1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>" or "<option>-X=</option>";
46 e.g. <option>-X=TemplateHaskell</option>. Before anything else is done, the string following
47 "<option>-X</option>" is normalised by removing hyphens and converting
48 to lower case. So <option>-X=TemplateHaskell</option>, <option>-XTemplateHaskell</option>, and
49 <option>-Xtemplate-haskell</option> are all equivalent.
52 <para> All the language options can be turned off by using the prefix "<option>No</option>";
53 e.g. "<option>-X=NoTemplateHaskell</option>".</para>
55 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
56 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
58 <para> All the language options can be introduced with "<option>-f</option>" as well as "<option>-X</option>",
59 but this is a deprecated feature for backward compatibility. Use the "<option>-X</option>"
60 or LANGUAGE-pragma form.</para>
62 <para>Turning on an option that enables special syntax
63 <emphasis>might</emphasis> cause working Haskell 98 code to fail
64 to compile, perhaps because it uses a variable name which has
65 become a reserved word. So, together with each option below, we
66 list the special syntax which is enabled by this option. We use
67 notation and nonterminal names from the Haskell 98 lexical syntax
68 (see the Haskell 98 Report). There are two classes of special
73 <para>New reserved words and symbols: character sequences
74 which are no longer available for use as identifiers in the
78 <para>Other special syntax: sequences of characters that have
79 a different meaning when this particular option is turned
84 <para>We are only listing syntax changes here that might affect
85 existing working programs (i.e. "stolen" syntax). Many of these
86 extensions will also enable new context-free syntax, but in all
87 cases programs written to use the new syntax would not be
88 compilable without the option enabled.</para>
94 <option>-fglasgow-exts</option>:
95 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
98 <para>This simultaneously enables all of the extensions to
99 Haskell 98 described in <xref
100 linkend="ghc-language-features"/>, except where otherwise
101 noted. We are trying to move away from this portmanteau flag,
102 and towards enabling features individaully.</para>
104 <para>New reserved words: <literal>forall</literal> (only in
105 types), <literal>mdo</literal>.</para>
107 <para>Other syntax stolen:
108 <replaceable>varid</replaceable>{<literal>#</literal>},
109 <replaceable>char</replaceable><literal>#</literal>,
110 <replaceable>string</replaceable><literal>#</literal>,
111 <replaceable>integer</replaceable><literal>#</literal>,
112 <replaceable>float</replaceable><literal>#</literal>,
113 <replaceable>float</replaceable><literal>##</literal>,
114 <literal>(#</literal>, <literal>#)</literal>,
115 <literal>|)</literal>, <literal>{|</literal>.</para>
117 <para>Implies these specific language options:
118 <option>-X=ForeignFunctionInterface</option>,
119 <option>-X=ImplicitParams</option>,
120 <option>-X=ScopedTypeVariables</option>,
121 <option>-X=GADTs</option>,
122 <option>-X=TypeFamilies</option>. </para>
128 <option>-X=ffi</option> and <option>-X=ForeignFunctionInterface</option>:
129 <indexterm><primary><option>-X=FFI</option></primary></indexterm>
132 <para>This option enables the language extension defined in the
133 Haskell 98 Foreign Function Interface Addendum.</para>
135 <para>New reserved words: <literal>foreign</literal>.</para>
141 <option>-X=MonomorphismRestriction</option>,<option>-X=MonoPatBinds</option>:
144 <para> These two flags control how generalisation is done.
145 See <xref linkend="monomorphism"/>.
152 <option>-X=ExtendedDefaultRules</option>:
153 <indexterm><primary><option>-X=ExtendedDefaultRules</option></primary></indexterm>
156 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
157 Independent of the <option>-fglasgow-exts</option>
164 <option>-X=AllowOverlappingInstances</option>
165 <indexterm><primary><option>-X=AllowOverlappingInstances</option></primary></indexterm>
168 <option>-X=AllowUndecidableInstances</option>
169 <indexterm><primary><option>-X=AllowUndecidableInstances</option></primary></indexterm>
172 <option>-X=AllowIncoherentInstances</option>
173 <indexterm><primary><option>-X=AllowIncoherentInstances</option></primary></indexterm>
176 <option>-fcontext-stack=N</option>
177 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
180 <para> See <xref linkend="instance-decls"/>. Only relevant
181 if you also use <option>-fglasgow-exts</option>.</para>
187 <option>-finline-phase</option>
188 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
191 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
192 you also use <option>-fglasgow-exts</option>.</para>
198 <option>-X=Arrows</option>
199 <indexterm><primary><option>-X=Arrows</option></primary></indexterm>
202 <para>See <xref linkend="arrow-notation"/>. Independent of
203 <option>-fglasgow-exts</option>.</para>
205 <para>New reserved words/symbols: <literal>rec</literal>,
206 <literal>proc</literal>, <literal>-<</literal>,
207 <literal>>-</literal>, <literal>-<<</literal>,
208 <literal>>>-</literal>.</para>
210 <para>Other syntax stolen: <literal>(|</literal>,
211 <literal>|)</literal>.</para>
217 <option>-X=Generics</option>
218 <indexterm><primary><option>-X=Generics</option></primary></indexterm>
221 <para>See <xref linkend="generic-classes"/>. Independent of
222 <option>-fglasgow-exts</option>.</para>
227 <term><option>-X=NoImplicitIrelude</option></term>
229 <para><indexterm><primary>-XnoImplicitPrelude
230 option</primary></indexterm> GHC normally imports
231 <filename>Prelude.hi</filename> files for you. If you'd
232 rather it didn't, then give it a
233 <option>-XnoImplicitPrelude</option> option. The idea is
234 that you can then import a Prelude of your own. (But don't
235 call it <literal>Prelude</literal>; the Haskell module
236 namespace is flat, and you must not conflict with any
237 Prelude module.)</para>
239 <para>Even though you have not imported the Prelude, most of
240 the built-in syntax still refers to the built-in Haskell
241 Prelude types and values, as specified by the Haskell
242 Report. For example, the type <literal>[Int]</literal>
243 still means <literal>Prelude.[] Int</literal>; tuples
244 continue to refer to the standard Prelude tuples; the
245 translation for list comprehensions continues to use
246 <literal>Prelude.map</literal> etc.</para>
248 <para>However, <option>-X=NoImplicitPrelude</option> does
249 change the handling of certain built-in syntax: see <xref
250 linkend="rebindable-syntax"/>.</para>
255 <term><option>-X=ImplicitParams</option></term>
257 <para>Enables implicit parameters (see <xref
258 linkend="implicit-parameters"/>). Currently also implied by
259 <option>-fglasgow-exts</option>.</para>
262 <literal>?<replaceable>varid</replaceable></literal>,
263 <literal>%<replaceable>varid</replaceable></literal>.</para>
268 <term><option>-X=OverloadedStrings</option></term>
270 <para>Enables overloaded string literals (see <xref
271 linkend="overloaded-strings"/>).</para>
276 <term><option>-X=ScopedTypeVariables</option></term>
278 <para>Enables lexically-scoped type variables (see <xref
279 linkend="scoped-type-variables"/>). Implied by
280 <option>-fglasgow-exts</option>.</para>
285 <term><option>-X=TH</option>, <option>-X=TemplateHaskell</option></term>
287 <para>Enables Template Haskell (see <xref
288 linkend="template-haskell"/>). This flag must
289 be given explicitly; it is no longer implied by
290 <option>-fglasgow-exts</option>.</para>
292 <para>Syntax stolen: <literal>[|</literal>,
293 <literal>[e|</literal>, <literal>[p|</literal>,
294 <literal>[d|</literal>, <literal>[t|</literal>,
295 <literal>$(</literal>,
296 <literal>$<replaceable>varid</replaceable></literal>.</para>
303 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
304 <sect1 id="primitives">
305 <title>Unboxed types and primitive operations</title>
307 <para>GHC is built on a raft of primitive data types and operations.
308 While you really can use this stuff to write fast code,
309 we generally find it a lot less painful, and more satisfying in the
310 long run, to use higher-level language features and libraries. With
311 any luck, the code you write will be optimised to the efficient
312 unboxed version in any case. And if it isn't, we'd like to know
315 <para>We do not currently have good, up-to-date documentation about the
316 primitives, perhaps because they are mainly intended for internal use.
317 There used to be a long section about them here in the User Guide, but it
318 became out of date, and wrong information is worse than none.</para>
320 <para>The Real Truth about what primitive types there are, and what operations
321 work over those types, is held in the file
322 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
323 This file is used directly to generate GHC's primitive-operation definitions, so
324 it is always correct! It is also intended for processing into text.</para>
327 the result of such processing is part of the description of the
329 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
330 Core language</ulink>.
331 So that document is a good place to look for a type-set version.
332 We would be very happy if someone wanted to volunteer to produce an SGML
333 back end to the program that processes <filename>primops.txt</filename> so that
334 we could include the results here in the User Guide.</para>
336 <para>What follows here is a brief summary of some main points.</para>
338 <sect2 id="glasgow-unboxed">
343 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
346 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
347 that values of that type are represented by a pointer to a heap
348 object. The representation of a Haskell <literal>Int</literal>, for
349 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
350 type, however, is represented by the value itself, no pointers or heap
351 allocation are involved.
355 Unboxed types correspond to the “raw machine” types you
356 would use in C: <literal>Int#</literal> (long int),
357 <literal>Double#</literal> (double), <literal>Addr#</literal>
358 (void *), etc. The <emphasis>primitive operations</emphasis>
359 (PrimOps) on these types are what you might expect; e.g.,
360 <literal>(+#)</literal> is addition on
361 <literal>Int#</literal>s, and is the machine-addition that we all
362 know and love—usually one instruction.
366 Primitive (unboxed) types cannot be defined in Haskell, and are
367 therefore built into the language and compiler. Primitive types are
368 always unlifted; that is, a value of a primitive type cannot be
369 bottom. We use the convention that primitive types, values, and
370 operations have a <literal>#</literal> suffix.
374 Primitive values are often represented by a simple bit-pattern, such
375 as <literal>Int#</literal>, <literal>Float#</literal>,
376 <literal>Double#</literal>. But this is not necessarily the case:
377 a primitive value might be represented by a pointer to a
378 heap-allocated object. Examples include
379 <literal>Array#</literal>, the type of primitive arrays. A
380 primitive array is heap-allocated because it is too big a value to fit
381 in a register, and would be too expensive to copy around; in a sense,
382 it is accidental that it is represented by a pointer. If a pointer
383 represents a primitive value, then it really does point to that value:
384 no unevaluated thunks, no indirections…nothing can be at the
385 other end of the pointer than the primitive value.
386 A numerically-intensive program using unboxed types can
387 go a <emphasis>lot</emphasis> faster than its “standard”
388 counterpart—we saw a threefold speedup on one example.
392 There are some restrictions on the use of primitive types:
394 <listitem><para>The main restriction
395 is that you can't pass a primitive value to a polymorphic
396 function or store one in a polymorphic data type. This rules out
397 things like <literal>[Int#]</literal> (i.e. lists of primitive
398 integers). The reason for this restriction is that polymorphic
399 arguments and constructor fields are assumed to be pointers: if an
400 unboxed integer is stored in one of these, the garbage collector would
401 attempt to follow it, leading to unpredictable space leaks. Or a
402 <function>seq</function> operation on the polymorphic component may
403 attempt to dereference the pointer, with disastrous results. Even
404 worse, the unboxed value might be larger than a pointer
405 (<literal>Double#</literal> for instance).
408 <listitem><para> You cannot define a newtype whose representation type
409 (the argument type of the data constructor) is an unboxed type. Thus,
415 <listitem><para> You cannot bind a variable with an unboxed type
416 in a <emphasis>top-level</emphasis> binding.
418 <listitem><para> You cannot bind a variable with an unboxed type
419 in a <emphasis>recursive</emphasis> binding.
421 <listitem><para> You may bind unboxed variables in a (non-recursive,
422 non-top-level) pattern binding, but any such variable causes the entire
424 to become strict. For example:
426 data Foo = Foo Int Int#
428 f x = let (Foo a b, w) = ..rhs.. in ..body..
430 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
432 is strict, and the program behaves as if you had written
434 data Foo = Foo Int Int#
436 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
445 <sect2 id="unboxed-tuples">
446 <title>Unboxed Tuples
450 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
451 they're available by default with <option>-fglasgow-exts</option>. An
452 unboxed tuple looks like this:
464 where <literal>e_1..e_n</literal> are expressions of any
465 type (primitive or non-primitive). The type of an unboxed tuple looks
470 Unboxed tuples are used for functions that need to return multiple
471 values, but they avoid the heap allocation normally associated with
472 using fully-fledged tuples. When an unboxed tuple is returned, the
473 components are put directly into registers or on the stack; the
474 unboxed tuple itself does not have a composite representation. Many
475 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
477 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
478 tuples to avoid unnecessary allocation during sequences of operations.
482 There are some pretty stringent restrictions on the use of unboxed tuples:
487 Values of unboxed tuple types are subject to the same restrictions as
488 other unboxed types; i.e. they may not be stored in polymorphic data
489 structures or passed to polymorphic functions.
496 No variable can have an unboxed tuple type, nor may a constructor or function
497 argument have an unboxed tuple type. The following are all illegal:
501 data Foo = Foo (# Int, Int #)
503 f :: (# Int, Int #) -> (# Int, Int #)
506 g :: (# Int, Int #) -> Int
509 h x = let y = (# x,x #) in ...
516 The typical use of unboxed tuples is simply to return multiple values,
517 binding those multiple results with a <literal>case</literal> expression, thus:
519 f x y = (# x+1, y-1 #)
520 g x = case f x x of { (# a, b #) -> a + b }
522 You can have an unboxed tuple in a pattern binding, thus
524 f x = let (# p,q #) = h x in ..body..
526 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
527 the resulting binding is lazy like any other Haskell pattern binding. The
528 above example desugars like this:
530 f x = let t = case h x o f{ (# p,q #) -> (p,q)
535 Indeed, the bindings can even be recursive.
542 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
544 <sect1 id="syntax-extns">
545 <title>Syntactic extensions</title>
547 <!-- ====================== HIERARCHICAL MODULES ======================= -->
549 <sect2 id="hierarchical-modules">
550 <title>Hierarchical Modules</title>
552 <para>GHC supports a small extension to the syntax of module
553 names: a module name is allowed to contain a dot
554 <literal>‘.’</literal>. This is also known as the
555 “hierarchical module namespace” extension, because
556 it extends the normally flat Haskell module namespace into a
557 more flexible hierarchy of modules.</para>
559 <para>This extension has very little impact on the language
560 itself; modules names are <emphasis>always</emphasis> fully
561 qualified, so you can just think of the fully qualified module
562 name as <quote>the module name</quote>. In particular, this
563 means that the full module name must be given after the
564 <literal>module</literal> keyword at the beginning of the
565 module; for example, the module <literal>A.B.C</literal> must
568 <programlisting>module A.B.C</programlisting>
571 <para>It is a common strategy to use the <literal>as</literal>
572 keyword to save some typing when using qualified names with
573 hierarchical modules. For example:</para>
576 import qualified Control.Monad.ST.Strict as ST
579 <para>For details on how GHC searches for source and interface
580 files in the presence of hierarchical modules, see <xref
581 linkend="search-path"/>.</para>
583 <para>GHC comes with a large collection of libraries arranged
584 hierarchically; see the accompanying <ulink
585 url="../libraries/index.html">library
586 documentation</ulink>. More libraries to install are available
588 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
591 <!-- ====================== PATTERN GUARDS ======================= -->
593 <sect2 id="pattern-guards">
594 <title>Pattern guards</title>
597 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
598 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
602 Suppose we have an abstract data type of finite maps, with a
606 lookup :: FiniteMap -> Int -> Maybe Int
609 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
610 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
614 clunky env var1 var2 | ok1 && ok2 = val1 + val2
615 | otherwise = var1 + var2
626 The auxiliary functions are
630 maybeToBool :: Maybe a -> Bool
631 maybeToBool (Just x) = True
632 maybeToBool Nothing = False
634 expectJust :: Maybe a -> a
635 expectJust (Just x) = x
636 expectJust Nothing = error "Unexpected Nothing"
640 What is <function>clunky</function> doing? The guard <literal>ok1 &&
641 ok2</literal> checks that both lookups succeed, using
642 <function>maybeToBool</function> to convert the <function>Maybe</function>
643 types to booleans. The (lazily evaluated) <function>expectJust</function>
644 calls extract the values from the results of the lookups, and binds the
645 returned values to <varname>val1</varname> and <varname>val2</varname>
646 respectively. If either lookup fails, then clunky takes the
647 <literal>otherwise</literal> case and returns the sum of its arguments.
651 This is certainly legal Haskell, but it is a tremendously verbose and
652 un-obvious way to achieve the desired effect. Arguably, a more direct way
653 to write clunky would be to use case expressions:
657 clunky env var1 var2 = case lookup env var1 of
659 Just val1 -> case lookup env var2 of
661 Just val2 -> val1 + val2
667 This is a bit shorter, but hardly better. Of course, we can rewrite any set
668 of pattern-matching, guarded equations as case expressions; that is
669 precisely what the compiler does when compiling equations! The reason that
670 Haskell provides guarded equations is because they allow us to write down
671 the cases we want to consider, one at a time, independently of each other.
672 This structure is hidden in the case version. Two of the right-hand sides
673 are really the same (<function>fail</function>), and the whole expression
674 tends to become more and more indented.
678 Here is how I would write clunky:
683 | Just val1 <- lookup env var1
684 , Just val2 <- lookup env var2
686 ...other equations for clunky...
690 The semantics should be clear enough. The qualifiers are matched in order.
691 For a <literal><-</literal> qualifier, which I call a pattern guard, the
692 right hand side is evaluated and matched against the pattern on the left.
693 If the match fails then the whole guard fails and the next equation is
694 tried. If it succeeds, then the appropriate binding takes place, and the
695 next qualifier is matched, in the augmented environment. Unlike list
696 comprehensions, however, the type of the expression to the right of the
697 <literal><-</literal> is the same as the type of the pattern to its
698 left. The bindings introduced by pattern guards scope over all the
699 remaining guard qualifiers, and over the right hand side of the equation.
703 Just as with list comprehensions, boolean expressions can be freely mixed
704 with among the pattern guards. For example:
715 Haskell's current guards therefore emerge as a special case, in which the
716 qualifier list has just one element, a boolean expression.
720 <!-- ===================== Recursive do-notation =================== -->
722 <sect2 id="mdo-notation">
723 <title>The recursive do-notation
726 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
727 "A recursive do for Haskell",
728 Levent Erkok, John Launchbury",
729 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
732 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
733 that is, the variables bound in a do-expression are visible only in the textually following
734 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
735 group. It turns out that several applications can benefit from recursive bindings in
736 the do-notation, and this extension provides the necessary syntactic support.
739 Here is a simple (yet contrived) example:
742 import Control.Monad.Fix
744 justOnes = mdo xs <- Just (1:xs)
748 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
752 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
755 class Monad m => MonadFix m where
756 mfix :: (a -> m a) -> m a
759 The function <literal>mfix</literal>
760 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
761 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
762 For details, see the above mentioned reference.
765 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
766 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
767 for Haskell's internal state monad (strict and lazy, respectively).
770 There are three important points in using the recursive-do notation:
773 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
774 than <literal>do</literal>).
778 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
784 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
785 contains up to date information on recursive monadic bindings.
789 Historical note: The old implementation of the mdo-notation (and most
790 of the existing documents) used the name
791 <literal>MonadRec</literal> for the class and the corresponding library.
792 This name is not supported by GHC.
798 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
800 <sect2 id="parallel-list-comprehensions">
801 <title>Parallel List Comprehensions</title>
802 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
804 <indexterm><primary>parallel list comprehensions</primary>
807 <para>Parallel list comprehensions are a natural extension to list
808 comprehensions. List comprehensions can be thought of as a nice
809 syntax for writing maps and filters. Parallel comprehensions
810 extend this to include the zipWith family.</para>
812 <para>A parallel list comprehension has multiple independent
813 branches of qualifier lists, each separated by a `|' symbol. For
814 example, the following zips together two lists:</para>
817 [ (x, y) | x <- xs | y <- ys ]
820 <para>The behavior of parallel list comprehensions follows that of
821 zip, in that the resulting list will have the same length as the
822 shortest branch.</para>
824 <para>We can define parallel list comprehensions by translation to
825 regular comprehensions. Here's the basic idea:</para>
827 <para>Given a parallel comprehension of the form: </para>
830 [ e | p1 <- e11, p2 <- e12, ...
831 | q1 <- e21, q2 <- e22, ...
836 <para>This will be translated to: </para>
839 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
840 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
845 <para>where `zipN' is the appropriate zip for the given number of
850 <sect2 id="rebindable-syntax">
851 <title>Rebindable syntax</title>
854 <para>GHC allows most kinds of built-in syntax to be rebound by
855 the user, to facilitate replacing the <literal>Prelude</literal>
856 with a home-grown version, for example.</para>
858 <para>You may want to define your own numeric class
859 hierarchy. It completely defeats that purpose if the
860 literal "1" means "<literal>Prelude.fromInteger
861 1</literal>", which is what the Haskell Report specifies.
862 So the <option>-X=NoImplicitPrelude</option> flag causes
863 the following pieces of built-in syntax to refer to
864 <emphasis>whatever is in scope</emphasis>, not the Prelude
869 <para>An integer literal <literal>368</literal> means
870 "<literal>fromInteger (368::Integer)</literal>", rather than
871 "<literal>Prelude.fromInteger (368::Integer)</literal>".
874 <listitem><para>Fractional literals are handed in just the same way,
875 except that the translation is
876 <literal>fromRational (3.68::Rational)</literal>.
879 <listitem><para>The equality test in an overloaded numeric pattern
880 uses whatever <literal>(==)</literal> is in scope.
883 <listitem><para>The subtraction operation, and the
884 greater-than-or-equal test, in <literal>n+k</literal> patterns
885 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
889 <para>Negation (e.g. "<literal>- (f x)</literal>")
890 means "<literal>negate (f x)</literal>", both in numeric
891 patterns, and expressions.
895 <para>"Do" notation is translated using whatever
896 functions <literal>(>>=)</literal>,
897 <literal>(>>)</literal>, and <literal>fail</literal>,
898 are in scope (not the Prelude
899 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
900 comprehensions, are unaffected. </para></listitem>
904 notation (see <xref linkend="arrow-notation"/>)
905 uses whatever <literal>arr</literal>,
906 <literal>(>>>)</literal>, <literal>first</literal>,
907 <literal>app</literal>, <literal>(|||)</literal> and
908 <literal>loop</literal> functions are in scope. But unlike the
909 other constructs, the types of these functions must match the
910 Prelude types very closely. Details are in flux; if you want
914 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
915 even if that is a little unexpected. For emample, the
916 static semantics of the literal <literal>368</literal>
917 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
918 <literal>fromInteger</literal> to have any of the types:
920 fromInteger :: Integer -> Integer
921 fromInteger :: forall a. Foo a => Integer -> a
922 fromInteger :: Num a => a -> Integer
923 fromInteger :: Integer -> Bool -> Bool
927 <para>Be warned: this is an experimental facility, with
928 fewer checks than usual. Use <literal>-dcore-lint</literal>
929 to typecheck the desugared program. If Core Lint is happy
930 you should be all right.</para>
934 <sect2 id="postfix-operators">
935 <title>Postfix operators</title>
938 GHC allows a small extension to the syntax of left operator sections, which
939 allows you to define postfix operators. The extension is this: the left section
943 is equivalent (from the point of view of both type checking and execution) to the expression
947 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
948 The strict Haskell 98 interpretation is that the section is equivalent to
952 That is, the operator must be a function of two arguments. GHC allows it to
953 take only one argument, and that in turn allows you to write the function
956 <para>Since this extension goes beyond Haskell 98, it should really be enabled
957 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
958 change their behaviour, of course.)
960 <para>The extension does not extend to the left-hand side of function
961 definitions; you must define such a function in prefix form.</para>
968 <!-- TYPE SYSTEM EXTENSIONS -->
969 <sect1 id="data-type-extensions">
970 <title>Extensions to data types and type synonyms</title>
972 <sect2 id="nullary-types">
973 <title>Data types with no constructors</title>
975 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
976 a data type with no constructors. For example:</para>
980 data T a -- T :: * -> *
983 <para>Syntactically, the declaration lacks the "= constrs" part. The
984 type can be parameterised over types of any kind, but if the kind is
985 not <literal>*</literal> then an explicit kind annotation must be used
986 (see <xref linkend="kinding"/>).</para>
988 <para>Such data types have only one value, namely bottom.
989 Nevertheless, they can be useful when defining "phantom types".</para>
992 <sect2 id="infix-tycons">
993 <title>Infix type constructors, classes, and type variables</title>
996 GHC allows type constructors, classes, and type variables to be operators, and
997 to be written infix, very much like expressions. More specifically:
1000 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1001 The lexical syntax is the same as that for data constructors.
1004 Data type and type-synonym declarations can be written infix, parenthesised
1005 if you want further arguments. E.g.
1007 data a :*: b = Foo a b
1008 type a :+: b = Either a b
1009 class a :=: b where ...
1011 data (a :**: b) x = Baz a b x
1012 type (a :++: b) y = Either (a,b) y
1016 Types, and class constraints, can be written infix. For example
1019 f :: (a :=: b) => a -> b
1023 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1024 The lexical syntax is the same as that for variable operators, excluding "(.)",
1025 "(!)", and "(*)". In a binding position, the operator must be
1026 parenthesised. For example:
1028 type T (+) = Int + Int
1032 liftA2 :: Arrow (~>)
1033 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1039 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1040 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1043 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1044 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1045 sets the fixity for a data constructor and the corresponding type constructor. For example:
1049 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1050 and similarly for <literal>:*:</literal>.
1051 <literal>Int `a` Bool</literal>.
1054 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1061 <sect2 id="type-synonyms">
1062 <title>Liberalised type synonyms</title>
1065 Type synonyms are like macros at the type level, and
1066 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1067 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1069 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1070 in a type synonym, thus:
1072 type Discard a = forall b. Show b => a -> b -> (a, String)
1077 g :: Discard Int -> (Int,String) -- A rank-2 type
1084 You can write an unboxed tuple in a type synonym:
1086 type Pr = (# Int, Int #)
1094 You can apply a type synonym to a forall type:
1096 type Foo a = a -> a -> Bool
1098 f :: Foo (forall b. b->b)
1100 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1102 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1107 You can apply a type synonym to a partially applied type synonym:
1109 type Generic i o = forall x. i x -> o x
1112 foo :: Generic Id []
1114 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1116 foo :: forall x. x -> [x]
1124 GHC currently does kind checking before expanding synonyms (though even that
1128 After expanding type synonyms, GHC does validity checking on types, looking for
1129 the following mal-formedness which isn't detected simply by kind checking:
1132 Type constructor applied to a type involving for-alls.
1135 Unboxed tuple on left of an arrow.
1138 Partially-applied type synonym.
1142 this will be rejected:
1144 type Pr = (# Int, Int #)
1149 because GHC does not allow unboxed tuples on the left of a function arrow.
1154 <sect2 id="existential-quantification">
1155 <title>Existentially quantified data constructors
1159 The idea of using existential quantification in data type declarations
1160 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1161 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1162 London, 1991). It was later formalised by Laufer and Odersky
1163 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1164 TOPLAS, 16(5), pp1411-1430, 1994).
1165 It's been in Lennart
1166 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1167 proved very useful. Here's the idea. Consider the declaration:
1173 data Foo = forall a. MkFoo a (a -> Bool)
1180 The data type <literal>Foo</literal> has two constructors with types:
1186 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1193 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1194 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1195 For example, the following expression is fine:
1201 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1207 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1208 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1209 isUpper</function> packages a character with a compatible function. These
1210 two things are each of type <literal>Foo</literal> and can be put in a list.
1214 What can we do with a value of type <literal>Foo</literal>?. In particular,
1215 what happens when we pattern-match on <function>MkFoo</function>?
1221 f (MkFoo val fn) = ???
1227 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1228 are compatible, the only (useful) thing we can do with them is to
1229 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1236 f (MkFoo val fn) = fn val
1242 What this allows us to do is to package heterogenous values
1243 together with a bunch of functions that manipulate them, and then treat
1244 that collection of packages in a uniform manner. You can express
1245 quite a bit of object-oriented-like programming this way.
1248 <sect3 id="existential">
1249 <title>Why existential?
1253 What has this to do with <emphasis>existential</emphasis> quantification?
1254 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1260 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1266 But Haskell programmers can safely think of the ordinary
1267 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1268 adding a new existential quantification construct.
1274 <title>Type classes</title>
1277 An easy extension is to allow
1278 arbitrary contexts before the constructor. For example:
1284 data Baz = forall a. Eq a => Baz1 a a
1285 | forall b. Show b => Baz2 b (b -> b)
1291 The two constructors have the types you'd expect:
1297 Baz1 :: forall a. Eq a => a -> a -> Baz
1298 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1304 But when pattern matching on <function>Baz1</function> the matched values can be compared
1305 for equality, and when pattern matching on <function>Baz2</function> the first matched
1306 value can be converted to a string (as well as applying the function to it).
1307 So this program is legal:
1314 f (Baz1 p q) | p == q = "Yes"
1316 f (Baz2 v fn) = show (fn v)
1322 Operationally, in a dictionary-passing implementation, the
1323 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1324 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1325 extract it on pattern matching.
1329 Notice the way that the syntax fits smoothly with that used for
1330 universal quantification earlier.
1335 <sect3 id="existential-records">
1336 <title>Record Constructors</title>
1339 GHC allows existentials to be used with records syntax as well. For example:
1342 data Counter a = forall self. NewCounter
1344 , _inc :: self -> self
1345 , _display :: self -> IO ()
1349 Here <literal>tag</literal> is a public field, with a well-typed selector
1350 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1351 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1352 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1353 compile-time error. In other words, <emphasis>GHC defines a record selector function
1354 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1355 (This example used an underscore in the fields for which record selectors
1356 will not be defined, but that is only programming style; GHC ignores them.)
1360 To make use of these hidden fields, we need to create some helper functions:
1363 inc :: Counter a -> Counter a
1364 inc (NewCounter x i d t) = NewCounter
1365 { _this = i x, _inc = i, _display = d, tag = t }
1367 display :: Counter a -> IO ()
1368 display NewCounter{ _this = x, _display = d } = d x
1371 Now we can define counters with different underlying implementations:
1374 counterA :: Counter String
1375 counterA = NewCounter
1376 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1378 counterB :: Counter String
1379 counterB = NewCounter
1380 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1383 display (inc counterA) -- prints "1"
1384 display (inc (inc counterB)) -- prints "##"
1387 At the moment, record update syntax is only supported for Haskell 98 data types,
1388 so the following function does <emphasis>not</emphasis> work:
1391 -- This is invalid; use explicit NewCounter instead for now
1392 setTag :: Counter a -> a -> Counter a
1393 setTag obj t = obj{ tag = t }
1402 <title>Restrictions</title>
1405 There are several restrictions on the ways in which existentially-quantified
1406 constructors can be use.
1415 When pattern matching, each pattern match introduces a new,
1416 distinct, type for each existential type variable. These types cannot
1417 be unified with any other type, nor can they escape from the scope of
1418 the pattern match. For example, these fragments are incorrect:
1426 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1427 is the result of <function>f1</function>. One way to see why this is wrong is to
1428 ask what type <function>f1</function> has:
1432 f1 :: Foo -> a -- Weird!
1436 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1441 f1 :: forall a. Foo -> a -- Wrong!
1445 The original program is just plain wrong. Here's another sort of error
1449 f2 (Baz1 a b) (Baz1 p q) = a==q
1453 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1454 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1455 from the two <function>Baz1</function> constructors.
1463 You can't pattern-match on an existentially quantified
1464 constructor in a <literal>let</literal> or <literal>where</literal> group of
1465 bindings. So this is illegal:
1469 f3 x = a==b where { Baz1 a b = x }
1472 Instead, use a <literal>case</literal> expression:
1475 f3 x = case x of Baz1 a b -> a==b
1478 In general, you can only pattern-match
1479 on an existentially-quantified constructor in a <literal>case</literal> expression or
1480 in the patterns of a function definition.
1482 The reason for this restriction is really an implementation one.
1483 Type-checking binding groups is already a nightmare without
1484 existentials complicating the picture. Also an existential pattern
1485 binding at the top level of a module doesn't make sense, because it's
1486 not clear how to prevent the existentially-quantified type "escaping".
1487 So for now, there's a simple-to-state restriction. We'll see how
1495 You can't use existential quantification for <literal>newtype</literal>
1496 declarations. So this is illegal:
1500 newtype T = forall a. Ord a => MkT a
1504 Reason: a value of type <literal>T</literal> must be represented as a
1505 pair of a dictionary for <literal>Ord t</literal> and a value of type
1506 <literal>t</literal>. That contradicts the idea that
1507 <literal>newtype</literal> should have no concrete representation.
1508 You can get just the same efficiency and effect by using
1509 <literal>data</literal> instead of <literal>newtype</literal>. If
1510 there is no overloading involved, then there is more of a case for
1511 allowing an existentially-quantified <literal>newtype</literal>,
1512 because the <literal>data</literal> version does carry an
1513 implementation cost, but single-field existentially quantified
1514 constructors aren't much use. So the simple restriction (no
1515 existential stuff on <literal>newtype</literal>) stands, unless there
1516 are convincing reasons to change it.
1524 You can't use <literal>deriving</literal> to define instances of a
1525 data type with existentially quantified data constructors.
1527 Reason: in most cases it would not make sense. For example:;
1530 data T = forall a. MkT [a] deriving( Eq )
1533 To derive <literal>Eq</literal> in the standard way we would need to have equality
1534 between the single component of two <function>MkT</function> constructors:
1538 (MkT a) == (MkT b) = ???
1541 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1542 It's just about possible to imagine examples in which the derived instance
1543 would make sense, but it seems altogether simpler simply to prohibit such
1544 declarations. Define your own instances!
1555 <!-- ====================== Generalised algebraic data types ======================= -->
1557 <sect2 id="gadt-style">
1558 <title>Declaring data types with explicit constructor signatures</title>
1560 <para>GHC allows you to declare an algebraic data type by
1561 giving the type signatures of constructors explicitly. For example:
1565 Just :: a -> Maybe a
1567 The form is called a "GADT-style declaration"
1568 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1569 can only be declared using this form.</para>
1570 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1571 For example, these two declarations are equivalent:
1573 data Foo = forall a. MkFoo a (a -> Bool)
1574 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1577 <para>Any data type that can be declared in standard Haskell-98 syntax
1578 can also be declared using GADT-style syntax.
1579 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1580 they treat class constraints on the data constructors differently.
1581 Specifically, if the constructor is given a type-class context, that
1582 context is made available by pattern matching. For example:
1585 MkSet :: Eq a => [a] -> Set a
1587 makeSet :: Eq a => [a] -> Set a
1588 makeSet xs = MkSet (nub xs)
1590 insert :: a -> Set a -> Set a
1591 insert a (MkSet as) | a `elem` as = MkSet as
1592 | otherwise = MkSet (a:as)
1594 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1595 gives rise to a <literal>(Eq a)</literal>
1596 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1597 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1598 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1599 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1600 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1601 In the example, the equality dictionary is used to satisfy the equality constraint
1602 generated by the call to <literal>elem</literal>, so that the type of
1603 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1605 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1606 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1607 In Haskell 98 the defintion
1609 data Eq a => Set' a = MkSet' [a]
1611 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1612 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1613 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1614 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1615 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1617 For example, a possible application of GHC's behaviour is to reify dictionaries:
1619 data NumInst a where
1620 MkNumInst :: Num a => NumInst a
1622 intInst :: NumInst Int
1625 plus :: NumInst a -> a -> a -> a
1626 plus MkNumInst p q = p + q
1628 Here, a value of type <literal>NumInst a</literal> is equivalent
1629 to an explicit <literal>(Num a)</literal> dictionary.
1633 The rest of this section gives further details about GADT-style data
1638 The result type of each data constructor must begin with the type constructor being defined.
1639 If the result type of all constructors
1640 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1641 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1642 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1646 The type signature of
1647 each constructor is independent, and is implicitly universally quantified as usual.
1648 Different constructors may have different universally-quantified type variables
1649 and different type-class constraints.
1650 For example, this is fine:
1653 T1 :: Eq b => b -> T b
1654 T2 :: (Show c, Ix c) => c -> [c] -> T c
1659 Unlike a Haskell-98-style
1660 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1661 have no scope. Indeed, one can write a kind signature instead:
1663 data Set :: * -> * where ...
1665 or even a mixture of the two:
1667 data Foo a :: (* -> *) -> * where ...
1669 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1672 data Foo a (b :: * -> *) where ...
1678 You can use strictness annotations, in the obvious places
1679 in the constructor type:
1682 Lit :: !Int -> Term Int
1683 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1684 Pair :: Term a -> Term b -> Term (a,b)
1689 You can use a <literal>deriving</literal> clause on a GADT-style data type
1690 declaration. For example, these two declarations are equivalent
1692 data Maybe1 a where {
1693 Nothing1 :: Maybe1 a ;
1694 Just1 :: a -> Maybe1 a
1695 } deriving( Eq, Ord )
1697 data Maybe2 a = Nothing2 | Just2 a
1703 You can use record syntax on a GADT-style data type declaration:
1707 Adult { name :: String, children :: [Person] } :: Person
1708 Child { name :: String } :: Person
1710 As usual, for every constructor that has a field <literal>f</literal>, the type of
1711 field <literal>f</literal> must be the same (modulo alpha conversion).
1714 At the moment, record updates are not yet possible with GADT-style declarations,
1715 so support is limited to record construction, selection and pattern matching.
1718 aPerson = Adult { name = "Fred", children = [] }
1720 shortName :: Person -> Bool
1721 hasChildren (Adult { children = kids }) = not (null kids)
1722 hasChildren (Child {}) = False
1727 As in the case of existentials declared using the Haskell-98-like record syntax
1728 (<xref linkend="existential-records"/>),
1729 record-selector functions are generated only for those fields that have well-typed
1731 Here is the example of that section, in GADT-style syntax:
1733 data Counter a where
1734 NewCounter { _this :: self
1735 , _inc :: self -> self
1736 , _display :: self -> IO ()
1741 As before, only one selector function is generated here, that for <literal>tag</literal>.
1742 Nevertheless, you can still use all the field names in pattern matching and record construction.
1744 </itemizedlist></para>
1748 <title>Generalised Algebraic Data Types (GADTs)</title>
1750 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1751 by allowing constructors to have richer return types. Here is an example:
1754 Lit :: Int -> Term Int
1755 Succ :: Term Int -> Term Int
1756 IsZero :: Term Int -> Term Bool
1757 If :: Term Bool -> Term a -> Term a -> Term a
1758 Pair :: Term a -> Term b -> Term (a,b)
1760 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1761 case with ordinary data types. This generality allows us to
1762 write a well-typed <literal>eval</literal> function
1763 for these <literal>Terms</literal>:
1767 eval (Succ t) = 1 + eval t
1768 eval (IsZero t) = eval t == 0
1769 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1770 eval (Pair e1 e2) = (eval e1, eval e2)
1772 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1773 For example, in the right hand side of the equation
1778 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1779 A precise specification of the type rules is beyond what this user manual aspires to,
1780 but the design closely follows that described in
1782 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1783 unification-based type inference for GADTs</ulink>,
1785 The general principle is this: <emphasis>type refinement is only carried out
1786 based on user-supplied type annotations</emphasis>.
1787 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1788 and lots of obscure error messages will
1789 occur. However, the refinement is quite general. For example, if we had:
1791 eval :: Term a -> a -> a
1792 eval (Lit i) j = i+j
1794 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1795 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1796 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1799 These and many other examples are given in papers by Hongwei Xi, and
1800 Tim Sheard. There is a longer introduction
1801 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1803 <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
1804 may use different notation to that implemented in GHC.
1807 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
1808 <option>-X=GADTs</option>.
1811 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1812 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1813 The result type of each constructor must begin with the type constructor being defined,
1814 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1815 For example, in the <literal>Term</literal> data
1816 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1817 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1822 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1823 an ordianary data type.
1827 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1831 Lit { val :: Int } :: Term Int
1832 Succ { num :: Term Int } :: Term Int
1833 Pred { num :: Term Int } :: Term Int
1834 IsZero { arg :: Term Int } :: Term Bool
1835 Pair { arg1 :: Term a
1838 If { cnd :: Term Bool
1843 However, for GADTs there is the following additional constraint:
1844 every constructor that has a field <literal>f</literal> must have
1845 the same result type (modulo alpha conversion)
1846 Hence, in the above example, we cannot merge the <literal>num</literal>
1847 and <literal>arg</literal> fields above into a
1848 single name. Although their field types are both <literal>Term Int</literal>,
1849 their selector functions actually have different types:
1852 num :: Term Int -> Term Int
1853 arg :: Term Bool -> Term Int
1862 <!-- ====================== End of Generalised algebraic data types ======================= -->
1865 <sect2 id="deriving-typeable">
1866 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1869 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1870 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1871 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1872 classes <literal>Eq</literal>, <literal>Ord</literal>,
1873 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1876 GHC extends this list with two more classes that may be automatically derived
1877 (provided the <option>-fglasgow-exts</option> flag is specified):
1878 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1879 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1880 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1882 <para>An instance of <literal>Typeable</literal> can only be derived if the
1883 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1884 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1886 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1887 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1889 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1890 are used, and only <literal>Typeable1</literal> up to
1891 <literal>Typeable7</literal> are provided in the library.)
1892 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1893 class, whose kind suits that of the data type constructor, and
1894 then writing the data type instance by hand.
1898 <sect2 id="newtype-deriving">
1899 <title>Generalised derived instances for newtypes</title>
1902 When you define an abstract type using <literal>newtype</literal>, you may want
1903 the new type to inherit some instances from its representation. In
1904 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1905 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1906 other classes you have to write an explicit instance declaration. For
1907 example, if you define
1910 newtype Dollars = Dollars Int
1913 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1914 explicitly define an instance of <literal>Num</literal>:
1917 instance Num Dollars where
1918 Dollars a + Dollars b = Dollars (a+b)
1921 All the instance does is apply and remove the <literal>newtype</literal>
1922 constructor. It is particularly galling that, since the constructor
1923 doesn't appear at run-time, this instance declaration defines a
1924 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1925 dictionary, only slower!
1929 <sect3> <title> Generalising the deriving clause </title>
1931 GHC now permits such instances to be derived instead, so one can write
1933 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1936 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1937 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1938 derives an instance declaration of the form
1941 instance Num Int => Num Dollars
1944 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1948 We can also derive instances of constructor classes in a similar
1949 way. For example, suppose we have implemented state and failure monad
1950 transformers, such that
1953 instance Monad m => Monad (State s m)
1954 instance Monad m => Monad (Failure m)
1956 In Haskell 98, we can define a parsing monad by
1958 type Parser tok m a = State [tok] (Failure m) a
1961 which is automatically a monad thanks to the instance declarations
1962 above. With the extension, we can make the parser type abstract,
1963 without needing to write an instance of class <literal>Monad</literal>, via
1966 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1969 In this case the derived instance declaration is of the form
1971 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1974 Notice that, since <literal>Monad</literal> is a constructor class, the
1975 instance is a <emphasis>partial application</emphasis> of the new type, not the
1976 entire left hand side. We can imagine that the type declaration is
1977 ``eta-converted'' to generate the context of the instance
1982 We can even derive instances of multi-parameter classes, provided the
1983 newtype is the last class parameter. In this case, a ``partial
1984 application'' of the class appears in the <literal>deriving</literal>
1985 clause. For example, given the class
1988 class StateMonad s m | m -> s where ...
1989 instance Monad m => StateMonad s (State s m) where ...
1991 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1993 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1994 deriving (Monad, StateMonad [tok])
1997 The derived instance is obtained by completing the application of the
1998 class to the new type:
2001 instance StateMonad [tok] (State [tok] (Failure m)) =>
2002 StateMonad [tok] (Parser tok m)
2007 As a result of this extension, all derived instances in newtype
2008 declarations are treated uniformly (and implemented just by reusing
2009 the dictionary for the representation type), <emphasis>except</emphasis>
2010 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2011 the newtype and its representation.
2015 <sect3> <title> A more precise specification </title>
2017 Derived instance declarations are constructed as follows. Consider the
2018 declaration (after expansion of any type synonyms)
2021 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2027 The <literal>ci</literal> are partial applications of
2028 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2029 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2032 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2035 The type <literal>t</literal> is an arbitrary type.
2038 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2039 nor in the <literal>ci</literal>, and
2042 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2043 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2044 should not "look through" the type or its constructor. You can still
2045 derive these classes for a newtype, but it happens in the usual way, not
2046 via this new mechanism.
2049 Then, for each <literal>ci</literal>, the derived instance
2052 instance ci t => ci (T v1...vk)
2054 As an example which does <emphasis>not</emphasis> work, consider
2056 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2058 Here we cannot derive the instance
2060 instance Monad (State s m) => Monad (NonMonad m)
2063 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2064 and so cannot be "eta-converted" away. It is a good thing that this
2065 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2066 not, in fact, a monad --- for the same reason. Try defining
2067 <literal>>>=</literal> with the correct type: you won't be able to.
2071 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2072 important, since we can only derive instances for the last one. If the
2073 <literal>StateMonad</literal> class above were instead defined as
2076 class StateMonad m s | m -> s where ...
2079 then we would not have been able to derive an instance for the
2080 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2081 classes usually have one "main" parameter for which deriving new
2082 instances is most interesting.
2084 <para>Lastly, all of this applies only for classes other than
2085 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2086 and <literal>Data</literal>, for which the built-in derivation applies (section
2087 4.3.3. of the Haskell Report).
2088 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2089 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2090 the standard method is used or the one described here.)
2096 <sect2 id="stand-alone-deriving">
2097 <title>Stand-alone deriving declarations</title>
2100 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2102 data Foo a = Bar a | Baz String
2104 derive instance Eq (Foo a)
2106 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2107 you can use it as a variable name elsewhere.</para>
2108 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2109 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2112 newtype Foo a = MkFoo (State Int a)
2114 derive instance MonadState Int Foo
2116 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2117 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2125 <!-- TYPE SYSTEM EXTENSIONS -->
2126 <sect1 id="other-type-extensions">
2127 <title>Other type system extensions</title>
2129 <sect2 id="multi-param-type-classes">
2130 <title>Class declarations</title>
2133 This section, and the next one, documents GHC's type-class extensions.
2134 There's lots of background in the paper <ulink
2135 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2136 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2137 Jones, Erik Meijer).
2140 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2144 <title>Multi-parameter type classes</title>
2146 Multi-parameter type classes are permitted. For example:
2150 class Collection c a where
2151 union :: c a -> c a -> c a
2159 <title>The superclasses of a class declaration</title>
2162 There are no restrictions on the context in a class declaration
2163 (which introduces superclasses), except that the class hierarchy must
2164 be acyclic. So these class declarations are OK:
2168 class Functor (m k) => FiniteMap m k where
2171 class (Monad m, Monad (t m)) => Transform t m where
2172 lift :: m a -> (t m) a
2178 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2179 of "acyclic" involves only the superclass relationships. For example,
2185 op :: D b => a -> b -> b
2188 class C a => D a where { ... }
2192 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2193 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2194 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2201 <sect3 id="class-method-types">
2202 <title>Class method types</title>
2205 Haskell 98 prohibits class method types to mention constraints on the
2206 class type variable, thus:
2209 fromList :: [a] -> s a
2210 elem :: Eq a => a -> s a -> Bool
2212 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2213 contains the constraint <literal>Eq a</literal>, constrains only the
2214 class type variable (in this case <literal>a</literal>).
2215 GHC lifts this restriction.
2222 <sect2 id="functional-dependencies">
2223 <title>Functional dependencies
2226 <para> Functional dependencies are implemented as described by Mark Jones
2227 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2228 In Proceedings of the 9th European Symposium on Programming,
2229 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2233 Functional dependencies are introduced by a vertical bar in the syntax of a
2234 class declaration; e.g.
2236 class (Monad m) => MonadState s m | m -> s where ...
2238 class Foo a b c | a b -> c where ...
2240 There should be more documentation, but there isn't (yet). Yell if you need it.
2243 <sect3><title>Rules for functional dependencies </title>
2245 In a class declaration, all of the class type variables must be reachable (in the sense
2246 mentioned in <xref linkend="type-restrictions"/>)
2247 from the free variables of each method type.
2251 class Coll s a where
2253 insert :: s -> a -> s
2256 is not OK, because the type of <literal>empty</literal> doesn't mention
2257 <literal>a</literal>. Functional dependencies can make the type variable
2260 class Coll s a | s -> a where
2262 insert :: s -> a -> s
2265 Alternatively <literal>Coll</literal> might be rewritten
2268 class Coll s a where
2270 insert :: s a -> a -> s a
2274 which makes the connection between the type of a collection of
2275 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2276 Occasionally this really doesn't work, in which case you can split the
2284 class CollE s => Coll s a where
2285 insert :: s -> a -> s
2292 <title>Background on functional dependencies</title>
2294 <para>The following description of the motivation and use of functional dependencies is taken
2295 from the Hugs user manual, reproduced here (with minor changes) by kind
2296 permission of Mark Jones.
2299 Consider the following class, intended as part of a
2300 library for collection types:
2302 class Collects e ce where
2304 insert :: e -> ce -> ce
2305 member :: e -> ce -> Bool
2307 The type variable e used here represents the element type, while ce is the type
2308 of the container itself. Within this framework, we might want to define
2309 instances of this class for lists or characteristic functions (both of which
2310 can be used to represent collections of any equality type), bit sets (which can
2311 be used to represent collections of characters), or hash tables (which can be
2312 used to represent any collection whose elements have a hash function). Omitting
2313 standard implementation details, this would lead to the following declarations:
2315 instance Eq e => Collects e [e] where ...
2316 instance Eq e => Collects e (e -> Bool) where ...
2317 instance Collects Char BitSet where ...
2318 instance (Hashable e, Collects a ce)
2319 => Collects e (Array Int ce) where ...
2321 All this looks quite promising; we have a class and a range of interesting
2322 implementations. Unfortunately, there are some serious problems with the class
2323 declaration. First, the empty function has an ambiguous type:
2325 empty :: Collects e ce => ce
2327 By "ambiguous" we mean that there is a type variable e that appears on the left
2328 of the <literal>=></literal> symbol, but not on the right. The problem with
2329 this is that, according to the theoretical foundations of Haskell overloading,
2330 we cannot guarantee a well-defined semantics for any term with an ambiguous
2334 We can sidestep this specific problem by removing the empty member from the
2335 class declaration. However, although the remaining members, insert and member,
2336 do not have ambiguous types, we still run into problems when we try to use
2337 them. For example, consider the following two functions:
2339 f x y = insert x . insert y
2342 for which GHC infers the following types:
2344 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2345 g :: (Collects Bool c, Collects Char c) => c -> c
2347 Notice that the type for f allows the two parameters x and y to be assigned
2348 different types, even though it attempts to insert each of the two values, one
2349 after the other, into the same collection. If we're trying to model collections
2350 that contain only one type of value, then this is clearly an inaccurate
2351 type. Worse still, the definition for g is accepted, without causing a type
2352 error. As a result, the error in this code will not be flagged at the point
2353 where it appears. Instead, it will show up only when we try to use g, which
2354 might even be in a different module.
2357 <sect4><title>An attempt to use constructor classes</title>
2360 Faced with the problems described above, some Haskell programmers might be
2361 tempted to use something like the following version of the class declaration:
2363 class Collects e c where
2365 insert :: e -> c e -> c e
2366 member :: e -> c e -> Bool
2368 The key difference here is that we abstract over the type constructor c that is
2369 used to form the collection type c e, and not over that collection type itself,
2370 represented by ce in the original class declaration. This avoids the immediate
2371 problems that we mentioned above: empty has type <literal>Collects e c => c
2372 e</literal>, which is not ambiguous.
2375 The function f from the previous section has a more accurate type:
2377 f :: (Collects e c) => e -> e -> c e -> c e
2379 The function g from the previous section is now rejected with a type error as
2380 we would hope because the type of f does not allow the two arguments to have
2382 This, then, is an example of a multiple parameter class that does actually work
2383 quite well in practice, without ambiguity problems.
2384 There is, however, a catch. This version of the Collects class is nowhere near
2385 as general as the original class seemed to be: only one of the four instances
2386 for <literal>Collects</literal>
2387 given above can be used with this version of Collects because only one of
2388 them---the instance for lists---has a collection type that can be written in
2389 the form c e, for some type constructor c, and element type e.
2393 <sect4><title>Adding functional dependencies</title>
2396 To get a more useful version of the Collects class, Hugs provides a mechanism
2397 that allows programmers to specify dependencies between the parameters of a
2398 multiple parameter class (For readers with an interest in theoretical
2399 foundations and previous work: The use of dependency information can be seen
2400 both as a generalization of the proposal for `parametric type classes' that was
2401 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2402 later framework for "improvement" of qualified types. The
2403 underlying ideas are also discussed in a more theoretical and abstract setting
2404 in a manuscript [implparam], where they are identified as one point in a
2405 general design space for systems of implicit parameterization.).
2407 To start with an abstract example, consider a declaration such as:
2409 class C a b where ...
2411 which tells us simply that C can be thought of as a binary relation on types
2412 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2413 included in the definition of classes to add information about dependencies
2414 between parameters, as in the following examples:
2416 class D a b | a -> b where ...
2417 class E a b | a -> b, b -> a where ...
2419 The notation <literal>a -> b</literal> used here between the | and where
2420 symbols --- not to be
2421 confused with a function type --- indicates that the a parameter uniquely
2422 determines the b parameter, and might be read as "a determines b." Thus D is
2423 not just a relation, but actually a (partial) function. Similarly, from the two
2424 dependencies that are included in the definition of E, we can see that E
2425 represents a (partial) one-one mapping between types.
2428 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2429 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2430 m>=0, meaning that the y parameters are uniquely determined by the x
2431 parameters. Spaces can be used as separators if more than one variable appears
2432 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2433 annotated with multiple dependencies using commas as separators, as in the
2434 definition of E above. Some dependencies that we can write in this notation are
2435 redundant, and will be rejected because they don't serve any useful
2436 purpose, and may instead indicate an error in the program. Examples of
2437 dependencies like this include <literal>a -> a </literal>,
2438 <literal>a -> a a </literal>,
2439 <literal>a -> </literal>, etc. There can also be
2440 some redundancy if multiple dependencies are given, as in
2441 <literal>a->b</literal>,
2442 <literal>b->c </literal>, <literal>a->c </literal>, and
2443 in which some subset implies the remaining dependencies. Examples like this are
2444 not treated as errors. Note that dependencies appear only in class
2445 declarations, and not in any other part of the language. In particular, the
2446 syntax for instance declarations, class constraints, and types is completely
2450 By including dependencies in a class declaration, we provide a mechanism for
2451 the programmer to specify each multiple parameter class more precisely. The
2452 compiler, on the other hand, is responsible for ensuring that the set of
2453 instances that are in scope at any given point in the program is consistent
2454 with any declared dependencies. For example, the following pair of instance
2455 declarations cannot appear together in the same scope because they violate the
2456 dependency for D, even though either one on its own would be acceptable:
2458 instance D Bool Int where ...
2459 instance D Bool Char where ...
2461 Note also that the following declaration is not allowed, even by itself:
2463 instance D [a] b where ...
2465 The problem here is that this instance would allow one particular choice of [a]
2466 to be associated with more than one choice for b, which contradicts the
2467 dependency specified in the definition of D. More generally, this means that,
2468 in any instance of the form:
2470 instance D t s where ...
2472 for some particular types t and s, the only variables that can appear in s are
2473 the ones that appear in t, and hence, if the type t is known, then s will be
2474 uniquely determined.
2477 The benefit of including dependency information is that it allows us to define
2478 more general multiple parameter classes, without ambiguity problems, and with
2479 the benefit of more accurate types. To illustrate this, we return to the
2480 collection class example, and annotate the original definition of <literal>Collects</literal>
2481 with a simple dependency:
2483 class Collects e ce | ce -> e where
2485 insert :: e -> ce -> ce
2486 member :: e -> ce -> Bool
2488 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2489 determined by the type of the collection ce. Note that both parameters of
2490 Collects are of kind *; there are no constructor classes here. Note too that
2491 all of the instances of Collects that we gave earlier can be used
2492 together with this new definition.
2495 What about the ambiguity problems that we encountered with the original
2496 definition? The empty function still has type Collects e ce => ce, but it is no
2497 longer necessary to regard that as an ambiguous type: Although the variable e
2498 does not appear on the right of the => symbol, the dependency for class
2499 Collects tells us that it is uniquely determined by ce, which does appear on
2500 the right of the => symbol. Hence the context in which empty is used can still
2501 give enough information to determine types for both ce and e, without
2502 ambiguity. More generally, we need only regard a type as ambiguous if it
2503 contains a variable on the left of the => that is not uniquely determined
2504 (either directly or indirectly) by the variables on the right.
2507 Dependencies also help to produce more accurate types for user defined
2508 functions, and hence to provide earlier detection of errors, and less cluttered
2509 types for programmers to work with. Recall the previous definition for a
2512 f x y = insert x y = insert x . insert y
2514 for which we originally obtained a type:
2516 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2518 Given the dependency information that we have for Collects, however, we can
2519 deduce that a and b must be equal because they both appear as the second
2520 parameter in a Collects constraint with the same first parameter c. Hence we
2521 can infer a shorter and more accurate type for f:
2523 f :: (Collects a c) => a -> a -> c -> c
2525 In a similar way, the earlier definition of g will now be flagged as a type error.
2528 Although we have given only a few examples here, it should be clear that the
2529 addition of dependency information can help to make multiple parameter classes
2530 more useful in practice, avoiding ambiguity problems, and allowing more general
2531 sets of instance declarations.
2537 <sect2 id="instance-decls">
2538 <title>Instance declarations</title>
2540 <sect3 id="instance-rules">
2541 <title>Relaxed rules for instance declarations</title>
2543 <para>An instance declaration has the form
2545 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 ...
2547 The part before the "<literal>=></literal>" is the
2548 <emphasis>context</emphasis>, while the part after the
2549 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2553 In Haskell 98 the head of an instance declaration
2554 must be of the form <literal>C (T a1 ... an)</literal>, where
2555 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2556 and the <literal>a1 ... an</literal> are distinct type variables.
2557 Furthermore, the assertions in the context of the instance declaration
2558 must be of the form <literal>C a</literal> where <literal>a</literal>
2559 is a type variable that occurs in the head.
2562 The <option>-fglasgow-exts</option> flag loosens these restrictions
2563 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2564 the context and head of the instance declaration can each consist of arbitrary
2565 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2569 The Paterson Conditions: for each assertion in the context
2571 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2572 <listitem><para>The assertion has fewer constructors and variables (taken together
2573 and counting repetitions) than the head</para></listitem>
2577 <listitem><para>The Coverage Condition. For each functional dependency,
2578 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2579 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2580 every type variable in
2581 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2582 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2583 substitution mapping each type variable in the class declaration to the
2584 corresponding type in the instance declaration.
2587 These restrictions ensure that context reduction terminates: each reduction
2588 step makes the problem smaller by at least one
2589 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2590 if you give the <option>-fallow-undecidable-instances</option>
2591 flag (<xref linkend="undecidable-instances"/>).
2592 You can find lots of background material about the reason for these
2593 restrictions in the paper <ulink
2594 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2595 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2598 For example, these are OK:
2600 instance C Int [a] -- Multiple parameters
2601 instance Eq (S [a]) -- Structured type in head
2603 -- Repeated type variable in head
2604 instance C4 a a => C4 [a] [a]
2605 instance Stateful (ST s) (MutVar s)
2607 -- Head can consist of type variables only
2609 instance (Eq a, Show b) => C2 a b
2611 -- Non-type variables in context
2612 instance Show (s a) => Show (Sized s a)
2613 instance C2 Int a => C3 Bool [a]
2614 instance C2 Int a => C3 [a] b
2618 -- Context assertion no smaller than head
2619 instance C a => C a where ...
2620 -- (C b b) has more more occurrences of b than the head
2621 instance C b b => Foo [b] where ...
2626 The same restrictions apply to instances generated by
2627 <literal>deriving</literal> clauses. Thus the following is accepted:
2629 data MinHeap h a = H a (h a)
2632 because the derived instance
2634 instance (Show a, Show (h a)) => Show (MinHeap h a)
2636 conforms to the above rules.
2640 A useful idiom permitted by the above rules is as follows.
2641 If one allows overlapping instance declarations then it's quite
2642 convenient to have a "default instance" declaration that applies if
2643 something more specific does not:
2651 <sect3 id="undecidable-instances">
2652 <title>Undecidable instances</title>
2655 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2656 For example, sometimes you might want to use the following to get the
2657 effect of a "class synonym":
2659 class (C1 a, C2 a, C3 a) => C a where { }
2661 instance (C1 a, C2 a, C3 a) => C a where { }
2663 This allows you to write shorter signatures:
2669 f :: (C1 a, C2 a, C3 a) => ...
2671 The restrictions on functional dependencies (<xref
2672 linkend="functional-dependencies"/>) are particularly troublesome.
2673 It is tempting to introduce type variables in the context that do not appear in
2674 the head, something that is excluded by the normal rules. For example:
2676 class HasConverter a b | a -> b where
2679 data Foo a = MkFoo a
2681 instance (HasConverter a b,Show b) => Show (Foo a) where
2682 show (MkFoo value) = show (convert value)
2684 This is dangerous territory, however. Here, for example, is a program that would make the
2689 instance F [a] [[a]]
2690 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2692 Similarly, it can be tempting to lift the coverage condition:
2694 class Mul a b c | a b -> c where
2695 (.*.) :: a -> b -> c
2697 instance Mul Int Int Int where (.*.) = (*)
2698 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2699 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2701 The third instance declaration does not obey the coverage condition;
2702 and indeed the (somewhat strange) definition:
2704 f = \ b x y -> if b then x .*. [y] else y
2706 makes instance inference go into a loop, because it requires the constraint
2707 <literal>(Mul a [b] b)</literal>.
2710 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2711 the experimental flag <option>-X=AllowUndecidableInstances</option>
2712 <indexterm><primary>-X=AllowUndecidableInstances</primary></indexterm>,
2713 both the Paterson Conditions and the Coverage Condition
2714 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2715 fixed-depth recursion stack. If you exceed the stack depth you get a
2716 sort of backtrace, and the opportunity to increase the stack depth
2717 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2723 <sect3 id="instance-overlap">
2724 <title>Overlapping instances</title>
2726 In general, <emphasis>GHC requires that that it be unambiguous which instance
2728 should be used to resolve a type-class constraint</emphasis>. This behaviour
2729 can be modified by two flags: <option>-X=AllowOverlappingInstances</option>
2730 <indexterm><primary>-X=AllowOverlappingInstances
2731 </primary></indexterm>
2732 and <option>-X=AllowIncoherentInstances</option>
2733 <indexterm><primary>-X=AllowIncoherentInstances
2734 </primary></indexterm>, as this section discusses. Both these
2735 flags are dynamic flags, and can be set on a per-module basis, using
2736 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2738 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2739 it tries to match every instance declaration against the
2741 by instantiating the head of the instance declaration. For example, consider
2744 instance context1 => C Int a where ... -- (A)
2745 instance context2 => C a Bool where ... -- (B)
2746 instance context3 => C Int [a] where ... -- (C)
2747 instance context4 => C Int [Int] where ... -- (D)
2749 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2750 but (C) and (D) do not. When matching, GHC takes
2751 no account of the context of the instance declaration
2752 (<literal>context1</literal> etc).
2753 GHC's default behaviour is that <emphasis>exactly one instance must match the
2754 constraint it is trying to resolve</emphasis>.
2755 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2756 including both declarations (A) and (B), say); an error is only reported if a
2757 particular constraint matches more than one.
2761 The <option>-X=AllowOverlappingInstances</option> flag instructs GHC to allow
2762 more than one instance to match, provided there is a most specific one. For
2763 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2764 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2765 most-specific match, the program is rejected.
2768 However, GHC is conservative about committing to an overlapping instance. For example:
2773 Suppose that from the RHS of <literal>f</literal> we get the constraint
2774 <literal>C Int [b]</literal>. But
2775 GHC does not commit to instance (C), because in a particular
2776 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2777 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2778 So GHC rejects the program. If you add the flag <option>-X=AllowIncoherentInstances</option>,
2779 GHC will instead pick (C), without complaining about
2780 the problem of subsequent instantiations.
2783 The willingness to be overlapped or incoherent is a property of
2784 the <emphasis>instance declaration</emphasis> itself, controlled by the
2785 presence or otherwise of the <option>-X=AllowOverlappingInstances</option>
2786 and <option>-X=AllowIncoherentInstances</option> flags when that mdodule is
2787 being defined. Neither flag is required in a module that imports and uses the
2788 instance declaration. Specifically, during the lookup process:
2791 An instance declaration is ignored during the lookup process if (a) a more specific
2792 match is found, and (b) the instance declaration was compiled with
2793 <option>-X=AllowOverlappingInstances</option>. The flag setting for the
2794 more-specific instance does not matter.
2797 Suppose an instance declaration does not matche the constraint being looked up, but
2798 does unify with it, so that it might match when the constraint is further
2799 instantiated. Usually GHC will regard this as a reason for not committing to
2800 some other constraint. But if the instance declaration was compiled with
2801 <option>-X=AllowIncoherentInstances</option>, GHC will skip the "does-it-unify?"
2802 check for that declaration.
2805 These rules make it possible for a library author to design a library that relies on
2806 overlapping instances without the library client having to know.
2809 If an instance declaration is compiled without
2810 <option>-X=AllowOverlappingInstances</option>,
2811 then that instance can never be overlapped. This could perhaps be
2812 inconvenient. Perhaps the rule should instead say that the
2813 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2814 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2815 at a usage site should be permitted regardless of how the instance declarations
2816 are compiled, if the <option>-X=AllowOverlappingInstances</option> flag is
2817 used at the usage site. (Mind you, the exact usage site can occasionally be
2818 hard to pin down.) We are interested to receive feedback on these points.
2820 <para>The <option>-X=AllowIncoherentInstances</option> flag implies the
2821 <option>-X=AllowOverlappingInstances</option> flag, but not vice versa.
2826 <title>Type synonyms in the instance head</title>
2829 <emphasis>Unlike Haskell 98, instance heads may use type
2830 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2831 As always, using a type synonym is just shorthand for
2832 writing the RHS of the type synonym definition. For example:
2836 type Point = (Int,Int)
2837 instance C Point where ...
2838 instance C [Point] where ...
2842 is legal. However, if you added
2846 instance C (Int,Int) where ...
2850 as well, then the compiler will complain about the overlapping
2851 (actually, identical) instance declarations. As always, type synonyms
2852 must be fully applied. You cannot, for example, write:
2857 instance Monad P where ...
2861 This design decision is independent of all the others, and easily
2862 reversed, but it makes sense to me.
2870 <sect2 id="type-restrictions">
2871 <title>Type signatures</title>
2873 <sect3><title>The context of a type signature</title>
2875 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2876 the form <emphasis>(class type-variable)</emphasis> or
2877 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2878 these type signatures are perfectly OK
2881 g :: Ord (T a ()) => ...
2885 GHC imposes the following restrictions on the constraints in a type signature.
2889 forall tv1..tvn (c1, ...,cn) => type
2892 (Here, we write the "foralls" explicitly, although the Haskell source
2893 language omits them; in Haskell 98, all the free type variables of an
2894 explicit source-language type signature are universally quantified,
2895 except for the class type variables in a class declaration. However,
2896 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2905 <emphasis>Each universally quantified type variable
2906 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2908 A type variable <literal>a</literal> is "reachable" if it it appears
2909 in the same constraint as either a type variable free in in
2910 <literal>type</literal>, or another reachable type variable.
2911 A value with a type that does not obey
2912 this reachability restriction cannot be used without introducing
2913 ambiguity; that is why the type is rejected.
2914 Here, for example, is an illegal type:
2918 forall a. Eq a => Int
2922 When a value with this type was used, the constraint <literal>Eq tv</literal>
2923 would be introduced where <literal>tv</literal> is a fresh type variable, and
2924 (in the dictionary-translation implementation) the value would be
2925 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2926 can never know which instance of <literal>Eq</literal> to use because we never
2927 get any more information about <literal>tv</literal>.
2931 that the reachability condition is weaker than saying that <literal>a</literal> is
2932 functionally dependent on a type variable free in
2933 <literal>type</literal> (see <xref
2934 linkend="functional-dependencies"/>). The reason for this is there
2935 might be a "hidden" dependency, in a superclass perhaps. So
2936 "reachable" is a conservative approximation to "functionally dependent".
2937 For example, consider:
2939 class C a b | a -> b where ...
2940 class C a b => D a b where ...
2941 f :: forall a b. D a b => a -> a
2943 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2944 but that is not immediately apparent from <literal>f</literal>'s type.
2950 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2951 universally quantified type variables <literal>tvi</literal></emphasis>.
2953 For example, this type is OK because <literal>C a b</literal> mentions the
2954 universally quantified type variable <literal>b</literal>:
2958 forall a. C a b => burble
2962 The next type is illegal because the constraint <literal>Eq b</literal> does not
2963 mention <literal>a</literal>:
2967 forall a. Eq b => burble
2971 The reason for this restriction is milder than the other one. The
2972 excluded types are never useful or necessary (because the offending
2973 context doesn't need to be witnessed at this point; it can be floated
2974 out). Furthermore, floating them out increases sharing. Lastly,
2975 excluding them is a conservative choice; it leaves a patch of
2976 territory free in case we need it later.
2990 <sect2 id="implicit-parameters">
2991 <title>Implicit parameters</title>
2993 <para> Implicit parameters are implemented as described in
2994 "Implicit parameters: dynamic scoping with static types",
2995 J Lewis, MB Shields, E Meijer, J Launchbury,
2996 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3000 <para>(Most of the following, stil rather incomplete, documentation is
3001 due to Jeff Lewis.)</para>
3003 <para>Implicit parameter support is enabled with the option
3004 <option>-X=ImplicitParams</option>.</para>
3007 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3008 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3009 context. In Haskell, all variables are statically bound. Dynamic
3010 binding of variables is a notion that goes back to Lisp, but was later
3011 discarded in more modern incarnations, such as Scheme. Dynamic binding
3012 can be very confusing in an untyped language, and unfortunately, typed
3013 languages, in particular Hindley-Milner typed languages like Haskell,
3014 only support static scoping of variables.
3017 However, by a simple extension to the type class system of Haskell, we
3018 can support dynamic binding. Basically, we express the use of a
3019 dynamically bound variable as a constraint on the type. These
3020 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3021 function uses a dynamically-bound variable <literal>?x</literal>
3022 of type <literal>t'</literal>". For
3023 example, the following expresses the type of a sort function,
3024 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3026 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3028 The dynamic binding constraints are just a new form of predicate in the type class system.
3031 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3032 where <literal>x</literal> is
3033 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3034 Use of this construct also introduces a new
3035 dynamic-binding constraint in the type of the expression.
3036 For example, the following definition
3037 shows how we can define an implicitly parameterized sort function in
3038 terms of an explicitly parameterized <literal>sortBy</literal> function:
3040 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3042 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3048 <title>Implicit-parameter type constraints</title>
3050 Dynamic binding constraints behave just like other type class
3051 constraints in that they are automatically propagated. Thus, when a
3052 function is used, its implicit parameters are inherited by the
3053 function that called it. For example, our <literal>sort</literal> function might be used
3054 to pick out the least value in a list:
3056 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3057 least xs = head (sort xs)
3059 Without lifting a finger, the <literal>?cmp</literal> parameter is
3060 propagated to become a parameter of <literal>least</literal> as well. With explicit
3061 parameters, the default is that parameters must always be explicit
3062 propagated. With implicit parameters, the default is to always
3066 An implicit-parameter type constraint differs from other type class constraints in the
3067 following way: All uses of a particular implicit parameter must have
3068 the same type. This means that the type of <literal>(?x, ?x)</literal>
3069 is <literal>(?x::a) => (a,a)</literal>, and not
3070 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3074 <para> You can't have an implicit parameter in the context of a class or instance
3075 declaration. For example, both these declarations are illegal:
3077 class (?x::Int) => C a where ...
3078 instance (?x::a) => Foo [a] where ...
3080 Reason: exactly which implicit parameter you pick up depends on exactly where
3081 you invoke a function. But the ``invocation'' of instance declarations is done
3082 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3083 Easiest thing is to outlaw the offending types.</para>
3085 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3087 f :: (?x :: [a]) => Int -> Int
3090 g :: (Read a, Show a) => String -> String
3093 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3094 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3095 quite unambiguous, and fixes the type <literal>a</literal>.
3100 <title>Implicit-parameter bindings</title>
3103 An implicit parameter is <emphasis>bound</emphasis> using the standard
3104 <literal>let</literal> or <literal>where</literal> binding forms.
3105 For example, we define the <literal>min</literal> function by binding
3106 <literal>cmp</literal>.
3109 min = let ?cmp = (<=) in least
3113 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3114 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3115 (including in a list comprehension, or do-notation, or pattern guards),
3116 or a <literal>where</literal> clause.
3117 Note the following points:
3120 An implicit-parameter binding group must be a
3121 collection of simple bindings to implicit-style variables (no
3122 function-style bindings, and no type signatures); these bindings are
3123 neither polymorphic or recursive.
3126 You may not mix implicit-parameter bindings with ordinary bindings in a
3127 single <literal>let</literal>
3128 expression; use two nested <literal>let</literal>s instead.
3129 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3133 You may put multiple implicit-parameter bindings in a
3134 single binding group; but they are <emphasis>not</emphasis> treated
3135 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3136 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3137 parameter. The bindings are not nested, and may be re-ordered without changing
3138 the meaning of the program.
3139 For example, consider:
3141 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3143 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3144 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3146 f :: (?x::Int) => Int -> Int
3154 <sect3><title>Implicit parameters and polymorphic recursion</title>
3157 Consider these two definitions:
3160 len1 xs = let ?acc = 0 in len_acc1 xs
3163 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3168 len2 xs = let ?acc = 0 in len_acc2 xs
3170 len_acc2 :: (?acc :: Int) => [a] -> Int
3172 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3174 The only difference between the two groups is that in the second group
3175 <literal>len_acc</literal> is given a type signature.
3176 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3177 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3178 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3179 has a type signature, the recursive call is made to the
3180 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3181 as an implicit parameter. So we get the following results in GHCi:
3188 Adding a type signature dramatically changes the result! This is a rather
3189 counter-intuitive phenomenon, worth watching out for.
3193 <sect3><title>Implicit parameters and monomorphism</title>
3195 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3196 Haskell Report) to implicit parameters. For example, consider:
3204 Since the binding for <literal>y</literal> falls under the Monomorphism
3205 Restriction it is not generalised, so the type of <literal>y</literal> is
3206 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3207 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3208 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3209 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3210 <literal>y</literal> in the body of the <literal>let</literal> will see the
3211 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3212 <literal>14</literal>.
3217 <!-- ======================= COMMENTED OUT ========================
3219 We intend to remove linear implicit parameters, so I'm at least removing
3220 them from the 6.6 user manual
3222 <sect2 id="linear-implicit-parameters">
3223 <title>Linear implicit parameters</title>
3225 Linear implicit parameters are an idea developed by Koen Claessen,
3226 Mark Shields, and Simon PJ. They address the long-standing
3227 problem that monads seem over-kill for certain sorts of problem, notably:
3230 <listitem> <para> distributing a supply of unique names </para> </listitem>
3231 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3232 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3236 Linear implicit parameters are just like ordinary implicit parameters,
3237 except that they are "linear"; that is, they cannot be copied, and
3238 must be explicitly "split" instead. Linear implicit parameters are
3239 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3240 (The '/' in the '%' suggests the split!)
3245 import GHC.Exts( Splittable )
3247 data NameSupply = ...
3249 splitNS :: NameSupply -> (NameSupply, NameSupply)
3250 newName :: NameSupply -> Name
3252 instance Splittable NameSupply where
3256 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3257 f env (Lam x e) = Lam x' (f env e)
3260 env' = extend env x x'
3261 ...more equations for f...
3263 Notice that the implicit parameter %ns is consumed
3265 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3266 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3270 So the translation done by the type checker makes
3271 the parameter explicit:
3273 f :: NameSupply -> Env -> Expr -> Expr
3274 f ns env (Lam x e) = Lam x' (f ns1 env e)
3276 (ns1,ns2) = splitNS ns
3278 env = extend env x x'
3280 Notice the call to 'split' introduced by the type checker.
3281 How did it know to use 'splitNS'? Because what it really did
3282 was to introduce a call to the overloaded function 'split',
3283 defined by the class <literal>Splittable</literal>:
3285 class Splittable a where
3288 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3289 split for name supplies. But we can simply write
3295 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3297 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3298 <literal>GHC.Exts</literal>.
3303 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3304 are entirely distinct implicit parameters: you
3305 can use them together and they won't intefere with each other. </para>
3308 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3310 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3311 in the context of a class or instance declaration. </para></listitem>
3315 <sect3><title>Warnings</title>
3318 The monomorphism restriction is even more important than usual.
3319 Consider the example above:
3321 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3322 f env (Lam x e) = Lam x' (f env e)
3325 env' = extend env x x'
3327 If we replaced the two occurrences of x' by (newName %ns), which is
3328 usually a harmless thing to do, we get:
3330 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3331 f env (Lam x e) = Lam (newName %ns) (f env e)
3333 env' = extend env x (newName %ns)
3335 But now the name supply is consumed in <emphasis>three</emphasis> places
3336 (the two calls to newName,and the recursive call to f), so
3337 the result is utterly different. Urk! We don't even have
3341 Well, this is an experimental change. With implicit
3342 parameters we have already lost beta reduction anyway, and
3343 (as John Launchbury puts it) we can't sensibly reason about
3344 Haskell programs without knowing their typing.
3349 <sect3><title>Recursive functions</title>
3350 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3353 foo :: %x::T => Int -> [Int]
3355 foo n = %x : foo (n-1)
3357 where T is some type in class Splittable.</para>
3359 Do you get a list of all the same T's or all different T's
3360 (assuming that split gives two distinct T's back)?
3362 If you supply the type signature, taking advantage of polymorphic
3363 recursion, you get what you'd probably expect. Here's the
3364 translated term, where the implicit param is made explicit:
3367 foo x n = let (x1,x2) = split x
3368 in x1 : foo x2 (n-1)
3370 But if you don't supply a type signature, GHC uses the Hindley
3371 Milner trick of using a single monomorphic instance of the function
3372 for the recursive calls. That is what makes Hindley Milner type inference
3373 work. So the translation becomes
3377 foom n = x : foom (n-1)
3381 Result: 'x' is not split, and you get a list of identical T's. So the
3382 semantics of the program depends on whether or not foo has a type signature.
3385 You may say that this is a good reason to dislike linear implicit parameters
3386 and you'd be right. That is why they are an experimental feature.
3392 ================ END OF Linear Implicit Parameters commented out -->
3394 <sect2 id="kinding">
3395 <title>Explicitly-kinded quantification</title>
3398 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3399 to give the kind explicitly as (machine-checked) documentation,
3400 just as it is nice to give a type signature for a function. On some occasions,
3401 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3402 John Hughes had to define the data type:
3404 data Set cxt a = Set [a]
3405 | Unused (cxt a -> ())
3407 The only use for the <literal>Unused</literal> constructor was to force the correct
3408 kind for the type variable <literal>cxt</literal>.
3411 GHC now instead allows you to specify the kind of a type variable directly, wherever
3412 a type variable is explicitly bound. Namely:
3414 <listitem><para><literal>data</literal> declarations:
3416 data Set (cxt :: * -> *) a = Set [a]
3417 </screen></para></listitem>
3418 <listitem><para><literal>type</literal> declarations:
3420 type T (f :: * -> *) = f Int
3421 </screen></para></listitem>
3422 <listitem><para><literal>class</literal> declarations:
3424 class (Eq a) => C (f :: * -> *) a where ...
3425 </screen></para></listitem>
3426 <listitem><para><literal>forall</literal>'s in type signatures:
3428 f :: forall (cxt :: * -> *). Set cxt Int
3429 </screen></para></listitem>
3434 The parentheses are required. Some of the spaces are required too, to
3435 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3436 will get a parse error, because "<literal>::*->*</literal>" is a
3437 single lexeme in Haskell.
3441 As part of the same extension, you can put kind annotations in types
3444 f :: (Int :: *) -> Int
3445 g :: forall a. a -> (a :: *)
3449 atype ::= '(' ctype '::' kind ')
3451 The parentheses are required.
3456 <sect2 id="universal-quantification">
3457 <title>Arbitrary-rank polymorphism
3461 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3462 allows us to say exactly what this means. For example:
3470 g :: forall b. (b -> b)
3472 The two are treated identically.
3476 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3477 explicit universal quantification in
3479 For example, all the following types are legal:
3481 f1 :: forall a b. a -> b -> a
3482 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3484 f2 :: (forall a. a->a) -> Int -> Int
3485 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3487 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3489 f4 :: Int -> (forall a. a -> a)
3491 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3492 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3493 The <literal>forall</literal> makes explicit the universal quantification that
3494 is implicitly added by Haskell.
3497 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3498 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3499 shows, the polymorphic type on the left of the function arrow can be overloaded.
3502 The function <literal>f3</literal> has a rank-3 type;
3503 it has rank-2 types on the left of a function arrow.
3506 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3507 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3508 that restriction has now been lifted.)
3509 In particular, a forall-type (also called a "type scheme"),
3510 including an operational type class context, is legal:
3512 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3513 of a function arrow </para> </listitem>
3514 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3515 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3516 field type signatures.</para> </listitem>
3517 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3518 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3520 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3521 a type variable any more!
3530 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3531 the types of the constructor arguments. Here are several examples:
3537 data T a = T1 (forall b. b -> b -> b) a
3539 data MonadT m = MkMonad { return :: forall a. a -> m a,
3540 bind :: forall a b. m a -> (a -> m b) -> m b
3543 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3549 The constructors have rank-2 types:
3555 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3556 MkMonad :: forall m. (forall a. a -> m a)
3557 -> (forall a b. m a -> (a -> m b) -> m b)
3559 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3565 Notice that you don't need to use a <literal>forall</literal> if there's an
3566 explicit context. For example in the first argument of the
3567 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3568 prefixed to the argument type. The implicit <literal>forall</literal>
3569 quantifies all type variables that are not already in scope, and are
3570 mentioned in the type quantified over.
3574 As for type signatures, implicit quantification happens for non-overloaded
3575 types too. So if you write this:
3578 data T a = MkT (Either a b) (b -> b)
3581 it's just as if you had written this:
3584 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3587 That is, since the type variable <literal>b</literal> isn't in scope, it's
3588 implicitly universally quantified. (Arguably, it would be better
3589 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3590 where that is what is wanted. Feedback welcomed.)
3594 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3595 the constructor to suitable values, just as usual. For example,
3606 a3 = MkSwizzle reverse
3609 a4 = let r x = Just x
3616 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3617 mkTs f x y = [T1 f x, T1 f y]
3623 The type of the argument can, as usual, be more general than the type
3624 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3625 does not need the <literal>Ord</literal> constraint.)
3629 When you use pattern matching, the bound variables may now have
3630 polymorphic types. For example:
3636 f :: T a -> a -> (a, Char)
3637 f (T1 w k) x = (w k x, w 'c' 'd')
3639 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3640 g (MkSwizzle s) xs f = s (map f (s xs))
3642 h :: MonadT m -> [m a] -> m [a]
3643 h m [] = return m []
3644 h m (x:xs) = bind m x $ \y ->
3645 bind m (h m xs) $ \ys ->
3652 In the function <function>h</function> we use the record selectors <literal>return</literal>
3653 and <literal>bind</literal> to extract the polymorphic bind and return functions
3654 from the <literal>MonadT</literal> data structure, rather than using pattern
3660 <title>Type inference</title>
3663 In general, type inference for arbitrary-rank types is undecidable.
3664 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3665 to get a decidable algorithm by requiring some help from the programmer.
3666 We do not yet have a formal specification of "some help" but the rule is this:
3669 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3670 provides an explicit polymorphic type for x, or GHC's type inference will assume
3671 that x's type has no foralls in it</emphasis>.
3674 What does it mean to "provide" an explicit type for x? You can do that by
3675 giving a type signature for x directly, using a pattern type signature
3676 (<xref linkend="scoped-type-variables"/>), thus:
3678 \ f :: (forall a. a->a) -> (f True, f 'c')
3680 Alternatively, you can give a type signature to the enclosing
3681 context, which GHC can "push down" to find the type for the variable:
3683 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3685 Here the type signature on the expression can be pushed inwards
3686 to give a type signature for f. Similarly, and more commonly,
3687 one can give a type signature for the function itself:
3689 h :: (forall a. a->a) -> (Bool,Char)
3690 h f = (f True, f 'c')
3692 You don't need to give a type signature if the lambda bound variable
3693 is a constructor argument. Here is an example we saw earlier:
3695 f :: T a -> a -> (a, Char)
3696 f (T1 w k) x = (w k x, w 'c' 'd')
3698 Here we do not need to give a type signature to <literal>w</literal>, because
3699 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3706 <sect3 id="implicit-quant">
3707 <title>Implicit quantification</title>
3710 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3711 user-written types, if and only if there is no explicit <literal>forall</literal>,
3712 GHC finds all the type variables mentioned in the type that are not already
3713 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3717 f :: forall a. a -> a
3724 h :: forall b. a -> b -> b
3730 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3733 f :: (a -> a) -> Int
3735 f :: forall a. (a -> a) -> Int
3737 f :: (forall a. a -> a) -> Int
3740 g :: (Ord a => a -> a) -> Int
3741 -- MEANS the illegal type
3742 g :: forall a. (Ord a => a -> a) -> Int
3744 g :: (forall a. Ord a => a -> a) -> Int
3746 The latter produces an illegal type, which you might think is silly,
3747 but at least the rule is simple. If you want the latter type, you
3748 can write your for-alls explicitly. Indeed, doing so is strongly advised
3755 <sect2 id="impredicative-polymorphism">
3756 <title>Impredicative polymorphism
3758 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3759 that you can call a polymorphic function at a polymorphic type, and
3760 parameterise data structures over polymorphic types. For example:
3762 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3763 f (Just g) = Just (g [3], g "hello")
3766 Notice here that the <literal>Maybe</literal> type is parameterised by the
3767 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3770 <para>The technical details of this extension are described in the paper
3771 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3772 type inference for higher-rank types and impredicativity</ulink>,
3773 which appeared at ICFP 2006.
3777 <sect2 id="scoped-type-variables">
3778 <title>Lexically scoped type variables
3782 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3783 which some type signatures are simply impossible to write. For example:
3785 f :: forall a. [a] -> [a]
3791 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3792 the entire definition of <literal>f</literal>.
3793 In particular, it is in scope at the type signature for <varname>ys</varname>.
3794 In Haskell 98 it is not possible to declare
3795 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3796 it becomes possible to do so.
3798 <para>Lexically-scoped type variables are enabled by
3799 <option>-fglasgow-exts</option>.
3801 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3802 variables work, compared to earlier releases. Read this section
3806 <title>Overview</title>
3808 <para>The design follows the following principles
3810 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3811 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3812 design.)</para></listitem>
3813 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3814 type variables. This means that every programmer-written type signature
3815 (includin one that contains free scoped type variables) denotes a
3816 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3817 checker, and no inference is involved.</para></listitem>
3818 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3819 changing the program.</para></listitem>
3823 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3825 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3826 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3827 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3828 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3832 In Haskell, a programmer-written type signature is implicitly quantifed over
3833 its free type variables (<ulink
3834 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3836 of the Haskel Report).
3837 Lexically scoped type variables affect this implicit quantification rules
3838 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3839 quantified. For example, if type variable <literal>a</literal> is in scope,
3842 (e :: a -> a) means (e :: a -> a)
3843 (e :: b -> b) means (e :: forall b. b->b)
3844 (e :: a -> b) means (e :: forall b. a->b)
3852 <sect3 id="decl-type-sigs">
3853 <title>Declaration type signatures</title>
3854 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3855 quantification (using <literal>forall</literal>) brings into scope the
3856 explicitly-quantified
3857 type variables, in the definition of the named function(s). For example:
3859 f :: forall a. [a] -> [a]
3860 f (x:xs) = xs ++ [ x :: a ]
3862 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3863 the definition of "<literal>f</literal>".
3865 <para>This only happens if the quantification in <literal>f</literal>'s type
3866 signature is explicit. For example:
3869 g (x:xs) = xs ++ [ x :: a ]
3871 This program will be rejected, because "<literal>a</literal>" does not scope
3872 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3873 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3874 quantification rules.
3878 <sect3 id="exp-type-sigs">
3879 <title>Expression type signatures</title>
3881 <para>An expression type signature that has <emphasis>explicit</emphasis>
3882 quantification (using <literal>forall</literal>) brings into scope the
3883 explicitly-quantified
3884 type variables, in the annotated expression. For example:
3886 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3888 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3889 type variable <literal>s</literal> into scope, in the annotated expression
3890 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3895 <sect3 id="pattern-type-sigs">
3896 <title>Pattern type signatures</title>
3898 A type signature may occur in any pattern; this is a <emphasis>pattern type
3899 signature</emphasis>.
3902 -- f and g assume that 'a' is already in scope
3903 f = \(x::Int, y::a) -> x
3905 h ((x,y) :: (Int,Bool)) = (y,x)
3907 In the case where all the type variables in the pattern type sigature are
3908 already in scope (i.e. bound by the enclosing context), matters are simple: the
3909 signature simply constrains the type of the pattern in the obvious way.
3912 There is only one situation in which you can write a pattern type signature that
3913 mentions a type variable that is not already in scope, namely in pattern match
3914 of an existential data constructor. For example:
3916 data T = forall a. MkT [a]
3919 k (MkT [t::a]) = MkT t3
3923 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3924 variable that is not already in scope. Indeed, it cannot already be in scope,
3925 because it is bound by the pattern match. GHC's rule is that in this situation
3926 (and only then), a pattern type signature can mention a type variable that is
3927 not already in scope; the effect is to bring it into scope, standing for the
3928 existentially-bound type variable.
3931 If this seems a little odd, we think so too. But we must have
3932 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3933 could not name existentially-bound type variables in subequent type signatures.
3936 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3937 signature is allowed to mention a lexical variable that is not already in
3939 For example, both <literal>f</literal> and <literal>g</literal> would be
3940 illegal if <literal>a</literal> was not already in scope.
3946 <!-- ==================== Commented out part about result type signatures
3948 <sect3 id="result-type-sigs">
3949 <title>Result type signatures</title>
3952 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3955 {- f assumes that 'a' is already in scope -}
3956 f x y :: [a] = [x,y,x]
3958 g = \ x :: [Int] -> [3,4]
3960 h :: forall a. [a] -> a
3964 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3965 the result of the function. Similarly, the body of the lambda in the RHS of
3966 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3967 alternative in <literal>h</literal> is <literal>a</literal>.
3969 <para> A result type signature never brings new type variables into scope.</para>
3971 There are a couple of syntactic wrinkles. First, notice that all three
3972 examples would parse quite differently with parentheses:
3974 {- f assumes that 'a' is already in scope -}
3975 f x (y :: [a]) = [x,y,x]
3977 g = \ (x :: [Int]) -> [3,4]
3979 h :: forall a. [a] -> a
3983 Now the signature is on the <emphasis>pattern</emphasis>; and
3984 <literal>h</literal> would certainly be ill-typed (since the pattern
3985 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3987 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3988 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3989 token or a parenthesised type of some sort). To see why,
3990 consider how one would parse this:
3999 <sect3 id="cls-inst-scoped-tyvars">
4000 <title>Class and instance declarations</title>
4003 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4004 scope over the methods defined in the <literal>where</literal> part. For example:
4022 <sect2 id="typing-binds">
4023 <title>Generalised typing of mutually recursive bindings</title>
4026 The Haskell Report specifies that a group of bindings (at top level, or in a
4027 <literal>let</literal> or <literal>where</literal>) should be sorted into
4028 strongly-connected components, and then type-checked in dependency order
4029 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4030 Report, Section 4.5.1</ulink>).
4031 As each group is type-checked, any binders of the group that
4033 an explicit type signature are put in the type environment with the specified
4035 and all others are monomorphic until the group is generalised
4036 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4039 <para>Following a suggestion of Mark Jones, in his paper
4040 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4042 GHC implements a more general scheme. If <option>-X=RelaxedPolyRec</option> is
4044 <emphasis>the dependency analysis ignores references to variables that have an explicit
4045 type signature</emphasis>.
4046 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4047 typecheck. For example, consider:
4049 f :: Eq a => a -> Bool
4050 f x = (x == x) || g True || g "Yes"
4052 g y = (y <= y) || f True
4054 This is rejected by Haskell 98, but under Jones's scheme the definition for
4055 <literal>g</literal> is typechecked first, separately from that for
4056 <literal>f</literal>,
4057 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4058 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4059 type is generalised, to get
4061 g :: Ord a => a -> Bool
4063 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4064 <literal>g</literal> in the type environment.
4068 The same refined dependency analysis also allows the type signatures of
4069 mutually-recursive functions to have different contexts, something that is illegal in
4070 Haskell 98 (Section 4.5.2, last sentence). With
4071 <option>-X=RelaxedPolyRec</option>
4072 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4073 type signatures; in practice this means that only variables bound by the same
4074 pattern binding must have the same context. For example, this is fine:
4076 f :: Eq a => a -> Bool
4077 f x = (x == x) || g True
4079 g :: Ord a => a -> Bool
4080 g y = (y <= y) || f True
4085 <sect2 id="overloaded-strings">
4086 <title>Overloaded string literals
4090 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4091 string literal has type <literal>String</literal>, but with overloaded string
4092 literals enabled (with <literal>-X=OverloadedStrings</literal>)
4093 a string literal has type <literal>(IsString a) => a</literal>.
4096 This means that the usual string syntax can be used, e.g., for packed strings
4097 and other variations of string like types. String literals behave very much
4098 like integer literals, i.e., they can be used in both expressions and patterns.
4099 If used in a pattern the literal with be replaced by an equality test, in the same
4100 way as an integer literal is.
4103 The class <literal>IsString</literal> is defined as:
4105 class IsString a where
4106 fromString :: String -> a
4108 The only predefined instance is the obvious one to make strings work as usual:
4110 instance IsString [Char] where
4113 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4114 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4115 from module <literal>GHC.Exts</literal>.
4118 Haskell's defaulting mechanism is extended to cover string literals, when <option>-X-OverloadedStrings</option> is specified.
4122 Each type in a default declaration must be an
4123 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4127 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4128 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4129 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4130 <emphasis>or</emphasis> <literal>IsString</literal>.
4139 import GHC.Exts( IsString(..) )
4141 newtype MyString = MyString String deriving (Eq, Show)
4142 instance IsString MyString where
4143 fromString = MyString
4145 greet :: MyString -> MyString
4146 greet "hello" = "world"
4150 print $ greet "hello"
4151 print $ greet "fool"
4155 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4156 to work since it gets translated into an equality comparison.
4160 <sect2 id="type-families">
4161 <title>Type families
4165 GHC supports the definition of type families indexed by types. They may be
4166 seen as an extension of Haskell 98's class-based overloading of values to
4167 types. When type families are declared in classes, they are also known as
4171 There are two forms of type families: data families and type synonym families.
4172 Currently, only the former are fully implemented, while we are still working
4173 on the latter. As a result, the specification of the language extension is
4174 also still to some degree in flux. Hence, a more detailed description of
4175 the language extension and its use is currently available
4176 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4177 wiki page on type families</ulink>. The material will be moved to this user's
4178 guide when it has stabilised.
4181 Type families are enabled by the flag <option>-X=TypeFamilies</option>.
4188 <!-- ==================== End of type system extensions ================= -->
4190 <!-- ====================== TEMPLATE HASKELL ======================= -->
4192 <sect1 id="template-haskell">
4193 <title>Template Haskell</title>
4195 <para>Template Haskell allows you to do compile-time meta-programming in
4198 the main technical innovations is discussed in "<ulink
4199 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4200 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4203 There is a Wiki page about
4204 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4205 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4209 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4210 Haskell library reference material</ulink>
4211 (search for the type ExpQ).
4212 [Temporary: many changes to the original design are described in
4213 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4214 Not all of these changes are in GHC 6.6.]
4217 <para> The first example from that paper is set out below as a worked example to help get you started.
4221 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4222 Tim Sheard is going to expand it.)
4226 <title>Syntax</title>
4228 <para> Template Haskell has the following new syntactic
4229 constructions. You need to use the flag
4230 <option>-X=TemplateHaskell</option> or <option>-X=TH</option>
4231 <indexterm><primary><option>-X=TemplateHaskell</option></primary>
4232 </indexterm>to switch these syntactic extensions on
4233 (<option>-X=TemplateHaskell</option> is no longer implied by
4234 <option>-fglasgow-exts</option>).</para>
4238 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4239 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4240 There must be no space between the "$" and the identifier or parenthesis. This use
4241 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4242 of "." as an infix operator. If you want the infix operator, put spaces around it.
4244 <para> A splice can occur in place of
4246 <listitem><para> an expression; the spliced expression must
4247 have type <literal>Q Exp</literal></para></listitem>
4248 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4249 <listitem><para> [Planned, but not implemented yet.] a
4250 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4252 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4253 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4259 A expression quotation is written in Oxford brackets, thus:
4261 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4262 the quotation has type <literal>Expr</literal>.</para></listitem>
4263 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4264 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4265 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4266 the quotation has type <literal>Type</literal>.</para></listitem>
4267 </itemizedlist></para></listitem>
4270 Reification is written thus:
4272 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4273 has type <literal>Dec</literal>. </para></listitem>
4274 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4275 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4276 <listitem><para> Still to come: fixities </para></listitem>
4278 </itemizedlist></para>
4285 <sect2> <title> Using Template Haskell </title>
4289 The data types and monadic constructor functions for Template Haskell are in the library
4290 <literal>Language.Haskell.THSyntax</literal>.
4294 You can only run a function at compile time if it is imported from another module. That is,
4295 you can't define a function in a module, and call it from within a splice in the same module.
4296 (It would make sense to do so, but it's hard to implement.)
4300 Furthermore, you can only run a function at compile time if it is imported
4301 from another module <emphasis>that is not part of a mutually-recursive group of modules
4302 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4303 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4304 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4308 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4311 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4312 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4313 compiles and runs a program, and then looks at the result. So it's important that
4314 the program it compiles produces results whose representations are identical to
4315 those of the compiler itself.
4319 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4320 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4325 <sect2> <title> A Template Haskell Worked Example </title>
4326 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4327 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4334 -- Import our template "pr"
4335 import Printf ( pr )
4337 -- The splice operator $ takes the Haskell source code
4338 -- generated at compile time by "pr" and splices it into
4339 -- the argument of "putStrLn".
4340 main = putStrLn ( $(pr "Hello") )
4346 -- Skeletal printf from the paper.
4347 -- It needs to be in a separate module to the one where
4348 -- you intend to use it.
4350 -- Import some Template Haskell syntax
4351 import Language.Haskell.TH
4353 -- Describe a format string
4354 data Format = D | S | L String
4356 -- Parse a format string. This is left largely to you
4357 -- as we are here interested in building our first ever
4358 -- Template Haskell program and not in building printf.
4359 parse :: String -> [Format]
4362 -- Generate Haskell source code from a parsed representation
4363 -- of the format string. This code will be spliced into
4364 -- the module which calls "pr", at compile time.
4365 gen :: [Format] -> ExpQ
4366 gen [D] = [| \n -> show n |]
4367 gen [S] = [| \s -> s |]
4368 gen [L s] = stringE s
4370 -- Here we generate the Haskell code for the splice
4371 -- from an input format string.
4372 pr :: String -> ExpQ
4373 pr s = gen (parse s)
4376 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4379 $ ghc --make -X=TemplateHaskell main.hs -o main.exe
4382 <para>Run "main.exe" and here is your output:</para>
4392 <title>Using Template Haskell with Profiling</title>
4393 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4395 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4396 interpreter to run the splice expressions. The bytecode interpreter
4397 runs the compiled expression on top of the same runtime on which GHC
4398 itself is running; this means that the compiled code referred to by
4399 the interpreted expression must be compatible with this runtime, and
4400 in particular this means that object code that is compiled for
4401 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4402 expression, because profiled object code is only compatible with the
4403 profiling version of the runtime.</para>
4405 <para>This causes difficulties if you have a multi-module program
4406 containing Template Haskell code and you need to compile it for
4407 profiling, because GHC cannot load the profiled object code and use it
4408 when executing the splices. Fortunately GHC provides a workaround.
4409 The basic idea is to compile the program twice:</para>
4413 <para>Compile the program or library first the normal way, without
4414 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4417 <para>Then compile it again with <option>-prof</option>, and
4418 additionally use <option>-osuf
4419 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4420 to name the object files differentliy (you can choose any suffix
4421 that isn't the normal object suffix here). GHC will automatically
4422 load the object files built in the first step when executing splice
4423 expressions. If you omit the <option>-osuf</option> flag when
4424 building with <option>-prof</option> and Template Haskell is used,
4425 GHC will emit an error message. </para>
4432 <!-- ===================== Arrow notation =================== -->
4434 <sect1 id="arrow-notation">
4435 <title>Arrow notation
4438 <para>Arrows are a generalization of monads introduced by John Hughes.
4439 For more details, see
4444 “Generalising Monads to Arrows”,
4445 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4446 pp67–111, May 2000.
4452 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4453 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4459 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4460 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4466 and the arrows web page at
4467 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4468 With the <option>-X=Arrows</option> flag, GHC supports the arrow
4469 notation described in the second of these papers.
4470 What follows is a brief introduction to the notation;
4471 it won't make much sense unless you've read Hughes's paper.
4472 This notation is translated to ordinary Haskell,
4473 using combinators from the
4474 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4478 <para>The extension adds a new kind of expression for defining arrows:
4480 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4481 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4483 where <literal>proc</literal> is a new keyword.
4484 The variables of the pattern are bound in the body of the
4485 <literal>proc</literal>-expression,
4486 which is a new sort of thing called a <firstterm>command</firstterm>.
4487 The syntax of commands is as follows:
4489 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4490 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4491 | <replaceable>cmd</replaceable><superscript>0</superscript>
4493 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4494 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4495 infix operators as for expressions, and
4497 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4498 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4499 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4500 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4501 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4502 | <replaceable>fcmd</replaceable>
4504 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4505 | ( <replaceable>cmd</replaceable> )
4506 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4508 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4509 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4510 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4511 | <replaceable>cmd</replaceable>
4513 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4514 except that the bodies are commands instead of expressions.
4518 Commands produce values, but (like monadic computations)
4519 may yield more than one value,
4520 or none, and may do other things as well.
4521 For the most part, familiarity with monadic notation is a good guide to
4523 However the values of expressions, even monadic ones,
4524 are determined by the values of the variables they contain;
4525 this is not necessarily the case for commands.
4529 A simple example of the new notation is the expression
4531 proc x -> f -< x+1
4533 We call this a <firstterm>procedure</firstterm> or
4534 <firstterm>arrow abstraction</firstterm>.
4535 As with a lambda expression, the variable <literal>x</literal>
4536 is a new variable bound within the <literal>proc</literal>-expression.
4537 It refers to the input to the arrow.
4538 In the above example, <literal>-<</literal> is not an identifier but an
4539 new reserved symbol used for building commands from an expression of arrow
4540 type and an expression to be fed as input to that arrow.
4541 (The weird look will make more sense later.)
4542 It may be read as analogue of application for arrows.
4543 The above example is equivalent to the Haskell expression
4545 arr (\ x -> x+1) >>> f
4547 That would make no sense if the expression to the left of
4548 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4549 More generally, the expression to the left of <literal>-<</literal>
4550 may not involve any <firstterm>local variable</firstterm>,
4551 i.e. a variable bound in the current arrow abstraction.
4552 For such a situation there is a variant <literal>-<<</literal>, as in
4554 proc x -> f x -<< x+1
4556 which is equivalent to
4558 arr (\ x -> (f x, x+1)) >>> app
4560 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4562 Such an arrow is equivalent to a monad, so if you're using this form
4563 you may find a monadic formulation more convenient.
4567 <title>do-notation for commands</title>
4570 Another form of command is a form of <literal>do</literal>-notation.
4571 For example, you can write
4580 You can read this much like ordinary <literal>do</literal>-notation,
4581 but with commands in place of monadic expressions.
4582 The first line sends the value of <literal>x+1</literal> as an input to
4583 the arrow <literal>f</literal>, and matches its output against
4584 <literal>y</literal>.
4585 In the next line, the output is discarded.
4586 The arrow <function>returnA</function> is defined in the
4587 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4588 module as <literal>arr id</literal>.
4589 The above example is treated as an abbreviation for
4591 arr (\ x -> (x, x)) >>>
4592 first (arr (\ x -> x+1) >>> f) >>>
4593 arr (\ (y, x) -> (y, (x, y))) >>>
4594 first (arr (\ y -> 2*y) >>> g) >>>
4596 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4597 first (arr (\ (x, z) -> x*z) >>> h) >>>
4598 arr (\ (t, z) -> t+z) >>>
4601 Note that variables not used later in the composition are projected out.
4602 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4604 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4605 module, this reduces to
4607 arr (\ x -> (x+1, x)) >>>
4609 arr (\ (y, x) -> (2*y, (x, y))) >>>
4611 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4613 arr (\ (t, z) -> t+z)
4615 which is what you might have written by hand.
4616 With arrow notation, GHC keeps track of all those tuples of variables for you.
4620 Note that although the above translation suggests that
4621 <literal>let</literal>-bound variables like <literal>z</literal> must be
4622 monomorphic, the actual translation produces Core,
4623 so polymorphic variables are allowed.
4627 It's also possible to have mutually recursive bindings,
4628 using the new <literal>rec</literal> keyword, as in the following example:
4630 counter :: ArrowCircuit a => a Bool Int
4631 counter = proc reset -> do
4632 rec output <- returnA -< if reset then 0 else next
4633 next <- delay 0 -< output+1
4634 returnA -< output
4636 The translation of such forms uses the <function>loop</function> combinator,
4637 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4643 <title>Conditional commands</title>
4646 In the previous example, we used a conditional expression to construct the
4648 Sometimes we want to conditionally execute different commands, as in
4655 which is translated to
4657 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4658 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4660 Since the translation uses <function>|||</function>,
4661 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4665 There are also <literal>case</literal> commands, like
4671 y <- h -< (x1, x2)
4675 The syntax is the same as for <literal>case</literal> expressions,
4676 except that the bodies of the alternatives are commands rather than expressions.
4677 The translation is similar to that of <literal>if</literal> commands.
4683 <title>Defining your own control structures</title>
4686 As we're seen, arrow notation provides constructs,
4687 modelled on those for expressions,
4688 for sequencing, value recursion and conditionals.
4689 But suitable combinators,
4690 which you can define in ordinary Haskell,
4691 may also be used to build new commands out of existing ones.
4692 The basic idea is that a command defines an arrow from environments to values.
4693 These environments assign values to the free local variables of the command.
4694 Thus combinators that produce arrows from arrows
4695 may also be used to build commands from commands.
4696 For example, the <literal>ArrowChoice</literal> class includes a combinator
4698 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4700 so we can use it to build commands:
4702 expr' = proc x -> do
4705 symbol Plus -< ()
4706 y <- term -< ()
4709 symbol Minus -< ()
4710 y <- term -< ()
4713 (The <literal>do</literal> on the first line is needed to prevent the first
4714 <literal><+> ...</literal> from being interpreted as part of the
4715 expression on the previous line.)
4716 This is equivalent to
4718 expr' = (proc x -> returnA -< x)
4719 <+> (proc x -> do
4720 symbol Plus -< ()
4721 y <- term -< ()
4723 <+> (proc x -> do
4724 symbol Minus -< ()
4725 y <- term -< ()
4728 It is essential that this operator be polymorphic in <literal>e</literal>
4729 (representing the environment input to the command
4730 and thence to its subcommands)
4731 and satisfy the corresponding naturality property
4733 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4735 at least for strict <literal>k</literal>.
4736 (This should be automatic if you're not using <function>seq</function>.)
4737 This ensures that environments seen by the subcommands are environments
4738 of the whole command,
4739 and also allows the translation to safely trim these environments.
4740 The operator must also not use any variable defined within the current
4745 We could define our own operator
4747 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4748 untilA body cond = proc x ->
4749 if cond x then returnA -< ()
4752 untilA body cond -< x
4754 and use it in the same way.
4755 Of course this infix syntax only makes sense for binary operators;
4756 there is also a more general syntax involving special brackets:
4760 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4767 <title>Primitive constructs</title>
4770 Some operators will need to pass additional inputs to their subcommands.
4771 For example, in an arrow type supporting exceptions,
4772 the operator that attaches an exception handler will wish to pass the
4773 exception that occurred to the handler.
4774 Such an operator might have a type
4776 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4778 where <literal>Ex</literal> is the type of exceptions handled.
4779 You could then use this with arrow notation by writing a command
4781 body `handleA` \ ex -> handler
4783 so that if an exception is raised in the command <literal>body</literal>,
4784 the variable <literal>ex</literal> is bound to the value of the exception
4785 and the command <literal>handler</literal>,
4786 which typically refers to <literal>ex</literal>, is entered.
4787 Though the syntax here looks like a functional lambda,
4788 we are talking about commands, and something different is going on.
4789 The input to the arrow represented by a command consists of values for
4790 the free local variables in the command, plus a stack of anonymous values.
4791 In all the prior examples, this stack was empty.
4792 In the second argument to <function>handleA</function>,
4793 this stack consists of one value, the value of the exception.
4794 The command form of lambda merely gives this value a name.
4799 the values on the stack are paired to the right of the environment.
4800 So operators like <function>handleA</function> that pass
4801 extra inputs to their subcommands can be designed for use with the notation
4802 by pairing the values with the environment in this way.
4803 More precisely, the type of each argument of the operator (and its result)
4804 should have the form
4806 a (...(e,t1), ... tn) t
4808 where <replaceable>e</replaceable> is a polymorphic variable
4809 (representing the environment)
4810 and <replaceable>ti</replaceable> are the types of the values on the stack,
4811 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4812 The polymorphic variable <replaceable>e</replaceable> must not occur in
4813 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4814 <replaceable>t</replaceable>.
4815 However the arrows involved need not be the same.
4816 Here are some more examples of suitable operators:
4818 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4819 runReader :: ... => a e c -> a' (e,State) c
4820 runState :: ... => a e c -> a' (e,State) (c,State)
4822 We can supply the extra input required by commands built with the last two
4823 by applying them to ordinary expressions, as in
4827 (|runReader (do { ... })|) s
4829 which adds <literal>s</literal> to the stack of inputs to the command
4830 built using <function>runReader</function>.
4834 The command versions of lambda abstraction and application are analogous to
4835 the expression versions.
4836 In particular, the beta and eta rules describe equivalences of commands.
4837 These three features (operators, lambda abstraction and application)
4838 are the core of the notation; everything else can be built using them,
4839 though the results would be somewhat clumsy.
4840 For example, we could simulate <literal>do</literal>-notation by defining
4842 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4843 u `bind` f = returnA &&& u >>> f
4845 bind_ :: Arrow a => a e b -> a e c -> a e c
4846 u `bind_` f = u `bind` (arr fst >>> f)
4848 We could simulate <literal>if</literal> by defining
4850 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4851 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4858 <title>Differences with the paper</title>
4863 <para>Instead of a single form of arrow application (arrow tail) with two
4864 translations, the implementation provides two forms
4865 <quote><literal>-<</literal></quote> (first-order)
4866 and <quote><literal>-<<</literal></quote> (higher-order).
4871 <para>User-defined operators are flagged with banana brackets instead of
4872 a new <literal>form</literal> keyword.
4881 <title>Portability</title>
4884 Although only GHC implements arrow notation directly,
4885 there is also a preprocessor
4887 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4888 that translates arrow notation into Haskell 98
4889 for use with other Haskell systems.
4890 You would still want to check arrow programs with GHC;
4891 tracing type errors in the preprocessor output is not easy.
4892 Modules intended for both GHC and the preprocessor must observe some
4893 additional restrictions:
4898 The module must import
4899 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4905 The preprocessor cannot cope with other Haskell extensions.
4906 These would have to go in separate modules.
4912 Because the preprocessor targets Haskell (rather than Core),
4913 <literal>let</literal>-bound variables are monomorphic.
4924 <!-- ==================== BANG PATTERNS ================= -->
4926 <sect1 id="bang-patterns">
4927 <title>Bang patterns
4928 <indexterm><primary>Bang patterns</primary></indexterm>
4930 <para>GHC supports an extension of pattern matching called <emphasis>bang
4931 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4933 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4934 prime feature description</ulink> contains more discussion and examples
4935 than the material below.
4938 Bang patterns are enabled by the flag <option>-X=BangPatterns</option>.
4941 <sect2 id="bang-patterns-informal">
4942 <title>Informal description of bang patterns
4945 The main idea is to add a single new production to the syntax of patterns:
4949 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4950 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4955 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4956 whereas without the bang it would be lazy.
4957 Bang patterns can be nested of course:
4961 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4962 <literal>y</literal>.
4963 A bang only really has an effect if it precedes a variable or wild-card pattern:
4968 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4969 forces evaluation anyway does nothing.
4971 Bang patterns work in <literal>case</literal> expressions too, of course:
4973 g5 x = let y = f x in body
4974 g6 x = case f x of { y -> body }
4975 g7 x = case f x of { !y -> body }
4977 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4978 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4979 result, and then evaluates <literal>body</literal>.
4981 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4982 definitions too. For example:
4986 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4987 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4988 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4989 in a function argument <literal>![x,y]</literal> means the
4990 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4991 is part of the syntax of <literal>let</literal> bindings.
4996 <sect2 id="bang-patterns-sem">
4997 <title>Syntax and semantics
5001 We add a single new production to the syntax of patterns:
5005 There is one problem with syntactic ambiguity. Consider:
5009 Is this a definition of the infix function "<literal>(!)</literal>",
5010 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5011 ambiguity in favour of the latter. If you want to define
5012 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5017 The semantics of Haskell pattern matching is described in <ulink
5018 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5019 Section 3.17.2</ulink> of the Haskell Report. To this description add
5020 one extra item 10, saying:
5021 <itemizedlist><listitem><para>Matching
5022 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5023 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5024 <listitem><para>otherwise, <literal>pat</literal> is matched against
5025 <literal>v</literal></para></listitem>
5027 </para></listitem></itemizedlist>
5028 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5029 Section 3.17.3</ulink>, add a new case (t):
5031 case v of { !pat -> e; _ -> e' }
5032 = v `seq` case v of { pat -> e; _ -> e' }
5035 That leaves let expressions, whose translation is given in
5036 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5038 of the Haskell Report.
5039 In the translation box, first apply
5040 the following transformation: for each pattern <literal>pi</literal> that is of
5041 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5042 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5043 have a bang at the top, apply the rules in the existing box.
5045 <para>The effect of the let rule is to force complete matching of the pattern
5046 <literal>qi</literal> before evaluation of the body is begun. The bang is
5047 retained in the translated form in case <literal>qi</literal> is a variable,
5055 The let-binding can be recursive. However, it is much more common for
5056 the let-binding to be non-recursive, in which case the following law holds:
5057 <literal>(let !p = rhs in body)</literal>
5059 <literal>(case rhs of !p -> body)</literal>
5062 A pattern with a bang at the outermost level is not allowed at the top level of
5068 <!-- ==================== ASSERTIONS ================= -->
5070 <sect1 id="assertions">
5072 <indexterm><primary>Assertions</primary></indexterm>
5076 If you want to make use of assertions in your standard Haskell code, you
5077 could define a function like the following:
5083 assert :: Bool -> a -> a
5084 assert False x = error "assertion failed!"
5091 which works, but gives you back a less than useful error message --
5092 an assertion failed, but which and where?
5096 One way out is to define an extended <function>assert</function> function which also
5097 takes a descriptive string to include in the error message and
5098 perhaps combine this with the use of a pre-processor which inserts
5099 the source location where <function>assert</function> was used.
5103 Ghc offers a helping hand here, doing all of this for you. For every
5104 use of <function>assert</function> in the user's source:
5110 kelvinToC :: Double -> Double
5111 kelvinToC k = assert (k >= 0.0) (k+273.15)
5117 Ghc will rewrite this to also include the source location where the
5124 assert pred val ==> assertError "Main.hs|15" pred val
5130 The rewrite is only performed by the compiler when it spots
5131 applications of <function>Control.Exception.assert</function>, so you
5132 can still define and use your own versions of
5133 <function>assert</function>, should you so wish. If not, import
5134 <literal>Control.Exception</literal> to make use
5135 <function>assert</function> in your code.
5139 GHC ignores assertions when optimisation is turned on with the
5140 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5141 <literal>assert pred e</literal> will be rewritten to
5142 <literal>e</literal>. You can also disable assertions using the
5143 <option>-fignore-asserts</option>
5144 option<indexterm><primary><option>-fignore-asserts</option></primary>
5145 </indexterm>.</para>
5148 Assertion failures can be caught, see the documentation for the
5149 <literal>Control.Exception</literal> library for the details.
5155 <!-- =============================== PRAGMAS =========================== -->
5157 <sect1 id="pragmas">
5158 <title>Pragmas</title>
5160 <indexterm><primary>pragma</primary></indexterm>
5162 <para>GHC supports several pragmas, or instructions to the
5163 compiler placed in the source code. Pragmas don't normally affect
5164 the meaning of the program, but they might affect the efficiency
5165 of the generated code.</para>
5167 <para>Pragmas all take the form
5169 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5171 where <replaceable>word</replaceable> indicates the type of
5172 pragma, and is followed optionally by information specific to that
5173 type of pragma. Case is ignored in
5174 <replaceable>word</replaceable>. The various values for
5175 <replaceable>word</replaceable> that GHC understands are described
5176 in the following sections; any pragma encountered with an
5177 unrecognised <replaceable>word</replaceable> is (silently)
5180 <sect2 id="deprecated-pragma">
5181 <title>DEPRECATED pragma</title>
5182 <indexterm><primary>DEPRECATED</primary>
5185 <para>The DEPRECATED pragma lets you specify that a particular
5186 function, class, or type, is deprecated. There are two
5191 <para>You can deprecate an entire module thus:</para>
5193 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5196 <para>When you compile any module that import
5197 <literal>Wibble</literal>, GHC will print the specified
5202 <para>You can deprecate a function, class, type, or data constructor, with the
5203 following top-level declaration:</para>
5205 {-# DEPRECATED f, C, T "Don't use these" #-}
5207 <para>When you compile any module that imports and uses any
5208 of the specified entities, GHC will print the specified
5210 <para> You can only depecate entities declared at top level in the module
5211 being compiled, and you can only use unqualified names in the list of
5212 entities being deprecated. A capitalised name, such as <literal>T</literal>
5213 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5214 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5215 both are in scope. If both are in scope, there is currently no way to deprecate
5216 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5219 Any use of the deprecated item, or of anything from a deprecated
5220 module, will be flagged with an appropriate message. However,
5221 deprecations are not reported for
5222 (a) uses of a deprecated function within its defining module, and
5223 (b) uses of a deprecated function in an export list.
5224 The latter reduces spurious complaints within a library
5225 in which one module gathers together and re-exports
5226 the exports of several others.
5228 <para>You can suppress the warnings with the flag
5229 <option>-fno-warn-deprecations</option>.</para>
5232 <sect2 id="include-pragma">
5233 <title>INCLUDE pragma</title>
5235 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5236 of C header files that should be <literal>#include</literal>'d into
5237 the C source code generated by the compiler for the current module (if
5238 compiling via C). For example:</para>
5241 {-# INCLUDE "foo.h" #-}
5242 {-# INCLUDE <stdio.h> #-}</programlisting>
5244 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5245 your source file with any <literal>OPTIONS_GHC</literal>
5248 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5249 to the <option>-#include</option> option (<xref
5250 linkend="options-C-compiler" />), because the
5251 <literal>INCLUDE</literal> pragma is understood by other
5252 compilers. Yet another alternative is to add the include file to each
5253 <literal>foreign import</literal> declaration in your code, but we
5254 don't recommend using this approach with GHC.</para>
5257 <sect2 id="inline-noinline-pragma">
5258 <title>INLINE and NOINLINE pragmas</title>
5260 <para>These pragmas control the inlining of function
5263 <sect3 id="inline-pragma">
5264 <title>INLINE pragma</title>
5265 <indexterm><primary>INLINE</primary></indexterm>
5267 <para>GHC (with <option>-O</option>, as always) tries to
5268 inline (or “unfold”) functions/values that are
5269 “small enough,” thus avoiding the call overhead
5270 and possibly exposing other more-wonderful optimisations.
5271 Normally, if GHC decides a function is “too
5272 expensive” to inline, it will not do so, nor will it
5273 export that unfolding for other modules to use.</para>
5275 <para>The sledgehammer you can bring to bear is the
5276 <literal>INLINE</literal><indexterm><primary>INLINE
5277 pragma</primary></indexterm> pragma, used thusly:</para>
5280 key_function :: Int -> String -> (Bool, Double)
5282 #ifdef __GLASGOW_HASKELL__
5283 {-# INLINE key_function #-}
5287 <para>(You don't need to do the C pre-processor carry-on
5288 unless you're going to stick the code through HBC—it
5289 doesn't like <literal>INLINE</literal> pragmas.)</para>
5291 <para>The major effect of an <literal>INLINE</literal> pragma
5292 is to declare a function's “cost” to be very low.
5293 The normal unfolding machinery will then be very keen to
5296 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5297 function can be put anywhere its type signature could be
5300 <para><literal>INLINE</literal> pragmas are a particularly
5302 <literal>then</literal>/<literal>return</literal> (or
5303 <literal>bind</literal>/<literal>unit</literal>) functions in
5304 a monad. For example, in GHC's own
5305 <literal>UniqueSupply</literal> monad code, we have:</para>
5308 #ifdef __GLASGOW_HASKELL__
5309 {-# INLINE thenUs #-}
5310 {-# INLINE returnUs #-}
5314 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5315 linkend="noinline-pragma"/>).</para>
5318 <sect3 id="noinline-pragma">
5319 <title>NOINLINE pragma</title>
5321 <indexterm><primary>NOINLINE</primary></indexterm>
5322 <indexterm><primary>NOTINLINE</primary></indexterm>
5324 <para>The <literal>NOINLINE</literal> pragma does exactly what
5325 you'd expect: it stops the named function from being inlined
5326 by the compiler. You shouldn't ever need to do this, unless
5327 you're very cautious about code size.</para>
5329 <para><literal>NOTINLINE</literal> is a synonym for
5330 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5331 specified by Haskell 98 as the standard way to disable
5332 inlining, so it should be used if you want your code to be
5336 <sect3 id="phase-control">
5337 <title>Phase control</title>
5339 <para> Sometimes you want to control exactly when in GHC's
5340 pipeline the INLINE pragma is switched on. Inlining happens
5341 only during runs of the <emphasis>simplifier</emphasis>. Each
5342 run of the simplifier has a different <emphasis>phase
5343 number</emphasis>; the phase number decreases towards zero.
5344 If you use <option>-dverbose-core2core</option> you'll see the
5345 sequence of phase numbers for successive runs of the
5346 simplifier. In an INLINE pragma you can optionally specify a
5350 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5351 <literal>f</literal>
5352 until phase <literal>k</literal>, but from phase
5353 <literal>k</literal> onwards be very keen to inline it.
5356 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5357 <literal>f</literal>
5358 until phase <literal>k</literal>, but from phase
5359 <literal>k</literal> onwards do not inline it.
5362 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5363 <literal>f</literal>
5364 until phase <literal>k</literal>, but from phase
5365 <literal>k</literal> onwards be willing to inline it (as if
5366 there was no pragma).
5369 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5370 <literal>f</literal>
5371 until phase <literal>k</literal>, but from phase
5372 <literal>k</literal> onwards do not inline it.
5375 The same information is summarised here:
5377 -- Before phase 2 Phase 2 and later
5378 {-# INLINE [2] f #-} -- No Yes
5379 {-# INLINE [~2] f #-} -- Yes No
5380 {-# NOINLINE [2] f #-} -- No Maybe
5381 {-# NOINLINE [~2] f #-} -- Maybe No
5383 {-# INLINE f #-} -- Yes Yes
5384 {-# NOINLINE f #-} -- No No
5386 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5387 function body is small, or it is applied to interesting-looking arguments etc).
5388 Another way to understand the semantics is this:
5390 <listitem><para>For both INLINE and NOINLINE, the phase number says
5391 when inlining is allowed at all.</para></listitem>
5392 <listitem><para>The INLINE pragma has the additional effect of making the
5393 function body look small, so that when inlining is allowed it is very likely to
5398 <para>The same phase-numbering control is available for RULES
5399 (<xref linkend="rewrite-rules"/>).</para>
5403 <sect2 id="language-pragma">
5404 <title>LANGUAGE pragma</title>
5406 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5407 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5409 <para>This allows language extensions to be enabled in a portable way.
5410 It is the intention that all Haskell compilers support the
5411 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5412 all extensions are supported by all compilers, of
5413 course. The <literal>LANGUAGE</literal> pragma should be used instead
5414 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5416 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5418 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5420 <para>Any extension from the <literal>Extension</literal> type defined in
5422 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>
5426 <sect2 id="line-pragma">
5427 <title>LINE pragma</title>
5429 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5430 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5431 <para>This pragma is similar to C's <literal>#line</literal>
5432 pragma, and is mainly for use in automatically generated Haskell
5433 code. It lets you specify the line number and filename of the
5434 original code; for example</para>
5436 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5438 <para>if you'd generated the current file from something called
5439 <filename>Foo.vhs</filename> and this line corresponds to line
5440 42 in the original. GHC will adjust its error messages to refer
5441 to the line/file named in the <literal>LINE</literal>
5445 <sect2 id="options-pragma">
5446 <title>OPTIONS_GHC pragma</title>
5447 <indexterm><primary>OPTIONS_GHC</primary>
5449 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5452 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5453 additional options that are given to the compiler when compiling
5454 this source file. See <xref linkend="source-file-options"/> for
5457 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5458 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5462 <title>RULES pragma</title>
5464 <para>The RULES pragma lets you specify rewrite rules. It is
5465 described in <xref linkend="rewrite-rules"/>.</para>
5468 <sect2 id="specialize-pragma">
5469 <title>SPECIALIZE pragma</title>
5471 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5472 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5473 <indexterm><primary>overloading, death to</primary></indexterm>
5475 <para>(UK spelling also accepted.) For key overloaded
5476 functions, you can create extra versions (NB: more code space)
5477 specialised to particular types. Thus, if you have an
5478 overloaded function:</para>
5481 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5484 <para>If it is heavily used on lists with
5485 <literal>Widget</literal> keys, you could specialise it as
5489 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5492 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5493 be put anywhere its type signature could be put.</para>
5495 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5496 (a) a specialised version of the function and (b) a rewrite rule
5497 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5498 un-specialised function into a call to the specialised one.</para>
5500 <para>The type in a SPECIALIZE pragma can be any type that is less
5501 polymorphic than the type of the original function. In concrete terms,
5502 if the original function is <literal>f</literal> then the pragma
5504 {-# SPECIALIZE f :: <type> #-}
5506 is valid if and only if the defintion
5508 f_spec :: <type>
5511 is valid. Here are some examples (where we only give the type signature
5512 for the original function, not its code):
5514 f :: Eq a => a -> b -> b
5515 {-# SPECIALISE f :: Int -> b -> b #-}
5517 g :: (Eq a, Ix b) => a -> b -> b
5518 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5520 h :: Eq a => a -> a -> a
5521 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5523 The last of these examples will generate a
5524 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5525 well. If you use this kind of specialisation, let us know how well it works.
5528 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5529 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5530 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5531 The <literal>INLINE</literal> pragma affects the specialised verison of the
5532 function (only), and applies even if the function is recursive. The motivating
5535 -- A GADT for arrays with type-indexed representation
5537 ArrInt :: !Int -> ByteArray# -> Arr Int
5538 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5540 (!:) :: Arr e -> Int -> e
5541 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5542 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5543 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5544 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5546 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5547 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5548 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5549 the specialised function will be inlined. It has two calls to
5550 <literal>(!:)</literal>,
5551 both at type <literal>Int</literal>. Both these calls fire the first
5552 specialisation, whose body is also inlined. The result is a type-based
5553 unrolling of the indexing function.</para>
5554 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5555 on an ordinarily-recursive function.</para>
5557 <para>Note: In earlier versions of GHC, it was possible to provide your own
5558 specialised function for a given type:
5561 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5564 This feature has been removed, as it is now subsumed by the
5565 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5569 <sect2 id="specialize-instance-pragma">
5570 <title>SPECIALIZE instance pragma
5574 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5575 <indexterm><primary>overloading, death to</primary></indexterm>
5576 Same idea, except for instance declarations. For example:
5579 instance (Eq a) => Eq (Foo a) where {
5580 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5584 The pragma must occur inside the <literal>where</literal> part
5585 of the instance declaration.
5588 Compatible with HBC, by the way, except perhaps in the placement
5594 <sect2 id="unpack-pragma">
5595 <title>UNPACK pragma</title>
5597 <indexterm><primary>UNPACK</primary></indexterm>
5599 <para>The <literal>UNPACK</literal> indicates to the compiler
5600 that it should unpack the contents of a constructor field into
5601 the constructor itself, removing a level of indirection. For
5605 data T = T {-# UNPACK #-} !Float
5606 {-# UNPACK #-} !Float
5609 <para>will create a constructor <literal>T</literal> containing
5610 two unboxed floats. This may not always be an optimisation: if
5611 the <function>T</function> constructor is scrutinised and the
5612 floats passed to a non-strict function for example, they will
5613 have to be reboxed (this is done automatically by the
5616 <para>Unpacking constructor fields should only be used in
5617 conjunction with <option>-O</option>, in order to expose
5618 unfoldings to the compiler so the reboxing can be removed as
5619 often as possible. For example:</para>
5623 f (T f1 f2) = f1 + f2
5626 <para>The compiler will avoid reboxing <function>f1</function>
5627 and <function>f2</function> by inlining <function>+</function>
5628 on floats, but only when <option>-O</option> is on.</para>
5630 <para>Any single-constructor data is eligible for unpacking; for
5634 data T = T {-# UNPACK #-} !(Int,Int)
5637 <para>will store the two <literal>Int</literal>s directly in the
5638 <function>T</function> constructor, by flattening the pair.
5639 Multi-level unpacking is also supported:</para>
5642 data T = T {-# UNPACK #-} !S
5643 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5646 <para>will store two unboxed <literal>Int#</literal>s
5647 directly in the <function>T</function> constructor. The
5648 unpacker can see through newtypes, too.</para>
5650 <para>If a field cannot be unpacked, you will not get a warning,
5651 so it might be an idea to check the generated code with
5652 <option>-ddump-simpl</option>.</para>
5654 <para>See also the <option>-funbox-strict-fields</option> flag,
5655 which essentially has the effect of adding
5656 <literal>{-# UNPACK #-}</literal> to every strict
5657 constructor field.</para>
5662 <!-- ======================= REWRITE RULES ======================== -->
5664 <sect1 id="rewrite-rules">
5665 <title>Rewrite rules
5667 <indexterm><primary>RULES pragma</primary></indexterm>
5668 <indexterm><primary>pragma, RULES</primary></indexterm>
5669 <indexterm><primary>rewrite rules</primary></indexterm></title>
5672 The programmer can specify rewrite rules as part of the source program
5673 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5674 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5675 and (b) the <option>-frules-off</option> flag
5676 (<xref linkend="options-f"/>) is not specified, and (c) the
5677 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5686 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5693 <title>Syntax</title>
5696 From a syntactic point of view:
5702 There may be zero or more rules in a <literal>RULES</literal> pragma.
5709 Each rule has a name, enclosed in double quotes. The name itself has
5710 no significance at all. It is only used when reporting how many times the rule fired.
5716 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5717 immediately after the name of the rule. Thus:
5720 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5723 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5724 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5733 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5734 is set, so you must lay out your rules starting in the same column as the
5735 enclosing definitions.
5742 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5743 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5744 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5745 by spaces, just like in a type <literal>forall</literal>.
5751 A pattern variable may optionally have a type signature.
5752 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5753 For example, here is the <literal>foldr/build</literal> rule:
5756 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5757 foldr k z (build g) = g k z
5760 Since <function>g</function> has a polymorphic type, it must have a type signature.
5767 The left hand side of a rule must consist of a top-level variable applied
5768 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5771 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5772 "wrong2" forall f. f True = True
5775 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5782 A rule does not need to be in the same module as (any of) the
5783 variables it mentions, though of course they need to be in scope.
5789 Rules are automatically exported from a module, just as instance declarations are.
5800 <title>Semantics</title>
5803 From a semantic point of view:
5809 Rules are only applied if you use the <option>-O</option> flag.
5815 Rules are regarded as left-to-right rewrite rules.
5816 When GHC finds an expression that is a substitution instance of the LHS
5817 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5818 By "a substitution instance" we mean that the LHS can be made equal to the
5819 expression by substituting for the pattern variables.
5826 The LHS and RHS of a rule are typechecked, and must have the
5834 GHC makes absolutely no attempt to verify that the LHS and RHS
5835 of a rule have the same meaning. That is undecidable in general, and
5836 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5843 GHC makes no attempt to make sure that the rules are confluent or
5844 terminating. For example:
5847 "loop" forall x,y. f x y = f y x
5850 This rule will cause the compiler to go into an infinite loop.
5857 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5863 GHC currently uses a very simple, syntactic, matching algorithm
5864 for matching a rule LHS with an expression. It seeks a substitution
5865 which makes the LHS and expression syntactically equal modulo alpha
5866 conversion. The pattern (rule), but not the expression, is eta-expanded if
5867 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5868 But not beta conversion (that's called higher-order matching).
5872 Matching is carried out on GHC's intermediate language, which includes
5873 type abstractions and applications. So a rule only matches if the
5874 types match too. See <xref linkend="rule-spec"/> below.
5880 GHC keeps trying to apply the rules as it optimises the program.
5881 For example, consider:
5890 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5891 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5892 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5893 not be substituted, and the rule would not fire.
5900 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5901 that appears on the LHS of a rule</emphasis>, because once you have substituted
5902 for something you can't match against it (given the simple minded
5903 matching). So if you write the rule
5906 "map/map" forall f,g. map f . map g = map (f.g)
5909 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5910 It will only match something written with explicit use of ".".
5911 Well, not quite. It <emphasis>will</emphasis> match the expression
5917 where <function>wibble</function> is defined:
5920 wibble f g = map f . map g
5923 because <function>wibble</function> will be inlined (it's small).
5925 Later on in compilation, GHC starts inlining even things on the
5926 LHS of rules, but still leaves the rules enabled. This inlining
5927 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5934 All rules are implicitly exported from the module, and are therefore
5935 in force in any module that imports the module that defined the rule, directly
5936 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5937 in force when compiling A.) The situation is very similar to that for instance
5949 <title>List fusion</title>
5952 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5953 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5954 intermediate list should be eliminated entirely.
5958 The following are good producers:
5970 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5976 Explicit lists (e.g. <literal>[True, False]</literal>)
5982 The cons constructor (e.g <literal>3:4:[]</literal>)
5988 <function>++</function>
5994 <function>map</function>
6000 <function>take</function>, <function>filter</function>
6006 <function>iterate</function>, <function>repeat</function>
6012 <function>zip</function>, <function>zipWith</function>
6021 The following are good consumers:
6033 <function>array</function> (on its second argument)
6039 <function>++</function> (on its first argument)
6045 <function>foldr</function>
6051 <function>map</function>
6057 <function>take</function>, <function>filter</function>
6063 <function>concat</function>
6069 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6075 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6076 will fuse with one but not the other)
6082 <function>partition</function>
6088 <function>head</function>
6094 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6100 <function>sequence_</function>
6106 <function>msum</function>
6112 <function>sortBy</function>
6121 So, for example, the following should generate no intermediate lists:
6124 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6130 This list could readily be extended; if there are Prelude functions that you use
6131 a lot which are not included, please tell us.
6135 If you want to write your own good consumers or producers, look at the
6136 Prelude definitions of the above functions to see how to do so.
6141 <sect2 id="rule-spec">
6142 <title>Specialisation
6146 Rewrite rules can be used to get the same effect as a feature
6147 present in earlier versions of GHC.
6148 For example, suppose that:
6151 genericLookup :: Ord a => Table a b -> a -> b
6152 intLookup :: Table Int b -> Int -> b
6155 where <function>intLookup</function> is an implementation of
6156 <function>genericLookup</function> that works very fast for
6157 keys of type <literal>Int</literal>. You might wish
6158 to tell GHC to use <function>intLookup</function> instead of
6159 <function>genericLookup</function> whenever the latter was called with
6160 type <literal>Table Int b -> Int -> b</literal>.
6161 It used to be possible to write
6164 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6167 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6170 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6173 This slightly odd-looking rule instructs GHC to replace
6174 <function>genericLookup</function> by <function>intLookup</function>
6175 <emphasis>whenever the types match</emphasis>.
6176 What is more, this rule does not need to be in the same
6177 file as <function>genericLookup</function>, unlike the
6178 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6179 have an original definition available to specialise).
6182 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6183 <function>intLookup</function> really behaves as a specialised version
6184 of <function>genericLookup</function>!!!</para>
6186 <para>An example in which using <literal>RULES</literal> for
6187 specialisation will Win Big:
6190 toDouble :: Real a => a -> Double
6191 toDouble = fromRational . toRational
6193 {-# RULES "toDouble/Int" toDouble = i2d #-}
6194 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6197 The <function>i2d</function> function is virtually one machine
6198 instruction; the default conversion—via an intermediate
6199 <literal>Rational</literal>—is obscenely expensive by
6206 <title>Controlling what's going on</title>
6214 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6220 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6221 If you add <option>-dppr-debug</option> you get a more detailed listing.
6227 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6230 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6231 {-# INLINE build #-}
6235 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6236 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6237 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6238 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6245 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6246 see how to write rules that will do fusion and yet give an efficient
6247 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6257 <sect2 id="core-pragma">
6258 <title>CORE pragma</title>
6260 <indexterm><primary>CORE pragma</primary></indexterm>
6261 <indexterm><primary>pragma, CORE</primary></indexterm>
6262 <indexterm><primary>core, annotation</primary></indexterm>
6265 The external core format supports <quote>Note</quote> annotations;
6266 the <literal>CORE</literal> pragma gives a way to specify what these
6267 should be in your Haskell source code. Syntactically, core
6268 annotations are attached to expressions and take a Haskell string
6269 literal as an argument. The following function definition shows an
6273 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6276 Semantically, this is equivalent to:
6284 However, when external for is generated (via
6285 <option>-fext-core</option>), there will be Notes attached to the
6286 expressions <function>show</function> and <varname>x</varname>.
6287 The core function declaration for <function>f</function> is:
6291 f :: %forall a . GHCziShow.ZCTShow a ->
6292 a -> GHCziBase.ZMZN GHCziBase.Char =
6293 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6295 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6297 (tpl1::GHCziBase.Int ->
6299 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6301 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6302 (tpl3::GHCziBase.ZMZN a ->
6303 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6311 Here, we can see that the function <function>show</function> (which
6312 has been expanded out to a case expression over the Show dictionary)
6313 has a <literal>%note</literal> attached to it, as does the
6314 expression <varname>eta</varname> (which used to be called
6315 <varname>x</varname>).
6322 <sect1 id="special-ids">
6323 <title>Special built-in functions</title>
6324 <para>GHC has a few built-in funcions with special behaviour,
6325 described in this section. All are exported by
6326 <literal>GHC.Exts</literal>.</para>
6328 <sect2> <title>The <literal>seq</literal> function </title>
6330 The function <literal>seq</literal> is as described in the Haskell98 Report.
6334 It evaluates its first argument to head normal form, and then returns its
6335 second argument as the result. The reason that it is documented here is
6336 that, despite <literal>seq</literal>'s polymorphism, its
6337 second argument can have an unboxed type, or
6338 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6339 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6340 to be instantiated to an unboxed type, which is not usually allowed.
6344 <sect2> <title>The <literal>inline</literal> function </title>
6346 The <literal>inline</literal> function is somewhat experimental.
6350 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6351 is inlined, regardless of its size. More precisely, the call
6352 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6354 This allows the programmer to control inlining from
6355 a particular <emphasis>call site</emphasis>
6356 rather than the <emphasis>definition site</emphasis> of the function
6357 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6360 This inlining occurs regardless of the argument to the call
6361 or the size of <literal>f</literal>'s definition; it is unconditional.
6362 The main caveat is that <literal>f</literal>'s definition must be
6363 visible to the compiler. That is, <literal>f</literal> must be
6364 let-bound in the current scope.
6365 If no inlining takes place, the <literal>inline</literal> function
6366 expands to the identity function in Phase zero; so its use imposes
6369 <para> If the function is defined in another
6370 module, GHC only exposes its inlining in the interface file if the
6371 function is sufficiently small that it <emphasis>might</emphasis> be
6372 inlined by the automatic mechanism. There is currently no way to tell
6373 GHC to expose arbitrarily-large functions in the interface file. (This
6374 shortcoming is something that could be fixed, with some kind of pragma.)
6378 <sect2> <title>The <literal>lazy</literal> function </title>
6380 The <literal>lazy</literal> function restrains strictness analysis a little:
6384 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6385 but <literal>lazy</literal> has a magical property so far as strictness
6386 analysis is concerned: it is lazy in its first argument,
6387 even though its semantics is strict. After strictness analysis has run,
6388 calls to <literal>lazy</literal> are inlined to be the identity function.
6391 This behaviour is occasionally useful when controlling evaluation order.
6392 Notably, <literal>lazy</literal> is used in the library definition of
6393 <literal>Control.Parallel.par</literal>:
6396 par x y = case (par# x) of { _ -> lazy y }
6398 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6399 look strict in <literal>y</literal> which would defeat the whole
6400 purpose of <literal>par</literal>.
6403 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6409 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6411 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6412 typechecker entirely. It has type
6414 unsafeCoerce# :: a -> b
6416 That is, it allows you to coerce any type into any other type. If you use this
6417 function, you had better get it right, otherwise segmentation faults await.
6418 It is generally used when you want to write a program that you know is
6419 well-typed, but where Haskell's type system is not expressive enough to prove
6420 that it is well typed.
6423 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6424 although extremely bad things will happen if you coerce a boxed type
6433 <sect1 id="generic-classes">
6434 <title>Generic classes</title>
6437 The ideas behind this extension are described in detail in "Derivable type classes",
6438 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6439 An example will give the idea:
6447 fromBin :: [Int] -> (a, [Int])
6449 toBin {| Unit |} Unit = []
6450 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6451 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6452 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6454 fromBin {| Unit |} bs = (Unit, bs)
6455 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6456 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6457 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6458 (y,bs'') = fromBin bs'
6461 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6462 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6463 which are defined thus in the library module <literal>Generics</literal>:
6467 data a :+: b = Inl a | Inr b
6468 data a :*: b = a :*: b
6471 Now you can make a data type into an instance of Bin like this:
6473 instance (Bin a, Bin b) => Bin (a,b)
6474 instance Bin a => Bin [a]
6476 That is, just leave off the "where" clause. Of course, you can put in the
6477 where clause and over-ride whichever methods you please.
6481 <title> Using generics </title>
6482 <para>To use generics you need to</para>
6485 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6486 <option>-X=Generics</option> (to generate extra per-data-type code),
6487 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6491 <para>Import the module <literal>Generics</literal> from the
6492 <literal>lang</literal> package. This import brings into
6493 scope the data types <literal>Unit</literal>,
6494 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6495 don't need this import if you don't mention these types
6496 explicitly; for example, if you are simply giving instance
6497 declarations.)</para>
6502 <sect2> <title> Changes wrt the paper </title>
6504 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6505 can be written infix (indeed, you can now use
6506 any operator starting in a colon as an infix type constructor). Also note that
6507 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6508 Finally, note that the syntax of the type patterns in the class declaration
6509 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6510 alone would ambiguous when they appear on right hand sides (an extension we
6511 anticipate wanting).
6515 <sect2> <title>Terminology and restrictions</title>
6517 Terminology. A "generic default method" in a class declaration
6518 is one that is defined using type patterns as above.
6519 A "polymorphic default method" is a default method defined as in Haskell 98.
6520 A "generic class declaration" is a class declaration with at least one
6521 generic default method.
6529 Alas, we do not yet implement the stuff about constructor names and
6536 A generic class can have only one parameter; you can't have a generic
6537 multi-parameter class.
6543 A default method must be defined entirely using type patterns, or entirely
6544 without. So this is illegal:
6547 op :: a -> (a, Bool)
6548 op {| Unit |} Unit = (Unit, True)
6551 However it is perfectly OK for some methods of a generic class to have
6552 generic default methods and others to have polymorphic default methods.
6558 The type variable(s) in the type pattern for a generic method declaration
6559 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:
6563 op {| p :*: q |} (x :*: y) = op (x :: p)
6571 The type patterns in a generic default method must take one of the forms:
6577 where "a" and "b" are type variables. Furthermore, all the type patterns for
6578 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6579 must use the same type variables. So this is illegal:
6583 op {| a :+: b |} (Inl x) = True
6584 op {| p :+: q |} (Inr y) = False
6586 The type patterns must be identical, even in equations for different methods of the class.
6587 So this too is illegal:
6591 op1 {| a :*: b |} (x :*: y) = True
6594 op2 {| p :*: q |} (x :*: y) = False
6596 (The reason for this restriction is that we gather all the equations for a particular type consructor
6597 into a single generic instance declaration.)
6603 A generic method declaration must give a case for each of the three type constructors.
6609 The type for a generic method can be built only from:
6611 <listitem> <para> Function arrows </para> </listitem>
6612 <listitem> <para> Type variables </para> </listitem>
6613 <listitem> <para> Tuples </para> </listitem>
6614 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6616 Here are some example type signatures for generic methods:
6619 op2 :: Bool -> (a,Bool)
6620 op3 :: [Int] -> a -> a
6623 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6627 This restriction is an implementation restriction: we just havn't got around to
6628 implementing the necessary bidirectional maps over arbitrary type constructors.
6629 It would be relatively easy to add specific type constructors, such as Maybe and list,
6630 to the ones that are allowed.</para>
6635 In an instance declaration for a generic class, the idea is that the compiler
6636 will fill in the methods for you, based on the generic templates. However it can only
6641 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6646 No constructor of the instance type has unboxed fields.
6650 (Of course, these things can only arise if you are already using GHC extensions.)
6651 However, you can still give an instance declarations for types which break these rules,
6652 provided you give explicit code to override any generic default methods.
6660 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6661 what the compiler does with generic declarations.
6666 <sect2> <title> Another example </title>
6668 Just to finish with, here's another example I rather like:
6672 nCons {| Unit |} _ = 1
6673 nCons {| a :*: b |} _ = 1
6674 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6677 tag {| Unit |} _ = 1
6678 tag {| a :*: b |} _ = 1
6679 tag {| a :+: b |} (Inl x) = tag x
6680 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6686 <sect1 id="monomorphism">
6687 <title>Control over monomorphism</title>
6689 <para>GHC supports two flags that control the way in which generalisation is
6690 carried out at let and where bindings.
6694 <title>Switching off the dreaded Monomorphism Restriction</title>
6695 <indexterm><primary><option>-X=NoMonomorphismRestriction</option></primary></indexterm>
6697 <para>Haskell's monomorphism restriction (see
6698 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6700 of the Haskell Report)
6701 can be completely switched off by
6702 <option>-X=NoMonomorphismRestriction</option>.
6707 <title>Monomorphic pattern bindings</title>
6708 <indexterm><primary><option>-X=NoMonoPatBinds</option></primary></indexterm>
6709 <indexterm><primary><option>-X=MonoPatBinds</option></primary></indexterm>
6711 <para> As an experimental change, we are exploring the possibility of
6712 making pattern bindings monomorphic; that is, not generalised at all.
6713 A pattern binding is a binding whose LHS has no function arguments,
6714 and is not a simple variable. For example:
6716 f x = x -- Not a pattern binding
6717 f = \x -> x -- Not a pattern binding
6718 f :: Int -> Int = \x -> x -- Not a pattern binding
6720 (g,h) = e -- A pattern binding
6721 (f) = e -- A pattern binding
6722 [x] = e -- A pattern binding
6724 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6725 default</emphasis>. Use <option>-X=MonoPatBinds</option> to recover the
6734 ;;; Local Variables: ***
6736 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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