1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individaully.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
296 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
297 <sect1 id="primitives">
298 <title>Unboxed types and primitive operations</title>
300 <para>GHC is built on a raft of primitive data types and operations.
301 While you really can use this stuff to write fast code,
302 we generally find it a lot less painful, and more satisfying in the
303 long run, to use higher-level language features and libraries. With
304 any luck, the code you write will be optimised to the efficient
305 unboxed version in any case. And if it isn't, we'd like to know
308 <para>We do not currently have good, up-to-date documentation about the
309 primitives, perhaps because they are mainly intended for internal use.
310 There used to be a long section about them here in the User Guide, but it
311 became out of date, and wrong information is worse than none.</para>
313 <para>The Real Truth about what primitive types there are, and what operations
314 work over those types, is held in the file
315 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
316 This file is used directly to generate GHC's primitive-operation definitions, so
317 it is always correct! It is also intended for processing into text.</para>
320 the result of such processing is part of the description of the
322 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
323 Core language</ulink>.
324 So that document is a good place to look for a type-set version.
325 We would be very happy if someone wanted to volunteer to produce an SGML
326 back end to the program that processes <filename>primops.txt</filename> so that
327 we could include the results here in the User Guide.</para>
329 <para>What follows here is a brief summary of some main points.</para>
331 <sect2 id="glasgow-unboxed">
336 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
339 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
340 that values of that type are represented by a pointer to a heap
341 object. The representation of a Haskell <literal>Int</literal>, for
342 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
343 type, however, is represented by the value itself, no pointers or heap
344 allocation are involved.
348 Unboxed types correspond to the “raw machine” types you
349 would use in C: <literal>Int#</literal> (long int),
350 <literal>Double#</literal> (double), <literal>Addr#</literal>
351 (void *), etc. The <emphasis>primitive operations</emphasis>
352 (PrimOps) on these types are what you might expect; e.g.,
353 <literal>(+#)</literal> is addition on
354 <literal>Int#</literal>s, and is the machine-addition that we all
355 know and love—usually one instruction.
359 Primitive (unboxed) types cannot be defined in Haskell, and are
360 therefore built into the language and compiler. Primitive types are
361 always unlifted; that is, a value of a primitive type cannot be
362 bottom. We use the convention that primitive types, values, and
363 operations have a <literal>#</literal> suffix.
367 Primitive values are often represented by a simple bit-pattern, such
368 as <literal>Int#</literal>, <literal>Float#</literal>,
369 <literal>Double#</literal>. But this is not necessarily the case:
370 a primitive value might be represented by a pointer to a
371 heap-allocated object. Examples include
372 <literal>Array#</literal>, the type of primitive arrays. A
373 primitive array is heap-allocated because it is too big a value to fit
374 in a register, and would be too expensive to copy around; in a sense,
375 it is accidental that it is represented by a pointer. If a pointer
376 represents a primitive value, then it really does point to that value:
377 no unevaluated thunks, no indirections…nothing can be at the
378 other end of the pointer than the primitive value.
379 A numerically-intensive program using unboxed types can
380 go a <emphasis>lot</emphasis> faster than its “standard”
381 counterpart—we saw a threefold speedup on one example.
385 There are some restrictions on the use of primitive types:
387 <listitem><para>The main restriction
388 is that you can't pass a primitive value to a polymorphic
389 function or store one in a polymorphic data type. This rules out
390 things like <literal>[Int#]</literal> (i.e. lists of primitive
391 integers). The reason for this restriction is that polymorphic
392 arguments and constructor fields are assumed to be pointers: if an
393 unboxed integer is stored in one of these, the garbage collector would
394 attempt to follow it, leading to unpredictable space leaks. Or a
395 <function>seq</function> operation on the polymorphic component may
396 attempt to dereference the pointer, with disastrous results. Even
397 worse, the unboxed value might be larger than a pointer
398 (<literal>Double#</literal> for instance).
401 <listitem><para> You cannot define a newtype whose representation type
402 (the argument type of the data constructor) is an unboxed type. Thus,
408 <listitem><para> You cannot bind a variable with an unboxed type
409 in a <emphasis>top-level</emphasis> binding.
411 <listitem><para> You cannot bind a variable with an unboxed type
412 in a <emphasis>recursive</emphasis> binding.
414 <listitem><para> You may bind unboxed variables in a (non-recursive,
415 non-top-level) pattern binding, but any such variable causes the entire
417 to become strict. For example:
419 data Foo = Foo Int Int#
421 f x = let (Foo a b, w) = ..rhs.. in ..body..
423 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
425 is strict, and the program behaves as if you had written
427 data Foo = Foo Int Int#
429 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
438 <sect2 id="unboxed-tuples">
439 <title>Unboxed Tuples
443 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
444 they're available by default with <option>-fglasgow-exts</option>. An
445 unboxed tuple looks like this:
457 where <literal>e_1..e_n</literal> are expressions of any
458 type (primitive or non-primitive). The type of an unboxed tuple looks
463 Unboxed tuples are used for functions that need to return multiple
464 values, but they avoid the heap allocation normally associated with
465 using fully-fledged tuples. When an unboxed tuple is returned, the
466 components are put directly into registers or on the stack; the
467 unboxed tuple itself does not have a composite representation. Many
468 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
470 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
471 tuples to avoid unnecessary allocation during sequences of operations.
475 There are some pretty stringent restrictions on the use of unboxed tuples:
480 Values of unboxed tuple types are subject to the same restrictions as
481 other unboxed types; i.e. they may not be stored in polymorphic data
482 structures or passed to polymorphic functions.
489 No variable can have an unboxed tuple type, nor may a constructor or function
490 argument have an unboxed tuple type. The following are all illegal:
494 data Foo = Foo (# Int, Int #)
496 f :: (# Int, Int #) -> (# Int, Int #)
499 g :: (# Int, Int #) -> Int
502 h x = let y = (# x,x #) in ...
509 The typical use of unboxed tuples is simply to return multiple values,
510 binding those multiple results with a <literal>case</literal> expression, thus:
512 f x y = (# x+1, y-1 #)
513 g x = case f x x of { (# a, b #) -> a + b }
515 You can have an unboxed tuple in a pattern binding, thus
517 f x = let (# p,q #) = h x in ..body..
519 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
520 the resulting binding is lazy like any other Haskell pattern binding. The
521 above example desugars like this:
523 f x = let t = case h x o f{ (# p,q #) -> (p,q)
528 Indeed, the bindings can even be recursive.
535 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
537 <sect1 id="syntax-extns">
538 <title>Syntactic extensions</title>
540 <!-- ====================== HIERARCHICAL MODULES ======================= -->
542 <sect2 id="hierarchical-modules">
543 <title>Hierarchical Modules</title>
545 <para>GHC supports a small extension to the syntax of module
546 names: a module name is allowed to contain a dot
547 <literal>‘.’</literal>. This is also known as the
548 “hierarchical module namespace” extension, because
549 it extends the normally flat Haskell module namespace into a
550 more flexible hierarchy of modules.</para>
552 <para>This extension has very little impact on the language
553 itself; modules names are <emphasis>always</emphasis> fully
554 qualified, so you can just think of the fully qualified module
555 name as <quote>the module name</quote>. In particular, this
556 means that the full module name must be given after the
557 <literal>module</literal> keyword at the beginning of the
558 module; for example, the module <literal>A.B.C</literal> must
561 <programlisting>module A.B.C</programlisting>
564 <para>It is a common strategy to use the <literal>as</literal>
565 keyword to save some typing when using qualified names with
566 hierarchical modules. For example:</para>
569 import qualified Control.Monad.ST.Strict as ST
572 <para>For details on how GHC searches for source and interface
573 files in the presence of hierarchical modules, see <xref
574 linkend="search-path"/>.</para>
576 <para>GHC comes with a large collection of libraries arranged
577 hierarchically; see the accompanying <ulink
578 url="../libraries/index.html">library
579 documentation</ulink>. More libraries to install are available
581 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
584 <!-- ====================== PATTERN GUARDS ======================= -->
586 <sect2 id="pattern-guards">
587 <title>Pattern guards</title>
590 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
591 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.)
595 Suppose we have an abstract data type of finite maps, with a
599 lookup :: FiniteMap -> Int -> Maybe Int
602 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
603 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
607 clunky env var1 var2 | ok1 && ok2 = val1 + val2
608 | otherwise = var1 + var2
619 The auxiliary functions are
623 maybeToBool :: Maybe a -> Bool
624 maybeToBool (Just x) = True
625 maybeToBool Nothing = False
627 expectJust :: Maybe a -> a
628 expectJust (Just x) = x
629 expectJust Nothing = error "Unexpected Nothing"
633 What is <function>clunky</function> doing? The guard <literal>ok1 &&
634 ok2</literal> checks that both lookups succeed, using
635 <function>maybeToBool</function> to convert the <function>Maybe</function>
636 types to booleans. The (lazily evaluated) <function>expectJust</function>
637 calls extract the values from the results of the lookups, and binds the
638 returned values to <varname>val1</varname> and <varname>val2</varname>
639 respectively. If either lookup fails, then clunky takes the
640 <literal>otherwise</literal> case and returns the sum of its arguments.
644 This is certainly legal Haskell, but it is a tremendously verbose and
645 un-obvious way to achieve the desired effect. Arguably, a more direct way
646 to write clunky would be to use case expressions:
650 clunky env var1 var2 = case lookup env var1 of
652 Just val1 -> case lookup env var2 of
654 Just val2 -> val1 + val2
660 This is a bit shorter, but hardly better. Of course, we can rewrite any set
661 of pattern-matching, guarded equations as case expressions; that is
662 precisely what the compiler does when compiling equations! The reason that
663 Haskell provides guarded equations is because they allow us to write down
664 the cases we want to consider, one at a time, independently of each other.
665 This structure is hidden in the case version. Two of the right-hand sides
666 are really the same (<function>fail</function>), and the whole expression
667 tends to become more and more indented.
671 Here is how I would write clunky:
676 | Just val1 <- lookup env var1
677 , Just val2 <- lookup env var2
679 ...other equations for clunky...
683 The semantics should be clear enough. The qualifiers are matched in order.
684 For a <literal><-</literal> qualifier, which I call a pattern guard, the
685 right hand side is evaluated and matched against the pattern on the left.
686 If the match fails then the whole guard fails and the next equation is
687 tried. If it succeeds, then the appropriate binding takes place, and the
688 next qualifier is matched, in the augmented environment. Unlike list
689 comprehensions, however, the type of the expression to the right of the
690 <literal><-</literal> is the same as the type of the pattern to its
691 left. The bindings introduced by pattern guards scope over all the
692 remaining guard qualifiers, and over the right hand side of the equation.
696 Just as with list comprehensions, boolean expressions can be freely mixed
697 with among the pattern guards. For example:
708 Haskell's current guards therefore emerge as a special case, in which the
709 qualifier list has just one element, a boolean expression.
713 <!-- ===================== Recursive do-notation =================== -->
715 <sect2 id="mdo-notation">
716 <title>The recursive do-notation
719 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
720 "A recursive do for Haskell",
721 Levent Erkok, John Launchbury",
722 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
725 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
726 that is, the variables bound in a do-expression are visible only in the textually following
727 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
728 group. It turns out that several applications can benefit from recursive bindings in
729 the do-notation, and this extension provides the necessary syntactic support.
732 Here is a simple (yet contrived) example:
735 import Control.Monad.Fix
737 justOnes = mdo xs <- Just (1:xs)
741 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
745 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
748 class Monad m => MonadFix m where
749 mfix :: (a -> m a) -> m a
752 The function <literal>mfix</literal>
753 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
754 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
755 For details, see the above mentioned reference.
758 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
759 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
760 for Haskell's internal state monad (strict and lazy, respectively).
763 There are three important points in using the recursive-do notation:
766 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
767 than <literal>do</literal>).
771 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
777 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
778 contains up to date information on recursive monadic bindings.
782 Historical note: The old implementation of the mdo-notation (and most
783 of the existing documents) used the name
784 <literal>MonadRec</literal> for the class and the corresponding library.
785 This name is not supported by GHC.
791 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
793 <sect2 id="parallel-list-comprehensions">
794 <title>Parallel List Comprehensions</title>
795 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
797 <indexterm><primary>parallel list comprehensions</primary>
800 <para>Parallel list comprehensions are a natural extension to list
801 comprehensions. List comprehensions can be thought of as a nice
802 syntax for writing maps and filters. Parallel comprehensions
803 extend this to include the zipWith family.</para>
805 <para>A parallel list comprehension has multiple independent
806 branches of qualifier lists, each separated by a `|' symbol. For
807 example, the following zips together two lists:</para>
810 [ (x, y) | x <- xs | y <- ys ]
813 <para>The behavior of parallel list comprehensions follows that of
814 zip, in that the resulting list will have the same length as the
815 shortest branch.</para>
817 <para>We can define parallel list comprehensions by translation to
818 regular comprehensions. Here's the basic idea:</para>
820 <para>Given a parallel comprehension of the form: </para>
823 [ e | p1 <- e11, p2 <- e12, ...
824 | q1 <- e21, q2 <- e22, ...
829 <para>This will be translated to: </para>
832 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
833 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
838 <para>where `zipN' is the appropriate zip for the given number of
843 <sect2 id="rebindable-syntax">
844 <title>Rebindable syntax</title>
847 <para>GHC allows most kinds of built-in syntax to be rebound by
848 the user, to facilitate replacing the <literal>Prelude</literal>
849 with a home-grown version, for example.</para>
851 <para>You may want to define your own numeric class
852 hierarchy. It completely defeats that purpose if the
853 literal "1" means "<literal>Prelude.fromInteger
854 1</literal>", which is what the Haskell Report specifies.
855 So the <option>-XNoImplicitPrelude</option> flag causes
856 the following pieces of built-in syntax to refer to
857 <emphasis>whatever is in scope</emphasis>, not the Prelude
862 <para>An integer literal <literal>368</literal> means
863 "<literal>fromInteger (368::Integer)</literal>", rather than
864 "<literal>Prelude.fromInteger (368::Integer)</literal>".
867 <listitem><para>Fractional literals are handed in just the same way,
868 except that the translation is
869 <literal>fromRational (3.68::Rational)</literal>.
872 <listitem><para>The equality test in an overloaded numeric pattern
873 uses whatever <literal>(==)</literal> is in scope.
876 <listitem><para>The subtraction operation, and the
877 greater-than-or-equal test, in <literal>n+k</literal> patterns
878 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
882 <para>Negation (e.g. "<literal>- (f x)</literal>")
883 means "<literal>negate (f x)</literal>", both in numeric
884 patterns, and expressions.
888 <para>"Do" notation is translated using whatever
889 functions <literal>(>>=)</literal>,
890 <literal>(>>)</literal>, and <literal>fail</literal>,
891 are in scope (not the Prelude
892 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
893 comprehensions, are unaffected. </para></listitem>
897 notation (see <xref linkend="arrow-notation"/>)
898 uses whatever <literal>arr</literal>,
899 <literal>(>>>)</literal>, <literal>first</literal>,
900 <literal>app</literal>, <literal>(|||)</literal> and
901 <literal>loop</literal> functions are in scope. But unlike the
902 other constructs, the types of these functions must match the
903 Prelude types very closely. Details are in flux; if you want
907 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
908 even if that is a little unexpected. For emample, the
909 static semantics of the literal <literal>368</literal>
910 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
911 <literal>fromInteger</literal> to have any of the types:
913 fromInteger :: Integer -> Integer
914 fromInteger :: forall a. Foo a => Integer -> a
915 fromInteger :: Num a => a -> Integer
916 fromInteger :: Integer -> Bool -> Bool
920 <para>Be warned: this is an experimental facility, with
921 fewer checks than usual. Use <literal>-dcore-lint</literal>
922 to typecheck the desugared program. If Core Lint is happy
923 you should be all right.</para>
927 <sect2 id="postfix-operators">
928 <title>Postfix operators</title>
931 GHC allows a small extension to the syntax of left operator sections, which
932 allows you to define postfix operators. The extension is this: the left section
936 is equivalent (from the point of view of both type checking and execution) to the expression
940 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
941 The strict Haskell 98 interpretation is that the section is equivalent to
945 That is, the operator must be a function of two arguments. GHC allows it to
946 take only one argument, and that in turn allows you to write the function
949 <para>Since this extension goes beyond Haskell 98, it should really be enabled
950 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
951 change their behaviour, of course.)
953 <para>The extension does not extend to the left-hand side of function
954 definitions; you must define such a function in prefix form.</para>
958 <sect2 id="disambiguate-fields">
959 <title>Record field disambiguation</title>
961 In record construction and record pattern matching
962 it is entirely unambiguous which field is referred to, even if there are two different
963 data types in scope with a common field name. For example:
966 data S = MkS { x :: Int, y :: Bool }
971 data T = MkT { x :: Int }
973 ok1 (MkS { x = n }) = n+1 -- Unambiguous
975 ok2 n = MkT { x = n+1 } -- Unambiguous
977 bad1 k = k { x = 3 } -- Ambiguous
978 bad2 k = x k -- Ambiguous
980 Even though there are two <literal>x</literal>'s in scope,
981 it is clear that the <literal>x</literal> in the pattern in the
982 definition of <literal>ok1</literal> can only mean the field
983 <literal>x</literal> from type <literal>S</literal>. Similarly for
984 the function <literal>ok2</literal>. However, in the record update
985 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
986 it is not clear which of the two types is intended.
989 Haskell 98 regards all four as ambiguous, but with the
990 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
991 the former two. The rules are precisely the same as those for instance
992 declarations in Haskell 98, where the method names on the left-hand side
993 of the method bindings in an instance declaration refer unambiguously
994 to the method of that class (provided they are in scope at all), even
995 if there are other variables in scope with the same name.
996 This reduces the clutter of qualified names when you import two
997 records from different modules that use the same field name.
1003 <!-- TYPE SYSTEM EXTENSIONS -->
1004 <sect1 id="data-type-extensions">
1005 <title>Extensions to data types and type synonyms</title>
1007 <sect2 id="nullary-types">
1008 <title>Data types with no constructors</title>
1010 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1011 a data type with no constructors. For example:</para>
1015 data T a -- T :: * -> *
1018 <para>Syntactically, the declaration lacks the "= constrs" part. The
1019 type can be parameterised over types of any kind, but if the kind is
1020 not <literal>*</literal> then an explicit kind annotation must be used
1021 (see <xref linkend="kinding"/>).</para>
1023 <para>Such data types have only one value, namely bottom.
1024 Nevertheless, they can be useful when defining "phantom types".</para>
1027 <sect2 id="infix-tycons">
1028 <title>Infix type constructors, classes, and type variables</title>
1031 GHC allows type constructors, classes, and type variables to be operators, and
1032 to be written infix, very much like expressions. More specifically:
1035 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1036 The lexical syntax is the same as that for data constructors.
1039 Data type and type-synonym declarations can be written infix, parenthesised
1040 if you want further arguments. E.g.
1042 data a :*: b = Foo a b
1043 type a :+: b = Either a b
1044 class a :=: b where ...
1046 data (a :**: b) x = Baz a b x
1047 type (a :++: b) y = Either (a,b) y
1051 Types, and class constraints, can be written infix. For example
1054 f :: (a :=: b) => a -> b
1058 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1059 The lexical syntax is the same as that for variable operators, excluding "(.)",
1060 "(!)", and "(*)". In a binding position, the operator must be
1061 parenthesised. For example:
1063 type T (+) = Int + Int
1067 liftA2 :: Arrow (~>)
1068 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1074 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1075 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1078 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1079 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1080 sets the fixity for a data constructor and the corresponding type constructor. For example:
1084 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1085 and similarly for <literal>:*:</literal>.
1086 <literal>Int `a` Bool</literal>.
1089 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1096 <sect2 id="type-synonyms">
1097 <title>Liberalised type synonyms</title>
1100 Type synonyms are like macros at the type level, and
1101 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1102 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1104 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1105 in a type synonym, thus:
1107 type Discard a = forall b. Show b => a -> b -> (a, String)
1112 g :: Discard Int -> (Int,String) -- A rank-2 type
1119 You can write an unboxed tuple in a type synonym:
1121 type Pr = (# Int, Int #)
1129 You can apply a type synonym to a forall type:
1131 type Foo a = a -> a -> Bool
1133 f :: Foo (forall b. b->b)
1135 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1137 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1142 You can apply a type synonym to a partially applied type synonym:
1144 type Generic i o = forall x. i x -> o x
1147 foo :: Generic Id []
1149 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1151 foo :: forall x. x -> [x]
1159 GHC currently does kind checking before expanding synonyms (though even that
1163 After expanding type synonyms, GHC does validity checking on types, looking for
1164 the following mal-formedness which isn't detected simply by kind checking:
1167 Type constructor applied to a type involving for-alls.
1170 Unboxed tuple on left of an arrow.
1173 Partially-applied type synonym.
1177 this will be rejected:
1179 type Pr = (# Int, Int #)
1184 because GHC does not allow unboxed tuples on the left of a function arrow.
1189 <sect2 id="existential-quantification">
1190 <title>Existentially quantified data constructors
1194 The idea of using existential quantification in data type declarations
1195 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1196 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1197 London, 1991). It was later formalised by Laufer and Odersky
1198 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1199 TOPLAS, 16(5), pp1411-1430, 1994).
1200 It's been in Lennart
1201 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1202 proved very useful. Here's the idea. Consider the declaration:
1208 data Foo = forall a. MkFoo a (a -> Bool)
1215 The data type <literal>Foo</literal> has two constructors with types:
1221 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1228 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1229 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1230 For example, the following expression is fine:
1236 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1242 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1243 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1244 isUpper</function> packages a character with a compatible function. These
1245 two things are each of type <literal>Foo</literal> and can be put in a list.
1249 What can we do with a value of type <literal>Foo</literal>?. In particular,
1250 what happens when we pattern-match on <function>MkFoo</function>?
1256 f (MkFoo val fn) = ???
1262 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1263 are compatible, the only (useful) thing we can do with them is to
1264 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1271 f (MkFoo val fn) = fn val
1277 What this allows us to do is to package heterogenous values
1278 together with a bunch of functions that manipulate them, and then treat
1279 that collection of packages in a uniform manner. You can express
1280 quite a bit of object-oriented-like programming this way.
1283 <sect3 id="existential">
1284 <title>Why existential?
1288 What has this to do with <emphasis>existential</emphasis> quantification?
1289 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1295 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1301 But Haskell programmers can safely think of the ordinary
1302 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1303 adding a new existential quantification construct.
1309 <title>Type classes</title>
1312 An easy extension is to allow
1313 arbitrary contexts before the constructor. For example:
1319 data Baz = forall a. Eq a => Baz1 a a
1320 | forall b. Show b => Baz2 b (b -> b)
1326 The two constructors have the types you'd expect:
1332 Baz1 :: forall a. Eq a => a -> a -> Baz
1333 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1339 But when pattern matching on <function>Baz1</function> the matched values can be compared
1340 for equality, and when pattern matching on <function>Baz2</function> the first matched
1341 value can be converted to a string (as well as applying the function to it).
1342 So this program is legal:
1349 f (Baz1 p q) | p == q = "Yes"
1351 f (Baz2 v fn) = show (fn v)
1357 Operationally, in a dictionary-passing implementation, the
1358 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1359 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1360 extract it on pattern matching.
1364 Notice the way that the syntax fits smoothly with that used for
1365 universal quantification earlier.
1370 <sect3 id="existential-records">
1371 <title>Record Constructors</title>
1374 GHC allows existentials to be used with records syntax as well. For example:
1377 data Counter a = forall self. NewCounter
1379 , _inc :: self -> self
1380 , _display :: self -> IO ()
1384 Here <literal>tag</literal> is a public field, with a well-typed selector
1385 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1386 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1387 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1388 compile-time error. In other words, <emphasis>GHC defines a record selector function
1389 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1390 (This example used an underscore in the fields for which record selectors
1391 will not be defined, but that is only programming style; GHC ignores them.)
1395 To make use of these hidden fields, we need to create some helper functions:
1398 inc :: Counter a -> Counter a
1399 inc (NewCounter x i d t) = NewCounter
1400 { _this = i x, _inc = i, _display = d, tag = t }
1402 display :: Counter a -> IO ()
1403 display NewCounter{ _this = x, _display = d } = d x
1406 Now we can define counters with different underlying implementations:
1409 counterA :: Counter String
1410 counterA = NewCounter
1411 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1413 counterB :: Counter String
1414 counterB = NewCounter
1415 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1418 display (inc counterA) -- prints "1"
1419 display (inc (inc counterB)) -- prints "##"
1422 At the moment, record update syntax is only supported for Haskell 98 data types,
1423 so the following function does <emphasis>not</emphasis> work:
1426 -- This is invalid; use explicit NewCounter instead for now
1427 setTag :: Counter a -> a -> Counter a
1428 setTag obj t = obj{ tag = t }
1437 <title>Restrictions</title>
1440 There are several restrictions on the ways in which existentially-quantified
1441 constructors can be use.
1450 When pattern matching, each pattern match introduces a new,
1451 distinct, type for each existential type variable. These types cannot
1452 be unified with any other type, nor can they escape from the scope of
1453 the pattern match. For example, these fragments are incorrect:
1461 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1462 is the result of <function>f1</function>. One way to see why this is wrong is to
1463 ask what type <function>f1</function> has:
1467 f1 :: Foo -> a -- Weird!
1471 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1476 f1 :: forall a. Foo -> a -- Wrong!
1480 The original program is just plain wrong. Here's another sort of error
1484 f2 (Baz1 a b) (Baz1 p q) = a==q
1488 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1489 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1490 from the two <function>Baz1</function> constructors.
1498 You can't pattern-match on an existentially quantified
1499 constructor in a <literal>let</literal> or <literal>where</literal> group of
1500 bindings. So this is illegal:
1504 f3 x = a==b where { Baz1 a b = x }
1507 Instead, use a <literal>case</literal> expression:
1510 f3 x = case x of Baz1 a b -> a==b
1513 In general, you can only pattern-match
1514 on an existentially-quantified constructor in a <literal>case</literal> expression or
1515 in the patterns of a function definition.
1517 The reason for this restriction is really an implementation one.
1518 Type-checking binding groups is already a nightmare without
1519 existentials complicating the picture. Also an existential pattern
1520 binding at the top level of a module doesn't make sense, because it's
1521 not clear how to prevent the existentially-quantified type "escaping".
1522 So for now, there's a simple-to-state restriction. We'll see how
1530 You can't use existential quantification for <literal>newtype</literal>
1531 declarations. So this is illegal:
1535 newtype T = forall a. Ord a => MkT a
1539 Reason: a value of type <literal>T</literal> must be represented as a
1540 pair of a dictionary for <literal>Ord t</literal> and a value of type
1541 <literal>t</literal>. That contradicts the idea that
1542 <literal>newtype</literal> should have no concrete representation.
1543 You can get just the same efficiency and effect by using
1544 <literal>data</literal> instead of <literal>newtype</literal>. If
1545 there is no overloading involved, then there is more of a case for
1546 allowing an existentially-quantified <literal>newtype</literal>,
1547 because the <literal>data</literal> version does carry an
1548 implementation cost, but single-field existentially quantified
1549 constructors aren't much use. So the simple restriction (no
1550 existential stuff on <literal>newtype</literal>) stands, unless there
1551 are convincing reasons to change it.
1559 You can't use <literal>deriving</literal> to define instances of a
1560 data type with existentially quantified data constructors.
1562 Reason: in most cases it would not make sense. For example:;
1565 data T = forall a. MkT [a] deriving( Eq )
1568 To derive <literal>Eq</literal> in the standard way we would need to have equality
1569 between the single component of two <function>MkT</function> constructors:
1573 (MkT a) == (MkT b) = ???
1576 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1577 It's just about possible to imagine examples in which the derived instance
1578 would make sense, but it seems altogether simpler simply to prohibit such
1579 declarations. Define your own instances!
1590 <!-- ====================== Generalised algebraic data types ======================= -->
1592 <sect2 id="gadt-style">
1593 <title>Declaring data types with explicit constructor signatures</title>
1595 <para>GHC allows you to declare an algebraic data type by
1596 giving the type signatures of constructors explicitly. For example:
1600 Just :: a -> Maybe a
1602 The form is called a "GADT-style declaration"
1603 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1604 can only be declared using this form.</para>
1605 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1606 For example, these two declarations are equivalent:
1608 data Foo = forall a. MkFoo a (a -> Bool)
1609 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1612 <para>Any data type that can be declared in standard Haskell-98 syntax
1613 can also be declared using GADT-style syntax.
1614 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1615 they treat class constraints on the data constructors differently.
1616 Specifically, if the constructor is given a type-class context, that
1617 context is made available by pattern matching. For example:
1620 MkSet :: Eq a => [a] -> Set a
1622 makeSet :: Eq a => [a] -> Set a
1623 makeSet xs = MkSet (nub xs)
1625 insert :: a -> Set a -> Set a
1626 insert a (MkSet as) | a `elem` as = MkSet as
1627 | otherwise = MkSet (a:as)
1629 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1630 gives rise to a <literal>(Eq a)</literal>
1631 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1632 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1633 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1634 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1635 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1636 In the example, the equality dictionary is used to satisfy the equality constraint
1637 generated by the call to <literal>elem</literal>, so that the type of
1638 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1640 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1641 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1642 In Haskell 98 the defintion
1644 data Eq a => Set' a = MkSet' [a]
1646 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1647 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1648 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1649 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1650 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1652 For example, a possible application of GHC's behaviour is to reify dictionaries:
1654 data NumInst a where
1655 MkNumInst :: Num a => NumInst a
1657 intInst :: NumInst Int
1660 plus :: NumInst a -> a -> a -> a
1661 plus MkNumInst p q = p + q
1663 Here, a value of type <literal>NumInst a</literal> is equivalent
1664 to an explicit <literal>(Num a)</literal> dictionary.
1668 The rest of this section gives further details about GADT-style data
1673 The result type of each data constructor must begin with the type constructor being defined.
1674 If the result type of all constructors
1675 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1676 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1677 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1681 The type signature of
1682 each constructor is independent, and is implicitly universally quantified as usual.
1683 Different constructors may have different universally-quantified type variables
1684 and different type-class constraints.
1685 For example, this is fine:
1688 T1 :: Eq b => b -> T b
1689 T2 :: (Show c, Ix c) => c -> [c] -> T c
1694 Unlike a Haskell-98-style
1695 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1696 have no scope. Indeed, one can write a kind signature instead:
1698 data Set :: * -> * where ...
1700 or even a mixture of the two:
1702 data Foo a :: (* -> *) -> * where ...
1704 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1707 data Foo a (b :: * -> *) where ...
1713 You can use strictness annotations, in the obvious places
1714 in the constructor type:
1717 Lit :: !Int -> Term Int
1718 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1719 Pair :: Term a -> Term b -> Term (a,b)
1724 You can use a <literal>deriving</literal> clause on a GADT-style data type
1725 declaration. For example, these two declarations are equivalent
1727 data Maybe1 a where {
1728 Nothing1 :: Maybe1 a ;
1729 Just1 :: a -> Maybe1 a
1730 } deriving( Eq, Ord )
1732 data Maybe2 a = Nothing2 | Just2 a
1738 You can use record syntax on a GADT-style data type declaration:
1742 Adult { name :: String, children :: [Person] } :: Person
1743 Child { name :: String } :: Person
1745 As usual, for every constructor that has a field <literal>f</literal>, the type of
1746 field <literal>f</literal> must be the same (modulo alpha conversion).
1749 At the moment, record updates are not yet possible with GADT-style declarations,
1750 so support is limited to record construction, selection and pattern matching.
1753 aPerson = Adult { name = "Fred", children = [] }
1755 shortName :: Person -> Bool
1756 hasChildren (Adult { children = kids }) = not (null kids)
1757 hasChildren (Child {}) = False
1762 As in the case of existentials declared using the Haskell-98-like record syntax
1763 (<xref linkend="existential-records"/>),
1764 record-selector functions are generated only for those fields that have well-typed
1766 Here is the example of that section, in GADT-style syntax:
1768 data Counter a where
1769 NewCounter { _this :: self
1770 , _inc :: self -> self
1771 , _display :: self -> IO ()
1776 As before, only one selector function is generated here, that for <literal>tag</literal>.
1777 Nevertheless, you can still use all the field names in pattern matching and record construction.
1779 </itemizedlist></para>
1783 <title>Generalised Algebraic Data Types (GADTs)</title>
1785 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1786 by allowing constructors to have richer return types. Here is an example:
1789 Lit :: Int -> Term Int
1790 Succ :: Term Int -> Term Int
1791 IsZero :: Term Int -> Term Bool
1792 If :: Term Bool -> Term a -> Term a -> Term a
1793 Pair :: Term a -> Term b -> Term (a,b)
1795 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1796 case with ordinary data types. This generality allows us to
1797 write a well-typed <literal>eval</literal> function
1798 for these <literal>Terms</literal>:
1802 eval (Succ t) = 1 + eval t
1803 eval (IsZero t) = eval t == 0
1804 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1805 eval (Pair e1 e2) = (eval e1, eval e2)
1807 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1808 For example, in the right hand side of the equation
1813 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1814 A precise specification of the type rules is beyond what this user manual aspires to,
1815 but the design closely follows that described in
1817 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1818 unification-based type inference for GADTs</ulink>,
1820 The general principle is this: <emphasis>type refinement is only carried out
1821 based on user-supplied type annotations</emphasis>.
1822 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1823 and lots of obscure error messages will
1824 occur. However, the refinement is quite general. For example, if we had:
1826 eval :: Term a -> a -> a
1827 eval (Lit i) j = i+j
1829 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1830 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1831 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1834 These and many other examples are given in papers by Hongwei Xi, and
1835 Tim Sheard. There is a longer introduction
1836 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1838 <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
1839 may use different notation to that implemented in GHC.
1842 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
1843 <option>-XGADTs</option>.
1846 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1847 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1848 The result type of each constructor must begin with the type constructor being defined,
1849 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1850 For example, in the <literal>Term</literal> data
1851 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1852 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1857 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1858 an ordianary data type.
1862 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1866 Lit { val :: Int } :: Term Int
1867 Succ { num :: Term Int } :: Term Int
1868 Pred { num :: Term Int } :: Term Int
1869 IsZero { arg :: Term Int } :: Term Bool
1870 Pair { arg1 :: Term a
1873 If { cnd :: Term Bool
1878 However, for GADTs there is the following additional constraint:
1879 every constructor that has a field <literal>f</literal> must have
1880 the same result type (modulo alpha conversion)
1881 Hence, in the above example, we cannot merge the <literal>num</literal>
1882 and <literal>arg</literal> fields above into a
1883 single name. Although their field types are both <literal>Term Int</literal>,
1884 their selector functions actually have different types:
1887 num :: Term Int -> Term Int
1888 arg :: Term Bool -> Term Int
1897 <!-- ====================== End of Generalised algebraic data types ======================= -->
1900 <sect2 id="deriving-typeable">
1901 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1904 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1905 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1906 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1907 classes <literal>Eq</literal>, <literal>Ord</literal>,
1908 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1911 GHC extends this list with two more classes that may be automatically derived
1912 (provided the <option>-fglasgow-exts</option> flag is specified):
1913 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1914 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1915 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1917 <para>An instance of <literal>Typeable</literal> can only be derived if the
1918 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1919 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1921 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1922 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1924 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1925 are used, and only <literal>Typeable1</literal> up to
1926 <literal>Typeable7</literal> are provided in the library.)
1927 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1928 class, whose kind suits that of the data type constructor, and
1929 then writing the data type instance by hand.
1933 <sect2 id="newtype-deriving">
1934 <title>Generalised derived instances for newtypes</title>
1937 When you define an abstract type using <literal>newtype</literal>, you may want
1938 the new type to inherit some instances from its representation. In
1939 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1940 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1941 other classes you have to write an explicit instance declaration. For
1942 example, if you define
1945 newtype Dollars = Dollars Int
1948 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1949 explicitly define an instance of <literal>Num</literal>:
1952 instance Num Dollars where
1953 Dollars a + Dollars b = Dollars (a+b)
1956 All the instance does is apply and remove the <literal>newtype</literal>
1957 constructor. It is particularly galling that, since the constructor
1958 doesn't appear at run-time, this instance declaration defines a
1959 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1960 dictionary, only slower!
1964 <sect3> <title> Generalising the deriving clause </title>
1966 GHC now permits such instances to be derived instead, so one can write
1968 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1971 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1972 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1973 derives an instance declaration of the form
1976 instance Num Int => Num Dollars
1979 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1983 We can also derive instances of constructor classes in a similar
1984 way. For example, suppose we have implemented state and failure monad
1985 transformers, such that
1988 instance Monad m => Monad (State s m)
1989 instance Monad m => Monad (Failure m)
1991 In Haskell 98, we can define a parsing monad by
1993 type Parser tok m a = State [tok] (Failure m) a
1996 which is automatically a monad thanks to the instance declarations
1997 above. With the extension, we can make the parser type abstract,
1998 without needing to write an instance of class <literal>Monad</literal>, via
2001 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2004 In this case the derived instance declaration is of the form
2006 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2009 Notice that, since <literal>Monad</literal> is a constructor class, the
2010 instance is a <emphasis>partial application</emphasis> of the new type, not the
2011 entire left hand side. We can imagine that the type declaration is
2012 ``eta-converted'' to generate the context of the instance
2017 We can even derive instances of multi-parameter classes, provided the
2018 newtype is the last class parameter. In this case, a ``partial
2019 application'' of the class appears in the <literal>deriving</literal>
2020 clause. For example, given the class
2023 class StateMonad s m | m -> s where ...
2024 instance Monad m => StateMonad s (State s m) where ...
2026 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2028 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2029 deriving (Monad, StateMonad [tok])
2032 The derived instance is obtained by completing the application of the
2033 class to the new type:
2036 instance StateMonad [tok] (State [tok] (Failure m)) =>
2037 StateMonad [tok] (Parser tok m)
2042 As a result of this extension, all derived instances in newtype
2043 declarations are treated uniformly (and implemented just by reusing
2044 the dictionary for the representation type), <emphasis>except</emphasis>
2045 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2046 the newtype and its representation.
2050 <sect3> <title> A more precise specification </title>
2052 Derived instance declarations are constructed as follows. Consider the
2053 declaration (after expansion of any type synonyms)
2056 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2062 The <literal>ci</literal> are partial applications of
2063 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2064 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2067 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2070 The type <literal>t</literal> is an arbitrary type.
2073 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2074 nor in the <literal>ci</literal>, and
2077 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2078 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2079 should not "look through" the type or its constructor. You can still
2080 derive these classes for a newtype, but it happens in the usual way, not
2081 via this new mechanism.
2084 Then, for each <literal>ci</literal>, the derived instance
2087 instance ci t => ci (T v1...vk)
2089 As an example which does <emphasis>not</emphasis> work, consider
2091 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2093 Here we cannot derive the instance
2095 instance Monad (State s m) => Monad (NonMonad m)
2098 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2099 and so cannot be "eta-converted" away. It is a good thing that this
2100 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2101 not, in fact, a monad --- for the same reason. Try defining
2102 <literal>>>=</literal> with the correct type: you won't be able to.
2106 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2107 important, since we can only derive instances for the last one. If the
2108 <literal>StateMonad</literal> class above were instead defined as
2111 class StateMonad m s | m -> s where ...
2114 then we would not have been able to derive an instance for the
2115 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2116 classes usually have one "main" parameter for which deriving new
2117 instances is most interesting.
2119 <para>Lastly, all of this applies only for classes other than
2120 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2121 and <literal>Data</literal>, for which the built-in derivation applies (section
2122 4.3.3. of the Haskell Report).
2123 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2124 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2125 the standard method is used or the one described here.)
2131 <sect2 id="stand-alone-deriving">
2132 <title>Stand-alone deriving declarations</title>
2135 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2137 data Foo a = Bar a | Baz String
2139 derive instance Eq (Foo a)
2141 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2142 you can use it as a variable name elsewhere.</para>
2143 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2144 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2147 newtype Foo a = MkFoo (State Int a)
2149 derive instance MonadState Int Foo
2151 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2152 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2160 <!-- TYPE SYSTEM EXTENSIONS -->
2161 <sect1 id="other-type-extensions">
2162 <title>Other type system extensions</title>
2164 <sect2 id="multi-param-type-classes">
2165 <title>Class declarations</title>
2168 This section, and the next one, documents GHC's type-class extensions.
2169 There's lots of background in the paper <ulink
2170 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2171 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2172 Jones, Erik Meijer).
2175 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2179 <title>Multi-parameter type classes</title>
2181 Multi-parameter type classes are permitted. For example:
2185 class Collection c a where
2186 union :: c a -> c a -> c a
2194 <title>The superclasses of a class declaration</title>
2197 There are no restrictions on the context in a class declaration
2198 (which introduces superclasses), except that the class hierarchy must
2199 be acyclic. So these class declarations are OK:
2203 class Functor (m k) => FiniteMap m k where
2206 class (Monad m, Monad (t m)) => Transform t m where
2207 lift :: m a -> (t m) a
2213 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2214 of "acyclic" involves only the superclass relationships. For example,
2220 op :: D b => a -> b -> b
2223 class C a => D a where { ... }
2227 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2228 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2229 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2236 <sect3 id="class-method-types">
2237 <title>Class method types</title>
2240 Haskell 98 prohibits class method types to mention constraints on the
2241 class type variable, thus:
2244 fromList :: [a] -> s a
2245 elem :: Eq a => a -> s a -> Bool
2247 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2248 contains the constraint <literal>Eq a</literal>, constrains only the
2249 class type variable (in this case <literal>a</literal>).
2250 GHC lifts this restriction.
2257 <sect2 id="functional-dependencies">
2258 <title>Functional dependencies
2261 <para> Functional dependencies are implemented as described by Mark Jones
2262 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2263 In Proceedings of the 9th European Symposium on Programming,
2264 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2268 Functional dependencies are introduced by a vertical bar in the syntax of a
2269 class declaration; e.g.
2271 class (Monad m) => MonadState s m | m -> s where ...
2273 class Foo a b c | a b -> c where ...
2275 There should be more documentation, but there isn't (yet). Yell if you need it.
2278 <sect3><title>Rules for functional dependencies </title>
2280 In a class declaration, all of the class type variables must be reachable (in the sense
2281 mentioned in <xref linkend="type-restrictions"/>)
2282 from the free variables of each method type.
2286 class Coll s a where
2288 insert :: s -> a -> s
2291 is not OK, because the type of <literal>empty</literal> doesn't mention
2292 <literal>a</literal>. Functional dependencies can make the type variable
2295 class Coll s a | s -> a where
2297 insert :: s -> a -> s
2300 Alternatively <literal>Coll</literal> might be rewritten
2303 class Coll s a where
2305 insert :: s a -> a -> s a
2309 which makes the connection between the type of a collection of
2310 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2311 Occasionally this really doesn't work, in which case you can split the
2319 class CollE s => Coll s a where
2320 insert :: s -> a -> s
2327 <title>Background on functional dependencies</title>
2329 <para>The following description of the motivation and use of functional dependencies is taken
2330 from the Hugs user manual, reproduced here (with minor changes) by kind
2331 permission of Mark Jones.
2334 Consider the following class, intended as part of a
2335 library for collection types:
2337 class Collects e ce where
2339 insert :: e -> ce -> ce
2340 member :: e -> ce -> Bool
2342 The type variable e used here represents the element type, while ce is the type
2343 of the container itself. Within this framework, we might want to define
2344 instances of this class for lists or characteristic functions (both of which
2345 can be used to represent collections of any equality type), bit sets (which can
2346 be used to represent collections of characters), or hash tables (which can be
2347 used to represent any collection whose elements have a hash function). Omitting
2348 standard implementation details, this would lead to the following declarations:
2350 instance Eq e => Collects e [e] where ...
2351 instance Eq e => Collects e (e -> Bool) where ...
2352 instance Collects Char BitSet where ...
2353 instance (Hashable e, Collects a ce)
2354 => Collects e (Array Int ce) where ...
2356 All this looks quite promising; we have a class and a range of interesting
2357 implementations. Unfortunately, there are some serious problems with the class
2358 declaration. First, the empty function has an ambiguous type:
2360 empty :: Collects e ce => ce
2362 By "ambiguous" we mean that there is a type variable e that appears on the left
2363 of the <literal>=></literal> symbol, but not on the right. The problem with
2364 this is that, according to the theoretical foundations of Haskell overloading,
2365 we cannot guarantee a well-defined semantics for any term with an ambiguous
2369 We can sidestep this specific problem by removing the empty member from the
2370 class declaration. However, although the remaining members, insert and member,
2371 do not have ambiguous types, we still run into problems when we try to use
2372 them. For example, consider the following two functions:
2374 f x y = insert x . insert y
2377 for which GHC infers the following types:
2379 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2380 g :: (Collects Bool c, Collects Char c) => c -> c
2382 Notice that the type for f allows the two parameters x and y to be assigned
2383 different types, even though it attempts to insert each of the two values, one
2384 after the other, into the same collection. If we're trying to model collections
2385 that contain only one type of value, then this is clearly an inaccurate
2386 type. Worse still, the definition for g is accepted, without causing a type
2387 error. As a result, the error in this code will not be flagged at the point
2388 where it appears. Instead, it will show up only when we try to use g, which
2389 might even be in a different module.
2392 <sect4><title>An attempt to use constructor classes</title>
2395 Faced with the problems described above, some Haskell programmers might be
2396 tempted to use something like the following version of the class declaration:
2398 class Collects e c where
2400 insert :: e -> c e -> c e
2401 member :: e -> c e -> Bool
2403 The key difference here is that we abstract over the type constructor c that is
2404 used to form the collection type c e, and not over that collection type itself,
2405 represented by ce in the original class declaration. This avoids the immediate
2406 problems that we mentioned above: empty has type <literal>Collects e c => c
2407 e</literal>, which is not ambiguous.
2410 The function f from the previous section has a more accurate type:
2412 f :: (Collects e c) => e -> e -> c e -> c e
2414 The function g from the previous section is now rejected with a type error as
2415 we would hope because the type of f does not allow the two arguments to have
2417 This, then, is an example of a multiple parameter class that does actually work
2418 quite well in practice, without ambiguity problems.
2419 There is, however, a catch. This version of the Collects class is nowhere near
2420 as general as the original class seemed to be: only one of the four instances
2421 for <literal>Collects</literal>
2422 given above can be used with this version of Collects because only one of
2423 them---the instance for lists---has a collection type that can be written in
2424 the form c e, for some type constructor c, and element type e.
2428 <sect4><title>Adding functional dependencies</title>
2431 To get a more useful version of the Collects class, Hugs provides a mechanism
2432 that allows programmers to specify dependencies between the parameters of a
2433 multiple parameter class (For readers with an interest in theoretical
2434 foundations and previous work: The use of dependency information can be seen
2435 both as a generalization of the proposal for `parametric type classes' that was
2436 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2437 later framework for "improvement" of qualified types. The
2438 underlying ideas are also discussed in a more theoretical and abstract setting
2439 in a manuscript [implparam], where they are identified as one point in a
2440 general design space for systems of implicit parameterization.).
2442 To start with an abstract example, consider a declaration such as:
2444 class C a b where ...
2446 which tells us simply that C can be thought of as a binary relation on types
2447 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2448 included in the definition of classes to add information about dependencies
2449 between parameters, as in the following examples:
2451 class D a b | a -> b where ...
2452 class E a b | a -> b, b -> a where ...
2454 The notation <literal>a -> b</literal> used here between the | and where
2455 symbols --- not to be
2456 confused with a function type --- indicates that the a parameter uniquely
2457 determines the b parameter, and might be read as "a determines b." Thus D is
2458 not just a relation, but actually a (partial) function. Similarly, from the two
2459 dependencies that are included in the definition of E, we can see that E
2460 represents a (partial) one-one mapping between types.
2463 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2464 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2465 m>=0, meaning that the y parameters are uniquely determined by the x
2466 parameters. Spaces can be used as separators if more than one variable appears
2467 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2468 annotated with multiple dependencies using commas as separators, as in the
2469 definition of E above. Some dependencies that we can write in this notation are
2470 redundant, and will be rejected because they don't serve any useful
2471 purpose, and may instead indicate an error in the program. Examples of
2472 dependencies like this include <literal>a -> a </literal>,
2473 <literal>a -> a a </literal>,
2474 <literal>a -> </literal>, etc. There can also be
2475 some redundancy if multiple dependencies are given, as in
2476 <literal>a->b</literal>,
2477 <literal>b->c </literal>, <literal>a->c </literal>, and
2478 in which some subset implies the remaining dependencies. Examples like this are
2479 not treated as errors. Note that dependencies appear only in class
2480 declarations, and not in any other part of the language. In particular, the
2481 syntax for instance declarations, class constraints, and types is completely
2485 By including dependencies in a class declaration, we provide a mechanism for
2486 the programmer to specify each multiple parameter class more precisely. The
2487 compiler, on the other hand, is responsible for ensuring that the set of
2488 instances that are in scope at any given point in the program is consistent
2489 with any declared dependencies. For example, the following pair of instance
2490 declarations cannot appear together in the same scope because they violate the
2491 dependency for D, even though either one on its own would be acceptable:
2493 instance D Bool Int where ...
2494 instance D Bool Char where ...
2496 Note also that the following declaration is not allowed, even by itself:
2498 instance D [a] b where ...
2500 The problem here is that this instance would allow one particular choice of [a]
2501 to be associated with more than one choice for b, which contradicts the
2502 dependency specified in the definition of D. More generally, this means that,
2503 in any instance of the form:
2505 instance D t s where ...
2507 for some particular types t and s, the only variables that can appear in s are
2508 the ones that appear in t, and hence, if the type t is known, then s will be
2509 uniquely determined.
2512 The benefit of including dependency information is that it allows us to define
2513 more general multiple parameter classes, without ambiguity problems, and with
2514 the benefit of more accurate types. To illustrate this, we return to the
2515 collection class example, and annotate the original definition of <literal>Collects</literal>
2516 with a simple dependency:
2518 class Collects e ce | ce -> e where
2520 insert :: e -> ce -> ce
2521 member :: e -> ce -> Bool
2523 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2524 determined by the type of the collection ce. Note that both parameters of
2525 Collects are of kind *; there are no constructor classes here. Note too that
2526 all of the instances of Collects that we gave earlier can be used
2527 together with this new definition.
2530 What about the ambiguity problems that we encountered with the original
2531 definition? The empty function still has type Collects e ce => ce, but it is no
2532 longer necessary to regard that as an ambiguous type: Although the variable e
2533 does not appear on the right of the => symbol, the dependency for class
2534 Collects tells us that it is uniquely determined by ce, which does appear on
2535 the right of the => symbol. Hence the context in which empty is used can still
2536 give enough information to determine types for both ce and e, without
2537 ambiguity. More generally, we need only regard a type as ambiguous if it
2538 contains a variable on the left of the => that is not uniquely determined
2539 (either directly or indirectly) by the variables on the right.
2542 Dependencies also help to produce more accurate types for user defined
2543 functions, and hence to provide earlier detection of errors, and less cluttered
2544 types for programmers to work with. Recall the previous definition for a
2547 f x y = insert x y = insert x . insert y
2549 for which we originally obtained a type:
2551 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2553 Given the dependency information that we have for Collects, however, we can
2554 deduce that a and b must be equal because they both appear as the second
2555 parameter in a Collects constraint with the same first parameter c. Hence we
2556 can infer a shorter and more accurate type for f:
2558 f :: (Collects a c) => a -> a -> c -> c
2560 In a similar way, the earlier definition of g will now be flagged as a type error.
2563 Although we have given only a few examples here, it should be clear that the
2564 addition of dependency information can help to make multiple parameter classes
2565 more useful in practice, avoiding ambiguity problems, and allowing more general
2566 sets of instance declarations.
2572 <sect2 id="instance-decls">
2573 <title>Instance declarations</title>
2575 <sect3 id="instance-rules">
2576 <title>Relaxed rules for instance declarations</title>
2578 <para>An instance declaration has the form
2580 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 ...
2582 The part before the "<literal>=></literal>" is the
2583 <emphasis>context</emphasis>, while the part after the
2584 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2588 In Haskell 98 the head of an instance declaration
2589 must be of the form <literal>C (T a1 ... an)</literal>, where
2590 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2591 and the <literal>a1 ... an</literal> are distinct type variables.
2592 Furthermore, the assertions in the context of the instance declaration
2593 must be of the form <literal>C a</literal> where <literal>a</literal>
2594 is a type variable that occurs in the head.
2597 The <option>-fglasgow-exts</option> flag loosens these restrictions
2598 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2599 the context and head of the instance declaration can each consist of arbitrary
2600 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2604 The Paterson Conditions: for each assertion in the context
2606 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2607 <listitem><para>The assertion has fewer constructors and variables (taken together
2608 and counting repetitions) than the head</para></listitem>
2612 <listitem><para>The Coverage Condition. For each functional dependency,
2613 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2614 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2615 every type variable in
2616 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2617 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2618 substitution mapping each type variable in the class declaration to the
2619 corresponding type in the instance declaration.
2622 These restrictions ensure that context reduction terminates: each reduction
2623 step makes the problem smaller by at least one
2624 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2625 if you give the <option>-fallow-undecidable-instances</option>
2626 flag (<xref linkend="undecidable-instances"/>).
2627 You can find lots of background material about the reason for these
2628 restrictions in the paper <ulink
2629 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2630 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2633 For example, these are OK:
2635 instance C Int [a] -- Multiple parameters
2636 instance Eq (S [a]) -- Structured type in head
2638 -- Repeated type variable in head
2639 instance C4 a a => C4 [a] [a]
2640 instance Stateful (ST s) (MutVar s)
2642 -- Head can consist of type variables only
2644 instance (Eq a, Show b) => C2 a b
2646 -- Non-type variables in context
2647 instance Show (s a) => Show (Sized s a)
2648 instance C2 Int a => C3 Bool [a]
2649 instance C2 Int a => C3 [a] b
2653 -- Context assertion no smaller than head
2654 instance C a => C a where ...
2655 -- (C b b) has more more occurrences of b than the head
2656 instance C b b => Foo [b] where ...
2661 The same restrictions apply to instances generated by
2662 <literal>deriving</literal> clauses. Thus the following is accepted:
2664 data MinHeap h a = H a (h a)
2667 because the derived instance
2669 instance (Show a, Show (h a)) => Show (MinHeap h a)
2671 conforms to the above rules.
2675 A useful idiom permitted by the above rules is as follows.
2676 If one allows overlapping instance declarations then it's quite
2677 convenient to have a "default instance" declaration that applies if
2678 something more specific does not:
2686 <sect3 id="undecidable-instances">
2687 <title>Undecidable instances</title>
2690 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2691 For example, sometimes you might want to use the following to get the
2692 effect of a "class synonym":
2694 class (C1 a, C2 a, C3 a) => C a where { }
2696 instance (C1 a, C2 a, C3 a) => C a where { }
2698 This allows you to write shorter signatures:
2704 f :: (C1 a, C2 a, C3 a) => ...
2706 The restrictions on functional dependencies (<xref
2707 linkend="functional-dependencies"/>) are particularly troublesome.
2708 It is tempting to introduce type variables in the context that do not appear in
2709 the head, something that is excluded by the normal rules. For example:
2711 class HasConverter a b | a -> b where
2714 data Foo a = MkFoo a
2716 instance (HasConverter a b,Show b) => Show (Foo a) where
2717 show (MkFoo value) = show (convert value)
2719 This is dangerous territory, however. Here, for example, is a program that would make the
2724 instance F [a] [[a]]
2725 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2727 Similarly, it can be tempting to lift the coverage condition:
2729 class Mul a b c | a b -> c where
2730 (.*.) :: a -> b -> c
2732 instance Mul Int Int Int where (.*.) = (*)
2733 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2734 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2736 The third instance declaration does not obey the coverage condition;
2737 and indeed the (somewhat strange) definition:
2739 f = \ b x y -> if b then x .*. [y] else y
2741 makes instance inference go into a loop, because it requires the constraint
2742 <literal>(Mul a [b] b)</literal>.
2745 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2746 the experimental flag <option>-XUndecidableInstances</option>
2747 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
2748 both the Paterson Conditions and the Coverage Condition
2749 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2750 fixed-depth recursion stack. If you exceed the stack depth you get a
2751 sort of backtrace, and the opportunity to increase the stack depth
2752 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2758 <sect3 id="instance-overlap">
2759 <title>Overlapping instances</title>
2761 In general, <emphasis>GHC requires that that it be unambiguous which instance
2763 should be used to resolve a type-class constraint</emphasis>. This behaviour
2764 can be modified by two flags: <option>-XOverlappingInstances</option>
2765 <indexterm><primary>-XOverlappingInstances
2766 </primary></indexterm>
2767 and <option>-XIncoherentInstances</option>
2768 <indexterm><primary>-XIncoherentInstances
2769 </primary></indexterm>, as this section discusses. Both these
2770 flags are dynamic flags, and can be set on a per-module basis, using
2771 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2773 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2774 it tries to match every instance declaration against the
2776 by instantiating the head of the instance declaration. For example, consider
2779 instance context1 => C Int a where ... -- (A)
2780 instance context2 => C a Bool where ... -- (B)
2781 instance context3 => C Int [a] where ... -- (C)
2782 instance context4 => C Int [Int] where ... -- (D)
2784 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2785 but (C) and (D) do not. When matching, GHC takes
2786 no account of the context of the instance declaration
2787 (<literal>context1</literal> etc).
2788 GHC's default behaviour is that <emphasis>exactly one instance must match the
2789 constraint it is trying to resolve</emphasis>.
2790 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2791 including both declarations (A) and (B), say); an error is only reported if a
2792 particular constraint matches more than one.
2796 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
2797 more than one instance to match, provided there is a most specific one. For
2798 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2799 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2800 most-specific match, the program is rejected.
2803 However, GHC is conservative about committing to an overlapping instance. For example:
2808 Suppose that from the RHS of <literal>f</literal> we get the constraint
2809 <literal>C Int [b]</literal>. But
2810 GHC does not commit to instance (C), because in a particular
2811 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2812 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2813 So GHC rejects the program.
2814 (If you add the flag <option>-XIncoherentInstances</option>,
2815 GHC will instead pick (C), without complaining about
2816 the problem of subsequent instantiations.)
2818 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
2819 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
2820 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
2821 it instead. In this case, GHC will refrain from
2822 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
2823 as before) but, rather than rejecting the program, it will infer the type
2825 f :: C Int b => [b] -> [b]
2827 That postpones the question of which instance to pick to the
2828 call site for <literal>f</literal>
2829 by which time more is known about the type <literal>b</literal>.
2832 The willingness to be overlapped or incoherent is a property of
2833 the <emphasis>instance declaration</emphasis> itself, controlled by the
2834 presence or otherwise of the <option>-XOverlappingInstances</option>
2835 and <option>-XIncoherentInstances</option> flags when that mdodule is
2836 being defined. Neither flag is required in a module that imports and uses the
2837 instance declaration. Specifically, during the lookup process:
2840 An instance declaration is ignored during the lookup process if (a) a more specific
2841 match is found, and (b) the instance declaration was compiled with
2842 <option>-XOverlappingInstances</option>. The flag setting for the
2843 more-specific instance does not matter.
2846 Suppose an instance declaration does not match the constraint being looked up, but
2847 does unify with it, so that it might match when the constraint is further
2848 instantiated. Usually GHC will regard this as a reason for not committing to
2849 some other constraint. But if the instance declaration was compiled with
2850 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
2851 check for that declaration.
2854 These rules make it possible for a library author to design a library that relies on
2855 overlapping instances without the library client having to know.
2858 If an instance declaration is compiled without
2859 <option>-XOverlappingInstances</option>,
2860 then that instance can never be overlapped. This could perhaps be
2861 inconvenient. Perhaps the rule should instead say that the
2862 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2863 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2864 at a usage site should be permitted regardless of how the instance declarations
2865 are compiled, if the <option>-XOverlappingInstances</option> flag is
2866 used at the usage site. (Mind you, the exact usage site can occasionally be
2867 hard to pin down.) We are interested to receive feedback on these points.
2869 <para>The <option>-XIncoherentInstances</option> flag implies the
2870 <option>-XOverlappingInstances</option> flag, but not vice versa.
2875 <title>Type synonyms in the instance head</title>
2878 <emphasis>Unlike Haskell 98, instance heads may use type
2879 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2880 As always, using a type synonym is just shorthand for
2881 writing the RHS of the type synonym definition. For example:
2885 type Point = (Int,Int)
2886 instance C Point where ...
2887 instance C [Point] where ...
2891 is legal. However, if you added
2895 instance C (Int,Int) where ...
2899 as well, then the compiler will complain about the overlapping
2900 (actually, identical) instance declarations. As always, type synonyms
2901 must be fully applied. You cannot, for example, write:
2906 instance Monad P where ...
2910 This design decision is independent of all the others, and easily
2911 reversed, but it makes sense to me.
2919 <sect2 id="type-restrictions">
2920 <title>Type signatures</title>
2922 <sect3><title>The context of a type signature</title>
2924 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2925 the form <emphasis>(class type-variable)</emphasis> or
2926 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2927 these type signatures are perfectly OK
2930 g :: Ord (T a ()) => ...
2934 GHC imposes the following restrictions on the constraints in a type signature.
2938 forall tv1..tvn (c1, ...,cn) => type
2941 (Here, we write the "foralls" explicitly, although the Haskell source
2942 language omits them; in Haskell 98, all the free type variables of an
2943 explicit source-language type signature are universally quantified,
2944 except for the class type variables in a class declaration. However,
2945 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2954 <emphasis>Each universally quantified type variable
2955 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2957 A type variable <literal>a</literal> is "reachable" if it it appears
2958 in the same constraint as either a type variable free in in
2959 <literal>type</literal>, or another reachable type variable.
2960 A value with a type that does not obey
2961 this reachability restriction cannot be used without introducing
2962 ambiguity; that is why the type is rejected.
2963 Here, for example, is an illegal type:
2967 forall a. Eq a => Int
2971 When a value with this type was used, the constraint <literal>Eq tv</literal>
2972 would be introduced where <literal>tv</literal> is a fresh type variable, and
2973 (in the dictionary-translation implementation) the value would be
2974 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2975 can never know which instance of <literal>Eq</literal> to use because we never
2976 get any more information about <literal>tv</literal>.
2980 that the reachability condition is weaker than saying that <literal>a</literal> is
2981 functionally dependent on a type variable free in
2982 <literal>type</literal> (see <xref
2983 linkend="functional-dependencies"/>). The reason for this is there
2984 might be a "hidden" dependency, in a superclass perhaps. So
2985 "reachable" is a conservative approximation to "functionally dependent".
2986 For example, consider:
2988 class C a b | a -> b where ...
2989 class C a b => D a b where ...
2990 f :: forall a b. D a b => a -> a
2992 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2993 but that is not immediately apparent from <literal>f</literal>'s type.
2999 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3000 universally quantified type variables <literal>tvi</literal></emphasis>.
3002 For example, this type is OK because <literal>C a b</literal> mentions the
3003 universally quantified type variable <literal>b</literal>:
3007 forall a. C a b => burble
3011 The next type is illegal because the constraint <literal>Eq b</literal> does not
3012 mention <literal>a</literal>:
3016 forall a. Eq b => burble
3020 The reason for this restriction is milder than the other one. The
3021 excluded types are never useful or necessary (because the offending
3022 context doesn't need to be witnessed at this point; it can be floated
3023 out). Furthermore, floating them out increases sharing. Lastly,
3024 excluding them is a conservative choice; it leaves a patch of
3025 territory free in case we need it later.
3039 <sect2 id="implicit-parameters">
3040 <title>Implicit parameters</title>
3042 <para> Implicit parameters are implemented as described in
3043 "Implicit parameters: dynamic scoping with static types",
3044 J Lewis, MB Shields, E Meijer, J Launchbury,
3045 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3049 <para>(Most of the following, stil rather incomplete, documentation is
3050 due to Jeff Lewis.)</para>
3052 <para>Implicit parameter support is enabled with the option
3053 <option>-XImplicitParams</option>.</para>
3056 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3057 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3058 context. In Haskell, all variables are statically bound. Dynamic
3059 binding of variables is a notion that goes back to Lisp, but was later
3060 discarded in more modern incarnations, such as Scheme. Dynamic binding
3061 can be very confusing in an untyped language, and unfortunately, typed
3062 languages, in particular Hindley-Milner typed languages like Haskell,
3063 only support static scoping of variables.
3066 However, by a simple extension to the type class system of Haskell, we
3067 can support dynamic binding. Basically, we express the use of a
3068 dynamically bound variable as a constraint on the type. These
3069 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3070 function uses a dynamically-bound variable <literal>?x</literal>
3071 of type <literal>t'</literal>". For
3072 example, the following expresses the type of a sort function,
3073 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3075 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3077 The dynamic binding constraints are just a new form of predicate in the type class system.
3080 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3081 where <literal>x</literal> is
3082 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3083 Use of this construct also introduces a new
3084 dynamic-binding constraint in the type of the expression.
3085 For example, the following definition
3086 shows how we can define an implicitly parameterized sort function in
3087 terms of an explicitly parameterized <literal>sortBy</literal> function:
3089 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3091 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3097 <title>Implicit-parameter type constraints</title>
3099 Dynamic binding constraints behave just like other type class
3100 constraints in that they are automatically propagated. Thus, when a
3101 function is used, its implicit parameters are inherited by the
3102 function that called it. For example, our <literal>sort</literal> function might be used
3103 to pick out the least value in a list:
3105 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3106 least xs = head (sort xs)
3108 Without lifting a finger, the <literal>?cmp</literal> parameter is
3109 propagated to become a parameter of <literal>least</literal> as well. With explicit
3110 parameters, the default is that parameters must always be explicit
3111 propagated. With implicit parameters, the default is to always
3115 An implicit-parameter type constraint differs from other type class constraints in the
3116 following way: All uses of a particular implicit parameter must have
3117 the same type. This means that the type of <literal>(?x, ?x)</literal>
3118 is <literal>(?x::a) => (a,a)</literal>, and not
3119 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3123 <para> You can't have an implicit parameter in the context of a class or instance
3124 declaration. For example, both these declarations are illegal:
3126 class (?x::Int) => C a where ...
3127 instance (?x::a) => Foo [a] where ...
3129 Reason: exactly which implicit parameter you pick up depends on exactly where
3130 you invoke a function. But the ``invocation'' of instance declarations is done
3131 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3132 Easiest thing is to outlaw the offending types.</para>
3134 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3136 f :: (?x :: [a]) => Int -> Int
3139 g :: (Read a, Show a) => String -> String
3142 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3143 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3144 quite unambiguous, and fixes the type <literal>a</literal>.
3149 <title>Implicit-parameter bindings</title>
3152 An implicit parameter is <emphasis>bound</emphasis> using the standard
3153 <literal>let</literal> or <literal>where</literal> binding forms.
3154 For example, we define the <literal>min</literal> function by binding
3155 <literal>cmp</literal>.
3158 min = let ?cmp = (<=) in least
3162 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3163 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3164 (including in a list comprehension, or do-notation, or pattern guards),
3165 or a <literal>where</literal> clause.
3166 Note the following points:
3169 An implicit-parameter binding group must be a
3170 collection of simple bindings to implicit-style variables (no
3171 function-style bindings, and no type signatures); these bindings are
3172 neither polymorphic or recursive.
3175 You may not mix implicit-parameter bindings with ordinary bindings in a
3176 single <literal>let</literal>
3177 expression; use two nested <literal>let</literal>s instead.
3178 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3182 You may put multiple implicit-parameter bindings in a
3183 single binding group; but they are <emphasis>not</emphasis> treated
3184 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3185 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3186 parameter. The bindings are not nested, and may be re-ordered without changing
3187 the meaning of the program.
3188 For example, consider:
3190 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3192 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3193 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3195 f :: (?x::Int) => Int -> Int
3203 <sect3><title>Implicit parameters and polymorphic recursion</title>
3206 Consider these two definitions:
3209 len1 xs = let ?acc = 0 in len_acc1 xs
3212 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3217 len2 xs = let ?acc = 0 in len_acc2 xs
3219 len_acc2 :: (?acc :: Int) => [a] -> Int
3221 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3223 The only difference between the two groups is that in the second group
3224 <literal>len_acc</literal> is given a type signature.
3225 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3226 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3227 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3228 has a type signature, the recursive call is made to the
3229 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3230 as an implicit parameter. So we get the following results in GHCi:
3237 Adding a type signature dramatically changes the result! This is a rather
3238 counter-intuitive phenomenon, worth watching out for.
3242 <sect3><title>Implicit parameters and monomorphism</title>
3244 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3245 Haskell Report) to implicit parameters. For example, consider:
3253 Since the binding for <literal>y</literal> falls under the Monomorphism
3254 Restriction it is not generalised, so the type of <literal>y</literal> is
3255 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3256 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3257 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3258 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3259 <literal>y</literal> in the body of the <literal>let</literal> will see the
3260 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3261 <literal>14</literal>.
3266 <!-- ======================= COMMENTED OUT ========================
3268 We intend to remove linear implicit parameters, so I'm at least removing
3269 them from the 6.6 user manual
3271 <sect2 id="linear-implicit-parameters">
3272 <title>Linear implicit parameters</title>
3274 Linear implicit parameters are an idea developed by Koen Claessen,
3275 Mark Shields, and Simon PJ. They address the long-standing
3276 problem that monads seem over-kill for certain sorts of problem, notably:
3279 <listitem> <para> distributing a supply of unique names </para> </listitem>
3280 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3281 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3285 Linear implicit parameters are just like ordinary implicit parameters,
3286 except that they are "linear"; that is, they cannot be copied, and
3287 must be explicitly "split" instead. Linear implicit parameters are
3288 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3289 (The '/' in the '%' suggests the split!)
3294 import GHC.Exts( Splittable )
3296 data NameSupply = ...
3298 splitNS :: NameSupply -> (NameSupply, NameSupply)
3299 newName :: NameSupply -> Name
3301 instance Splittable NameSupply where
3305 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3306 f env (Lam x e) = Lam x' (f env e)
3309 env' = extend env x x'
3310 ...more equations for f...
3312 Notice that the implicit parameter %ns is consumed
3314 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3315 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3319 So the translation done by the type checker makes
3320 the parameter explicit:
3322 f :: NameSupply -> Env -> Expr -> Expr
3323 f ns env (Lam x e) = Lam x' (f ns1 env e)
3325 (ns1,ns2) = splitNS ns
3327 env = extend env x x'
3329 Notice the call to 'split' introduced by the type checker.
3330 How did it know to use 'splitNS'? Because what it really did
3331 was to introduce a call to the overloaded function 'split',
3332 defined by the class <literal>Splittable</literal>:
3334 class Splittable a where
3337 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3338 split for name supplies. But we can simply write
3344 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3346 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3347 <literal>GHC.Exts</literal>.
3352 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3353 are entirely distinct implicit parameters: you
3354 can use them together and they won't intefere with each other. </para>
3357 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3359 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3360 in the context of a class or instance declaration. </para></listitem>
3364 <sect3><title>Warnings</title>
3367 The monomorphism restriction is even more important than usual.
3368 Consider the example above:
3370 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3371 f env (Lam x e) = Lam x' (f env e)
3374 env' = extend env x x'
3376 If we replaced the two occurrences of x' by (newName %ns), which is
3377 usually a harmless thing to do, we get:
3379 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3380 f env (Lam x e) = Lam (newName %ns) (f env e)
3382 env' = extend env x (newName %ns)
3384 But now the name supply is consumed in <emphasis>three</emphasis> places
3385 (the two calls to newName,and the recursive call to f), so
3386 the result is utterly different. Urk! We don't even have
3390 Well, this is an experimental change. With implicit
3391 parameters we have already lost beta reduction anyway, and
3392 (as John Launchbury puts it) we can't sensibly reason about
3393 Haskell programs without knowing their typing.
3398 <sect3><title>Recursive functions</title>
3399 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3402 foo :: %x::T => Int -> [Int]
3404 foo n = %x : foo (n-1)
3406 where T is some type in class Splittable.</para>
3408 Do you get a list of all the same T's or all different T's
3409 (assuming that split gives two distinct T's back)?
3411 If you supply the type signature, taking advantage of polymorphic
3412 recursion, you get what you'd probably expect. Here's the
3413 translated term, where the implicit param is made explicit:
3416 foo x n = let (x1,x2) = split x
3417 in x1 : foo x2 (n-1)
3419 But if you don't supply a type signature, GHC uses the Hindley
3420 Milner trick of using a single monomorphic instance of the function
3421 for the recursive calls. That is what makes Hindley Milner type inference
3422 work. So the translation becomes
3426 foom n = x : foom (n-1)
3430 Result: 'x' is not split, and you get a list of identical T's. So the
3431 semantics of the program depends on whether or not foo has a type signature.
3434 You may say that this is a good reason to dislike linear implicit parameters
3435 and you'd be right. That is why they are an experimental feature.
3441 ================ END OF Linear Implicit Parameters commented out -->
3443 <sect2 id="kinding">
3444 <title>Explicitly-kinded quantification</title>
3447 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3448 to give the kind explicitly as (machine-checked) documentation,
3449 just as it is nice to give a type signature for a function. On some occasions,
3450 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3451 John Hughes had to define the data type:
3453 data Set cxt a = Set [a]
3454 | Unused (cxt a -> ())
3456 The only use for the <literal>Unused</literal> constructor was to force the correct
3457 kind for the type variable <literal>cxt</literal>.
3460 GHC now instead allows you to specify the kind of a type variable directly, wherever
3461 a type variable is explicitly bound. Namely:
3463 <listitem><para><literal>data</literal> declarations:
3465 data Set (cxt :: * -> *) a = Set [a]
3466 </screen></para></listitem>
3467 <listitem><para><literal>type</literal> declarations:
3469 type T (f :: * -> *) = f Int
3470 </screen></para></listitem>
3471 <listitem><para><literal>class</literal> declarations:
3473 class (Eq a) => C (f :: * -> *) a where ...
3474 </screen></para></listitem>
3475 <listitem><para><literal>forall</literal>'s in type signatures:
3477 f :: forall (cxt :: * -> *). Set cxt Int
3478 </screen></para></listitem>
3483 The parentheses are required. Some of the spaces are required too, to
3484 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3485 will get a parse error, because "<literal>::*->*</literal>" is a
3486 single lexeme in Haskell.
3490 As part of the same extension, you can put kind annotations in types
3493 f :: (Int :: *) -> Int
3494 g :: forall a. a -> (a :: *)
3498 atype ::= '(' ctype '::' kind ')
3500 The parentheses are required.
3505 <sect2 id="universal-quantification">
3506 <title>Arbitrary-rank polymorphism
3510 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3511 allows us to say exactly what this means. For example:
3519 g :: forall b. (b -> b)
3521 The two are treated identically.
3525 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3526 explicit universal quantification in
3528 For example, all the following types are legal:
3530 f1 :: forall a b. a -> b -> a
3531 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3533 f2 :: (forall a. a->a) -> Int -> Int
3534 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3536 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3538 f4 :: Int -> (forall a. a -> a)
3540 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3541 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3542 The <literal>forall</literal> makes explicit the universal quantification that
3543 is implicitly added by Haskell.
3546 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3547 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3548 shows, the polymorphic type on the left of the function arrow can be overloaded.
3551 The function <literal>f3</literal> has a rank-3 type;
3552 it has rank-2 types on the left of a function arrow.
3555 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3556 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3557 that restriction has now been lifted.)
3558 In particular, a forall-type (also called a "type scheme"),
3559 including an operational type class context, is legal:
3561 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3562 of a function arrow </para> </listitem>
3563 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3564 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3565 field type signatures.</para> </listitem>
3566 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3567 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3569 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3570 a type variable any more!
3579 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3580 the types of the constructor arguments. Here are several examples:
3586 data T a = T1 (forall b. b -> b -> b) a
3588 data MonadT m = MkMonad { return :: forall a. a -> m a,
3589 bind :: forall a b. m a -> (a -> m b) -> m b
3592 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3598 The constructors have rank-2 types:
3604 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3605 MkMonad :: forall m. (forall a. a -> m a)
3606 -> (forall a b. m a -> (a -> m b) -> m b)
3608 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3614 Notice that you don't need to use a <literal>forall</literal> if there's an
3615 explicit context. For example in the first argument of the
3616 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3617 prefixed to the argument type. The implicit <literal>forall</literal>
3618 quantifies all type variables that are not already in scope, and are
3619 mentioned in the type quantified over.
3623 As for type signatures, implicit quantification happens for non-overloaded
3624 types too. So if you write this:
3627 data T a = MkT (Either a b) (b -> b)
3630 it's just as if you had written this:
3633 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3636 That is, since the type variable <literal>b</literal> isn't in scope, it's
3637 implicitly universally quantified. (Arguably, it would be better
3638 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3639 where that is what is wanted. Feedback welcomed.)
3643 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3644 the constructor to suitable values, just as usual. For example,
3655 a3 = MkSwizzle reverse
3658 a4 = let r x = Just x
3665 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3666 mkTs f x y = [T1 f x, T1 f y]
3672 The type of the argument can, as usual, be more general than the type
3673 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3674 does not need the <literal>Ord</literal> constraint.)
3678 When you use pattern matching, the bound variables may now have
3679 polymorphic types. For example:
3685 f :: T a -> a -> (a, Char)
3686 f (T1 w k) x = (w k x, w 'c' 'd')
3688 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3689 g (MkSwizzle s) xs f = s (map f (s xs))
3691 h :: MonadT m -> [m a] -> m [a]
3692 h m [] = return m []
3693 h m (x:xs) = bind m x $ \y ->
3694 bind m (h m xs) $ \ys ->
3701 In the function <function>h</function> we use the record selectors <literal>return</literal>
3702 and <literal>bind</literal> to extract the polymorphic bind and return functions
3703 from the <literal>MonadT</literal> data structure, rather than using pattern
3709 <title>Type inference</title>
3712 In general, type inference for arbitrary-rank types is undecidable.
3713 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3714 to get a decidable algorithm by requiring some help from the programmer.
3715 We do not yet have a formal specification of "some help" but the rule is this:
3718 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3719 provides an explicit polymorphic type for x, or GHC's type inference will assume
3720 that x's type has no foralls in it</emphasis>.
3723 What does it mean to "provide" an explicit type for x? You can do that by
3724 giving a type signature for x directly, using a pattern type signature
3725 (<xref linkend="scoped-type-variables"/>), thus:
3727 \ f :: (forall a. a->a) -> (f True, f 'c')
3729 Alternatively, you can give a type signature to the enclosing
3730 context, which GHC can "push down" to find the type for the variable:
3732 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3734 Here the type signature on the expression can be pushed inwards
3735 to give a type signature for f. Similarly, and more commonly,
3736 one can give a type signature for the function itself:
3738 h :: (forall a. a->a) -> (Bool,Char)
3739 h f = (f True, f 'c')
3741 You don't need to give a type signature if the lambda bound variable
3742 is a constructor argument. Here is an example we saw earlier:
3744 f :: T a -> a -> (a, Char)
3745 f (T1 w k) x = (w k x, w 'c' 'd')
3747 Here we do not need to give a type signature to <literal>w</literal>, because
3748 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3755 <sect3 id="implicit-quant">
3756 <title>Implicit quantification</title>
3759 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3760 user-written types, if and only if there is no explicit <literal>forall</literal>,
3761 GHC finds all the type variables mentioned in the type that are not already
3762 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3766 f :: forall a. a -> a
3773 h :: forall b. a -> b -> b
3779 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3782 f :: (a -> a) -> Int
3784 f :: forall a. (a -> a) -> Int
3786 f :: (forall a. a -> a) -> Int
3789 g :: (Ord a => a -> a) -> Int
3790 -- MEANS the illegal type
3791 g :: forall a. (Ord a => a -> a) -> Int
3793 g :: (forall a. Ord a => a -> a) -> Int
3795 The latter produces an illegal type, which you might think is silly,
3796 but at least the rule is simple. If you want the latter type, you
3797 can write your for-alls explicitly. Indeed, doing so is strongly advised
3804 <sect2 id="impredicative-polymorphism">
3805 <title>Impredicative polymorphism
3807 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3808 that you can call a polymorphic function at a polymorphic type, and
3809 parameterise data structures over polymorphic types. For example:
3811 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3812 f (Just g) = Just (g [3], g "hello")
3815 Notice here that the <literal>Maybe</literal> type is parameterised by the
3816 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3819 <para>The technical details of this extension are described in the paper
3820 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3821 type inference for higher-rank types and impredicativity</ulink>,
3822 which appeared at ICFP 2006.
3826 <sect2 id="scoped-type-variables">
3827 <title>Lexically scoped type variables
3831 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3832 which some type signatures are simply impossible to write. For example:
3834 f :: forall a. [a] -> [a]
3840 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3841 the entire definition of <literal>f</literal>.
3842 In particular, it is in scope at the type signature for <varname>ys</varname>.
3843 In Haskell 98 it is not possible to declare
3844 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3845 it becomes possible to do so.
3847 <para>Lexically-scoped type variables are enabled by
3848 <option>-fglasgow-exts</option>.
3850 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3851 variables work, compared to earlier releases. Read this section
3855 <title>Overview</title>
3857 <para>The design follows the following principles
3859 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3860 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3861 design.)</para></listitem>
3862 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3863 type variables. This means that every programmer-written type signature
3864 (includin one that contains free scoped type variables) denotes a
3865 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3866 checker, and no inference is involved.</para></listitem>
3867 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3868 changing the program.</para></listitem>
3872 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3874 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3875 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3876 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3877 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3881 In Haskell, a programmer-written type signature is implicitly quantifed over
3882 its free type variables (<ulink
3883 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3885 of the Haskel Report).
3886 Lexically scoped type variables affect this implicit quantification rules
3887 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3888 quantified. For example, if type variable <literal>a</literal> is in scope,
3891 (e :: a -> a) means (e :: a -> a)
3892 (e :: b -> b) means (e :: forall b. b->b)
3893 (e :: a -> b) means (e :: forall b. a->b)
3901 <sect3 id="decl-type-sigs">
3902 <title>Declaration type signatures</title>
3903 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3904 quantification (using <literal>forall</literal>) brings into scope the
3905 explicitly-quantified
3906 type variables, in the definition of the named function(s). For example:
3908 f :: forall a. [a] -> [a]
3909 f (x:xs) = xs ++ [ x :: a ]
3911 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3912 the definition of "<literal>f</literal>".
3914 <para>This only happens if the quantification in <literal>f</literal>'s type
3915 signature is explicit. For example:
3918 g (x:xs) = xs ++ [ x :: a ]
3920 This program will be rejected, because "<literal>a</literal>" does not scope
3921 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3922 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3923 quantification rules.
3927 <sect3 id="exp-type-sigs">
3928 <title>Expression type signatures</title>
3930 <para>An expression type signature that has <emphasis>explicit</emphasis>
3931 quantification (using <literal>forall</literal>) brings into scope the
3932 explicitly-quantified
3933 type variables, in the annotated expression. For example:
3935 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3937 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3938 type variable <literal>s</literal> into scope, in the annotated expression
3939 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3944 <sect3 id="pattern-type-sigs">
3945 <title>Pattern type signatures</title>
3947 A type signature may occur in any pattern; this is a <emphasis>pattern type
3948 signature</emphasis>.
3951 -- f and g assume that 'a' is already in scope
3952 f = \(x::Int, y::a) -> x
3954 h ((x,y) :: (Int,Bool)) = (y,x)
3956 In the case where all the type variables in the pattern type sigature are
3957 already in scope (i.e. bound by the enclosing context), matters are simple: the
3958 signature simply constrains the type of the pattern in the obvious way.
3961 There is only one situation in which you can write a pattern type signature that
3962 mentions a type variable that is not already in scope, namely in pattern match
3963 of an existential data constructor. For example:
3965 data T = forall a. MkT [a]
3968 k (MkT [t::a]) = MkT t3
3972 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3973 variable that is not already in scope. Indeed, it cannot already be in scope,
3974 because it is bound by the pattern match. GHC's rule is that in this situation
3975 (and only then), a pattern type signature can mention a type variable that is
3976 not already in scope; the effect is to bring it into scope, standing for the
3977 existentially-bound type variable.
3980 If this seems a little odd, we think so too. But we must have
3981 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3982 could not name existentially-bound type variables in subequent type signatures.
3985 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3986 signature is allowed to mention a lexical variable that is not already in
3988 For example, both <literal>f</literal> and <literal>g</literal> would be
3989 illegal if <literal>a</literal> was not already in scope.
3995 <!-- ==================== Commented out part about result type signatures
3997 <sect3 id="result-type-sigs">
3998 <title>Result type signatures</title>
4001 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4004 {- f assumes that 'a' is already in scope -}
4005 f x y :: [a] = [x,y,x]
4007 g = \ x :: [Int] -> [3,4]
4009 h :: forall a. [a] -> a
4013 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4014 the result of the function. Similarly, the body of the lambda in the RHS of
4015 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4016 alternative in <literal>h</literal> is <literal>a</literal>.
4018 <para> A result type signature never brings new type variables into scope.</para>
4020 There are a couple of syntactic wrinkles. First, notice that all three
4021 examples would parse quite differently with parentheses:
4023 {- f assumes that 'a' is already in scope -}
4024 f x (y :: [a]) = [x,y,x]
4026 g = \ (x :: [Int]) -> [3,4]
4028 h :: forall a. [a] -> a
4032 Now the signature is on the <emphasis>pattern</emphasis>; and
4033 <literal>h</literal> would certainly be ill-typed (since the pattern
4034 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4036 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4037 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4038 token or a parenthesised type of some sort). To see why,
4039 consider how one would parse this:
4048 <sect3 id="cls-inst-scoped-tyvars">
4049 <title>Class and instance declarations</title>
4052 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4053 scope over the methods defined in the <literal>where</literal> part. For example:
4071 <sect2 id="typing-binds">
4072 <title>Generalised typing of mutually recursive bindings</title>
4075 The Haskell Report specifies that a group of bindings (at top level, or in a
4076 <literal>let</literal> or <literal>where</literal>) should be sorted into
4077 strongly-connected components, and then type-checked in dependency order
4078 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4079 Report, Section 4.5.1</ulink>).
4080 As each group is type-checked, any binders of the group that
4082 an explicit type signature are put in the type environment with the specified
4084 and all others are monomorphic until the group is generalised
4085 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4088 <para>Following a suggestion of Mark Jones, in his paper
4089 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4091 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4093 <emphasis>the dependency analysis ignores references to variables that have an explicit
4094 type signature</emphasis>.
4095 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4096 typecheck. For example, consider:
4098 f :: Eq a => a -> Bool
4099 f x = (x == x) || g True || g "Yes"
4101 g y = (y <= y) || f True
4103 This is rejected by Haskell 98, but under Jones's scheme the definition for
4104 <literal>g</literal> is typechecked first, separately from that for
4105 <literal>f</literal>,
4106 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4107 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4108 type is generalised, to get
4110 g :: Ord a => a -> Bool
4112 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4113 <literal>g</literal> in the type environment.
4117 The same refined dependency analysis also allows the type signatures of
4118 mutually-recursive functions to have different contexts, something that is illegal in
4119 Haskell 98 (Section 4.5.2, last sentence). With
4120 <option>-XRelaxedPolyRec</option>
4121 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4122 type signatures; in practice this means that only variables bound by the same
4123 pattern binding must have the same context. For example, this is fine:
4125 f :: Eq a => a -> Bool
4126 f x = (x == x) || g True
4128 g :: Ord a => a -> Bool
4129 g y = (y <= y) || f True
4134 <sect2 id="overloaded-strings">
4135 <title>Overloaded string literals
4139 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4140 string literal has type <literal>String</literal>, but with overloaded string
4141 literals enabled (with <literal>-XOverloadedStrings</literal>)
4142 a string literal has type <literal>(IsString a) => a</literal>.
4145 This means that the usual string syntax can be used, e.g., for packed strings
4146 and other variations of string like types. String literals behave very much
4147 like integer literals, i.e., they can be used in both expressions and patterns.
4148 If used in a pattern the literal with be replaced by an equality test, in the same
4149 way as an integer literal is.
4152 The class <literal>IsString</literal> is defined as:
4154 class IsString a where
4155 fromString :: String -> a
4157 The only predefined instance is the obvious one to make strings work as usual:
4159 instance IsString [Char] where
4162 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4163 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4164 from module <literal>GHC.Exts</literal>.
4167 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4171 Each type in a default declaration must be an
4172 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4176 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4177 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4178 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4179 <emphasis>or</emphasis> <literal>IsString</literal>.
4188 import GHC.Exts( IsString(..) )
4190 newtype MyString = MyString String deriving (Eq, Show)
4191 instance IsString MyString where
4192 fromString = MyString
4194 greet :: MyString -> MyString
4195 greet "hello" = "world"
4199 print $ greet "hello"
4200 print $ greet "fool"
4204 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4205 to work since it gets translated into an equality comparison.
4209 <sect2 id="type-families">
4210 <title>Type families
4214 GHC supports the definition of type families indexed by types. They may be
4215 seen as an extension of Haskell 98's class-based overloading of values to
4216 types. When type families are declared in classes, they are also known as
4220 There are two forms of type families: data families and type synonym families.
4221 Currently, only the former are fully implemented, while we are still working
4222 on the latter. As a result, the specification of the language extension is
4223 also still to some degree in flux. Hence, a more detailed description of
4224 the language extension and its use is currently available
4225 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4226 wiki page on type families</ulink>. The material will be moved to this user's
4227 guide when it has stabilised.
4230 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4237 <!-- ==================== End of type system extensions ================= -->
4239 <!-- ====================== TEMPLATE HASKELL ======================= -->
4241 <sect1 id="template-haskell">
4242 <title>Template Haskell</title>
4244 <para>Template Haskell allows you to do compile-time meta-programming in
4247 the main technical innovations is discussed in "<ulink
4248 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4249 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4252 There is a Wiki page about
4253 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4254 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4258 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4259 Haskell library reference material</ulink>
4260 (search for the type ExpQ).
4261 [Temporary: many changes to the original design are described in
4262 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4263 Not all of these changes are in GHC 6.6.]
4266 <para> The first example from that paper is set out below as a worked example to help get you started.
4270 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4271 Tim Sheard is going to expand it.)
4275 <title>Syntax</title>
4277 <para> Template Haskell has the following new syntactic
4278 constructions. You need to use the flag
4279 <option>-XTemplateHaskell</option>
4280 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4281 </indexterm>to switch these syntactic extensions on
4282 (<option>-XTemplateHaskell</option> is no longer implied by
4283 <option>-fglasgow-exts</option>).</para>
4287 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4288 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4289 There must be no space between the "$" and the identifier or parenthesis. This use
4290 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4291 of "." as an infix operator. If you want the infix operator, put spaces around it.
4293 <para> A splice can occur in place of
4295 <listitem><para> an expression; the spliced expression must
4296 have type <literal>Q Exp</literal></para></listitem>
4297 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4298 <listitem><para> [Planned, but not implemented yet.] a
4299 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4301 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4302 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4308 A expression quotation is written in Oxford brackets, thus:
4310 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4311 the quotation has type <literal>Expr</literal>.</para></listitem>
4312 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4313 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4314 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4315 the quotation has type <literal>Type</literal>.</para></listitem>
4316 </itemizedlist></para></listitem>
4319 Reification is written thus:
4321 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4322 has type <literal>Dec</literal>. </para></listitem>
4323 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4324 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4325 <listitem><para> Still to come: fixities </para></listitem>
4327 </itemizedlist></para>
4334 <sect2> <title> Using Template Haskell </title>
4338 The data types and monadic constructor functions for Template Haskell are in the library
4339 <literal>Language.Haskell.THSyntax</literal>.
4343 You can only run a function at compile time if it is imported from another module. That is,
4344 you can't define a function in a module, and call it from within a splice in the same module.
4345 (It would make sense to do so, but it's hard to implement.)
4349 Furthermore, you can only run a function at compile time if it is imported
4350 from another module <emphasis>that is not part of a mutually-recursive group of modules
4351 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4352 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4353 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4357 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4360 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4361 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4362 compiles and runs a program, and then looks at the result. So it's important that
4363 the program it compiles produces results whose representations are identical to
4364 those of the compiler itself.
4368 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4369 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4374 <sect2> <title> A Template Haskell Worked Example </title>
4375 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4376 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4383 -- Import our template "pr"
4384 import Printf ( pr )
4386 -- The splice operator $ takes the Haskell source code
4387 -- generated at compile time by "pr" and splices it into
4388 -- the argument of "putStrLn".
4389 main = putStrLn ( $(pr "Hello") )
4395 -- Skeletal printf from the paper.
4396 -- It needs to be in a separate module to the one where
4397 -- you intend to use it.
4399 -- Import some Template Haskell syntax
4400 import Language.Haskell.TH
4402 -- Describe a format string
4403 data Format = D | S | L String
4405 -- Parse a format string. This is left largely to you
4406 -- as we are here interested in building our first ever
4407 -- Template Haskell program and not in building printf.
4408 parse :: String -> [Format]
4411 -- Generate Haskell source code from a parsed representation
4412 -- of the format string. This code will be spliced into
4413 -- the module which calls "pr", at compile time.
4414 gen :: [Format] -> ExpQ
4415 gen [D] = [| \n -> show n |]
4416 gen [S] = [| \s -> s |]
4417 gen [L s] = stringE s
4419 -- Here we generate the Haskell code for the splice
4420 -- from an input format string.
4421 pr :: String -> ExpQ
4422 pr s = gen (parse s)
4425 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4428 $ ghc --make -XTemplateHaskell main.hs -o main.exe
4431 <para>Run "main.exe" and here is your output:</para>
4441 <title>Using Template Haskell with Profiling</title>
4442 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4444 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4445 interpreter to run the splice expressions. The bytecode interpreter
4446 runs the compiled expression on top of the same runtime on which GHC
4447 itself is running; this means that the compiled code referred to by
4448 the interpreted expression must be compatible with this runtime, and
4449 in particular this means that object code that is compiled for
4450 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4451 expression, because profiled object code is only compatible with the
4452 profiling version of the runtime.</para>
4454 <para>This causes difficulties if you have a multi-module program
4455 containing Template Haskell code and you need to compile it for
4456 profiling, because GHC cannot load the profiled object code and use it
4457 when executing the splices. Fortunately GHC provides a workaround.
4458 The basic idea is to compile the program twice:</para>
4462 <para>Compile the program or library first the normal way, without
4463 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4466 <para>Then compile it again with <option>-prof</option>, and
4467 additionally use <option>-osuf
4468 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4469 to name the object files differentliy (you can choose any suffix
4470 that isn't the normal object suffix here). GHC will automatically
4471 load the object files built in the first step when executing splice
4472 expressions. If you omit the <option>-osuf</option> flag when
4473 building with <option>-prof</option> and Template Haskell is used,
4474 GHC will emit an error message. </para>
4481 <!-- ===================== Arrow notation =================== -->
4483 <sect1 id="arrow-notation">
4484 <title>Arrow notation
4487 <para>Arrows are a generalization of monads introduced by John Hughes.
4488 For more details, see
4493 “Generalising Monads to Arrows”,
4494 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4495 pp67–111, May 2000.
4501 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4502 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4508 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4509 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4515 and the arrows web page at
4516 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4517 With the <option>-XArrows</option> flag, GHC supports the arrow
4518 notation described in the second of these papers.
4519 What follows is a brief introduction to the notation;
4520 it won't make much sense unless you've read Hughes's paper.
4521 This notation is translated to ordinary Haskell,
4522 using combinators from the
4523 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4527 <para>The extension adds a new kind of expression for defining arrows:
4529 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4530 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4532 where <literal>proc</literal> is a new keyword.
4533 The variables of the pattern are bound in the body of the
4534 <literal>proc</literal>-expression,
4535 which is a new sort of thing called a <firstterm>command</firstterm>.
4536 The syntax of commands is as follows:
4538 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4539 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4540 | <replaceable>cmd</replaceable><superscript>0</superscript>
4542 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4543 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4544 infix operators as for expressions, and
4546 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4547 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4548 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4549 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4550 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4551 | <replaceable>fcmd</replaceable>
4553 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4554 | ( <replaceable>cmd</replaceable> )
4555 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4557 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4558 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4559 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4560 | <replaceable>cmd</replaceable>
4562 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4563 except that the bodies are commands instead of expressions.
4567 Commands produce values, but (like monadic computations)
4568 may yield more than one value,
4569 or none, and may do other things as well.
4570 For the most part, familiarity with monadic notation is a good guide to
4572 However the values of expressions, even monadic ones,
4573 are determined by the values of the variables they contain;
4574 this is not necessarily the case for commands.
4578 A simple example of the new notation is the expression
4580 proc x -> f -< x+1
4582 We call this a <firstterm>procedure</firstterm> or
4583 <firstterm>arrow abstraction</firstterm>.
4584 As with a lambda expression, the variable <literal>x</literal>
4585 is a new variable bound within the <literal>proc</literal>-expression.
4586 It refers to the input to the arrow.
4587 In the above example, <literal>-<</literal> is not an identifier but an
4588 new reserved symbol used for building commands from an expression of arrow
4589 type and an expression to be fed as input to that arrow.
4590 (The weird look will make more sense later.)
4591 It may be read as analogue of application for arrows.
4592 The above example is equivalent to the Haskell expression
4594 arr (\ x -> x+1) >>> f
4596 That would make no sense if the expression to the left of
4597 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4598 More generally, the expression to the left of <literal>-<</literal>
4599 may not involve any <firstterm>local variable</firstterm>,
4600 i.e. a variable bound in the current arrow abstraction.
4601 For such a situation there is a variant <literal>-<<</literal>, as in
4603 proc x -> f x -<< x+1
4605 which is equivalent to
4607 arr (\ x -> (f x, x+1)) >>> app
4609 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4611 Such an arrow is equivalent to a monad, so if you're using this form
4612 you may find a monadic formulation more convenient.
4616 <title>do-notation for commands</title>
4619 Another form of command is a form of <literal>do</literal>-notation.
4620 For example, you can write
4629 You can read this much like ordinary <literal>do</literal>-notation,
4630 but with commands in place of monadic expressions.
4631 The first line sends the value of <literal>x+1</literal> as an input to
4632 the arrow <literal>f</literal>, and matches its output against
4633 <literal>y</literal>.
4634 In the next line, the output is discarded.
4635 The arrow <function>returnA</function> is defined in the
4636 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4637 module as <literal>arr id</literal>.
4638 The above example is treated as an abbreviation for
4640 arr (\ x -> (x, x)) >>>
4641 first (arr (\ x -> x+1) >>> f) >>>
4642 arr (\ (y, x) -> (y, (x, y))) >>>
4643 first (arr (\ y -> 2*y) >>> g) >>>
4645 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4646 first (arr (\ (x, z) -> x*z) >>> h) >>>
4647 arr (\ (t, z) -> t+z) >>>
4650 Note that variables not used later in the composition are projected out.
4651 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4653 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4654 module, this reduces to
4656 arr (\ x -> (x+1, x)) >>>
4658 arr (\ (y, x) -> (2*y, (x, y))) >>>
4660 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4662 arr (\ (t, z) -> t+z)
4664 which is what you might have written by hand.
4665 With arrow notation, GHC keeps track of all those tuples of variables for you.
4669 Note that although the above translation suggests that
4670 <literal>let</literal>-bound variables like <literal>z</literal> must be
4671 monomorphic, the actual translation produces Core,
4672 so polymorphic variables are allowed.
4676 It's also possible to have mutually recursive bindings,
4677 using the new <literal>rec</literal> keyword, as in the following example:
4679 counter :: ArrowCircuit a => a Bool Int
4680 counter = proc reset -> do
4681 rec output <- returnA -< if reset then 0 else next
4682 next <- delay 0 -< output+1
4683 returnA -< output
4685 The translation of such forms uses the <function>loop</function> combinator,
4686 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4692 <title>Conditional commands</title>
4695 In the previous example, we used a conditional expression to construct the
4697 Sometimes we want to conditionally execute different commands, as in
4704 which is translated to
4706 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4707 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4709 Since the translation uses <function>|||</function>,
4710 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4714 There are also <literal>case</literal> commands, like
4720 y <- h -< (x1, x2)
4724 The syntax is the same as for <literal>case</literal> expressions,
4725 except that the bodies of the alternatives are commands rather than expressions.
4726 The translation is similar to that of <literal>if</literal> commands.
4732 <title>Defining your own control structures</title>
4735 As we're seen, arrow notation provides constructs,
4736 modelled on those for expressions,
4737 for sequencing, value recursion and conditionals.
4738 But suitable combinators,
4739 which you can define in ordinary Haskell,
4740 may also be used to build new commands out of existing ones.
4741 The basic idea is that a command defines an arrow from environments to values.
4742 These environments assign values to the free local variables of the command.
4743 Thus combinators that produce arrows from arrows
4744 may also be used to build commands from commands.
4745 For example, the <literal>ArrowChoice</literal> class includes a combinator
4747 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4749 so we can use it to build commands:
4751 expr' = proc x -> do
4754 symbol Plus -< ()
4755 y <- term -< ()
4758 symbol Minus -< ()
4759 y <- term -< ()
4762 (The <literal>do</literal> on the first line is needed to prevent the first
4763 <literal><+> ...</literal> from being interpreted as part of the
4764 expression on the previous line.)
4765 This is equivalent to
4767 expr' = (proc x -> returnA -< x)
4768 <+> (proc x -> do
4769 symbol Plus -< ()
4770 y <- term -< ()
4772 <+> (proc x -> do
4773 symbol Minus -< ()
4774 y <- term -< ()
4777 It is essential that this operator be polymorphic in <literal>e</literal>
4778 (representing the environment input to the command
4779 and thence to its subcommands)
4780 and satisfy the corresponding naturality property
4782 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4784 at least for strict <literal>k</literal>.
4785 (This should be automatic if you're not using <function>seq</function>.)
4786 This ensures that environments seen by the subcommands are environments
4787 of the whole command,
4788 and also allows the translation to safely trim these environments.
4789 The operator must also not use any variable defined within the current
4794 We could define our own operator
4796 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4797 untilA body cond = proc x ->
4798 if cond x then returnA -< ()
4801 untilA body cond -< x
4803 and use it in the same way.
4804 Of course this infix syntax only makes sense for binary operators;
4805 there is also a more general syntax involving special brackets:
4809 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4816 <title>Primitive constructs</title>
4819 Some operators will need to pass additional inputs to their subcommands.
4820 For example, in an arrow type supporting exceptions,
4821 the operator that attaches an exception handler will wish to pass the
4822 exception that occurred to the handler.
4823 Such an operator might have a type
4825 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4827 where <literal>Ex</literal> is the type of exceptions handled.
4828 You could then use this with arrow notation by writing a command
4830 body `handleA` \ ex -> handler
4832 so that if an exception is raised in the command <literal>body</literal>,
4833 the variable <literal>ex</literal> is bound to the value of the exception
4834 and the command <literal>handler</literal>,
4835 which typically refers to <literal>ex</literal>, is entered.
4836 Though the syntax here looks like a functional lambda,
4837 we are talking about commands, and something different is going on.
4838 The input to the arrow represented by a command consists of values for
4839 the free local variables in the command, plus a stack of anonymous values.
4840 In all the prior examples, this stack was empty.
4841 In the second argument to <function>handleA</function>,
4842 this stack consists of one value, the value of the exception.
4843 The command form of lambda merely gives this value a name.
4848 the values on the stack are paired to the right of the environment.
4849 So operators like <function>handleA</function> that pass
4850 extra inputs to their subcommands can be designed for use with the notation
4851 by pairing the values with the environment in this way.
4852 More precisely, the type of each argument of the operator (and its result)
4853 should have the form
4855 a (...(e,t1), ... tn) t
4857 where <replaceable>e</replaceable> is a polymorphic variable
4858 (representing the environment)
4859 and <replaceable>ti</replaceable> are the types of the values on the stack,
4860 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4861 The polymorphic variable <replaceable>e</replaceable> must not occur in
4862 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4863 <replaceable>t</replaceable>.
4864 However the arrows involved need not be the same.
4865 Here are some more examples of suitable operators:
4867 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4868 runReader :: ... => a e c -> a' (e,State) c
4869 runState :: ... => a e c -> a' (e,State) (c,State)
4871 We can supply the extra input required by commands built with the last two
4872 by applying them to ordinary expressions, as in
4876 (|runReader (do { ... })|) s
4878 which adds <literal>s</literal> to the stack of inputs to the command
4879 built using <function>runReader</function>.
4883 The command versions of lambda abstraction and application are analogous to
4884 the expression versions.
4885 In particular, the beta and eta rules describe equivalences of commands.
4886 These three features (operators, lambda abstraction and application)
4887 are the core of the notation; everything else can be built using them,
4888 though the results would be somewhat clumsy.
4889 For example, we could simulate <literal>do</literal>-notation by defining
4891 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4892 u `bind` f = returnA &&& u >>> f
4894 bind_ :: Arrow a => a e b -> a e c -> a e c
4895 u `bind_` f = u `bind` (arr fst >>> f)
4897 We could simulate <literal>if</literal> by defining
4899 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4900 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4907 <title>Differences with the paper</title>
4912 <para>Instead of a single form of arrow application (arrow tail) with two
4913 translations, the implementation provides two forms
4914 <quote><literal>-<</literal></quote> (first-order)
4915 and <quote><literal>-<<</literal></quote> (higher-order).
4920 <para>User-defined operators are flagged with banana brackets instead of
4921 a new <literal>form</literal> keyword.
4930 <title>Portability</title>
4933 Although only GHC implements arrow notation directly,
4934 there is also a preprocessor
4936 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4937 that translates arrow notation into Haskell 98
4938 for use with other Haskell systems.
4939 You would still want to check arrow programs with GHC;
4940 tracing type errors in the preprocessor output is not easy.
4941 Modules intended for both GHC and the preprocessor must observe some
4942 additional restrictions:
4947 The module must import
4948 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4954 The preprocessor cannot cope with other Haskell extensions.
4955 These would have to go in separate modules.
4961 Because the preprocessor targets Haskell (rather than Core),
4962 <literal>let</literal>-bound variables are monomorphic.
4973 <!-- ==================== BANG PATTERNS ================= -->
4975 <sect1 id="bang-patterns">
4976 <title>Bang patterns
4977 <indexterm><primary>Bang patterns</primary></indexterm>
4979 <para>GHC supports an extension of pattern matching called <emphasis>bang
4980 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4982 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4983 prime feature description</ulink> contains more discussion and examples
4984 than the material below.
4987 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
4990 <sect2 id="bang-patterns-informal">
4991 <title>Informal description of bang patterns
4994 The main idea is to add a single new production to the syntax of patterns:
4998 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4999 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5004 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5005 whereas without the bang it would be lazy.
5006 Bang patterns can be nested of course:
5010 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5011 <literal>y</literal>.
5012 A bang only really has an effect if it precedes a variable or wild-card pattern:
5017 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5018 forces evaluation anyway does nothing.
5020 Bang patterns work in <literal>case</literal> expressions too, of course:
5022 g5 x = let y = f x in body
5023 g6 x = case f x of { y -> body }
5024 g7 x = case f x of { !y -> body }
5026 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5027 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
5028 result, and then evaluates <literal>body</literal>.
5030 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5031 definitions too. For example:
5035 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5036 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5037 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5038 in a function argument <literal>![x,y]</literal> means the
5039 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5040 is part of the syntax of <literal>let</literal> bindings.
5045 <sect2 id="bang-patterns-sem">
5046 <title>Syntax and semantics
5050 We add a single new production to the syntax of patterns:
5054 There is one problem with syntactic ambiguity. Consider:
5058 Is this a definition of the infix function "<literal>(!)</literal>",
5059 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5060 ambiguity in favour of the latter. If you want to define
5061 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5066 The semantics of Haskell pattern matching is described in <ulink
5067 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5068 Section 3.17.2</ulink> of the Haskell Report. To this description add
5069 one extra item 10, saying:
5070 <itemizedlist><listitem><para>Matching
5071 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5072 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5073 <listitem><para>otherwise, <literal>pat</literal> is matched against
5074 <literal>v</literal></para></listitem>
5076 </para></listitem></itemizedlist>
5077 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5078 Section 3.17.3</ulink>, add a new case (t):
5080 case v of { !pat -> e; _ -> e' }
5081 = v `seq` case v of { pat -> e; _ -> e' }
5084 That leaves let expressions, whose translation is given in
5085 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5087 of the Haskell Report.
5088 In the translation box, first apply
5089 the following transformation: for each pattern <literal>pi</literal> that is of
5090 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5091 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5092 have a bang at the top, apply the rules in the existing box.
5094 <para>The effect of the let rule is to force complete matching of the pattern
5095 <literal>qi</literal> before evaluation of the body is begun. The bang is
5096 retained in the translated form in case <literal>qi</literal> is a variable,
5104 The let-binding can be recursive. However, it is much more common for
5105 the let-binding to be non-recursive, in which case the following law holds:
5106 <literal>(let !p = rhs in body)</literal>
5108 <literal>(case rhs of !p -> body)</literal>
5111 A pattern with a bang at the outermost level is not allowed at the top level of
5117 <!-- ==================== ASSERTIONS ================= -->
5119 <sect1 id="assertions">
5121 <indexterm><primary>Assertions</primary></indexterm>
5125 If you want to make use of assertions in your standard Haskell code, you
5126 could define a function like the following:
5132 assert :: Bool -> a -> a
5133 assert False x = error "assertion failed!"
5140 which works, but gives you back a less than useful error message --
5141 an assertion failed, but which and where?
5145 One way out is to define an extended <function>assert</function> function which also
5146 takes a descriptive string to include in the error message and
5147 perhaps combine this with the use of a pre-processor which inserts
5148 the source location where <function>assert</function> was used.
5152 Ghc offers a helping hand here, doing all of this for you. For every
5153 use of <function>assert</function> in the user's source:
5159 kelvinToC :: Double -> Double
5160 kelvinToC k = assert (k >= 0.0) (k+273.15)
5166 Ghc will rewrite this to also include the source location where the
5173 assert pred val ==> assertError "Main.hs|15" pred val
5179 The rewrite is only performed by the compiler when it spots
5180 applications of <function>Control.Exception.assert</function>, so you
5181 can still define and use your own versions of
5182 <function>assert</function>, should you so wish. If not, import
5183 <literal>Control.Exception</literal> to make use
5184 <function>assert</function> in your code.
5188 GHC ignores assertions when optimisation is turned on with the
5189 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5190 <literal>assert pred e</literal> will be rewritten to
5191 <literal>e</literal>. You can also disable assertions using the
5192 <option>-fignore-asserts</option>
5193 option<indexterm><primary><option>-fignore-asserts</option></primary>
5194 </indexterm>.</para>
5197 Assertion failures can be caught, see the documentation for the
5198 <literal>Control.Exception</literal> library for the details.
5204 <!-- =============================== PRAGMAS =========================== -->
5206 <sect1 id="pragmas">
5207 <title>Pragmas</title>
5209 <indexterm><primary>pragma</primary></indexterm>
5211 <para>GHC supports several pragmas, or instructions to the
5212 compiler placed in the source code. Pragmas don't normally affect
5213 the meaning of the program, but they might affect the efficiency
5214 of the generated code.</para>
5216 <para>Pragmas all take the form
5218 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5220 where <replaceable>word</replaceable> indicates the type of
5221 pragma, and is followed optionally by information specific to that
5222 type of pragma. Case is ignored in
5223 <replaceable>word</replaceable>. The various values for
5224 <replaceable>word</replaceable> that GHC understands are described
5225 in the following sections; any pragma encountered with an
5226 unrecognised <replaceable>word</replaceable> is (silently)
5229 <sect2 id="deprecated-pragma">
5230 <title>DEPRECATED pragma</title>
5231 <indexterm><primary>DEPRECATED</primary>
5234 <para>The DEPRECATED pragma lets you specify that a particular
5235 function, class, or type, is deprecated. There are two
5240 <para>You can deprecate an entire module thus:</para>
5242 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5245 <para>When you compile any module that import
5246 <literal>Wibble</literal>, GHC will print the specified
5251 <para>You can deprecate a function, class, type, or data constructor, with the
5252 following top-level declaration:</para>
5254 {-# DEPRECATED f, C, T "Don't use these" #-}
5256 <para>When you compile any module that imports and uses any
5257 of the specified entities, GHC will print the specified
5259 <para> You can only depecate entities declared at top level in the module
5260 being compiled, and you can only use unqualified names in the list of
5261 entities being deprecated. A capitalised name, such as <literal>T</literal>
5262 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5263 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5264 both are in scope. If both are in scope, there is currently no way to deprecate
5265 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5268 Any use of the deprecated item, or of anything from a deprecated
5269 module, will be flagged with an appropriate message. However,
5270 deprecations are not reported for
5271 (a) uses of a deprecated function within its defining module, and
5272 (b) uses of a deprecated function in an export list.
5273 The latter reduces spurious complaints within a library
5274 in which one module gathers together and re-exports
5275 the exports of several others.
5277 <para>You can suppress the warnings with the flag
5278 <option>-fno-warn-deprecations</option>.</para>
5281 <sect2 id="include-pragma">
5282 <title>INCLUDE pragma</title>
5284 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5285 of C header files that should be <literal>#include</literal>'d into
5286 the C source code generated by the compiler for the current module (if
5287 compiling via C). For example:</para>
5290 {-# INCLUDE "foo.h" #-}
5291 {-# INCLUDE <stdio.h> #-}</programlisting>
5293 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5294 your source file with any <literal>OPTIONS_GHC</literal>
5297 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5298 to the <option>-#include</option> option (<xref
5299 linkend="options-C-compiler" />), because the
5300 <literal>INCLUDE</literal> pragma is understood by other
5301 compilers. Yet another alternative is to add the include file to each
5302 <literal>foreign import</literal> declaration in your code, but we
5303 don't recommend using this approach with GHC.</para>
5306 <sect2 id="inline-noinline-pragma">
5307 <title>INLINE and NOINLINE pragmas</title>
5309 <para>These pragmas control the inlining of function
5312 <sect3 id="inline-pragma">
5313 <title>INLINE pragma</title>
5314 <indexterm><primary>INLINE</primary></indexterm>
5316 <para>GHC (with <option>-O</option>, as always) tries to
5317 inline (or “unfold”) functions/values that are
5318 “small enough,” thus avoiding the call overhead
5319 and possibly exposing other more-wonderful optimisations.
5320 Normally, if GHC decides a function is “too
5321 expensive” to inline, it will not do so, nor will it
5322 export that unfolding for other modules to use.</para>
5324 <para>The sledgehammer you can bring to bear is the
5325 <literal>INLINE</literal><indexterm><primary>INLINE
5326 pragma</primary></indexterm> pragma, used thusly:</para>
5329 key_function :: Int -> String -> (Bool, Double)
5331 #ifdef __GLASGOW_HASKELL__
5332 {-# INLINE key_function #-}
5336 <para>(You don't need to do the C pre-processor carry-on
5337 unless you're going to stick the code through HBC—it
5338 doesn't like <literal>INLINE</literal> pragmas.)</para>
5340 <para>The major effect of an <literal>INLINE</literal> pragma
5341 is to declare a function's “cost” to be very low.
5342 The normal unfolding machinery will then be very keen to
5345 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5346 function can be put anywhere its type signature could be
5349 <para><literal>INLINE</literal> pragmas are a particularly
5351 <literal>then</literal>/<literal>return</literal> (or
5352 <literal>bind</literal>/<literal>unit</literal>) functions in
5353 a monad. For example, in GHC's own
5354 <literal>UniqueSupply</literal> monad code, we have:</para>
5357 #ifdef __GLASGOW_HASKELL__
5358 {-# INLINE thenUs #-}
5359 {-# INLINE returnUs #-}
5363 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5364 linkend="noinline-pragma"/>).</para>
5367 <sect3 id="noinline-pragma">
5368 <title>NOINLINE pragma</title>
5370 <indexterm><primary>NOINLINE</primary></indexterm>
5371 <indexterm><primary>NOTINLINE</primary></indexterm>
5373 <para>The <literal>NOINLINE</literal> pragma does exactly what
5374 you'd expect: it stops the named function from being inlined
5375 by the compiler. You shouldn't ever need to do this, unless
5376 you're very cautious about code size.</para>
5378 <para><literal>NOTINLINE</literal> is a synonym for
5379 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5380 specified by Haskell 98 as the standard way to disable
5381 inlining, so it should be used if you want your code to be
5385 <sect3 id="phase-control">
5386 <title>Phase control</title>
5388 <para> Sometimes you want to control exactly when in GHC's
5389 pipeline the INLINE pragma is switched on. Inlining happens
5390 only during runs of the <emphasis>simplifier</emphasis>. Each
5391 run of the simplifier has a different <emphasis>phase
5392 number</emphasis>; the phase number decreases towards zero.
5393 If you use <option>-dverbose-core2core</option> you'll see the
5394 sequence of phase numbers for successive runs of the
5395 simplifier. In an INLINE pragma you can optionally specify a
5399 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5400 <literal>f</literal>
5401 until phase <literal>k</literal>, but from phase
5402 <literal>k</literal> onwards be very keen to inline it.
5405 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5406 <literal>f</literal>
5407 until phase <literal>k</literal>, but from phase
5408 <literal>k</literal> onwards do not inline it.
5411 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5412 <literal>f</literal>
5413 until phase <literal>k</literal>, but from phase
5414 <literal>k</literal> onwards be willing to inline it (as if
5415 there was no pragma).
5418 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5419 <literal>f</literal>
5420 until phase <literal>k</literal>, but from phase
5421 <literal>k</literal> onwards do not inline it.
5424 The same information is summarised here:
5426 -- Before phase 2 Phase 2 and later
5427 {-# INLINE [2] f #-} -- No Yes
5428 {-# INLINE [~2] f #-} -- Yes No
5429 {-# NOINLINE [2] f #-} -- No Maybe
5430 {-# NOINLINE [~2] f #-} -- Maybe No
5432 {-# INLINE f #-} -- Yes Yes
5433 {-# NOINLINE f #-} -- No No
5435 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5436 function body is small, or it is applied to interesting-looking arguments etc).
5437 Another way to understand the semantics is this:
5439 <listitem><para>For both INLINE and NOINLINE, the phase number says
5440 when inlining is allowed at all.</para></listitem>
5441 <listitem><para>The INLINE pragma has the additional effect of making the
5442 function body look small, so that when inlining is allowed it is very likely to
5447 <para>The same phase-numbering control is available for RULES
5448 (<xref linkend="rewrite-rules"/>).</para>
5452 <sect2 id="language-pragma">
5453 <title>LANGUAGE pragma</title>
5455 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5456 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5458 <para>This allows language extensions to be enabled in a portable way.
5459 It is the intention that all Haskell compilers support the
5460 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5461 all extensions are supported by all compilers, of
5462 course. The <literal>LANGUAGE</literal> pragma should be used instead
5463 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5465 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5467 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5469 <para>Any extension from the <literal>Extension</literal> type defined in
5471 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>
5475 <sect2 id="line-pragma">
5476 <title>LINE pragma</title>
5478 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5479 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5480 <para>This pragma is similar to C's <literal>#line</literal>
5481 pragma, and is mainly for use in automatically generated Haskell
5482 code. It lets you specify the line number and filename of the
5483 original code; for example</para>
5485 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5487 <para>if you'd generated the current file from something called
5488 <filename>Foo.vhs</filename> and this line corresponds to line
5489 42 in the original. GHC will adjust its error messages to refer
5490 to the line/file named in the <literal>LINE</literal>
5494 <sect2 id="options-pragma">
5495 <title>OPTIONS_GHC pragma</title>
5496 <indexterm><primary>OPTIONS_GHC</primary>
5498 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5501 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5502 additional options that are given to the compiler when compiling
5503 this source file. See <xref linkend="source-file-options"/> for
5506 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5507 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5511 <title>RULES pragma</title>
5513 <para>The RULES pragma lets you specify rewrite rules. It is
5514 described in <xref linkend="rewrite-rules"/>.</para>
5517 <sect2 id="specialize-pragma">
5518 <title>SPECIALIZE pragma</title>
5520 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5521 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5522 <indexterm><primary>overloading, death to</primary></indexterm>
5524 <para>(UK spelling also accepted.) For key overloaded
5525 functions, you can create extra versions (NB: more code space)
5526 specialised to particular types. Thus, if you have an
5527 overloaded function:</para>
5530 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5533 <para>If it is heavily used on lists with
5534 <literal>Widget</literal> keys, you could specialise it as
5538 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5541 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5542 be put anywhere its type signature could be put.</para>
5544 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5545 (a) a specialised version of the function and (b) a rewrite rule
5546 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5547 un-specialised function into a call to the specialised one.</para>
5549 <para>The type in a SPECIALIZE pragma can be any type that is less
5550 polymorphic than the type of the original function. In concrete terms,
5551 if the original function is <literal>f</literal> then the pragma
5553 {-# SPECIALIZE f :: <type> #-}
5555 is valid if and only if the defintion
5557 f_spec :: <type>
5560 is valid. Here are some examples (where we only give the type signature
5561 for the original function, not its code):
5563 f :: Eq a => a -> b -> b
5564 {-# SPECIALISE f :: Int -> b -> b #-}
5566 g :: (Eq a, Ix b) => a -> b -> b
5567 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5569 h :: Eq a => a -> a -> a
5570 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5572 The last of these examples will generate a
5573 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5574 well. If you use this kind of specialisation, let us know how well it works.
5577 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5578 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5579 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5580 The <literal>INLINE</literal> pragma affects the specialised verison of the
5581 function (only), and applies even if the function is recursive. The motivating
5584 -- A GADT for arrays with type-indexed representation
5586 ArrInt :: !Int -> ByteArray# -> Arr Int
5587 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5589 (!:) :: Arr e -> Int -> e
5590 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5591 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5592 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5593 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5595 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5596 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5597 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5598 the specialised function will be inlined. It has two calls to
5599 <literal>(!:)</literal>,
5600 both at type <literal>Int</literal>. Both these calls fire the first
5601 specialisation, whose body is also inlined. The result is a type-based
5602 unrolling of the indexing function.</para>
5603 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5604 on an ordinarily-recursive function.</para>
5606 <para>Note: In earlier versions of GHC, it was possible to provide your own
5607 specialised function for a given type:
5610 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5613 This feature has been removed, as it is now subsumed by the
5614 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5618 <sect2 id="specialize-instance-pragma">
5619 <title>SPECIALIZE instance pragma
5623 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5624 <indexterm><primary>overloading, death to</primary></indexterm>
5625 Same idea, except for instance declarations. For example:
5628 instance (Eq a) => Eq (Foo a) where {
5629 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5633 The pragma must occur inside the <literal>where</literal> part
5634 of the instance declaration.
5637 Compatible with HBC, by the way, except perhaps in the placement
5643 <sect2 id="unpack-pragma">
5644 <title>UNPACK pragma</title>
5646 <indexterm><primary>UNPACK</primary></indexterm>
5648 <para>The <literal>UNPACK</literal> indicates to the compiler
5649 that it should unpack the contents of a constructor field into
5650 the constructor itself, removing a level of indirection. For
5654 data T = T {-# UNPACK #-} !Float
5655 {-# UNPACK #-} !Float
5658 <para>will create a constructor <literal>T</literal> containing
5659 two unboxed floats. This may not always be an optimisation: if
5660 the <function>T</function> constructor is scrutinised and the
5661 floats passed to a non-strict function for example, they will
5662 have to be reboxed (this is done automatically by the
5665 <para>Unpacking constructor fields should only be used in
5666 conjunction with <option>-O</option>, in order to expose
5667 unfoldings to the compiler so the reboxing can be removed as
5668 often as possible. For example:</para>
5672 f (T f1 f2) = f1 + f2
5675 <para>The compiler will avoid reboxing <function>f1</function>
5676 and <function>f2</function> by inlining <function>+</function>
5677 on floats, but only when <option>-O</option> is on.</para>
5679 <para>Any single-constructor data is eligible for unpacking; for
5683 data T = T {-# UNPACK #-} !(Int,Int)
5686 <para>will store the two <literal>Int</literal>s directly in the
5687 <function>T</function> constructor, by flattening the pair.
5688 Multi-level unpacking is also supported:</para>
5691 data T = T {-# UNPACK #-} !S
5692 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5695 <para>will store two unboxed <literal>Int#</literal>s
5696 directly in the <function>T</function> constructor. The
5697 unpacker can see through newtypes, too.</para>
5699 <para>If a field cannot be unpacked, you will not get a warning,
5700 so it might be an idea to check the generated code with
5701 <option>-ddump-simpl</option>.</para>
5703 <para>See also the <option>-funbox-strict-fields</option> flag,
5704 which essentially has the effect of adding
5705 <literal>{-# UNPACK #-}</literal> to every strict
5706 constructor field.</para>
5711 <!-- ======================= REWRITE RULES ======================== -->
5713 <sect1 id="rewrite-rules">
5714 <title>Rewrite rules
5716 <indexterm><primary>RULES pragma</primary></indexterm>
5717 <indexterm><primary>pragma, RULES</primary></indexterm>
5718 <indexterm><primary>rewrite rules</primary></indexterm></title>
5721 The programmer can specify rewrite rules as part of the source program
5722 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5723 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5724 and (b) the <option>-frules-off</option> flag
5725 (<xref linkend="options-f"/>) is not specified, and (c) the
5726 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5735 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5742 <title>Syntax</title>
5745 From a syntactic point of view:
5751 There may be zero or more rules in a <literal>RULES</literal> pragma.
5758 Each rule has a name, enclosed in double quotes. The name itself has
5759 no significance at all. It is only used when reporting how many times the rule fired.
5765 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5766 immediately after the name of the rule. Thus:
5769 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5772 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5773 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5782 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5783 is set, so you must lay out your rules starting in the same column as the
5784 enclosing definitions.
5791 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5792 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5793 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5794 by spaces, just like in a type <literal>forall</literal>.
5800 A pattern variable may optionally have a type signature.
5801 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5802 For example, here is the <literal>foldr/build</literal> rule:
5805 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5806 foldr k z (build g) = g k z
5809 Since <function>g</function> has a polymorphic type, it must have a type signature.
5816 The left hand side of a rule must consist of a top-level variable applied
5817 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5820 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5821 "wrong2" forall f. f True = True
5824 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5831 A rule does not need to be in the same module as (any of) the
5832 variables it mentions, though of course they need to be in scope.
5838 Rules are automatically exported from a module, just as instance declarations are.
5849 <title>Semantics</title>
5852 From a semantic point of view:
5858 Rules are only applied if you use the <option>-O</option> flag.
5864 Rules are regarded as left-to-right rewrite rules.
5865 When GHC finds an expression that is a substitution instance of the LHS
5866 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5867 By "a substitution instance" we mean that the LHS can be made equal to the
5868 expression by substituting for the pattern variables.
5875 The LHS and RHS of a rule are typechecked, and must have the
5883 GHC makes absolutely no attempt to verify that the LHS and RHS
5884 of a rule have the same meaning. That is undecidable in general, and
5885 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5892 GHC makes no attempt to make sure that the rules are confluent or
5893 terminating. For example:
5896 "loop" forall x,y. f x y = f y x
5899 This rule will cause the compiler to go into an infinite loop.
5906 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5912 GHC currently uses a very simple, syntactic, matching algorithm
5913 for matching a rule LHS with an expression. It seeks a substitution
5914 which makes the LHS and expression syntactically equal modulo alpha
5915 conversion. The pattern (rule), but not the expression, is eta-expanded if
5916 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5917 But not beta conversion (that's called higher-order matching).
5921 Matching is carried out on GHC's intermediate language, which includes
5922 type abstractions and applications. So a rule only matches if the
5923 types match too. See <xref linkend="rule-spec"/> below.
5929 GHC keeps trying to apply the rules as it optimises the program.
5930 For example, consider:
5939 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5940 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5941 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5942 not be substituted, and the rule would not fire.
5949 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5950 that appears on the LHS of a rule</emphasis>, because once you have substituted
5951 for something you can't match against it (given the simple minded
5952 matching). So if you write the rule
5955 "map/map" forall f,g. map f . map g = map (f.g)
5958 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5959 It will only match something written with explicit use of ".".
5960 Well, not quite. It <emphasis>will</emphasis> match the expression
5966 where <function>wibble</function> is defined:
5969 wibble f g = map f . map g
5972 because <function>wibble</function> will be inlined (it's small).
5974 Later on in compilation, GHC starts inlining even things on the
5975 LHS of rules, but still leaves the rules enabled. This inlining
5976 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5983 All rules are implicitly exported from the module, and are therefore
5984 in force in any module that imports the module that defined the rule, directly
5985 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5986 in force when compiling A.) The situation is very similar to that for instance
5998 <title>List fusion</title>
6001 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6002 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6003 intermediate list should be eliminated entirely.
6007 The following are good producers:
6019 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6025 Explicit lists (e.g. <literal>[True, False]</literal>)
6031 The cons constructor (e.g <literal>3:4:[]</literal>)
6037 <function>++</function>
6043 <function>map</function>
6049 <function>take</function>, <function>filter</function>
6055 <function>iterate</function>, <function>repeat</function>
6061 <function>zip</function>, <function>zipWith</function>
6070 The following are good consumers:
6082 <function>array</function> (on its second argument)
6088 <function>++</function> (on its first argument)
6094 <function>foldr</function>
6100 <function>map</function>
6106 <function>take</function>, <function>filter</function>
6112 <function>concat</function>
6118 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6124 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6125 will fuse with one but not the other)
6131 <function>partition</function>
6137 <function>head</function>
6143 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6149 <function>sequence_</function>
6155 <function>msum</function>
6161 <function>sortBy</function>
6170 So, for example, the following should generate no intermediate lists:
6173 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6179 This list could readily be extended; if there are Prelude functions that you use
6180 a lot which are not included, please tell us.
6184 If you want to write your own good consumers or producers, look at the
6185 Prelude definitions of the above functions to see how to do so.
6190 <sect2 id="rule-spec">
6191 <title>Specialisation
6195 Rewrite rules can be used to get the same effect as a feature
6196 present in earlier versions of GHC.
6197 For example, suppose that:
6200 genericLookup :: Ord a => Table a b -> a -> b
6201 intLookup :: Table Int b -> Int -> b
6204 where <function>intLookup</function> is an implementation of
6205 <function>genericLookup</function> that works very fast for
6206 keys of type <literal>Int</literal>. You might wish
6207 to tell GHC to use <function>intLookup</function> instead of
6208 <function>genericLookup</function> whenever the latter was called with
6209 type <literal>Table Int b -> Int -> b</literal>.
6210 It used to be possible to write
6213 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6216 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6219 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6222 This slightly odd-looking rule instructs GHC to replace
6223 <function>genericLookup</function> by <function>intLookup</function>
6224 <emphasis>whenever the types match</emphasis>.
6225 What is more, this rule does not need to be in the same
6226 file as <function>genericLookup</function>, unlike the
6227 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6228 have an original definition available to specialise).
6231 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6232 <function>intLookup</function> really behaves as a specialised version
6233 of <function>genericLookup</function>!!!</para>
6235 <para>An example in which using <literal>RULES</literal> for
6236 specialisation will Win Big:
6239 toDouble :: Real a => a -> Double
6240 toDouble = fromRational . toRational
6242 {-# RULES "toDouble/Int" toDouble = i2d #-}
6243 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6246 The <function>i2d</function> function is virtually one machine
6247 instruction; the default conversion—via an intermediate
6248 <literal>Rational</literal>—is obscenely expensive by
6255 <title>Controlling what's going on</title>
6263 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6269 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6270 If you add <option>-dppr-debug</option> you get a more detailed listing.
6276 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6279 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6280 {-# INLINE build #-}
6284 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6285 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6286 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6287 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6294 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6295 see how to write rules that will do fusion and yet give an efficient
6296 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6306 <sect2 id="core-pragma">
6307 <title>CORE pragma</title>
6309 <indexterm><primary>CORE pragma</primary></indexterm>
6310 <indexterm><primary>pragma, CORE</primary></indexterm>
6311 <indexterm><primary>core, annotation</primary></indexterm>
6314 The external core format supports <quote>Note</quote> annotations;
6315 the <literal>CORE</literal> pragma gives a way to specify what these
6316 should be in your Haskell source code. Syntactically, core
6317 annotations are attached to expressions and take a Haskell string
6318 literal as an argument. The following function definition shows an
6322 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6325 Semantically, this is equivalent to:
6333 However, when external for is generated (via
6334 <option>-fext-core</option>), there will be Notes attached to the
6335 expressions <function>show</function> and <varname>x</varname>.
6336 The core function declaration for <function>f</function> is:
6340 f :: %forall a . GHCziShow.ZCTShow a ->
6341 a -> GHCziBase.ZMZN GHCziBase.Char =
6342 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6344 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6346 (tpl1::GHCziBase.Int ->
6348 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6350 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6351 (tpl3::GHCziBase.ZMZN a ->
6352 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6360 Here, we can see that the function <function>show</function> (which
6361 has been expanded out to a case expression over the Show dictionary)
6362 has a <literal>%note</literal> attached to it, as does the
6363 expression <varname>eta</varname> (which used to be called
6364 <varname>x</varname>).
6371 <sect1 id="special-ids">
6372 <title>Special built-in functions</title>
6373 <para>GHC has a few built-in funcions with special behaviour,
6374 described in this section. All are exported by
6375 <literal>GHC.Exts</literal>.</para>
6377 <sect2> <title>The <literal>seq</literal> function </title>
6379 The function <literal>seq</literal> is as described in the Haskell98 Report.
6383 It evaluates its first argument to head normal form, and then returns its
6384 second argument as the result. The reason that it is documented here is
6385 that, despite <literal>seq</literal>'s polymorphism, its
6386 second argument can have an unboxed type, or
6387 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6388 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6389 to be instantiated to an unboxed type, which is not usually allowed.
6393 <sect2> <title>The <literal>inline</literal> function </title>
6395 The <literal>inline</literal> function is somewhat experimental.
6399 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6400 is inlined, regardless of its size. More precisely, the call
6401 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6403 This allows the programmer to control inlining from
6404 a particular <emphasis>call site</emphasis>
6405 rather than the <emphasis>definition site</emphasis> of the function
6406 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6409 This inlining occurs regardless of the argument to the call
6410 or the size of <literal>f</literal>'s definition; it is unconditional.
6411 The main caveat is that <literal>f</literal>'s definition must be
6412 visible to the compiler. That is, <literal>f</literal> must be
6413 let-bound in the current scope.
6414 If no inlining takes place, the <literal>inline</literal> function
6415 expands to the identity function in Phase zero; so its use imposes
6418 <para> If the function is defined in another
6419 module, GHC only exposes its inlining in the interface file if the
6420 function is sufficiently small that it <emphasis>might</emphasis> be
6421 inlined by the automatic mechanism. There is currently no way to tell
6422 GHC to expose arbitrarily-large functions in the interface file. (This
6423 shortcoming is something that could be fixed, with some kind of pragma.)
6427 <sect2> <title>The <literal>lazy</literal> function </title>
6429 The <literal>lazy</literal> function restrains strictness analysis a little:
6433 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6434 but <literal>lazy</literal> has a magical property so far as strictness
6435 analysis is concerned: it is lazy in its first argument,
6436 even though its semantics is strict. After strictness analysis has run,
6437 calls to <literal>lazy</literal> are inlined to be the identity function.
6440 This behaviour is occasionally useful when controlling evaluation order.
6441 Notably, <literal>lazy</literal> is used in the library definition of
6442 <literal>Control.Parallel.par</literal>:
6445 par x y = case (par# x) of { _ -> lazy y }
6447 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6448 look strict in <literal>y</literal> which would defeat the whole
6449 purpose of <literal>par</literal>.
6452 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6458 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6460 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6461 typechecker entirely. It has type
6463 unsafeCoerce# :: a -> b
6465 That is, it allows you to coerce any type into any other type. If you use this
6466 function, you had better get it right, otherwise segmentation faults await.
6467 It is generally used when you want to write a program that you know is
6468 well-typed, but where Haskell's type system is not expressive enough to prove
6469 that it is well typed.
6472 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6473 although extremely bad things will happen if you coerce a boxed type
6482 <sect1 id="generic-classes">
6483 <title>Generic classes</title>
6486 The ideas behind this extension are described in detail in "Derivable type classes",
6487 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6488 An example will give the idea:
6496 fromBin :: [Int] -> (a, [Int])
6498 toBin {| Unit |} Unit = []
6499 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6500 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6501 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6503 fromBin {| Unit |} bs = (Unit, bs)
6504 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6505 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6506 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6507 (y,bs'') = fromBin bs'
6510 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6511 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6512 which are defined thus in the library module <literal>Generics</literal>:
6516 data a :+: b = Inl a | Inr b
6517 data a :*: b = a :*: b
6520 Now you can make a data type into an instance of Bin like this:
6522 instance (Bin a, Bin b) => Bin (a,b)
6523 instance Bin a => Bin [a]
6525 That is, just leave off the "where" clause. Of course, you can put in the
6526 where clause and over-ride whichever methods you please.
6530 <title> Using generics </title>
6531 <para>To use generics you need to</para>
6534 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6535 <option>-XGenerics</option> (to generate extra per-data-type code),
6536 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6540 <para>Import the module <literal>Generics</literal> from the
6541 <literal>lang</literal> package. This import brings into
6542 scope the data types <literal>Unit</literal>,
6543 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6544 don't need this import if you don't mention these types
6545 explicitly; for example, if you are simply giving instance
6546 declarations.)</para>
6551 <sect2> <title> Changes wrt the paper </title>
6553 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6554 can be written infix (indeed, you can now use
6555 any operator starting in a colon as an infix type constructor). Also note that
6556 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6557 Finally, note that the syntax of the type patterns in the class declaration
6558 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6559 alone would ambiguous when they appear on right hand sides (an extension we
6560 anticipate wanting).
6564 <sect2> <title>Terminology and restrictions</title>
6566 Terminology. A "generic default method" in a class declaration
6567 is one that is defined using type patterns as above.
6568 A "polymorphic default method" is a default method defined as in Haskell 98.
6569 A "generic class declaration" is a class declaration with at least one
6570 generic default method.
6578 Alas, we do not yet implement the stuff about constructor names and
6585 A generic class can have only one parameter; you can't have a generic
6586 multi-parameter class.
6592 A default method must be defined entirely using type patterns, or entirely
6593 without. So this is illegal:
6596 op :: a -> (a, Bool)
6597 op {| Unit |} Unit = (Unit, True)
6600 However it is perfectly OK for some methods of a generic class to have
6601 generic default methods and others to have polymorphic default methods.
6607 The type variable(s) in the type pattern for a generic method declaration
6608 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:
6612 op {| p :*: q |} (x :*: y) = op (x :: p)
6620 The type patterns in a generic default method must take one of the forms:
6626 where "a" and "b" are type variables. Furthermore, all the type patterns for
6627 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6628 must use the same type variables. So this is illegal:
6632 op {| a :+: b |} (Inl x) = True
6633 op {| p :+: q |} (Inr y) = False
6635 The type patterns must be identical, even in equations for different methods of the class.
6636 So this too is illegal:
6640 op1 {| a :*: b |} (x :*: y) = True
6643 op2 {| p :*: q |} (x :*: y) = False
6645 (The reason for this restriction is that we gather all the equations for a particular type consructor
6646 into a single generic instance declaration.)
6652 A generic method declaration must give a case for each of the three type constructors.
6658 The type for a generic method can be built only from:
6660 <listitem> <para> Function arrows </para> </listitem>
6661 <listitem> <para> Type variables </para> </listitem>
6662 <listitem> <para> Tuples </para> </listitem>
6663 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6665 Here are some example type signatures for generic methods:
6668 op2 :: Bool -> (a,Bool)
6669 op3 :: [Int] -> a -> a
6672 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6676 This restriction is an implementation restriction: we just havn't got around to
6677 implementing the necessary bidirectional maps over arbitrary type constructors.
6678 It would be relatively easy to add specific type constructors, such as Maybe and list,
6679 to the ones that are allowed.</para>
6684 In an instance declaration for a generic class, the idea is that the compiler
6685 will fill in the methods for you, based on the generic templates. However it can only
6690 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6695 No constructor of the instance type has unboxed fields.
6699 (Of course, these things can only arise if you are already using GHC extensions.)
6700 However, you can still give an instance declarations for types which break these rules,
6701 provided you give explicit code to override any generic default methods.
6709 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6710 what the compiler does with generic declarations.
6715 <sect2> <title> Another example </title>
6717 Just to finish with, here's another example I rather like:
6721 nCons {| Unit |} _ = 1
6722 nCons {| a :*: b |} _ = 1
6723 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6726 tag {| Unit |} _ = 1
6727 tag {| a :*: b |} _ = 1
6728 tag {| a :+: b |} (Inl x) = tag x
6729 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6735 <sect1 id="monomorphism">
6736 <title>Control over monomorphism</title>
6738 <para>GHC supports two flags that control the way in which generalisation is
6739 carried out at let and where bindings.
6743 <title>Switching off the dreaded Monomorphism Restriction</title>
6744 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
6746 <para>Haskell's monomorphism restriction (see
6747 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6749 of the Haskell Report)
6750 can be completely switched off by
6751 <option>-XNoMonomorphismRestriction</option>.
6756 <title>Monomorphic pattern bindings</title>
6757 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
6758 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
6760 <para> As an experimental change, we are exploring the possibility of
6761 making pattern bindings monomorphic; that is, not generalised at all.
6762 A pattern binding is a binding whose LHS has no function arguments,
6763 and is not a simple variable. For example:
6765 f x = x -- Not a pattern binding
6766 f = \x -> x -- Not a pattern binding
6767 f :: Int -> Int = \x -> x -- Not a pattern binding
6769 (g,h) = e -- A pattern binding
6770 (f) = e -- A pattern binding
6771 [x] = e -- A pattern binding
6773 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6774 default</emphasis>. Use <option>-XMonoPatBinds</option> to recover the
6783 ;;; Local Variables: ***
6785 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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