be removed as
5661 often as possible. For example:</para>
5665 f (T f1 f2) = f1 + f2
5668 <para>The compiler will avoid reboxing <function>f1</function>
5669 and <function>f2</function> by inlining <function>+</function>
5670 on floats, but only when <option>-O</option> is on.</para>
5672 <para>Any single-constructor data is eligible for unpacking; for
5676 data T = T {-# UNPACK #-} !(Int,Int)
5679 <para>will store the two <literal>Int</literal>s directly in the
5680 <function>T</function> constructor, by flattening the pair.
5681 Multi-level unpacking is also supported:</para>
5684 data T = T {-# UNPACK #-} !S
5685 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5688 <para>will store two unboxed <literal>Int#</literal>s
5689 directly in the <function>T</function> constructor. The
5690 unpacker can see through newtypes, too.</para>
5692 <para>If a field cannot be unpacked, you will not get a warning,
5693 so it might be an idea to check the generated code with
5694 <option>-ddump-simpl</option>.</para>
5696 <para>See also the <option>-funbox-strict-fields</option> flag,
5697 which essentially has the effect of adding
5698 <literal>{-# UNPACK #-}</literal> to every strict
5699 constructor field.</para>
5704 <!-- ======================= REWRITE RULES ======================== -->
5706 <sect1 id="rewrite-rules">
5707 <title>Rewrite rules
5709 <indexterm><primary>RULES pragma</primary></indexterm>
5710 <indexterm><primary>pragma, RULES</primary></indexterm>
5711 <indexterm><primary>rewrite rules</primary></indexterm></title>
5714 The programmer can specify rewrite rules as part of the source program
5715 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5716 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5717 and (b) the <option>-frules-off</option> flag
5718 (<xref linkend="options-f"/>) is not specified, and (c) the
5719 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5728 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5735 <title>Syntax</title>
5738 From a syntactic point of view:
5744 There may be zero or more rules in a <literal>RULES</literal> pragma.
5751 Each rule has a name, enclosed in double quotes. The name itself has
5752 no significance at all. It is only used when reporting how many times the rule fired.
5758 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5759 immediately after the name of the rule. Thus:
5762 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5765 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5766 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5775 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5776 is set, so you must lay out your rules starting in the same column as the
5777 enclosing definitions.
5784 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5785 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5786 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5787 by spaces, just like in a type <literal>forall</literal>.
5793 A pattern variable may optionally have a type signature.
5794 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5795 For example, here is the <literal>foldr/build</literal> rule:
5798 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5799 foldr k z (build g) = g k z
5802 Since <function>g</function> has a polymorphic type, it must have a type signature.
5809 The left hand side of a rule must consist of a top-level variable applied
5810 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5813 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5814 "wrong2" forall f. f True = True
5817 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5824 A rule does not need to be in the same module as (any of) the
5825 variables it mentions, though of course they need to be in scope.
5831 Rules are automatically exported from a module, just as instance declarations are.
5842 <title>Semantics</title>
5845 From a semantic point of view:
5851 Rules are only applied if you use the <option>-O</option> flag.
5857 Rules are regarded as left-to-right rewrite rules.
5858 When GHC finds an expression that is a substitution instance of the LHS
5859 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5860 By "a substitution instance" we mean that the LHS can be made equal to the
5861 expression by substituting for the pattern variables.
5868 The LHS and RHS of a rule are typechecked, and must have the
5876 GHC makes absolutely no attempt to verify that the LHS and RHS
5877 of a rule have the same meaning. That is undecidable in general, and
5878 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5885 GHC makes no attempt to make sure that the rules are confluent or
5886 terminating. For example:
5889 "loop" forall x,y. f x y = f y x
5892 This rule will cause the compiler to go into an infinite loop.
5899 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5905 GHC currently uses a very simple, syntactic, matching algorithm
5906 for matching a rule LHS with an expression. It seeks a substitution
5907 which makes the LHS and expression syntactically equal modulo alpha
5908 conversion. The pattern (rule), but not the expression, is eta-expanded if
5909 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5910 But not beta conversion (that's called higher-order matching).
5914 Matching is carried out on GHC's intermediate language, which includes
5915 type abstractions and applications. So a rule only matches if the
5916 types match too. See <xref linkend="rule-spec"/> below.
5922 GHC keeps trying to apply the rules as it optimises the program.
5923 For example, consider:
5932 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5933 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5934 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5935 not be substituted, and the rule would not fire.
5942 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5943 that appears on the LHS of a rule</emphasis>, because once you have substituted
5944 for something you can't match against it (given the simple minded
5945 matching). So if you write the rule
5948 "map/map" forall f,g. map f . map g = map (f.g)
5951 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5952 It will only match something written with explicit use of ".".
5953 Well, not quite. It <emphasis>will</emphasis> match the expression
5959 where <function>wibble</function> is defined:
5962 wibble f g = map f . map g
5965 because <function>wibble</function> will be inlined (it's small).
5967 Later on in compilation, GHC starts inlining even things on the
5968 LHS of rules, but still leaves the rules enabled. This inlining
5969 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5976 All rules are implicitly exported from the module, and are therefore
5977 in force in any module that imports the module that defined the rule, directly
5978 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5979 in force when compiling A.) The situation is very similar to that for instance
5991 <title>List fusion</title>
5994 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5995 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5996 intermediate list should be eliminated entirely.
6000 The following are good producers:
6012 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6018 Explicit lists (e.g. <literal>[True, False]</literal>)
6024 The cons constructor (e.g <literal>3:4:[]</literal>)
6030 <function>++</function>
6036 <function>map</function>
6042 <function>take</function>, <function>filter</function>
6048 <function>iterate</function>, <function>repeat</function>
6054 <function>zip</function>, <function>zipWith</function>
6063 The following are good consumers:
6075 <function>array</function> (on its second argument)
6081 <function>++</function> (on its first argument)
6087 <function>foldr</function>
6093 <function>map</function>
6099 <function>take</function>, <function>filter</function>
6105 <function>concat</function>
6111 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6117 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6118 will fuse with one but not the other)
6124 <function>partition</function>
6130 <function>head</function>
6136 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6142 <function>sequence_</function>
6148 <function>msum</function>
6154 <function>sortBy</function>
6163 So, for example, the following should generate no intermediate lists:
6166 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6172 This list could readily be extended; if there are Prelude functions that you use
6173 a lot which are not included, please tell us.
6177 If you want to write your own good consumers or producers, look at the
6178 Prelude definitions of the above functions to see how to do so.
6183 <sect2 id="rule-spec">
6184 <title>Specialisation
6188 Rewrite rules can be used to get the same effect as a feature
6189 present in earlier versions of GHC.
6190 For example, suppose that:
6193 genericLookup :: Ord a => Table a b -> a -> b
6194 intLookup :: Table Int b -> Int -> b
6197 where <function>intLookup</function> is an implementation of
6198 <function>genericLookup</function> that works very fast for
6199 keys of type <literal>Int</literal>. You might wish
6200 to tell GHC to use <function>intLookup</function> instead of
6201 <function>genericLookup</function> whenever the latter was called with
6202 type <literal>Table Int b -> Int -> b</literal>.
6203 It used to be possible to write
6206 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6209 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6212 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6215 This slightly odd-looking rule instructs GHC to replace
6216 <function>genericLookup</function> by <function>intLookup</function>
6217 <emphasis>whenever the types match</emphasis>.
6218 What is more, this rule does not need to be in the same
6219 file as <function>genericLookup</function>, unlike the
6220 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6221 have an original definition available to specialise).
6224 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6225 <function>intLookup</function> really behaves as a specialised version
6226 of <function>genericLookup</function>!!!</para>
6228 <para>An example in which using <literal>RULES</literal> for
6229 specialisation will Win Big:
6232 toDouble :: Real a => a -> Double
6233 toDouble = fromRational . toRational
6235 {-# RULES "toDouble/Int" toDouble = i2d #-}
6236 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6239 The <function>i2d</function> function is virtually one machine
6240 instruction; the default conversion—via an intermediate
6241 <literal>Rational</literal>—is obscenely expensive by
6248 <title>Controlling what's going on</title>
6256 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6262 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6263 If you add <option>-dppr-debug</option> you get a more detailed listing.
6269 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6272 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6273 {-# INLINE build #-}
6277 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6278 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6279 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6280 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6287 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6288 see how to write rules that will do fusion and yet give an efficient
6289 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6299 <sect2 id="core-pragma">
6300 <title>CORE pragma</title>
6302 <indexterm><primary>CORE pragma</primary></indexterm>
6303 <indexterm><primary>pragma, CORE</primary></indexterm>
6304 <indexterm><primary>core, annotation</primary></indexterm>
6307 The external core format supports <quote>Note</quote> annotations;
6308 the <literal>CORE</literal> pragma gives a way to specify what these
6309 should be in your Haskell source code. Syntactically, core
6310 annotations are attached to expressions and take a Haskell string
6311 literal as an argument. The following function definition shows an
6315 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6318 Semantically, this is equivalent to:
6326 However, when external for is generated (via
6327 <option>-fext-core</option>), there will be Notes attached to the
6328 expressions <function>show</function> and <varname>x</varname>.
6329 The core function declaration for <function>f</function> is:
6333 f :: %forall a . GHCziShow.ZCTShow a ->
6334 a -> GHCziBase.ZMZN GHCziBase.Char =
6335 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6337 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6339 (tpl1::GHCziBase.Int ->
6341 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6343 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6344 (tpl3::GHCziBase.ZMZN a ->
6345 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6353 Here, we can see that the function <function>show</function> (which
6354 has been expanded out to a case expression over the Show dictionary)
6355 has a <literal>%note</literal> attached to it, as does the
6356 expression <varname>eta</varname> (which used to be called
6357 <varname>x</varname>).
6364 <sect1 id="special-ids">
6365 <title>Special built-in functions</title>
6366 <para>GHC has a few built-in funcions with special behaviour,
6367 described in this section. All are exported by
6368 <literal>GHC.Exts</literal>.</para>
6370 <sect2> <title>The <literal>seq</literal> function </title>
6372 The function <literal>seq</literal> is as described in the Haskell98 Report.
6376 It evaluates its first argument to head normal form, and then returns its
6377 second argument as the result. The reason that it is documented here is
6378 that, despite <literal>seq</literal>'s polymorphism, its
6379 second argument can have an unboxed type, or
6380 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6381 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6382 to be instantiated to an unboxed type, which is not usually allowed.
6386 <sect2> <title>The <literal>inline</literal> function </title>
6388 The <literal>inline</literal> function is somewhat experimental.
6392 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6393 is inlined, regardless of its size. More precisely, the call
6394 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6396 This allows the programmer to control inlining from
6397 a particular <emphasis>call site</emphasis>
6398 rather than the <emphasis>definition site</emphasis> of the function
6399 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6402 This inlining occurs regardless of the argument to the call
6403 or the size of <literal>f</literal>'s definition; it is unconditional.
6404 The main caveat is that <literal>f</literal>'s definition must be
6405 visible to the compiler. That is, <literal>f</literal> must be
6406 let-bound in the current scope.
6407 If no inlining takes place, the <literal>inline</literal> function
6408 expands to the identity function in Phase zero; so its use imposes
6411 <para> If the function is defined in another
6412 module, GHC only exposes its inlining in the interface file if the
6413 function is sufficiently small that it <emphasis>might</emphasis> be
6414 inlined by the automatic mechanism. There is currently no way to tell
6415 GHC to expose arbitrarily-large functions in the interface file. (This
6416 shortcoming is something that could be fixed, with some kind of pragma.)
6420 <sect2> <title>The <literal>lazy</literal> function </title>
6422 The <literal>lazy</literal> function restrains strictness analysis a little:
6426 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6427 but <literal>lazy</literal> has a magical property so far as strictness
6428 analysis is concerned: it is lazy in its first argument,
6429 even though its semantics is strict. After strictness analysis has run,
6430 calls to <literal>lazy</literal> are inlined to be the identity function.
6433 This behaviour is occasionally useful when controlling evaluation order.
6434 Notably, <literal>lazy</literal> is used in the library definition of
6435 <literal>Control.Parallel.par</literal>:
6438 par x y = case (par# x) of { _ -> lazy y }
6440 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6441 look strict in <literal>y</literal> which would defeat the whole
6442 purpose of <literal>par</literal>.
6445 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6451 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6453 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6454 typechecker entirely. It has type
6456 unsafeCoerce# :: a -> b
6458 That is, it allows you to coerce any type into any other type. If you use this
6459 function, you had better get it right, otherwise segmentation faults await.
6460 It is generally used when you want to write a program that you know is
6461 well-typed, but where Haskell's type system is not expressive enough to prove
6462 that it is well typed.
6465 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6466 although extremely bad things will happen if you coerce a boxed type
6475 <sect1 id="generic-classes">
6476 <title>Generic classes</title>
6479 The ideas behind this extension are described in detail in "Derivable type classes",
6480 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6481 An example will give the idea:
6489 fromBin :: [Int] -> (a, [Int])
6491 toBin {| Unit |} Unit = []
6492 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6493 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6494 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6496 fromBin {| Unit |} bs = (Unit, bs)
6497 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6498 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6499 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6500 (y,bs'') = fromBin bs'
6503 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6504 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6505 which are defined thus in the library module <literal>Generics</literal>:
6509 data a :+: b = Inl a | Inr b
6510 data a :*: b = a :*: b
6513 Now you can make a data type into an instance of Bin like this:
6515 instance (Bin a, Bin b) => Bin (a,b)
6516 instance Bin a => Bin [a]
6518 That is, just leave off the "where" clause. Of course, you can put in the
6519 where clause and over-ride whichever methods you please.
6523 <title> Using generics </title>
6524 <para>To use generics you need to</para>
6527 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6528 <option>-X=Generics</option> (to generate extra per-data-type code),
6529 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6533 <para>Import the module <literal>Generics</literal> from the
6534 <literal>lang</literal> package. This import brings into
6535 scope the data types <literal>Unit</literal>,
6536 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6537 don't need this import if you don't mention these types
6538 explicitly; for example, if you are simply giving instance
6539 declarations.)</para>
6544 <sect2> <title> Changes wrt the paper </title>
6546 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6547 can be written infix (indeed, you can now use
6548 any operator starting in a colon as an infix type constructor). Also note that
6549 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6550 Finally, note that the syntax of the type patterns in the class declaration
6551 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6552 alone would ambiguous when they appear on right hand sides (an extension we
6553 anticipate wanting).
6557 <sect2> <title>Terminology and restrictions</title>
6559 Terminology. A "generic default method" in a class declaration
6560 is one that is defined using type patterns as above.
6561 A "polymorphic default method" is a default method defined as in Haskell 98.
6562 A "generic class declaration" is a class declaration with at least one
6563 generic default method.
6571 Alas, we do not yet implement the stuff about constructor names and
6578 A generic class can have only one parameter; you can't have a generic
6579 multi-parameter class.
6585 A default method must be defined entirely using type patterns, or entirely
6586 without. So this is illegal:
6589 op :: a -> (a, Bool)
6590 op {| Unit |} Unit = (Unit, True)
6593 However it is perfectly OK for some methods of a generic class to have
6594 generic default methods and others to have polymorphic default methods.
6600 The type variable(s) in the type pattern for a generic method declaration
6601 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:
6605 op {| p :*: q |} (x :*: y) = op (x :: p)
6613 The type patterns in a generic default method must take one of the forms:
6619 where "a" and "b" are type variables. Furthermore, all the type patterns for
6620 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6621 must use the same type variables. So this is illegal:
6625 op {| a :+: b |} (Inl x) = True
6626 op {| p :+: q |} (Inr y) = False
6628 The type patterns must be identical, even in equations for different methods of the class.
6629 So this too is illegal:
6633 op1 {| a :*: b |} (x :*: y) = True
6636 op2 {| p :*: q |} (x :*: y) = False
6638 (The reason for this restriction is that we gather all the equations for a particular type consructor
6639 into a single generic instance declaration.)
6645 A generic method declaration must give a case for each of the three type constructors.
6651 The type for a generic method can be built only from:
6653 <listitem> <para> Function arrows </para> </listitem>
6654 <listitem> <para> Type variables </para> </listitem>
6655 <listitem> <para> Tuples </para> </listitem>
6656 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6658 Here are some example type signatures for generic methods:
6661 op2 :: Bool -> (a,Bool)
6662 op3 :: [Int] -> a -> a
6665 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6669 This restriction is an implementation restriction: we just havn't got around to
6670 implementing the necessary bidirectional maps over arbitrary type constructors.
6671 It would be relatively easy to add specific type constructors, such as Maybe and list,
6672 to the ones that are allowed.</para>
6677 In an instance declaration for a generic class, the idea is that the compiler
6678 will fill in the methods for you, based on the generic templates. However it can only
6683 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6688 No constructor of the instance type has unboxed fields.
6692 (Of course, these things can only arise if you are already using GHC extensions.)
6693 However, you can still give an instance declarations for types which break these rules,
6694 provided you give explicit code to override any generic default methods.
6702 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6703 what the compiler does with generic declarations.
6708 <sect2> <title> Another example </title>
6710 Just to finish with, here's another example I rather like:
6714 nCons {| Unit |} _ = 1
6715 nCons {| a :*: b |} _ = 1
6716 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6719 tag {| Unit |} _ = 1
6720 tag {| a :*: b |} _ = 1
6721 tag {| a :+: b |} (Inl x) = tag x
6722 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6728 <sect1 id="monomorphism">
6729 <title>Control over monomorphism</title>
6731 <para>GHC supports two flags that control the way in which generalisation is
6732 carried out at let and where bindings.
6736 <title>Switching off the dreaded Monomorphism Restriction</title>
6737 <indexterm><primary><option>-X=NoMonomorphismRestriction</option></primary></indexterm>
6739 <para>Haskell's monomorphism restriction (see
6740 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6742 of the Haskell Report)
6743 can be completely switched off by
6744 <option>-X=NoMonomorphismRestriction</option>.
6749 <title>Monomorphic pattern bindings</title>
6750 <indexterm><primary><option>-X=NoMonoPatBinds</option></primary></indexterm>
6751 <indexterm><primary><option>-X=MonoPatBinds</option></primary></indexterm>
6753 <para> As an experimental change, we are exploring the possibility of
6754 making pattern bindings monomorphic; that is, not generalised at all.
6755 A pattern binding is a binding whose LHS has no function arguments,
6756 and is not a simple variable. For example:
6758 f x = x -- Not a pattern binding
6759 f = \x -> x -- Not a pattern binding
6760 f :: Int -> Int = \x -> x -- Not a pattern binding
6762 (g,h) = e -- A pattern binding
6763 (f) = e -- A pattern binding
6764 [x] = e -- A pattern binding
6766 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6767 default</emphasis>. Use <option>-X=MonoPatBinds</option> to recover the
6776 ;;; Local Variables: ***
6778 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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