1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flag control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Generally speaking, all the language options are introduced by "<option>-X</option>",
46 e.g. <option>-XTemplateHaskell</option>.
49 <para> All the language options can be turned off by using the prefix "<option>No</option>";
50 e.g. "<option>-XNoTemplateHaskell</option>".</para>
52 <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
53 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
55 <para>Turning on an option that enables special syntax
56 <emphasis>might</emphasis> cause working Haskell 98 code to fail
57 to compile, perhaps because it uses a variable name which has
58 become a reserved word. So, together with each option below, we
59 list the special syntax which is enabled by this option. We use
60 notation and nonterminal names from the Haskell 98 lexical syntax
61 (see the Haskell 98 Report). There are two classes of special
66 <para>New reserved words and symbols: character sequences
67 which are no longer available for use as identifiers in the
71 <para>Other special syntax: sequences of characters that have
72 a different meaning when this particular option is turned
77 <para>We are only listing syntax changes here that might affect
78 existing working programs (i.e. "stolen" syntax). Many of these
79 extensions will also enable new context-free syntax, but in all
80 cases programs written to use the new syntax would not be
81 compilable without the option enabled.</para>
87 <option>-fglasgow-exts</option>:
88 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
91 <para>This simultaneously enables all of the extensions to
92 Haskell 98 described in <xref
93 linkend="ghc-language-features"/>, except where otherwise
94 noted. We are trying to move away from this portmanteau flag,
95 and towards enabling features individaully.</para>
97 <para>New reserved words: <literal>forall</literal> (only in
98 types), <literal>mdo</literal>.</para>
100 <para>Other syntax stolen:
101 <replaceable>varid</replaceable>{<literal>#</literal>},
102 <replaceable>char</replaceable><literal>#</literal>,
103 <replaceable>string</replaceable><literal>#</literal>,
104 <replaceable>integer</replaceable><literal>#</literal>,
105 <replaceable>float</replaceable><literal>#</literal>,
106 <replaceable>float</replaceable><literal>##</literal>,
107 <literal>(#</literal>, <literal>#)</literal>,
108 <literal>|)</literal>, <literal>{|</literal>.</para>
110 <para>Implies these specific language options:
111 <option>-XForeignFunctionInterface</option>,
112 <option>-XImplicitParams</option>,
113 <option>-XScopedTypeVariables</option>,
114 <option>-XGADTs</option>,
115 <option>-XTypeFamilies</option>. </para>
121 <option>-XForeignFunctionInterface</option>:
122 <indexterm><primary><option>-XForeignFunctionInterface</option></primary></indexterm>
125 <para>This option enables the language extension defined in the
126 Haskell 98 Foreign Function Interface Addendum.</para>
128 <para>New reserved words: <literal>foreign</literal>.</para>
134 <option>-XMonomorphismRestriction</option>,<option>-XMonoPatBinds</option>:
137 <para> These two flags control how generalisation is done.
138 See <xref linkend="monomorphism"/>.
145 <option>-XExtendedDefaultRules</option>:
146 <indexterm><primary><option>-XExtendedDefaultRules</option></primary></indexterm>
149 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
150 Independent of the <option>-fglasgow-exts</option>
157 <option>-XOverlappingInstances</option>
158 <indexterm><primary><option>-XOverlappingInstances</option></primary></indexterm>
161 <option>-XUndecidableInstances</option>
162 <indexterm><primary><option>-XUndecidableInstances</option></primary></indexterm>
165 <option>-XIncoherentInstances</option>
166 <indexterm><primary><option>-XIncoherentInstances</option></primary></indexterm>
169 <option>-fcontext-stack=N</option>
170 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
173 <para> See <xref linkend="instance-decls"/>. Only relevant
174 if you also use <option>-fglasgow-exts</option>.</para>
180 <option>-finline-phase</option>
181 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
184 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
185 you also use <option>-fglasgow-exts</option>.</para>
191 <option>-XArrows</option>
192 <indexterm><primary><option>-XArrows</option></primary></indexterm>
195 <para>See <xref linkend="arrow-notation"/>. Independent of
196 <option>-fglasgow-exts</option>.</para>
198 <para>New reserved words/symbols: <literal>rec</literal>,
199 <literal>proc</literal>, <literal>-<</literal>,
200 <literal>>-</literal>, <literal>-<<</literal>,
201 <literal>>>-</literal>.</para>
203 <para>Other syntax stolen: <literal>(|</literal>,
204 <literal>|)</literal>.</para>
210 <option>-XGenerics</option>
211 <indexterm><primary><option>-XGenerics</option></primary></indexterm>
214 <para>See <xref linkend="generic-classes"/>. Independent of
215 <option>-fglasgow-exts</option>.</para>
220 <term><option>-XNoImplicitPrelude</option></term>
222 <para><indexterm><primary>-XNoImplicitPrelude
223 option</primary></indexterm> GHC normally imports
224 <filename>Prelude.hi</filename> files for you. If you'd
225 rather it didn't, then give it a
226 <option>-XNoImplicitPrelude</option> option. The idea is
227 that you can then import a Prelude of your own. (But don't
228 call it <literal>Prelude</literal>; the Haskell module
229 namespace is flat, and you must not conflict with any
230 Prelude module.)</para>
232 <para>Even though you have not imported the Prelude, most of
233 the built-in syntax still refers to the built-in Haskell
234 Prelude types and values, as specified by the Haskell
235 Report. For example, the type <literal>[Int]</literal>
236 still means <literal>Prelude.[] Int</literal>; tuples
237 continue to refer to the standard Prelude tuples; the
238 translation for list comprehensions continues to use
239 <literal>Prelude.map</literal> etc.</para>
241 <para>However, <option>-XNoImplicitPrelude</option> does
242 change the handling of certain built-in syntax: see <xref
243 linkend="rebindable-syntax"/>.</para>
248 <term><option>-XImplicitParams</option></term>
250 <para>Enables implicit parameters (see <xref
251 linkend="implicit-parameters"/>). Currently also implied by
252 <option>-fglasgow-exts</option>.</para>
255 <literal>?<replaceable>varid</replaceable></literal>,
256 <literal>%<replaceable>varid</replaceable></literal>.</para>
261 <term><option>-XOverloadedStrings</option></term>
263 <para>Enables overloaded string literals (see <xref
264 linkend="overloaded-strings"/>).</para>
269 <term><option>-XScopedTypeVariables</option></term>
271 <para>Enables lexically-scoped type variables (see <xref
272 linkend="scoped-type-variables"/>). Implied by
273 <option>-fglasgow-exts</option>.</para>
278 <term><option>-XTemplateHaskell</option></term>
280 <para>Enables Template Haskell (see <xref
281 linkend="template-haskell"/>). This flag must
282 be given explicitly; it is no longer implied by
283 <option>-fglasgow-exts</option>.</para>
285 <para>Syntax stolen: <literal>[|</literal>,
286 <literal>[e|</literal>, <literal>[p|</literal>,
287 <literal>[d|</literal>, <literal>[t|</literal>,
288 <literal>$(</literal>,
289 <literal>$<replaceable>varid</replaceable></literal>.</para>
296 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
297 <sect1 id="primitives">
298 <title>Unboxed types and primitive operations</title>
300 <para>GHC is built on a raft of primitive data types and operations.
301 While you really can use this stuff to write fast code,
302 we generally find it a lot less painful, and more satisfying in the
303 long run, to use higher-level language features and libraries. With
304 any luck, the code you write will be optimised to the efficient
305 unboxed version in any case. And if it isn't, we'd like to know
308 <para>We do not currently have good, up-to-date documentation about the
309 primitives, perhaps because they are mainly intended for internal use.
310 There used to be a long section about them here in the User Guide, but it
311 became out of date, and wrong information is worse than none.</para>
313 <para>The Real Truth about what primitive types there are, and what operations
314 work over those types, is held in the file
315 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
316 This file is used directly to generate GHC's primitive-operation definitions, so
317 it is always correct! It is also intended for processing into text.</para>
320 the result of such processing is part of the description of the
322 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
323 Core language</ulink>.
324 So that document is a good place to look for a type-set version.
325 We would be very happy if someone wanted to volunteer to produce an SGML
326 back end to the program that processes <filename>primops.txt</filename> so that
327 we could include the results here in the User Guide.</para>
329 <para>What follows here is a brief summary of some main points.</para>
331 <sect2 id="glasgow-unboxed">
336 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
339 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
340 that values of that type are represented by a pointer to a heap
341 object. The representation of a Haskell <literal>Int</literal>, for
342 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
343 type, however, is represented by the value itself, no pointers or heap
344 allocation are involved.
348 Unboxed types correspond to the “raw machine” types you
349 would use in C: <literal>Int#</literal> (long int),
350 <literal>Double#</literal> (double), <literal>Addr#</literal>
351 (void *), etc. The <emphasis>primitive operations</emphasis>
352 (PrimOps) on these types are what you might expect; e.g.,
353 <literal>(+#)</literal> is addition on
354 <literal>Int#</literal>s, and is the machine-addition that we all
355 know and love—usually one instruction.
359 Primitive (unboxed) types cannot be defined in Haskell, and are
360 therefore built into the language and compiler. Primitive types are
361 always unlifted; that is, a value of a primitive type cannot be
362 bottom. We use the convention that primitive types, values, and
363 operations have a <literal>#</literal> suffix.
367 Primitive values are often represented by a simple bit-pattern, such
368 as <literal>Int#</literal>, <literal>Float#</literal>,
369 <literal>Double#</literal>. But this is not necessarily the case:
370 a primitive value might be represented by a pointer to a
371 heap-allocated object. Examples include
372 <literal>Array#</literal>, the type of primitive arrays. A
373 primitive array is heap-allocated because it is too big a value to fit
374 in a register, and would be too expensive to copy around; in a sense,
375 it is accidental that it is represented by a pointer. If a pointer
376 represents a primitive value, then it really does point to that value:
377 no unevaluated thunks, no indirections…nothing can be at the
378 other end of the pointer than the primitive value.
379 A numerically-intensive program using unboxed types can
380 go a <emphasis>lot</emphasis> faster than its “standard”
381 counterpart—we saw a threefold speedup on one example.
385 There are some restrictions on the use of primitive types:
387 <listitem><para>The main restriction
388 is that you can't pass a primitive value to a polymorphic
389 function or store one in a polymorphic data type. This rules out
390 things like <literal>[Int#]</literal> (i.e. lists of primitive
391 integers). The reason for this restriction is that polymorphic
392 arguments and constructor fields are assumed to be pointers: if an
393 unboxed integer is stored in one of these, the garbage collector would
394 attempt to follow it, leading to unpredictable space leaks. Or a
395 <function>seq</function> operation on the polymorphic component may
396 attempt to dereference the pointer, with disastrous results. Even
397 worse, the unboxed value might be larger than a pointer
398 (<literal>Double#</literal> for instance).
401 <listitem><para> You cannot define a newtype whose representation type
402 (the argument type of the data constructor) is an unboxed type. Thus,
408 <listitem><para> You cannot bind a variable with an unboxed type
409 in a <emphasis>top-level</emphasis> binding.
411 <listitem><para> You cannot bind a variable with an unboxed type
412 in a <emphasis>recursive</emphasis> binding.
414 <listitem><para> You may bind unboxed variables in a (non-recursive,
415 non-top-level) pattern binding, but any such variable causes the entire
417 to become strict. For example:
419 data Foo = Foo Int Int#
421 f x = let (Foo a b, w) = ..rhs.. in ..body..
423 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
425 is strict, and the program behaves as if you had written
427 data Foo = Foo Int Int#
429 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
438 <sect2 id="unboxed-tuples">
439 <title>Unboxed Tuples
443 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
444 they're available by default with <option>-fglasgow-exts</option>. An
445 unboxed tuple looks like this:
457 where <literal>e_1..e_n</literal> are expressions of any
458 type (primitive or non-primitive). The type of an unboxed tuple looks
463 Unboxed tuples are used for functions that need to return multiple
464 values, but they avoid the heap allocation normally associated with
465 using fully-fledged tuples. When an unboxed tuple is returned, the
466 components are put directly into registers or on the stack; the
467 unboxed tuple itself does not have a composite representation. Many
468 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
470 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
471 tuples to avoid unnecessary allocation during sequences of operations.
475 There are some pretty stringent restrictions on the use of unboxed tuples:
480 Values of unboxed tuple types are subject to the same restrictions as
481 other unboxed types; i.e. they may not be stored in polymorphic data
482 structures or passed to polymorphic functions.
489 No variable can have an unboxed tuple type, nor may a constructor or function
490 argument have an unboxed tuple type. The following are all illegal:
494 data Foo = Foo (# Int, Int #)
496 f :: (# Int, Int #) -> (# Int, Int #)
499 g :: (# Int, Int #) -> Int
502 h x = let y = (# x,x #) in ...
509 The typical use of unboxed tuples is simply to return multiple values,
510 binding those multiple results with a <literal>case</literal> expression, thus:
512 f x y = (# x+1, y-1 #)
513 g x = case f x x of { (# a, b #) -> a + b }
515 You can have an unboxed tuple in a pattern binding, thus
517 f x = let (# p,q #) = h x in ..body..
519 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
520 the resulting binding is lazy like any other Haskell pattern binding. The
521 above example desugars like this:
523 f x = let t = case h x o f{ (# p,q #) -> (p,q)
528 Indeed, the bindings can even be recursive.
535 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
537 <sect1 id="syntax-extns">
538 <title>Syntactic extensions</title>
540 <!-- ====================== HIERARCHICAL MODULES ======================= -->
542 <sect2 id="hierarchical-modules">
543 <title>Hierarchical Modules</title>
545 <para>GHC supports a small extension to the syntax of module
546 names: a module name is allowed to contain a dot
547 <literal>‘.’</literal>. This is also known as the
548 “hierarchical module namespace” extension, because
549 it extends the normally flat Haskell module namespace into a
550 more flexible hierarchy of modules.</para>
552 <para>This extension has very little impact on the language
553 itself; modules names are <emphasis>always</emphasis> fully
554 qualified, so you can just think of the fully qualified module
555 name as <quote>the module name</quote>. In particular, this
556 means that the full module name must be given after the
557 <literal>module</literal> keyword at the beginning of the
558 module; for example, the module <literal>A.B.C</literal> must
561 <programlisting>module A.B.C</programlisting>
564 <para>It is a common strategy to use the <literal>as</literal>
565 keyword to save some typing when using qualified names with
566 hierarchical modules. For example:</para>
569 import qualified Control.Monad.ST.Strict as ST
572 <para>For details on how GHC searches for source and interface
573 files in the presence of hierarchical modules, see <xref
574 linkend="search-path"/>.</para>
576 <para>GHC comes with a large collection of libraries arranged
577 hierarchically; see the accompanying <ulink
578 url="../libraries/index.html">library
579 documentation</ulink>. More libraries to install are available
581 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
584 <!-- ====================== PATTERN GUARDS ======================= -->
586 <sect2 id="pattern-guards">
587 <title>Pattern guards</title>
590 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
591 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
595 Suppose we have an abstract data type of finite maps, with a
599 lookup :: FiniteMap -> Int -> Maybe Int
602 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
603 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
607 clunky env var1 var2 | ok1 && ok2 = val1 + val2
608 | otherwise = var1 + var2
619 The auxiliary functions are
623 maybeToBool :: Maybe a -> Bool
624 maybeToBool (Just x) = True
625 maybeToBool Nothing = False
627 expectJust :: Maybe a -> a
628 expectJust (Just x) = x
629 expectJust Nothing = error "Unexpected Nothing"
633 What is <function>clunky</function> doing? The guard <literal>ok1 &&
634 ok2</literal> checks that both lookups succeed, using
635 <function>maybeToBool</function> to convert the <function>Maybe</function>
636 types to booleans. The (lazily evaluated) <function>expectJust</function>
637 calls extract the values from the results of the lookups, and binds the
638 returned values to <varname>val1</varname> and <varname>val2</varname>
639 respectively. If either lookup fails, then clunky takes the
640 <literal>otherwise</literal> case and returns the sum of its arguments.
644 This is certainly legal Haskell, but it is a tremendously verbose and
645 un-obvious way to achieve the desired effect. Arguably, a more direct way
646 to write clunky would be to use case expressions:
650 clunky env var1 var2 = case lookup env var1 of
652 Just val1 -> case lookup env var2 of
654 Just val2 -> val1 + val2
660 This is a bit shorter, but hardly better. Of course, we can rewrite any set
661 of pattern-matching, guarded equations as case expressions; that is
662 precisely what the compiler does when compiling equations! The reason that
663 Haskell provides guarded equations is because they allow us to write down
664 the cases we want to consider, one at a time, independently of each other.
665 This structure is hidden in the case version. Two of the right-hand sides
666 are really the same (<function>fail</function>), and the whole expression
667 tends to become more and more indented.
671 Here is how I would write clunky:
676 | Just val1 <- lookup env var1
677 , Just val2 <- lookup env var2
679 ...other equations for clunky...
683 The semantics should be clear enough. The qualifiers are matched in order.
684 For a <literal><-</literal> qualifier, which I call a pattern guard, the
685 right hand side is evaluated and matched against the pattern on the left.
686 If the match fails then the whole guard fails and the next equation is
687 tried. If it succeeds, then the appropriate binding takes place, and the
688 next qualifier is matched, in the augmented environment. Unlike list
689 comprehensions, however, the type of the expression to the right of the
690 <literal><-</literal> is the same as the type of the pattern to its
691 left. The bindings introduced by pattern guards scope over all the
692 remaining guard qualifiers, and over the right hand side of the equation.
696 Just as with list comprehensions, boolean expressions can be freely mixed
697 with among the pattern guards. For example:
708 Haskell's current guards therefore emerge as a special case, in which the
709 qualifier list has just one element, a boolean expression.
713 <!-- ===================== Recursive do-notation =================== -->
715 <sect2 id="mdo-notation">
716 <title>The recursive do-notation
719 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
720 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
721 by Levent Erkok, John Launchbury,
722 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
723 This paper is essential reading for anyone making non-trivial use of mdo-notation,
724 and we do not repeat it here.
727 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
728 that is, the variables bound in a do-expression are visible only in the textually following
729 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
730 group. It turns out that several applications can benefit from recursive bindings in
731 the do-notation, and this extension provides the necessary syntactic support.
734 Here is a simple (yet contrived) example:
737 import Control.Monad.Fix
739 justOnes = mdo xs <- Just (1:xs)
743 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
747 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
750 class Monad m => MonadFix m where
751 mfix :: (a -> m a) -> m a
754 The function <literal>mfix</literal>
755 dictates how the required recursion operation should be performed. For example,
756 <literal>justOnes</literal> desugars as follows:
758 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
760 For full details of the way in which mdo is typechecked and desugared, see
761 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
762 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
765 If recursive bindings are required for a monad,
766 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
767 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
768 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
769 for Haskell's internal state monad (strict and lazy, respectively).
772 There are three important points in using the recursive-do notation:
775 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
776 than <literal>do</literal>).
780 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
786 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
787 contains up to date information on recursive monadic bindings.
791 Historical note: The old implementation of the mdo-notation (and most
792 of the existing documents) used the name
793 <literal>MonadRec</literal> for the class and the corresponding library.
794 This name is not supported by GHC.
800 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
802 <sect2 id="parallel-list-comprehensions">
803 <title>Parallel List Comprehensions</title>
804 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
806 <indexterm><primary>parallel list comprehensions</primary>
809 <para>Parallel list comprehensions are a natural extension to list
810 comprehensions. List comprehensions can be thought of as a nice
811 syntax for writing maps and filters. Parallel comprehensions
812 extend this to include the zipWith family.</para>
814 <para>A parallel list comprehension has multiple independent
815 branches of qualifier lists, each separated by a `|' symbol. For
816 example, the following zips together two lists:</para>
819 [ (x, y) | x <- xs | y <- ys ]
822 <para>The behavior of parallel list comprehensions follows that of
823 zip, in that the resulting list will have the same length as the
824 shortest branch.</para>
826 <para>We can define parallel list comprehensions by translation to
827 regular comprehensions. Here's the basic idea:</para>
829 <para>Given a parallel comprehension of the form: </para>
832 [ e | p1 <- e11, p2 <- e12, ...
833 | q1 <- e21, q2 <- e22, ...
838 <para>This will be translated to: </para>
841 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
842 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
847 <para>where `zipN' is the appropriate zip for the given number of
852 <sect2 id="rebindable-syntax">
853 <title>Rebindable syntax</title>
856 <para>GHC allows most kinds of built-in syntax to be rebound by
857 the user, to facilitate replacing the <literal>Prelude</literal>
858 with a home-grown version, for example.</para>
860 <para>You may want to define your own numeric class
861 hierarchy. It completely defeats that purpose if the
862 literal "1" means "<literal>Prelude.fromInteger
863 1</literal>", which is what the Haskell Report specifies.
864 So the <option>-XNoImplicitPrelude</option> flag causes
865 the following pieces of built-in syntax to refer to
866 <emphasis>whatever is in scope</emphasis>, not the Prelude
871 <para>An integer literal <literal>368</literal> means
872 "<literal>fromInteger (368::Integer)</literal>", rather than
873 "<literal>Prelude.fromInteger (368::Integer)</literal>".
876 <listitem><para>Fractional literals are handed in just the same way,
877 except that the translation is
878 <literal>fromRational (3.68::Rational)</literal>.
881 <listitem><para>The equality test in an overloaded numeric pattern
882 uses whatever <literal>(==)</literal> is in scope.
885 <listitem><para>The subtraction operation, and the
886 greater-than-or-equal test, in <literal>n+k</literal> patterns
887 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
891 <para>Negation (e.g. "<literal>- (f x)</literal>")
892 means "<literal>negate (f x)</literal>", both in numeric
893 patterns, and expressions.
897 <para>"Do" notation is translated using whatever
898 functions <literal>(>>=)</literal>,
899 <literal>(>>)</literal>, and <literal>fail</literal>,
900 are in scope (not the Prelude
901 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
902 comprehensions, are unaffected. </para></listitem>
906 notation (see <xref linkend="arrow-notation"/>)
907 uses whatever <literal>arr</literal>,
908 <literal>(>>>)</literal>, <literal>first</literal>,
909 <literal>app</literal>, <literal>(|||)</literal> and
910 <literal>loop</literal> functions are in scope. But unlike the
911 other constructs, the types of these functions must match the
912 Prelude types very closely. Details are in flux; if you want
916 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
917 even if that is a little unexpected. For emample, the
918 static semantics of the literal <literal>368</literal>
919 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
920 <literal>fromInteger</literal> to have any of the types:
922 fromInteger :: Integer -> Integer
923 fromInteger :: forall a. Foo a => Integer -> a
924 fromInteger :: Num a => a -> Integer
925 fromInteger :: Integer -> Bool -> Bool
929 <para>Be warned: this is an experimental facility, with
930 fewer checks than usual. Use <literal>-dcore-lint</literal>
931 to typecheck the desugared program. If Core Lint is happy
932 you should be all right.</para>
936 <sect2 id="postfix-operators">
937 <title>Postfix operators</title>
940 GHC allows a small extension to the syntax of left operator sections, which
941 allows you to define postfix operators. The extension is this: the left section
945 is equivalent (from the point of view of both type checking and execution) to the expression
949 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
950 The strict Haskell 98 interpretation is that the section is equivalent to
954 That is, the operator must be a function of two arguments. GHC allows it to
955 take only one argument, and that in turn allows you to write the function
958 <para>Since this extension goes beyond Haskell 98, it should really be enabled
959 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
960 change their behaviour, of course.)
962 <para>The extension does not extend to the left-hand side of function
963 definitions; you must define such a function in prefix form.</para>
967 <sect2 id="disambiguate-fields">
968 <title>Record field disambiguation</title>
970 In record construction and record pattern matching
971 it is entirely unambiguous which field is referred to, even if there are two different
972 data types in scope with a common field name. For example:
975 data S = MkS { x :: Int, y :: Bool }
980 data T = MkT { x :: Int }
982 ok1 (MkS { x = n }) = n+1 -- Unambiguous
984 ok2 n = MkT { x = n+1 } -- Unambiguous
986 bad1 k = k { x = 3 } -- Ambiguous
987 bad2 k = x k -- Ambiguous
989 Even though there are two <literal>x</literal>'s in scope,
990 it is clear that the <literal>x</literal> in the pattern in the
991 definition of <literal>ok1</literal> can only mean the field
992 <literal>x</literal> from type <literal>S</literal>. Similarly for
993 the function <literal>ok2</literal>. However, in the record update
994 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
995 it is not clear which of the two types is intended.
998 Haskell 98 regards all four as ambiguous, but with the
999 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1000 the former two. The rules are precisely the same as those for instance
1001 declarations in Haskell 98, where the method names on the left-hand side
1002 of the method bindings in an instance declaration refer unambiguously
1003 to the method of that class (provided they are in scope at all), even
1004 if there are other variables in scope with the same name.
1005 This reduces the clutter of qualified names when you import two
1006 records from different modules that use the same field name.
1012 <!-- TYPE SYSTEM EXTENSIONS -->
1013 <sect1 id="data-type-extensions">
1014 <title>Extensions to data types and type synonyms</title>
1016 <sect2 id="nullary-types">
1017 <title>Data types with no constructors</title>
1019 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1020 a data type with no constructors. For example:</para>
1024 data T a -- T :: * -> *
1027 <para>Syntactically, the declaration lacks the "= constrs" part. The
1028 type can be parameterised over types of any kind, but if the kind is
1029 not <literal>*</literal> then an explicit kind annotation must be used
1030 (see <xref linkend="kinding"/>).</para>
1032 <para>Such data types have only one value, namely bottom.
1033 Nevertheless, they can be useful when defining "phantom types".</para>
1036 <sect2 id="infix-tycons">
1037 <title>Infix type constructors, classes, and type variables</title>
1040 GHC allows type constructors, classes, and type variables to be operators, and
1041 to be written infix, very much like expressions. More specifically:
1044 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1045 The lexical syntax is the same as that for data constructors.
1048 Data type and type-synonym declarations can be written infix, parenthesised
1049 if you want further arguments. E.g.
1051 data a :*: b = Foo a b
1052 type a :+: b = Either a b
1053 class a :=: b where ...
1055 data (a :**: b) x = Baz a b x
1056 type (a :++: b) y = Either (a,b) y
1060 Types, and class constraints, can be written infix. For example
1063 f :: (a :=: b) => a -> b
1067 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1068 The lexical syntax is the same as that for variable operators, excluding "(.)",
1069 "(!)", and "(*)". In a binding position, the operator must be
1070 parenthesised. For example:
1072 type T (+) = Int + Int
1076 liftA2 :: Arrow (~>)
1077 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1083 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1084 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1087 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1088 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1089 sets the fixity for a data constructor and the corresponding type constructor. For example:
1093 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1094 and similarly for <literal>:*:</literal>.
1095 <literal>Int `a` Bool</literal>.
1098 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1105 <sect2 id="type-synonyms">
1106 <title>Liberalised type synonyms</title>
1109 Type synonyms are like macros at the type level, and
1110 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1111 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1113 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1114 in a type synonym, thus:
1116 type Discard a = forall b. Show b => a -> b -> (a, String)
1121 g :: Discard Int -> (Int,String) -- A rank-2 type
1128 You can write an unboxed tuple in a type synonym:
1130 type Pr = (# Int, Int #)
1138 You can apply a type synonym to a forall type:
1140 type Foo a = a -> a -> Bool
1142 f :: Foo (forall b. b->b)
1144 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1146 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1151 You can apply a type synonym to a partially applied type synonym:
1153 type Generic i o = forall x. i x -> o x
1156 foo :: Generic Id []
1158 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1160 foo :: forall x. x -> [x]
1168 GHC currently does kind checking before expanding synonyms (though even that
1172 After expanding type synonyms, GHC does validity checking on types, looking for
1173 the following mal-formedness which isn't detected simply by kind checking:
1176 Type constructor applied to a type involving for-alls.
1179 Unboxed tuple on left of an arrow.
1182 Partially-applied type synonym.
1186 this will be rejected:
1188 type Pr = (# Int, Int #)
1193 because GHC does not allow unboxed tuples on the left of a function arrow.
1198 <sect2 id="existential-quantification">
1199 <title>Existentially quantified data constructors
1203 The idea of using existential quantification in data type declarations
1204 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1205 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1206 London, 1991). It was later formalised by Laufer and Odersky
1207 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1208 TOPLAS, 16(5), pp1411-1430, 1994).
1209 It's been in Lennart
1210 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1211 proved very useful. Here's the idea. Consider the declaration:
1217 data Foo = forall a. MkFoo a (a -> Bool)
1224 The data type <literal>Foo</literal> has two constructors with types:
1230 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1237 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1238 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1239 For example, the following expression is fine:
1245 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1251 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1252 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1253 isUpper</function> packages a character with a compatible function. These
1254 two things are each of type <literal>Foo</literal> and can be put in a list.
1258 What can we do with a value of type <literal>Foo</literal>?. In particular,
1259 what happens when we pattern-match on <function>MkFoo</function>?
1265 f (MkFoo val fn) = ???
1271 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1272 are compatible, the only (useful) thing we can do with them is to
1273 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1280 f (MkFoo val fn) = fn val
1286 What this allows us to do is to package heterogenous values
1287 together with a bunch of functions that manipulate them, and then treat
1288 that collection of packages in a uniform manner. You can express
1289 quite a bit of object-oriented-like programming this way.
1292 <sect3 id="existential">
1293 <title>Why existential?
1297 What has this to do with <emphasis>existential</emphasis> quantification?
1298 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1304 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1310 But Haskell programmers can safely think of the ordinary
1311 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1312 adding a new existential quantification construct.
1318 <title>Type classes</title>
1321 An easy extension is to allow
1322 arbitrary contexts before the constructor. For example:
1328 data Baz = forall a. Eq a => Baz1 a a
1329 | forall b. Show b => Baz2 b (b -> b)
1335 The two constructors have the types you'd expect:
1341 Baz1 :: forall a. Eq a => a -> a -> Baz
1342 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1348 But when pattern matching on <function>Baz1</function> the matched values can be compared
1349 for equality, and when pattern matching on <function>Baz2</function> the first matched
1350 value can be converted to a string (as well as applying the function to it).
1351 So this program is legal:
1358 f (Baz1 p q) | p == q = "Yes"
1360 f (Baz2 v fn) = show (fn v)
1366 Operationally, in a dictionary-passing implementation, the
1367 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1368 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1369 extract it on pattern matching.
1373 Notice the way that the syntax fits smoothly with that used for
1374 universal quantification earlier.
1379 <sect3 id="existential-records">
1380 <title>Record Constructors</title>
1383 GHC allows existentials to be used with records syntax as well. For example:
1386 data Counter a = forall self. NewCounter
1388 , _inc :: self -> self
1389 , _display :: self -> IO ()
1393 Here <literal>tag</literal> is a public field, with a well-typed selector
1394 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1395 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1396 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1397 compile-time error. In other words, <emphasis>GHC defines a record selector function
1398 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1399 (This example used an underscore in the fields for which record selectors
1400 will not be defined, but that is only programming style; GHC ignores them.)
1404 To make use of these hidden fields, we need to create some helper functions:
1407 inc :: Counter a -> Counter a
1408 inc (NewCounter x i d t) = NewCounter
1409 { _this = i x, _inc = i, _display = d, tag = t }
1411 display :: Counter a -> IO ()
1412 display NewCounter{ _this = x, _display = d } = d x
1415 Now we can define counters with different underlying implementations:
1418 counterA :: Counter String
1419 counterA = NewCounter
1420 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1422 counterB :: Counter String
1423 counterB = NewCounter
1424 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1427 display (inc counterA) -- prints "1"
1428 display (inc (inc counterB)) -- prints "##"
1431 At the moment, record update syntax is only supported for Haskell 98 data types,
1432 so the following function does <emphasis>not</emphasis> work:
1435 -- This is invalid; use explicit NewCounter instead for now
1436 setTag :: Counter a -> a -> Counter a
1437 setTag obj t = obj{ tag = t }
1446 <title>Restrictions</title>
1449 There are several restrictions on the ways in which existentially-quantified
1450 constructors can be use.
1459 When pattern matching, each pattern match introduces a new,
1460 distinct, type for each existential type variable. These types cannot
1461 be unified with any other type, nor can they escape from the scope of
1462 the pattern match. For example, these fragments are incorrect:
1470 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1471 is the result of <function>f1</function>. One way to see why this is wrong is to
1472 ask what type <function>f1</function> has:
1476 f1 :: Foo -> a -- Weird!
1480 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1485 f1 :: forall a. Foo -> a -- Wrong!
1489 The original program is just plain wrong. Here's another sort of error
1493 f2 (Baz1 a b) (Baz1 p q) = a==q
1497 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1498 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1499 from the two <function>Baz1</function> constructors.
1507 You can't pattern-match on an existentially quantified
1508 constructor in a <literal>let</literal> or <literal>where</literal> group of
1509 bindings. So this is illegal:
1513 f3 x = a==b where { Baz1 a b = x }
1516 Instead, use a <literal>case</literal> expression:
1519 f3 x = case x of Baz1 a b -> a==b
1522 In general, you can only pattern-match
1523 on an existentially-quantified constructor in a <literal>case</literal> expression or
1524 in the patterns of a function definition.
1526 The reason for this restriction is really an implementation one.
1527 Type-checking binding groups is already a nightmare without
1528 existentials complicating the picture. Also an existential pattern
1529 binding at the top level of a module doesn't make sense, because it's
1530 not clear how to prevent the existentially-quantified type "escaping".
1531 So for now, there's a simple-to-state restriction. We'll see how
1539 You can't use existential quantification for <literal>newtype</literal>
1540 declarations. So this is illegal:
1544 newtype T = forall a. Ord a => MkT a
1548 Reason: a value of type <literal>T</literal> must be represented as a
1549 pair of a dictionary for <literal>Ord t</literal> and a value of type
1550 <literal>t</literal>. That contradicts the idea that
1551 <literal>newtype</literal> should have no concrete representation.
1552 You can get just the same efficiency and effect by using
1553 <literal>data</literal> instead of <literal>newtype</literal>. If
1554 there is no overloading involved, then there is more of a case for
1555 allowing an existentially-quantified <literal>newtype</literal>,
1556 because the <literal>data</literal> version does carry an
1557 implementation cost, but single-field existentially quantified
1558 constructors aren't much use. So the simple restriction (no
1559 existential stuff on <literal>newtype</literal>) stands, unless there
1560 are convincing reasons to change it.
1568 You can't use <literal>deriving</literal> to define instances of a
1569 data type with existentially quantified data constructors.
1571 Reason: in most cases it would not make sense. For example:;
1574 data T = forall a. MkT [a] deriving( Eq )
1577 To derive <literal>Eq</literal> in the standard way we would need to have equality
1578 between the single component of two <function>MkT</function> constructors:
1582 (MkT a) == (MkT b) = ???
1585 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1586 It's just about possible to imagine examples in which the derived instance
1587 would make sense, but it seems altogether simpler simply to prohibit such
1588 declarations. Define your own instances!
1599 <!-- ====================== Generalised algebraic data types ======================= -->
1601 <sect2 id="gadt-style">
1602 <title>Declaring data types with explicit constructor signatures</title>
1604 <para>GHC allows you to declare an algebraic data type by
1605 giving the type signatures of constructors explicitly. For example:
1609 Just :: a -> Maybe a
1611 The form is called a "GADT-style declaration"
1612 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1613 can only be declared using this form.</para>
1614 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1615 For example, these two declarations are equivalent:
1617 data Foo = forall a. MkFoo a (a -> Bool)
1618 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1621 <para>Any data type that can be declared in standard Haskell-98 syntax
1622 can also be declared using GADT-style syntax.
1623 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1624 they treat class constraints on the data constructors differently.
1625 Specifically, if the constructor is given a type-class context, that
1626 context is made available by pattern matching. For example:
1629 MkSet :: Eq a => [a] -> Set a
1631 makeSet :: Eq a => [a] -> Set a
1632 makeSet xs = MkSet (nub xs)
1634 insert :: a -> Set a -> Set a
1635 insert a (MkSet as) | a `elem` as = MkSet as
1636 | otherwise = MkSet (a:as)
1638 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1639 gives rise to a <literal>(Eq a)</literal>
1640 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1641 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1642 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1643 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1644 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1645 In the example, the equality dictionary is used to satisfy the equality constraint
1646 generated by the call to <literal>elem</literal>, so that the type of
1647 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1649 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1650 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1651 In Haskell 98 the defintion
1653 data Eq a => Set' a = MkSet' [a]
1655 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1656 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1657 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1658 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1659 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1661 For example, a possible application of GHC's behaviour is to reify dictionaries:
1663 data NumInst a where
1664 MkNumInst :: Num a => NumInst a
1666 intInst :: NumInst Int
1669 plus :: NumInst a -> a -> a -> a
1670 plus MkNumInst p q = p + q
1672 Here, a value of type <literal>NumInst a</literal> is equivalent
1673 to an explicit <literal>(Num a)</literal> dictionary.
1677 The rest of this section gives further details about GADT-style data
1682 The result type of each data constructor must begin with the type constructor being defined.
1683 If the result type of all constructors
1684 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1685 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1686 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1690 The type signature of
1691 each constructor is independent, and is implicitly universally quantified as usual.
1692 Different constructors may have different universally-quantified type variables
1693 and different type-class constraints.
1694 For example, this is fine:
1697 T1 :: Eq b => b -> T b
1698 T2 :: (Show c, Ix c) => c -> [c] -> T c
1703 Unlike a Haskell-98-style
1704 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1705 have no scope. Indeed, one can write a kind signature instead:
1707 data Set :: * -> * where ...
1709 or even a mixture of the two:
1711 data Foo a :: (* -> *) -> * where ...
1713 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1716 data Foo a (b :: * -> *) where ...
1722 You can use strictness annotations, in the obvious places
1723 in the constructor type:
1726 Lit :: !Int -> Term Int
1727 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1728 Pair :: Term a -> Term b -> Term (a,b)
1733 You can use a <literal>deriving</literal> clause on a GADT-style data type
1734 declaration. For example, these two declarations are equivalent
1736 data Maybe1 a where {
1737 Nothing1 :: Maybe1 a ;
1738 Just1 :: a -> Maybe1 a
1739 } deriving( Eq, Ord )
1741 data Maybe2 a = Nothing2 | Just2 a
1747 You can use record syntax on a GADT-style data type declaration:
1751 Adult { name :: String, children :: [Person] } :: Person
1752 Child { name :: String } :: Person
1754 As usual, for every constructor that has a field <literal>f</literal>, the type of
1755 field <literal>f</literal> must be the same (modulo alpha conversion).
1758 At the moment, record updates are not yet possible with GADT-style declarations,
1759 so support is limited to record construction, selection and pattern matching.
1762 aPerson = Adult { name = "Fred", children = [] }
1764 shortName :: Person -> Bool
1765 hasChildren (Adult { children = kids }) = not (null kids)
1766 hasChildren (Child {}) = False
1771 As in the case of existentials declared using the Haskell-98-like record syntax
1772 (<xref linkend="existential-records"/>),
1773 record-selector functions are generated only for those fields that have well-typed
1775 Here is the example of that section, in GADT-style syntax:
1777 data Counter a where
1778 NewCounter { _this :: self
1779 , _inc :: self -> self
1780 , _display :: self -> IO ()
1785 As before, only one selector function is generated here, that for <literal>tag</literal>.
1786 Nevertheless, you can still use all the field names in pattern matching and record construction.
1788 </itemizedlist></para>
1792 <title>Generalised Algebraic Data Types (GADTs)</title>
1794 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1795 by allowing constructors to have richer return types. Here is an example:
1798 Lit :: Int -> Term Int
1799 Succ :: Term Int -> Term Int
1800 IsZero :: Term Int -> Term Bool
1801 If :: Term Bool -> Term a -> Term a -> Term a
1802 Pair :: Term a -> Term b -> Term (a,b)
1804 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1805 case with ordinary data types. This generality allows us to
1806 write a well-typed <literal>eval</literal> function
1807 for these <literal>Terms</literal>:
1811 eval (Succ t) = 1 + eval t
1812 eval (IsZero t) = eval t == 0
1813 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1814 eval (Pair e1 e2) = (eval e1, eval e2)
1816 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1817 For example, in the right hand side of the equation
1822 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1823 A precise specification of the type rules is beyond what this user manual aspires to,
1824 but the design closely follows that described in
1826 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1827 unification-based type inference for GADTs</ulink>,
1829 The general principle is this: <emphasis>type refinement is only carried out
1830 based on user-supplied type annotations</emphasis>.
1831 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1832 and lots of obscure error messages will
1833 occur. However, the refinement is quite general. For example, if we had:
1835 eval :: Term a -> a -> a
1836 eval (Lit i) j = i+j
1838 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1839 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1840 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1843 These and many other examples are given in papers by Hongwei Xi, and
1844 Tim Sheard. There is a longer introduction
1845 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1847 <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
1848 may use different notation to that implemented in GHC.
1851 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
1852 <option>-XGADTs</option>.
1855 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1856 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1857 The result type of each constructor must begin with the type constructor being defined,
1858 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1859 For example, in the <literal>Term</literal> data
1860 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1861 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1866 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1867 an ordianary data type.
1871 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1875 Lit { val :: Int } :: Term Int
1876 Succ { num :: Term Int } :: Term Int
1877 Pred { num :: Term Int } :: Term Int
1878 IsZero { arg :: Term Int } :: Term Bool
1879 Pair { arg1 :: Term a
1882 If { cnd :: Term Bool
1887 However, for GADTs there is the following additional constraint:
1888 every constructor that has a field <literal>f</literal> must have
1889 the same result type (modulo alpha conversion)
1890 Hence, in the above example, we cannot merge the <literal>num</literal>
1891 and <literal>arg</literal> fields above into a
1892 single name. Although their field types are both <literal>Term Int</literal>,
1893 their selector functions actually have different types:
1896 num :: Term Int -> Term Int
1897 arg :: Term Bool -> Term Int
1906 <!-- ====================== End of Generalised algebraic data types ======================= -->
1909 <sect2 id="deriving-typeable">
1910 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1913 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1914 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1915 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1916 classes <literal>Eq</literal>, <literal>Ord</literal>,
1917 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1920 GHC extends this list with two more classes that may be automatically derived
1921 (provided the <option>-fglasgow-exts</option> flag is specified):
1922 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1923 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1924 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1926 <para>An instance of <literal>Typeable</literal> can only be derived if the
1927 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1928 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1930 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1931 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1933 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1934 are used, and only <literal>Typeable1</literal> up to
1935 <literal>Typeable7</literal> are provided in the library.)
1936 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1937 class, whose kind suits that of the data type constructor, and
1938 then writing the data type instance by hand.
1942 <sect2 id="newtype-deriving">
1943 <title>Generalised derived instances for newtypes</title>
1946 When you define an abstract type using <literal>newtype</literal>, you may want
1947 the new type to inherit some instances from its representation. In
1948 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1949 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1950 other classes you have to write an explicit instance declaration. For
1951 example, if you define
1954 newtype Dollars = Dollars Int
1957 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1958 explicitly define an instance of <literal>Num</literal>:
1961 instance Num Dollars where
1962 Dollars a + Dollars b = Dollars (a+b)
1965 All the instance does is apply and remove the <literal>newtype</literal>
1966 constructor. It is particularly galling that, since the constructor
1967 doesn't appear at run-time, this instance declaration defines a
1968 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1969 dictionary, only slower!
1973 <sect3> <title> Generalising the deriving clause </title>
1975 GHC now permits such instances to be derived instead, so one can write
1977 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1980 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1981 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1982 derives an instance declaration of the form
1985 instance Num Int => Num Dollars
1988 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1992 We can also derive instances of constructor classes in a similar
1993 way. For example, suppose we have implemented state and failure monad
1994 transformers, such that
1997 instance Monad m => Monad (State s m)
1998 instance Monad m => Monad (Failure m)
2000 In Haskell 98, we can define a parsing monad by
2002 type Parser tok m a = State [tok] (Failure m) a
2005 which is automatically a monad thanks to the instance declarations
2006 above. With the extension, we can make the parser type abstract,
2007 without needing to write an instance of class <literal>Monad</literal>, via
2010 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2013 In this case the derived instance declaration is of the form
2015 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2018 Notice that, since <literal>Monad</literal> is a constructor class, the
2019 instance is a <emphasis>partial application</emphasis> of the new type, not the
2020 entire left hand side. We can imagine that the type declaration is
2021 ``eta-converted'' to generate the context of the instance
2026 We can even derive instances of multi-parameter classes, provided the
2027 newtype is the last class parameter. In this case, a ``partial
2028 application'' of the class appears in the <literal>deriving</literal>
2029 clause. For example, given the class
2032 class StateMonad s m | m -> s where ...
2033 instance Monad m => StateMonad s (State s m) where ...
2035 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2037 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2038 deriving (Monad, StateMonad [tok])
2041 The derived instance is obtained by completing the application of the
2042 class to the new type:
2045 instance StateMonad [tok] (State [tok] (Failure m)) =>
2046 StateMonad [tok] (Parser tok m)
2051 As a result of this extension, all derived instances in newtype
2052 declarations are treated uniformly (and implemented just by reusing
2053 the dictionary for the representation type), <emphasis>except</emphasis>
2054 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2055 the newtype and its representation.
2059 <sect3> <title> A more precise specification </title>
2061 Derived instance declarations are constructed as follows. Consider the
2062 declaration (after expansion of any type synonyms)
2065 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2071 The <literal>ci</literal> are partial applications of
2072 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2073 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2076 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2079 The type <literal>t</literal> is an arbitrary type.
2082 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2083 nor in the <literal>ci</literal>, and
2086 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2087 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2088 should not "look through" the type or its constructor. You can still
2089 derive these classes for a newtype, but it happens in the usual way, not
2090 via this new mechanism.
2093 Then, for each <literal>ci</literal>, the derived instance
2096 instance ci t => ci (T v1...vk)
2098 As an example which does <emphasis>not</emphasis> work, consider
2100 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2102 Here we cannot derive the instance
2104 instance Monad (State s m) => Monad (NonMonad m)
2107 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2108 and so cannot be "eta-converted" away. It is a good thing that this
2109 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2110 not, in fact, a monad --- for the same reason. Try defining
2111 <literal>>>=</literal> with the correct type: you won't be able to.
2115 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2116 important, since we can only derive instances for the last one. If the
2117 <literal>StateMonad</literal> class above were instead defined as
2120 class StateMonad m s | m -> s where ...
2123 then we would not have been able to derive an instance for the
2124 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2125 classes usually have one "main" parameter for which deriving new
2126 instances is most interesting.
2128 <para>Lastly, all of this applies only for classes other than
2129 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2130 and <literal>Data</literal>, for which the built-in derivation applies (section
2131 4.3.3. of the Haskell Report).
2132 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2133 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2134 the standard method is used or the one described here.)
2140 <sect2 id="stand-alone-deriving">
2141 <title>Stand-alone deriving declarations</title>
2144 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2146 data Foo a = Bar a | Baz String
2148 derive instance Eq (Foo a)
2150 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2151 you can use it as a variable name elsewhere.</para>
2152 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2153 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2156 newtype Foo a = MkFoo (State Int a)
2158 derive instance MonadState Int Foo
2160 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2161 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2169 <!-- TYPE SYSTEM EXTENSIONS -->
2170 <sect1 id="other-type-extensions">
2171 <title>Other type system extensions</title>
2173 <sect2 id="multi-param-type-classes">
2174 <title>Class declarations</title>
2177 This section, and the next one, documents GHC's type-class extensions.
2178 There's lots of background in the paper <ulink
2179 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2180 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2181 Jones, Erik Meijer).
2184 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2188 <title>Multi-parameter type classes</title>
2190 Multi-parameter type classes are permitted. For example:
2194 class Collection c a where
2195 union :: c a -> c a -> c a
2203 <title>The superclasses of a class declaration</title>
2206 There are no restrictions on the context in a class declaration
2207 (which introduces superclasses), except that the class hierarchy must
2208 be acyclic. So these class declarations are OK:
2212 class Functor (m k) => FiniteMap m k where
2215 class (Monad m, Monad (t m)) => Transform t m where
2216 lift :: m a -> (t m) a
2222 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2223 of "acyclic" involves only the superclass relationships. For example,
2229 op :: D b => a -> b -> b
2232 class C a => D a where { ... }
2236 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2237 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2238 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2245 <sect3 id="class-method-types">
2246 <title>Class method types</title>
2249 Haskell 98 prohibits class method types to mention constraints on the
2250 class type variable, thus:
2253 fromList :: [a] -> s a
2254 elem :: Eq a => a -> s a -> Bool
2256 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2257 contains the constraint <literal>Eq a</literal>, constrains only the
2258 class type variable (in this case <literal>a</literal>).
2259 GHC lifts this restriction.
2266 <sect2 id="functional-dependencies">
2267 <title>Functional dependencies
2270 <para> Functional dependencies are implemented as described by Mark Jones
2271 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2272 In Proceedings of the 9th European Symposium on Programming,
2273 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2277 Functional dependencies are introduced by a vertical bar in the syntax of a
2278 class declaration; e.g.
2280 class (Monad m) => MonadState s m | m -> s where ...
2282 class Foo a b c | a b -> c where ...
2284 There should be more documentation, but there isn't (yet). Yell if you need it.
2287 <sect3><title>Rules for functional dependencies </title>
2289 In a class declaration, all of the class type variables must be reachable (in the sense
2290 mentioned in <xref linkend="type-restrictions"/>)
2291 from the free variables of each method type.
2295 class Coll s a where
2297 insert :: s -> a -> s
2300 is not OK, because the type of <literal>empty</literal> doesn't mention
2301 <literal>a</literal>. Functional dependencies can make the type variable
2304 class Coll s a | s -> a where
2306 insert :: s -> a -> s
2309 Alternatively <literal>Coll</literal> might be rewritten
2312 class Coll s a where
2314 insert :: s a -> a -> s a
2318 which makes the connection between the type of a collection of
2319 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2320 Occasionally this really doesn't work, in which case you can split the
2328 class CollE s => Coll s a where
2329 insert :: s -> a -> s
2336 <title>Background on functional dependencies</title>
2338 <para>The following description of the motivation and use of functional dependencies is taken
2339 from the Hugs user manual, reproduced here (with minor changes) by kind
2340 permission of Mark Jones.
2343 Consider the following class, intended as part of a
2344 library for collection types:
2346 class Collects e ce where
2348 insert :: e -> ce -> ce
2349 member :: e -> ce -> Bool
2351 The type variable e used here represents the element type, while ce is the type
2352 of the container itself. Within this framework, we might want to define
2353 instances of this class for lists or characteristic functions (both of which
2354 can be used to represent collections of any equality type), bit sets (which can
2355 be used to represent collections of characters), or hash tables (which can be
2356 used to represent any collection whose elements have a hash function). Omitting
2357 standard implementation details, this would lead to the following declarations:
2359 instance Eq e => Collects e [e] where ...
2360 instance Eq e => Collects e (e -> Bool) where ...
2361 instance Collects Char BitSet where ...
2362 instance (Hashable e, Collects a ce)
2363 => Collects e (Array Int ce) where ...
2365 All this looks quite promising; we have a class and a range of interesting
2366 implementations. Unfortunately, there are some serious problems with the class
2367 declaration. First, the empty function has an ambiguous type:
2369 empty :: Collects e ce => ce
2371 By "ambiguous" we mean that there is a type variable e that appears on the left
2372 of the <literal>=></literal> symbol, but not on the right. The problem with
2373 this is that, according to the theoretical foundations of Haskell overloading,
2374 we cannot guarantee a well-defined semantics for any term with an ambiguous
2378 We can sidestep this specific problem by removing the empty member from the
2379 class declaration. However, although the remaining members, insert and member,
2380 do not have ambiguous types, we still run into problems when we try to use
2381 them. For example, consider the following two functions:
2383 f x y = insert x . insert y
2386 for which GHC infers the following types:
2388 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2389 g :: (Collects Bool c, Collects Char c) => c -> c
2391 Notice that the type for f allows the two parameters x and y to be assigned
2392 different types, even though it attempts to insert each of the two values, one
2393 after the other, into the same collection. If we're trying to model collections
2394 that contain only one type of value, then this is clearly an inaccurate
2395 type. Worse still, the definition for g is accepted, without causing a type
2396 error. As a result, the error in this code will not be flagged at the point
2397 where it appears. Instead, it will show up only when we try to use g, which
2398 might even be in a different module.
2401 <sect4><title>An attempt to use constructor classes</title>
2404 Faced with the problems described above, some Haskell programmers might be
2405 tempted to use something like the following version of the class declaration:
2407 class Collects e c where
2409 insert :: e -> c e -> c e
2410 member :: e -> c e -> Bool
2412 The key difference here is that we abstract over the type constructor c that is
2413 used to form the collection type c e, and not over that collection type itself,
2414 represented by ce in the original class declaration. This avoids the immediate
2415 problems that we mentioned above: empty has type <literal>Collects e c => c
2416 e</literal>, which is not ambiguous.
2419 The function f from the previous section has a more accurate type:
2421 f :: (Collects e c) => e -> e -> c e -> c e
2423 The function g from the previous section is now rejected with a type error as
2424 we would hope because the type of f does not allow the two arguments to have
2426 This, then, is an example of a multiple parameter class that does actually work
2427 quite well in practice, without ambiguity problems.
2428 There is, however, a catch. This version of the Collects class is nowhere near
2429 as general as the original class seemed to be: only one of the four instances
2430 for <literal>Collects</literal>
2431 given above can be used with this version of Collects because only one of
2432 them---the instance for lists---has a collection type that can be written in
2433 the form c e, for some type constructor c, and element type e.
2437 <sect4><title>Adding functional dependencies</title>
2440 To get a more useful version of the Collects class, Hugs provides a mechanism
2441 that allows programmers to specify dependencies between the parameters of a
2442 multiple parameter class (For readers with an interest in theoretical
2443 foundations and previous work: The use of dependency information can be seen
2444 both as a generalization of the proposal for `parametric type classes' that was
2445 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2446 later framework for "improvement" of qualified types. The
2447 underlying ideas are also discussed in a more theoretical and abstract setting
2448 in a manuscript [implparam], where they are identified as one point in a
2449 general design space for systems of implicit parameterization.).
2451 To start with an abstract example, consider a declaration such as:
2453 class C a b where ...
2455 which tells us simply that C can be thought of as a binary relation on types
2456 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2457 included in the definition of classes to add information about dependencies
2458 between parameters, as in the following examples:
2460 class D a b | a -> b where ...
2461 class E a b | a -> b, b -> a where ...
2463 The notation <literal>a -> b</literal> used here between the | and where
2464 symbols --- not to be
2465 confused with a function type --- indicates that the a parameter uniquely
2466 determines the b parameter, and might be read as "a determines b." Thus D is
2467 not just a relation, but actually a (partial) function. Similarly, from the two
2468 dependencies that are included in the definition of E, we can see that E
2469 represents a (partial) one-one mapping between types.
2472 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2473 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2474 m>=0, meaning that the y parameters are uniquely determined by the x
2475 parameters. Spaces can be used as separators if more than one variable appears
2476 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2477 annotated with multiple dependencies using commas as separators, as in the
2478 definition of E above. Some dependencies that we can write in this notation are
2479 redundant, and will be rejected because they don't serve any useful
2480 purpose, and may instead indicate an error in the program. Examples of
2481 dependencies like this include <literal>a -> a </literal>,
2482 <literal>a -> a a </literal>,
2483 <literal>a -> </literal>, etc. There can also be
2484 some redundancy if multiple dependencies are given, as in
2485 <literal>a->b</literal>,
2486 <literal>b->c </literal>, <literal>a->c </literal>, and
2487 in which some subset implies the remaining dependencies. Examples like this are
2488 not treated as errors. Note that dependencies appear only in class
2489 declarations, and not in any other part of the language. In particular, the
2490 syntax for instance declarations, class constraints, and types is completely
2494 By including dependencies in a class declaration, we provide a mechanism for
2495 the programmer to specify each multiple parameter class more precisely. The
2496 compiler, on the other hand, is responsible for ensuring that the set of
2497 instances that are in scope at any given point in the program is consistent
2498 with any declared dependencies. For example, the following pair of instance
2499 declarations cannot appear together in the same scope because they violate the
2500 dependency for D, even though either one on its own would be acceptable:
2502 instance D Bool Int where ...
2503 instance D Bool Char where ...
2505 Note also that the following declaration is not allowed, even by itself:
2507 instance D [a] b where ...
2509 The problem here is that this instance would allow one particular choice of [a]
2510 to be associated with more than one choice for b, which contradicts the
2511 dependency specified in the definition of D. More generally, this means that,
2512 in any instance of the form:
2514 instance D t s where ...
2516 for some particular types t and s, the only variables that can appear in s are
2517 the ones that appear in t, and hence, if the type t is known, then s will be
2518 uniquely determined.
2521 The benefit of including dependency information is that it allows us to define
2522 more general multiple parameter classes, without ambiguity problems, and with
2523 the benefit of more accurate types. To illustrate this, we return to the
2524 collection class example, and annotate the original definition of <literal>Collects</literal>
2525 with a simple dependency:
2527 class Collects e ce | ce -> e where
2529 insert :: e -> ce -> ce
2530 member :: e -> ce -> Bool
2532 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2533 determined by the type of the collection ce. Note that both parameters of
2534 Collects are of kind *; there are no constructor classes here. Note too that
2535 all of the instances of Collects that we gave earlier can be used
2536 together with this new definition.
2539 What about the ambiguity problems that we encountered with the original
2540 definition? The empty function still has type Collects e ce => ce, but it is no
2541 longer necessary to regard that as an ambiguous type: Although the variable e
2542 does not appear on the right of the => symbol, the dependency for class
2543 Collects tells us that it is uniquely determined by ce, which does appear on
2544 the right of the => symbol. Hence the context in which empty is used can still
2545 give enough information to determine types for both ce and e, without
2546 ambiguity. More generally, we need only regard a type as ambiguous if it
2547 contains a variable on the left of the => that is not uniquely determined
2548 (either directly or indirectly) by the variables on the right.
2551 Dependencies also help to produce more accurate types for user defined
2552 functions, and hence to provide earlier detection of errors, and less cluttered
2553 types for programmers to work with. Recall the previous definition for a
2556 f x y = insert x y = insert x . insert y
2558 for which we originally obtained a type:
2560 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2562 Given the dependency information that we have for Collects, however, we can
2563 deduce that a and b must be equal because they both appear as the second
2564 parameter in a Collects constraint with the same first parameter c. Hence we
2565 can infer a shorter and more accurate type for f:
2567 f :: (Collects a c) => a -> a -> c -> c
2569 In a similar way, the earlier definition of g will now be flagged as a type error.
2572 Although we have given only a few examples here, it should be clear that the
2573 addition of dependency information can help to make multiple parameter classes
2574 more useful in practice, avoiding ambiguity problems, and allowing more general
2575 sets of instance declarations.
2581 <sect2 id="instance-decls">
2582 <title>Instance declarations</title>
2584 <sect3 id="instance-rules">
2585 <title>Relaxed rules for instance declarations</title>
2587 <para>An instance declaration has the form
2589 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 ...
2591 The part before the "<literal>=></literal>" is the
2592 <emphasis>context</emphasis>, while the part after the
2593 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2597 In Haskell 98 the head of an instance declaration
2598 must be of the form <literal>C (T a1 ... an)</literal>, where
2599 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2600 and the <literal>a1 ... an</literal> are distinct type variables.
2601 Furthermore, the assertions in the context of the instance declaration
2602 must be of the form <literal>C a</literal> where <literal>a</literal>
2603 is a type variable that occurs in the head.
2606 The <option>-fglasgow-exts</option> flag loosens these restrictions
2607 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2608 the context and head of the instance declaration can each consist of arbitrary
2609 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2613 The Paterson Conditions: for each assertion in the context
2615 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2616 <listitem><para>The assertion has fewer constructors and variables (taken together
2617 and counting repetitions) than the head</para></listitem>
2621 <listitem><para>The Coverage Condition. For each functional dependency,
2622 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2623 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2624 every type variable in
2625 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2626 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2627 substitution mapping each type variable in the class declaration to the
2628 corresponding type in the instance declaration.
2631 These restrictions ensure that context reduction terminates: each reduction
2632 step makes the problem smaller by at least one
2633 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2634 if you give the <option>-fallow-undecidable-instances</option>
2635 flag (<xref linkend="undecidable-instances"/>).
2636 You can find lots of background material about the reason for these
2637 restrictions in the paper <ulink
2638 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2639 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2642 For example, these are OK:
2644 instance C Int [a] -- Multiple parameters
2645 instance Eq (S [a]) -- Structured type in head
2647 -- Repeated type variable in head
2648 instance C4 a a => C4 [a] [a]
2649 instance Stateful (ST s) (MutVar s)
2651 -- Head can consist of type variables only
2653 instance (Eq a, Show b) => C2 a b
2655 -- Non-type variables in context
2656 instance Show (s a) => Show (Sized s a)
2657 instance C2 Int a => C3 Bool [a]
2658 instance C2 Int a => C3 [a] b
2662 -- Context assertion no smaller than head
2663 instance C a => C a where ...
2664 -- (C b b) has more more occurrences of b than the head
2665 instance C b b => Foo [b] where ...
2670 The same restrictions apply to instances generated by
2671 <literal>deriving</literal> clauses. Thus the following is accepted:
2673 data MinHeap h a = H a (h a)
2676 because the derived instance
2678 instance (Show a, Show (h a)) => Show (MinHeap h a)
2680 conforms to the above rules.
2684 A useful idiom permitted by the above rules is as follows.
2685 If one allows overlapping instance declarations then it's quite
2686 convenient to have a "default instance" declaration that applies if
2687 something more specific does not:
2695 <sect3 id="undecidable-instances">
2696 <title>Undecidable instances</title>
2699 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2700 For example, sometimes you might want to use the following to get the
2701 effect of a "class synonym":
2703 class (C1 a, C2 a, C3 a) => C a where { }
2705 instance (C1 a, C2 a, C3 a) => C a where { }
2707 This allows you to write shorter signatures:
2713 f :: (C1 a, C2 a, C3 a) => ...
2715 The restrictions on functional dependencies (<xref
2716 linkend="functional-dependencies"/>) are particularly troublesome.
2717 It is tempting to introduce type variables in the context that do not appear in
2718 the head, something that is excluded by the normal rules. For example:
2720 class HasConverter a b | a -> b where
2723 data Foo a = MkFoo a
2725 instance (HasConverter a b,Show b) => Show (Foo a) where
2726 show (MkFoo value) = show (convert value)
2728 This is dangerous territory, however. Here, for example, is a program that would make the
2733 instance F [a] [[a]]
2734 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2736 Similarly, it can be tempting to lift the coverage condition:
2738 class Mul a b c | a b -> c where
2739 (.*.) :: a -> b -> c
2741 instance Mul Int Int Int where (.*.) = (*)
2742 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2743 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2745 The third instance declaration does not obey the coverage condition;
2746 and indeed the (somewhat strange) definition:
2748 f = \ b x y -> if b then x .*. [y] else y
2750 makes instance inference go into a loop, because it requires the constraint
2751 <literal>(Mul a [b] b)</literal>.
2754 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2755 the experimental flag <option>-XUndecidableInstances</option>
2756 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
2757 both the Paterson Conditions and the Coverage Condition
2758 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2759 fixed-depth recursion stack. If you exceed the stack depth you get a
2760 sort of backtrace, and the opportunity to increase the stack depth
2761 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2767 <sect3 id="instance-overlap">
2768 <title>Overlapping instances</title>
2770 In general, <emphasis>GHC requires that that it be unambiguous which instance
2772 should be used to resolve a type-class constraint</emphasis>. This behaviour
2773 can be modified by two flags: <option>-XOverlappingInstances</option>
2774 <indexterm><primary>-XOverlappingInstances
2775 </primary></indexterm>
2776 and <option>-XIncoherentInstances</option>
2777 <indexterm><primary>-XIncoherentInstances
2778 </primary></indexterm>, as this section discusses. Both these
2779 flags are dynamic flags, and can be set on a per-module basis, using
2780 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2782 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2783 it tries to match every instance declaration against the
2785 by instantiating the head of the instance declaration. For example, consider
2788 instance context1 => C Int a where ... -- (A)
2789 instance context2 => C a Bool where ... -- (B)
2790 instance context3 => C Int [a] where ... -- (C)
2791 instance context4 => C Int [Int] where ... -- (D)
2793 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2794 but (C) and (D) do not. When matching, GHC takes
2795 no account of the context of the instance declaration
2796 (<literal>context1</literal> etc).
2797 GHC's default behaviour is that <emphasis>exactly one instance must match the
2798 constraint it is trying to resolve</emphasis>.
2799 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2800 including both declarations (A) and (B), say); an error is only reported if a
2801 particular constraint matches more than one.
2805 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
2806 more than one instance to match, provided there is a most specific one. For
2807 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2808 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2809 most-specific match, the program is rejected.
2812 However, GHC is conservative about committing to an overlapping instance. For example:
2817 Suppose that from the RHS of <literal>f</literal> we get the constraint
2818 <literal>C Int [b]</literal>. But
2819 GHC does not commit to instance (C), because in a particular
2820 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2821 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2822 So GHC rejects the program.
2823 (If you add the flag <option>-XIncoherentInstances</option>,
2824 GHC will instead pick (C), without complaining about
2825 the problem of subsequent instantiations.)
2828 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
2829 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
2830 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
2831 it instead. In this case, GHC will refrain from
2832 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
2833 as before) but, rather than rejecting the program, it will infer the type
2835 f :: C Int b => [b] -> [b]
2837 That postpones the question of which instance to pick to the
2838 call site for <literal>f</literal>
2839 by which time more is known about the type <literal>b</literal>.
2842 The willingness to be overlapped or incoherent is a property of
2843 the <emphasis>instance declaration</emphasis> itself, controlled by the
2844 presence or otherwise of the <option>-XOverlappingInstances</option>
2845 and <option>-XIncoherentInstances</option> flags when that mdodule is
2846 being defined. Neither flag is required in a module that imports and uses the
2847 instance declaration. Specifically, during the lookup process:
2850 An instance declaration is ignored during the lookup process if (a) a more specific
2851 match is found, and (b) the instance declaration was compiled with
2852 <option>-XOverlappingInstances</option>. The flag setting for the
2853 more-specific instance does not matter.
2856 Suppose an instance declaration does not match the constraint being looked up, but
2857 does unify with it, so that it might match when the constraint is further
2858 instantiated. Usually GHC will regard this as a reason for not committing to
2859 some other constraint. But if the instance declaration was compiled with
2860 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
2861 check for that declaration.
2864 These rules make it possible for a library author to design a library that relies on
2865 overlapping instances without the library client having to know.
2868 If an instance declaration is compiled without
2869 <option>-XOverlappingInstances</option>,
2870 then that instance can never be overlapped. This could perhaps be
2871 inconvenient. Perhaps the rule should instead say that the
2872 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2873 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2874 at a usage site should be permitted regardless of how the instance declarations
2875 are compiled, if the <option>-XOverlappingInstances</option> flag is
2876 used at the usage site. (Mind you, the exact usage site can occasionally be
2877 hard to pin down.) We are interested to receive feedback on these points.
2879 <para>The <option>-XIncoherentInstances</option> flag implies the
2880 <option>-XOverlappingInstances</option> flag, but not vice versa.
2885 <title>Type synonyms in the instance head</title>
2888 <emphasis>Unlike Haskell 98, instance heads may use type
2889 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2890 As always, using a type synonym is just shorthand for
2891 writing the RHS of the type synonym definition. For example:
2895 type Point = (Int,Int)
2896 instance C Point where ...
2897 instance C [Point] where ...
2901 is legal. However, if you added
2905 instance C (Int,Int) where ...
2909 as well, then the compiler will complain about the overlapping
2910 (actually, identical) instance declarations. As always, type synonyms
2911 must be fully applied. You cannot, for example, write:
2916 instance Monad P where ...
2920 This design decision is independent of all the others, and easily
2921 reversed, but it makes sense to me.
2929 <sect2 id="type-restrictions">
2930 <title>Type signatures</title>
2932 <sect3><title>The context of a type signature</title>
2934 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2935 the form <emphasis>(class type-variable)</emphasis> or
2936 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2937 these type signatures are perfectly OK
2940 g :: Ord (T a ()) => ...
2944 GHC imposes the following restrictions on the constraints in a type signature.
2948 forall tv1..tvn (c1, ...,cn) => type
2951 (Here, we write the "foralls" explicitly, although the Haskell source
2952 language omits them; in Haskell 98, all the free type variables of an
2953 explicit source-language type signature are universally quantified,
2954 except for the class type variables in a class declaration. However,
2955 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2964 <emphasis>Each universally quantified type variable
2965 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2967 A type variable <literal>a</literal> is "reachable" if it it appears
2968 in the same constraint as either a type variable free in in
2969 <literal>type</literal>, or another reachable type variable.
2970 A value with a type that does not obey
2971 this reachability restriction cannot be used without introducing
2972 ambiguity; that is why the type is rejected.
2973 Here, for example, is an illegal type:
2977 forall a. Eq a => Int
2981 When a value with this type was used, the constraint <literal>Eq tv</literal>
2982 would be introduced where <literal>tv</literal> is a fresh type variable, and
2983 (in the dictionary-translation implementation) the value would be
2984 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2985 can never know which instance of <literal>Eq</literal> to use because we never
2986 get any more information about <literal>tv</literal>.
2990 that the reachability condition is weaker than saying that <literal>a</literal> is
2991 functionally dependent on a type variable free in
2992 <literal>type</literal> (see <xref
2993 linkend="functional-dependencies"/>). The reason for this is there
2994 might be a "hidden" dependency, in a superclass perhaps. So
2995 "reachable" is a conservative approximation to "functionally dependent".
2996 For example, consider:
2998 class C a b | a -> b where ...
2999 class C a b => D a b where ...
3000 f :: forall a b. D a b => a -> a
3002 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3003 but that is not immediately apparent from <literal>f</literal>'s type.
3009 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3010 universally quantified type variables <literal>tvi</literal></emphasis>.
3012 For example, this type is OK because <literal>C a b</literal> mentions the
3013 universally quantified type variable <literal>b</literal>:
3017 forall a. C a b => burble
3021 The next type is illegal because the constraint <literal>Eq b</literal> does not
3022 mention <literal>a</literal>:
3026 forall a. Eq b => burble
3030 The reason for this restriction is milder than the other one. The
3031 excluded types are never useful or necessary (because the offending
3032 context doesn't need to be witnessed at this point; it can be floated
3033 out). Furthermore, floating them out increases sharing. Lastly,
3034 excluding them is a conservative choice; it leaves a patch of
3035 territory free in case we need it later.
3049 <sect2 id="implicit-parameters">
3050 <title>Implicit parameters</title>
3052 <para> Implicit parameters are implemented as described in
3053 "Implicit parameters: dynamic scoping with static types",
3054 J Lewis, MB Shields, E Meijer, J Launchbury,
3055 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3059 <para>(Most of the following, stil rather incomplete, documentation is
3060 due to Jeff Lewis.)</para>
3062 <para>Implicit parameter support is enabled with the option
3063 <option>-XImplicitParams</option>.</para>
3066 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3067 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3068 context. In Haskell, all variables are statically bound. Dynamic
3069 binding of variables is a notion that goes back to Lisp, but was later
3070 discarded in more modern incarnations, such as Scheme. Dynamic binding
3071 can be very confusing in an untyped language, and unfortunately, typed
3072 languages, in particular Hindley-Milner typed languages like Haskell,
3073 only support static scoping of variables.
3076 However, by a simple extension to the type class system of Haskell, we
3077 can support dynamic binding. Basically, we express the use of a
3078 dynamically bound variable as a constraint on the type. These
3079 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3080 function uses a dynamically-bound variable <literal>?x</literal>
3081 of type <literal>t'</literal>". For
3082 example, the following expresses the type of a sort function,
3083 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3085 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3087 The dynamic binding constraints are just a new form of predicate in the type class system.
3090 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3091 where <literal>x</literal> is
3092 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3093 Use of this construct also introduces a new
3094 dynamic-binding constraint in the type of the expression.
3095 For example, the following definition
3096 shows how we can define an implicitly parameterized sort function in
3097 terms of an explicitly parameterized <literal>sortBy</literal> function:
3099 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3101 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3107 <title>Implicit-parameter type constraints</title>
3109 Dynamic binding constraints behave just like other type class
3110 constraints in that they are automatically propagated. Thus, when a
3111 function is used, its implicit parameters are inherited by the
3112 function that called it. For example, our <literal>sort</literal> function might be used
3113 to pick out the least value in a list:
3115 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3116 least xs = head (sort xs)
3118 Without lifting a finger, the <literal>?cmp</literal> parameter is
3119 propagated to become a parameter of <literal>least</literal> as well. With explicit
3120 parameters, the default is that parameters must always be explicit
3121 propagated. With implicit parameters, the default is to always
3125 An implicit-parameter type constraint differs from other type class constraints in the
3126 following way: All uses of a particular implicit parameter must have
3127 the same type. This means that the type of <literal>(?x, ?x)</literal>
3128 is <literal>(?x::a) => (a,a)</literal>, and not
3129 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3133 <para> You can't have an implicit parameter in the context of a class or instance
3134 declaration. For example, both these declarations are illegal:
3136 class (?x::Int) => C a where ...
3137 instance (?x::a) => Foo [a] where ...
3139 Reason: exactly which implicit parameter you pick up depends on exactly where
3140 you invoke a function. But the ``invocation'' of instance declarations is done
3141 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3142 Easiest thing is to outlaw the offending types.</para>
3144 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3146 f :: (?x :: [a]) => Int -> Int
3149 g :: (Read a, Show a) => String -> String
3152 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3153 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3154 quite unambiguous, and fixes the type <literal>a</literal>.
3159 <title>Implicit-parameter bindings</title>
3162 An implicit parameter is <emphasis>bound</emphasis> using the standard
3163 <literal>let</literal> or <literal>where</literal> binding forms.
3164 For example, we define the <literal>min</literal> function by binding
3165 <literal>cmp</literal>.
3168 min = let ?cmp = (<=) in least
3172 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3173 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3174 (including in a list comprehension, or do-notation, or pattern guards),
3175 or a <literal>where</literal> clause.
3176 Note the following points:
3179 An implicit-parameter binding group must be a
3180 collection of simple bindings to implicit-style variables (no
3181 function-style bindings, and no type signatures); these bindings are
3182 neither polymorphic or recursive.
3185 You may not mix implicit-parameter bindings with ordinary bindings in a
3186 single <literal>let</literal>
3187 expression; use two nested <literal>let</literal>s instead.
3188 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3192 You may put multiple implicit-parameter bindings in a
3193 single binding group; but they are <emphasis>not</emphasis> treated
3194 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3195 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3196 parameter. The bindings are not nested, and may be re-ordered without changing
3197 the meaning of the program.
3198 For example, consider:
3200 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3202 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3203 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3205 f :: (?x::Int) => Int -> Int
3213 <sect3><title>Implicit parameters and polymorphic recursion</title>
3216 Consider these two definitions:
3219 len1 xs = let ?acc = 0 in len_acc1 xs
3222 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3227 len2 xs = let ?acc = 0 in len_acc2 xs
3229 len_acc2 :: (?acc :: Int) => [a] -> Int
3231 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3233 The only difference between the two groups is that in the second group
3234 <literal>len_acc</literal> is given a type signature.
3235 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3236 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3237 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3238 has a type signature, the recursive call is made to the
3239 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3240 as an implicit parameter. So we get the following results in GHCi:
3247 Adding a type signature dramatically changes the result! This is a rather
3248 counter-intuitive phenomenon, worth watching out for.
3252 <sect3><title>Implicit parameters and monomorphism</title>
3254 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3255 Haskell Report) to implicit parameters. For example, consider:
3263 Since the binding for <literal>y</literal> falls under the Monomorphism
3264 Restriction it is not generalised, so the type of <literal>y</literal> is
3265 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3266 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3267 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3268 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3269 <literal>y</literal> in the body of the <literal>let</literal> will see the
3270 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3271 <literal>14</literal>.
3276 <!-- ======================= COMMENTED OUT ========================
3278 We intend to remove linear implicit parameters, so I'm at least removing
3279 them from the 6.6 user manual
3281 <sect2 id="linear-implicit-parameters">
3282 <title>Linear implicit parameters</title>
3284 Linear implicit parameters are an idea developed by Koen Claessen,
3285 Mark Shields, and Simon PJ. They address the long-standing
3286 problem that monads seem over-kill for certain sorts of problem, notably:
3289 <listitem> <para> distributing a supply of unique names </para> </listitem>
3290 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3291 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3295 Linear implicit parameters are just like ordinary implicit parameters,
3296 except that they are "linear"; that is, they cannot be copied, and
3297 must be explicitly "split" instead. Linear implicit parameters are
3298 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3299 (The '/' in the '%' suggests the split!)
3304 import GHC.Exts( Splittable )
3306 data NameSupply = ...
3308 splitNS :: NameSupply -> (NameSupply, NameSupply)
3309 newName :: NameSupply -> Name
3311 instance Splittable NameSupply where
3315 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3316 f env (Lam x e) = Lam x' (f env e)
3319 env' = extend env x x'
3320 ...more equations for f...
3322 Notice that the implicit parameter %ns is consumed
3324 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3325 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3329 So the translation done by the type checker makes
3330 the parameter explicit:
3332 f :: NameSupply -> Env -> Expr -> Expr
3333 f ns env (Lam x e) = Lam x' (f ns1 env e)
3335 (ns1,ns2) = splitNS ns
3337 env = extend env x x'
3339 Notice the call to 'split' introduced by the type checker.
3340 How did it know to use 'splitNS'? Because what it really did
3341 was to introduce a call to the overloaded function 'split',
3342 defined by the class <literal>Splittable</literal>:
3344 class Splittable a where
3347 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3348 split for name supplies. But we can simply write
3354 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3356 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3357 <literal>GHC.Exts</literal>.
3362 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3363 are entirely distinct implicit parameters: you
3364 can use them together and they won't intefere with each other. </para>
3367 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3369 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3370 in the context of a class or instance declaration. </para></listitem>
3374 <sect3><title>Warnings</title>
3377 The monomorphism restriction is even more important than usual.
3378 Consider the example above:
3380 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3381 f env (Lam x e) = Lam x' (f env e)
3384 env' = extend env x x'
3386 If we replaced the two occurrences of x' by (newName %ns), which is
3387 usually a harmless thing to do, we get:
3389 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3390 f env (Lam x e) = Lam (newName %ns) (f env e)
3392 env' = extend env x (newName %ns)
3394 But now the name supply is consumed in <emphasis>three</emphasis> places
3395 (the two calls to newName,and the recursive call to f), so
3396 the result is utterly different. Urk! We don't even have
3400 Well, this is an experimental change. With implicit
3401 parameters we have already lost beta reduction anyway, and
3402 (as John Launchbury puts it) we can't sensibly reason about
3403 Haskell programs without knowing their typing.
3408 <sect3><title>Recursive functions</title>
3409 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3412 foo :: %x::T => Int -> [Int]
3414 foo n = %x : foo (n-1)
3416 where T is some type in class Splittable.</para>
3418 Do you get a list of all the same T's or all different T's
3419 (assuming that split gives two distinct T's back)?
3421 If you supply the type signature, taking advantage of polymorphic
3422 recursion, you get what you'd probably expect. Here's the
3423 translated term, where the implicit param is made explicit:
3426 foo x n = let (x1,x2) = split x
3427 in x1 : foo x2 (n-1)
3429 But if you don't supply a type signature, GHC uses the Hindley
3430 Milner trick of using a single monomorphic instance of the function
3431 for the recursive calls. That is what makes Hindley Milner type inference
3432 work. So the translation becomes
3436 foom n = x : foom (n-1)
3440 Result: 'x' is not split, and you get a list of identical T's. So the
3441 semantics of the program depends on whether or not foo has a type signature.
3444 You may say that this is a good reason to dislike linear implicit parameters
3445 and you'd be right. That is why they are an experimental feature.
3451 ================ END OF Linear Implicit Parameters commented out -->
3453 <sect2 id="kinding">
3454 <title>Explicitly-kinded quantification</title>
3457 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3458 to give the kind explicitly as (machine-checked) documentation,
3459 just as it is nice to give a type signature for a function. On some occasions,
3460 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3461 John Hughes had to define the data type:
3463 data Set cxt a = Set [a]
3464 | Unused (cxt a -> ())
3466 The only use for the <literal>Unused</literal> constructor was to force the correct
3467 kind for the type variable <literal>cxt</literal>.
3470 GHC now instead allows you to specify the kind of a type variable directly, wherever
3471 a type variable is explicitly bound. Namely:
3473 <listitem><para><literal>data</literal> declarations:
3475 data Set (cxt :: * -> *) a = Set [a]
3476 </screen></para></listitem>
3477 <listitem><para><literal>type</literal> declarations:
3479 type T (f :: * -> *) = f Int
3480 </screen></para></listitem>
3481 <listitem><para><literal>class</literal> declarations:
3483 class (Eq a) => C (f :: * -> *) a where ...
3484 </screen></para></listitem>
3485 <listitem><para><literal>forall</literal>'s in type signatures:
3487 f :: forall (cxt :: * -> *). Set cxt Int
3488 </screen></para></listitem>
3493 The parentheses are required. Some of the spaces are required too, to
3494 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3495 will get a parse error, because "<literal>::*->*</literal>" is a
3496 single lexeme in Haskell.
3500 As part of the same extension, you can put kind annotations in types
3503 f :: (Int :: *) -> Int
3504 g :: forall a. a -> (a :: *)
3508 atype ::= '(' ctype '::' kind ')
3510 The parentheses are required.
3515 <sect2 id="universal-quantification">
3516 <title>Arbitrary-rank polymorphism
3520 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3521 allows us to say exactly what this means. For example:
3529 g :: forall b. (b -> b)
3531 The two are treated identically.
3535 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3536 explicit universal quantification in
3538 For example, all the following types are legal:
3540 f1 :: forall a b. a -> b -> a
3541 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3543 f2 :: (forall a. a->a) -> Int -> Int
3544 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3546 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3548 f4 :: Int -> (forall a. a -> a)
3550 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3551 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3552 The <literal>forall</literal> makes explicit the universal quantification that
3553 is implicitly added by Haskell.
3556 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3557 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3558 shows, the polymorphic type on the left of the function arrow can be overloaded.
3561 The function <literal>f3</literal> has a rank-3 type;
3562 it has rank-2 types on the left of a function arrow.
3565 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3566 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3567 that restriction has now been lifted.)
3568 In particular, a forall-type (also called a "type scheme"),
3569 including an operational type class context, is legal:
3571 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3572 of a function arrow </para> </listitem>
3573 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3574 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3575 field type signatures.</para> </listitem>
3576 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3577 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3579 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3580 a type variable any more!
3589 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3590 the types of the constructor arguments. Here are several examples:
3596 data T a = T1 (forall b. b -> b -> b) a
3598 data MonadT m = MkMonad { return :: forall a. a -> m a,
3599 bind :: forall a b. m a -> (a -> m b) -> m b
3602 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3608 The constructors have rank-2 types:
3614 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3615 MkMonad :: forall m. (forall a. a -> m a)
3616 -> (forall a b. m a -> (a -> m b) -> m b)
3618 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3624 Notice that you don't need to use a <literal>forall</literal> if there's an
3625 explicit context. For example in the first argument of the
3626 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3627 prefixed to the argument type. The implicit <literal>forall</literal>
3628 quantifies all type variables that are not already in scope, and are
3629 mentioned in the type quantified over.
3633 As for type signatures, implicit quantification happens for non-overloaded
3634 types too. So if you write this:
3637 data T a = MkT (Either a b) (b -> b)
3640 it's just as if you had written this:
3643 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3646 That is, since the type variable <literal>b</literal> isn't in scope, it's
3647 implicitly universally quantified. (Arguably, it would be better
3648 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3649 where that is what is wanted. Feedback welcomed.)
3653 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3654 the constructor to suitable values, just as usual. For example,
3665 a3 = MkSwizzle reverse
3668 a4 = let r x = Just x
3675 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3676 mkTs f x y = [T1 f x, T1 f y]
3682 The type of the argument can, as usual, be more general than the type
3683 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3684 does not need the <literal>Ord</literal> constraint.)
3688 When you use pattern matching, the bound variables may now have
3689 polymorphic types. For example:
3695 f :: T a -> a -> (a, Char)
3696 f (T1 w k) x = (w k x, w 'c' 'd')
3698 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3699 g (MkSwizzle s) xs f = s (map f (s xs))
3701 h :: MonadT m -> [m a] -> m [a]
3702 h m [] = return m []
3703 h m (x:xs) = bind m x $ \y ->
3704 bind m (h m xs) $ \ys ->
3711 In the function <function>h</function> we use the record selectors <literal>return</literal>
3712 and <literal>bind</literal> to extract the polymorphic bind and return functions
3713 from the <literal>MonadT</literal> data structure, rather than using pattern
3719 <title>Type inference</title>
3722 In general, type inference for arbitrary-rank types is undecidable.
3723 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3724 to get a decidable algorithm by requiring some help from the programmer.
3725 We do not yet have a formal specification of "some help" but the rule is this:
3728 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3729 provides an explicit polymorphic type for x, or GHC's type inference will assume
3730 that x's type has no foralls in it</emphasis>.
3733 What does it mean to "provide" an explicit type for x? You can do that by
3734 giving a type signature for x directly, using a pattern type signature
3735 (<xref linkend="scoped-type-variables"/>), thus:
3737 \ f :: (forall a. a->a) -> (f True, f 'c')
3739 Alternatively, you can give a type signature to the enclosing
3740 context, which GHC can "push down" to find the type for the variable:
3742 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3744 Here the type signature on the expression can be pushed inwards
3745 to give a type signature for f. Similarly, and more commonly,
3746 one can give a type signature for the function itself:
3748 h :: (forall a. a->a) -> (Bool,Char)
3749 h f = (f True, f 'c')
3751 You don't need to give a type signature if the lambda bound variable
3752 is a constructor argument. Here is an example we saw earlier:
3754 f :: T a -> a -> (a, Char)
3755 f (T1 w k) x = (w k x, w 'c' 'd')
3757 Here we do not need to give a type signature to <literal>w</literal>, because
3758 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3765 <sect3 id="implicit-quant">
3766 <title>Implicit quantification</title>
3769 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3770 user-written types, if and only if there is no explicit <literal>forall</literal>,
3771 GHC finds all the type variables mentioned in the type that are not already
3772 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3776 f :: forall a. a -> a
3783 h :: forall b. a -> b -> b
3789 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3792 f :: (a -> a) -> Int
3794 f :: forall a. (a -> a) -> Int
3796 f :: (forall a. a -> a) -> Int
3799 g :: (Ord a => a -> a) -> Int
3800 -- MEANS the illegal type
3801 g :: forall a. (Ord a => a -> a) -> Int
3803 g :: (forall a. Ord a => a -> a) -> Int
3805 The latter produces an illegal type, which you might think is silly,
3806 but at least the rule is simple. If you want the latter type, you
3807 can write your for-alls explicitly. Indeed, doing so is strongly advised
3814 <sect2 id="impredicative-polymorphism">
3815 <title>Impredicative polymorphism
3817 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3818 that you can call a polymorphic function at a polymorphic type, and
3819 parameterise data structures over polymorphic types. For example:
3821 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3822 f (Just g) = Just (g [3], g "hello")
3825 Notice here that the <literal>Maybe</literal> type is parameterised by the
3826 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3829 <para>The technical details of this extension are described in the paper
3830 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3831 type inference for higher-rank types and impredicativity</ulink>,
3832 which appeared at ICFP 2006.
3836 <sect2 id="scoped-type-variables">
3837 <title>Lexically scoped type variables
3841 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3842 which some type signatures are simply impossible to write. For example:
3844 f :: forall a. [a] -> [a]
3850 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3851 the entire definition of <literal>f</literal>.
3852 In particular, it is in scope at the type signature for <varname>ys</varname>.
3853 In Haskell 98 it is not possible to declare
3854 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3855 it becomes possible to do so.
3857 <para>Lexically-scoped type variables are enabled by
3858 <option>-fglasgow-exts</option>.
3860 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3861 variables work, compared to earlier releases. Read this section
3865 <title>Overview</title>
3867 <para>The design follows the following principles
3869 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3870 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3871 design.)</para></listitem>
3872 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3873 type variables. This means that every programmer-written type signature
3874 (includin one that contains free scoped type variables) denotes a
3875 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3876 checker, and no inference is involved.</para></listitem>
3877 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3878 changing the program.</para></listitem>
3882 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3884 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3885 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3886 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3887 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3891 In Haskell, a programmer-written type signature is implicitly quantifed over
3892 its free type variables (<ulink
3893 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3895 of the Haskel Report).
3896 Lexically scoped type variables affect this implicit quantification rules
3897 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3898 quantified. For example, if type variable <literal>a</literal> is in scope,
3901 (e :: a -> a) means (e :: a -> a)
3902 (e :: b -> b) means (e :: forall b. b->b)
3903 (e :: a -> b) means (e :: forall b. a->b)
3911 <sect3 id="decl-type-sigs">
3912 <title>Declaration type signatures</title>
3913 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3914 quantification (using <literal>forall</literal>) brings into scope the
3915 explicitly-quantified
3916 type variables, in the definition of the named function(s). For example:
3918 f :: forall a. [a] -> [a]
3919 f (x:xs) = xs ++ [ x :: a ]
3921 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3922 the definition of "<literal>f</literal>".
3924 <para>This only happens if the quantification in <literal>f</literal>'s type
3925 signature is explicit. For example:
3928 g (x:xs) = xs ++ [ x :: a ]
3930 This program will be rejected, because "<literal>a</literal>" does not scope
3931 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3932 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3933 quantification rules.
3937 <sect3 id="exp-type-sigs">
3938 <title>Expression type signatures</title>
3940 <para>An expression type signature that has <emphasis>explicit</emphasis>
3941 quantification (using <literal>forall</literal>) brings into scope the
3942 explicitly-quantified
3943 type variables, in the annotated expression. For example:
3945 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3947 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3948 type variable <literal>s</literal> into scope, in the annotated expression
3949 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3954 <sect3 id="pattern-type-sigs">
3955 <title>Pattern type signatures</title>
3957 A type signature may occur in any pattern; this is a <emphasis>pattern type
3958 signature</emphasis>.
3961 -- f and g assume that 'a' is already in scope
3962 f = \(x::Int, y::a) -> x
3964 h ((x,y) :: (Int,Bool)) = (y,x)
3966 In the case where all the type variables in the pattern type sigature are
3967 already in scope (i.e. bound by the enclosing context), matters are simple: the
3968 signature simply constrains the type of the pattern in the obvious way.
3971 There is only one situation in which you can write a pattern type signature that
3972 mentions a type variable that is not already in scope, namely in pattern match
3973 of an existential data constructor. For example:
3975 data T = forall a. MkT [a]
3978 k (MkT [t::a]) = MkT t3
3982 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3983 variable that is not already in scope. Indeed, it cannot already be in scope,
3984 because it is bound by the pattern match. GHC's rule is that in this situation
3985 (and only then), a pattern type signature can mention a type variable that is
3986 not already in scope; the effect is to bring it into scope, standing for the
3987 existentially-bound type variable.
3990 If this seems a little odd, we think so too. But we must have
3991 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3992 could not name existentially-bound type variables in subequent type signatures.
3995 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3996 signature is allowed to mention a lexical variable that is not already in
3998 For example, both <literal>f</literal> and <literal>g</literal> would be
3999 illegal if <literal>a</literal> was not already in scope.
4005 <!-- ==================== Commented out part about result type signatures
4007 <sect3 id="result-type-sigs">
4008 <title>Result type signatures</title>
4011 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4014 {- f assumes that 'a' is already in scope -}
4015 f x y :: [a] = [x,y,x]
4017 g = \ x :: [Int] -> [3,4]
4019 h :: forall a. [a] -> a
4023 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4024 the result of the function. Similarly, the body of the lambda in the RHS of
4025 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4026 alternative in <literal>h</literal> is <literal>a</literal>.
4028 <para> A result type signature never brings new type variables into scope.</para>
4030 There are a couple of syntactic wrinkles. First, notice that all three
4031 examples would parse quite differently with parentheses:
4033 {- f assumes that 'a' is already in scope -}
4034 f x (y :: [a]) = [x,y,x]
4036 g = \ (x :: [Int]) -> [3,4]
4038 h :: forall a. [a] -> a
4042 Now the signature is on the <emphasis>pattern</emphasis>; and
4043 <literal>h</literal> would certainly be ill-typed (since the pattern
4044 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4046 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4047 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4048 token or a parenthesised type of some sort). To see why,
4049 consider how one would parse this:
4058 <sect3 id="cls-inst-scoped-tyvars">
4059 <title>Class and instance declarations</title>
4062 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4063 scope over the methods defined in the <literal>where</literal> part. For example:
4081 <sect2 id="typing-binds">
4082 <title>Generalised typing of mutually recursive bindings</title>
4085 The Haskell Report specifies that a group of bindings (at top level, or in a
4086 <literal>let</literal> or <literal>where</literal>) should be sorted into
4087 strongly-connected components, and then type-checked in dependency order
4088 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4089 Report, Section 4.5.1</ulink>).
4090 As each group is type-checked, any binders of the group that
4092 an explicit type signature are put in the type environment with the specified
4094 and all others are monomorphic until the group is generalised
4095 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4098 <para>Following a suggestion of Mark Jones, in his paper
4099 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4101 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4103 <emphasis>the dependency analysis ignores references to variables that have an explicit
4104 type signature</emphasis>.
4105 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4106 typecheck. For example, consider:
4108 f :: Eq a => a -> Bool
4109 f x = (x == x) || g True || g "Yes"
4111 g y = (y <= y) || f True
4113 This is rejected by Haskell 98, but under Jones's scheme the definition for
4114 <literal>g</literal> is typechecked first, separately from that for
4115 <literal>f</literal>,
4116 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4117 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4118 type is generalised, to get
4120 g :: Ord a => a -> Bool
4122 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4123 <literal>g</literal> in the type environment.
4127 The same refined dependency analysis also allows the type signatures of
4128 mutually-recursive functions to have different contexts, something that is illegal in
4129 Haskell 98 (Section 4.5.2, last sentence). With
4130 <option>-XRelaxedPolyRec</option>
4131 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4132 type signatures; in practice this means that only variables bound by the same
4133 pattern binding must have the same context. For example, this is fine:
4135 f :: Eq a => a -> Bool
4136 f x = (x == x) || g True
4138 g :: Ord a => a -> Bool
4139 g y = (y <= y) || f True
4144 <sect2 id="overloaded-strings">
4145 <title>Overloaded string literals
4149 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4150 string literal has type <literal>String</literal>, but with overloaded string
4151 literals enabled (with <literal>-XOverloadedStrings</literal>)
4152 a string literal has type <literal>(IsString a) => a</literal>.
4155 This means that the usual string syntax can be used, e.g., for packed strings
4156 and other variations of string like types. String literals behave very much
4157 like integer literals, i.e., they can be used in both expressions and patterns.
4158 If used in a pattern the literal with be replaced by an equality test, in the same
4159 way as an integer literal is.
4162 The class <literal>IsString</literal> is defined as:
4164 class IsString a where
4165 fromString :: String -> a
4167 The only predefined instance is the obvious one to make strings work as usual:
4169 instance IsString [Char] where
4172 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4173 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4174 from module <literal>GHC.Exts</literal>.
4177 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4181 Each type in a default declaration must be an
4182 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4186 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4187 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4188 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4189 <emphasis>or</emphasis> <literal>IsString</literal>.
4198 import GHC.Exts( IsString(..) )
4200 newtype MyString = MyString String deriving (Eq, Show)
4201 instance IsString MyString where
4202 fromString = MyString
4204 greet :: MyString -> MyString
4205 greet "hello" = "world"
4209 print $ greet "hello"
4210 print $ greet "fool"
4214 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4215 to work since it gets translated into an equality comparison.
4219 <sect2 id="type-families">
4220 <title>Type families
4224 GHC supports the definition of type families indexed by types. They may be
4225 seen as an extension of Haskell 98's class-based overloading of values to
4226 types. When type families are declared in classes, they are also known as
4230 There are two forms of type families: data families and type synonym families.
4231 Currently, only the former are fully implemented, while we are still working
4232 on the latter. As a result, the specification of the language extension is
4233 also still to some degree in flux. Hence, a more detailed description of
4234 the language extension and its use is currently available
4235 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4236 wiki page on type families</ulink>. The material will be moved to this user's
4237 guide when it has stabilised.
4240 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4247 <!-- ==================== End of type system extensions ================= -->
4249 <!-- ====================== TEMPLATE HASKELL ======================= -->
4251 <sect1 id="template-haskell">
4252 <title>Template Haskell</title>
4254 <para>Template Haskell allows you to do compile-time meta-programming in
4257 the main technical innovations is discussed in "<ulink
4258 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4259 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4262 There is a Wiki page about
4263 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4264 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4268 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4269 Haskell library reference material</ulink>
4270 (search for the type ExpQ).
4271 [Temporary: many changes to the original design are described in
4272 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4273 Not all of these changes are in GHC 6.6.]
4276 <para> The first example from that paper is set out below as a worked example to help get you started.
4280 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4281 Tim Sheard is going to expand it.)
4285 <title>Syntax</title>
4287 <para> Template Haskell has the following new syntactic
4288 constructions. You need to use the flag
4289 <option>-XTemplateHaskell</option>
4290 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4291 </indexterm>to switch these syntactic extensions on
4292 (<option>-XTemplateHaskell</option> is no longer implied by
4293 <option>-fglasgow-exts</option>).</para>
4297 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4298 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4299 There must be no space between the "$" and the identifier or parenthesis. This use
4300 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4301 of "." as an infix operator. If you want the infix operator, put spaces around it.
4303 <para> A splice can occur in place of
4305 <listitem><para> an expression; the spliced expression must
4306 have type <literal>Q Exp</literal></para></listitem>
4307 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4308 <listitem><para> [Planned, but not implemented yet.] a
4309 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4311 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4312 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4318 A expression quotation is written in Oxford brackets, thus:
4320 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4321 the quotation has type <literal>Expr</literal>.</para></listitem>
4322 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4323 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4324 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4325 the quotation has type <literal>Type</literal>.</para></listitem>
4326 </itemizedlist></para></listitem>
4329 Reification is written thus:
4331 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4332 has type <literal>Dec</literal>. </para></listitem>
4333 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4334 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4335 <listitem><para> Still to come: fixities </para></listitem>
4337 </itemizedlist></para>
4344 <sect2> <title> Using Template Haskell </title>
4348 The data types and monadic constructor functions for Template Haskell are in the library
4349 <literal>Language.Haskell.THSyntax</literal>.
4353 You can only run a function at compile time if it is imported from another module. That is,
4354 you can't define a function in a module, and call it from within a splice in the same module.
4355 (It would make sense to do so, but it's hard to implement.)
4359 Furthermore, you can only run a function at compile time if it is imported
4360 from another module <emphasis>that is not part of a mutually-recursive group of modules
4361 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4362 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4363 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4367 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4370 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4371 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4372 compiles and runs a program, and then looks at the result. So it's important that
4373 the program it compiles produces results whose representations are identical to
4374 those of the compiler itself.
4378 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4379 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4384 <sect2> <title> A Template Haskell Worked Example </title>
4385 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4386 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4393 -- Import our template "pr"
4394 import Printf ( pr )
4396 -- The splice operator $ takes the Haskell source code
4397 -- generated at compile time by "pr" and splices it into
4398 -- the argument of "putStrLn".
4399 main = putStrLn ( $(pr "Hello") )
4405 -- Skeletal printf from the paper.
4406 -- It needs to be in a separate module to the one where
4407 -- you intend to use it.
4409 -- Import some Template Haskell syntax
4410 import Language.Haskell.TH
4412 -- Describe a format string
4413 data Format = D | S | L String
4415 -- Parse a format string. This is left largely to you
4416 -- as we are here interested in building our first ever
4417 -- Template Haskell program and not in building printf.
4418 parse :: String -> [Format]
4421 -- Generate Haskell source code from a parsed representation
4422 -- of the format string. This code will be spliced into
4423 -- the module which calls "pr", at compile time.
4424 gen :: [Format] -> ExpQ
4425 gen [D] = [| \n -> show n |]
4426 gen [S] = [| \s -> s |]
4427 gen [L s] = stringE s
4429 -- Here we generate the Haskell code for the splice
4430 -- from an input format string.
4431 pr :: String -> ExpQ
4432 pr s = gen (parse s)
4435 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4438 $ ghc --make -XTemplateHaskell main.hs -o main.exe
4441 <para>Run "main.exe" and here is your output:</para>
4451 <title>Using Template Haskell with Profiling</title>
4452 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4454 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4455 interpreter to run the splice expressions. The bytecode interpreter
4456 runs the compiled expression on top of the same runtime on which GHC
4457 itself is running; this means that the compiled code referred to by
4458 the interpreted expression must be compatible with this runtime, and
4459 in particular this means that object code that is compiled for
4460 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4461 expression, because profiled object code is only compatible with the
4462 profiling version of the runtime.</para>
4464 <para>This causes difficulties if you have a multi-module program
4465 containing Template Haskell code and you need to compile it for
4466 profiling, because GHC cannot load the profiled object code and use it
4467 when executing the splices. Fortunately GHC provides a workaround.
4468 The basic idea is to compile the program twice:</para>
4472 <para>Compile the program or library first the normal way, without
4473 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4476 <para>Then compile it again with <option>-prof</option>, and
4477 additionally use <option>-osuf
4478 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4479 to name the object files differentliy (you can choose any suffix
4480 that isn't the normal object suffix here). GHC will automatically
4481 load the object files built in the first step when executing splice
4482 expressions. If you omit the <option>-osuf</option> flag when
4483 building with <option>-prof</option> and Template Haskell is used,
4484 GHC will emit an error message. </para>
4491 <!-- ===================== Arrow notation =================== -->
4493 <sect1 id="arrow-notation">
4494 <title>Arrow notation
4497 <para>Arrows are a generalization of monads introduced by John Hughes.
4498 For more details, see
4503 “Generalising Monads to Arrows”,
4504 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4505 pp67–111, May 2000.
4511 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4512 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4518 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4519 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4525 and the arrows web page at
4526 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4527 With the <option>-XArrows</option> flag, GHC supports the arrow
4528 notation described in the second of these papers.
4529 What follows is a brief introduction to the notation;
4530 it won't make much sense unless you've read Hughes's paper.
4531 This notation is translated to ordinary Haskell,
4532 using combinators from the
4533 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4537 <para>The extension adds a new kind of expression for defining arrows:
4539 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4540 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4542 where <literal>proc</literal> is a new keyword.
4543 The variables of the pattern are bound in the body of the
4544 <literal>proc</literal>-expression,
4545 which is a new sort of thing called a <firstterm>command</firstterm>.
4546 The syntax of commands is as follows:
4548 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4549 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4550 | <replaceable>cmd</replaceable><superscript>0</superscript>
4552 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4553 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4554 infix operators as for expressions, and
4556 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4557 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4558 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4559 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4560 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4561 | <replaceable>fcmd</replaceable>
4563 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4564 | ( <replaceable>cmd</replaceable> )
4565 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4567 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4568 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4569 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4570 | <replaceable>cmd</replaceable>
4572 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4573 except that the bodies are commands instead of expressions.
4577 Commands produce values, but (like monadic computations)
4578 may yield more than one value,
4579 or none, and may do other things as well.
4580 For the most part, familiarity with monadic notation is a good guide to
4582 However the values of expressions, even monadic ones,
4583 are determined by the values of the variables they contain;
4584 this is not necessarily the case for commands.
4588 A simple example of the new notation is the expression
4590 proc x -> f -< x+1
4592 We call this a <firstterm>procedure</firstterm> or
4593 <firstterm>arrow abstraction</firstterm>.
4594 As with a lambda expression, the variable <literal>x</literal>
4595 is a new variable bound within the <literal>proc</literal>-expression.
4596 It refers to the input to the arrow.
4597 In the above example, <literal>-<</literal> is not an identifier but an
4598 new reserved symbol used for building commands from an expression of arrow
4599 type and an expression to be fed as input to that arrow.
4600 (The weird look will make more sense later.)
4601 It may be read as analogue of application for arrows.
4602 The above example is equivalent to the Haskell expression
4604 arr (\ x -> x+1) >>> f
4606 That would make no sense if the expression to the left of
4607 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4608 More generally, the expression to the left of <literal>-<</literal>
4609 may not involve any <firstterm>local variable</firstterm>,
4610 i.e. a variable bound in the current arrow abstraction.
4611 For such a situation there is a variant <literal>-<<</literal>, as in
4613 proc x -> f x -<< x+1
4615 which is equivalent to
4617 arr (\ x -> (f x, x+1)) >>> app
4619 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4621 Such an arrow is equivalent to a monad, so if you're using this form
4622 you may find a monadic formulation more convenient.
4626 <title>do-notation for commands</title>
4629 Another form of command is a form of <literal>do</literal>-notation.
4630 For example, you can write
4639 You can read this much like ordinary <literal>do</literal>-notation,
4640 but with commands in place of monadic expressions.
4641 The first line sends the value of <literal>x+1</literal> as an input to
4642 the arrow <literal>f</literal>, and matches its output against
4643 <literal>y</literal>.
4644 In the next line, the output is discarded.
4645 The arrow <function>returnA</function> is defined in the
4646 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4647 module as <literal>arr id</literal>.
4648 The above example is treated as an abbreviation for
4650 arr (\ x -> (x, x)) >>>
4651 first (arr (\ x -> x+1) >>> f) >>>
4652 arr (\ (y, x) -> (y, (x, y))) >>>
4653 first (arr (\ y -> 2*y) >>> g) >>>
4655 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4656 first (arr (\ (x, z) -> x*z) >>> h) >>>
4657 arr (\ (t, z) -> t+z) >>>
4660 Note that variables not used later in the composition are projected out.
4661 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4663 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4664 module, this reduces to
4666 arr (\ x -> (x+1, x)) >>>
4668 arr (\ (y, x) -> (2*y, (x, y))) >>>
4670 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4672 arr (\ (t, z) -> t+z)
4674 which is what you might have written by hand.
4675 With arrow notation, GHC keeps track of all those tuples of variables for you.
4679 Note that although the above translation suggests that
4680 <literal>let</literal>-bound variables like <literal>z</literal> must be
4681 monomorphic, the actual translation produces Core,
4682 so polymorphic variables are allowed.
4686 It's also possible to have mutually recursive bindings,
4687 using the new <literal>rec</literal> keyword, as in the following example:
4689 counter :: ArrowCircuit a => a Bool Int
4690 counter = proc reset -> do
4691 rec output <- returnA -< if reset then 0 else next
4692 next <- delay 0 -< output+1
4693 returnA -< output
4695 The translation of such forms uses the <function>loop</function> combinator,
4696 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4702 <title>Conditional commands</title>
4705 In the previous example, we used a conditional expression to construct the
4707 Sometimes we want to conditionally execute different commands, as in
4714 which is translated to
4716 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4717 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4719 Since the translation uses <function>|||</function>,
4720 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4724 There are also <literal>case</literal> commands, like
4730 y <- h -< (x1, x2)
4734 The syntax is the same as for <literal>case</literal> expressions,
4735 except that the bodies of the alternatives are commands rather than expressions.
4736 The translation is similar to that of <literal>if</literal> commands.
4742 <title>Defining your own control structures</title>
4745 As we're seen, arrow notation provides constructs,
4746 modelled on those for expressions,
4747 for sequencing, value recursion and conditionals.
4748 But suitable combinators,
4749 which you can define in ordinary Haskell,
4750 may also be used to build new commands out of existing ones.
4751 The basic idea is that a command defines an arrow from environments to values.
4752 These environments assign values to the free local variables of the command.
4753 Thus combinators that produce arrows from arrows
4754 may also be used to build commands from commands.
4755 For example, the <literal>ArrowChoice</literal> class includes a combinator
4757 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4759 so we can use it to build commands:
4761 expr' = proc x -> do
4764 symbol Plus -< ()
4765 y <- term -< ()
4768 symbol Minus -< ()
4769 y <- term -< ()
4772 (The <literal>do</literal> on the first line is needed to prevent the first
4773 <literal><+> ...</literal> from being interpreted as part of the
4774 expression on the previous line.)
4775 This is equivalent to
4777 expr' = (proc x -> returnA -< x)
4778 <+> (proc x -> do
4779 symbol Plus -< ()
4780 y <- term -< ()
4782 <+> (proc x -> do
4783 symbol Minus -< ()
4784 y <- term -< ()
4787 It is essential that this operator be polymorphic in <literal>e</literal>
4788 (representing the environment input to the command
4789 and thence to its subcommands)
4790 and satisfy the corresponding naturality property
4792 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4794 at least for strict <literal>k</literal>.
4795 (This should be automatic if you're not using <function>seq</function>.)
4796 This ensures that environments seen by the subcommands are environments
4797 of the whole command,
4798 and also allows the translation to safely trim these environments.
4799 The operator must also not use any variable defined within the current
4804 We could define our own operator
4806 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4807 untilA body cond = proc x ->
4808 if cond x then returnA -< ()
4811 untilA body cond -< x
4813 and use it in the same way.
4814 Of course this infix syntax only makes sense for binary operators;
4815 there is also a more general syntax involving special brackets:
4819 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4826 <title>Primitive constructs</title>
4829 Some operators will need to pass additional inputs to their subcommands.
4830 For example, in an arrow type supporting exceptions,
4831 the operator that attaches an exception handler will wish to pass the
4832 exception that occurred to the handler.
4833 Such an operator might have a type
4835 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4837 where <literal>Ex</literal> is the type of exceptions handled.
4838 You could then use this with arrow notation by writing a command
4840 body `handleA` \ ex -> handler
4842 so that if an exception is raised in the command <literal>body</literal>,
4843 the variable <literal>ex</literal> is bound to the value of the exception
4844 and the command <literal>handler</literal>,
4845 which typically refers to <literal>ex</literal>, is entered.
4846 Though the syntax here looks like a functional lambda,
4847 we are talking about commands, and something different is going on.
4848 The input to the arrow represented by a command consists of values for
4849 the free local variables in the command, plus a stack of anonymous values.
4850 In all the prior examples, this stack was empty.
4851 In the second argument to <function>handleA</function>,
4852 this stack consists of one value, the value of the exception.
4853 The command form of lambda merely gives this value a name.
4858 the values on the stack are paired to the right of the environment.
4859 So operators like <function>handleA</function> that pass
4860 extra inputs to their subcommands can be designed for use with the notation
4861 by pairing the values with the environment in this way.
4862 More precisely, the type of each argument of the operator (and its result)
4863 should have the form
4865 a (...(e,t1), ... tn) t
4867 where <replaceable>e</replaceable> is a polymorphic variable
4868 (representing the environment)
4869 and <replaceable>ti</replaceable> are the types of the values on the stack,
4870 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4871 The polymorphic variable <replaceable>e</replaceable> must not occur in
4872 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4873 <replaceable>t</replaceable>.
4874 However the arrows involved need not be the same.
4875 Here are some more examples of suitable operators:
4877 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4878 runReader :: ... => a e c -> a' (e,State) c
4879 runState :: ... => a e c -> a' (e,State) (c,State)
4881 We can supply the extra input required by commands built with the last two
4882 by applying them to ordinary expressions, as in
4886 (|runReader (do { ... })|) s
4888 which adds <literal>s</literal> to the stack of inputs to the command
4889 built using <function>runReader</function>.
4893 The command versions of lambda abstraction and application are analogous to
4894 the expression versions.
4895 In particular, the beta and eta rules describe equivalences of commands.
4896 These three features (operators, lambda abstraction and application)
4897 are the core of the notation; everything else can be built using them,
4898 though the results would be somewhat clumsy.
4899 For example, we could simulate <literal>do</literal>-notation by defining
4901 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4902 u `bind` f = returnA &&& u >>> f
4904 bind_ :: Arrow a => a e b -> a e c -> a e c
4905 u `bind_` f = u `bind` (arr fst >>> f)
4907 We could simulate <literal>if</literal> by defining
4909 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4910 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4917 <title>Differences with the paper</title>
4922 <para>Instead of a single form of arrow application (arrow tail) with two
4923 translations, the implementation provides two forms
4924 <quote><literal>-<</literal></quote> (first-order)
4925 and <quote><literal>-<<</literal></quote> (higher-order).
4930 <para>User-defined operators are flagged with banana brackets instead of
4931 a new <literal>form</literal> keyword.
4940 <title>Portability</title>
4943 Although only GHC implements arrow notation directly,
4944 there is also a preprocessor
4946 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4947 that translates arrow notation into Haskell 98
4948 for use with other Haskell systems.
4949 You would still want to check arrow programs with GHC;
4950 tracing type errors in the preprocessor output is not easy.
4951 Modules intended for both GHC and the preprocessor must observe some
4952 additional restrictions:
4957 The module must import
4958 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4964 The preprocessor cannot cope with other Haskell extensions.
4965 These would have to go in separate modules.
4971 Because the preprocessor targets Haskell (rather than Core),
4972 <literal>let</literal>-bound variables are monomorphic.
4983 <!-- ==================== BANG PATTERNS ================= -->
4985 <sect1 id="bang-patterns">
4986 <title>Bang patterns
4987 <indexterm><primary>Bang patterns</primary></indexterm>
4989 <para>GHC supports an extension of pattern matching called <emphasis>bang
4990 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4992 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4993 prime feature description</ulink> contains more discussion and examples
4994 than the material below.
4997 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5000 <sect2 id="bang-patterns-informal">
5001 <title>Informal description of bang patterns
5004 The main idea is to add a single new production to the syntax of patterns:
5008 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5009 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5014 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5015 whereas without the bang it would be lazy.
5016 Bang patterns can be nested of course:
5020 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5021 <literal>y</literal>.
5022 A bang only really has an effect if it precedes a variable or wild-card pattern:
5027 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5028 forces evaluation anyway does nothing.
5030 Bang patterns work in <literal>case</literal> expressions too, of course:
5032 g5 x = let y = f x in body
5033 g6 x = case f x of { y -> body }
5034 g7 x = case f x of { !y -> body }
5036 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5037 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
5038 result, and then evaluates <literal>body</literal>.
5040 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5041 definitions too. For example:
5045 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5046 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5047 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5048 in a function argument <literal>![x,y]</literal> means the
5049 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5050 is part of the syntax of <literal>let</literal> bindings.
5055 <sect2 id="bang-patterns-sem">
5056 <title>Syntax and semantics
5060 We add a single new production to the syntax of patterns:
5064 There is one problem with syntactic ambiguity. Consider:
5068 Is this a definition of the infix function "<literal>(!)</literal>",
5069 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5070 ambiguity in favour of the latter. If you want to define
5071 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5076 The semantics of Haskell pattern matching is described in <ulink
5077 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5078 Section 3.17.2</ulink> of the Haskell Report. To this description add
5079 one extra item 10, saying:
5080 <itemizedlist><listitem><para>Matching
5081 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5082 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5083 <listitem><para>otherwise, <literal>pat</literal> is matched against
5084 <literal>v</literal></para></listitem>
5086 </para></listitem></itemizedlist>
5087 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5088 Section 3.17.3</ulink>, add a new case (t):
5090 case v of { !pat -> e; _ -> e' }
5091 = v `seq` case v of { pat -> e; _ -> e' }
5094 That leaves let expressions, whose translation is given in
5095 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5097 of the Haskell Report.
5098 In the translation box, first apply
5099 the following transformation: for each pattern <literal>pi</literal> that is of
5100 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5101 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5102 have a bang at the top, apply the rules in the existing box.
5104 <para>The effect of the let rule is to force complete matching of the pattern
5105 <literal>qi</literal> before evaluation of the body is begun. The bang is
5106 retained in the translated form in case <literal>qi</literal> is a variable,
5114 The let-binding can be recursive. However, it is much more common for
5115 the let-binding to be non-recursive, in which case the following law holds:
5116 <literal>(let !p = rhs in body)</literal>
5118 <literal>(case rhs of !p -> body)</literal>
5121 A pattern with a bang at the outermost level is not allowed at the top level of
5127 <!-- ==================== ASSERTIONS ================= -->
5129 <sect1 id="assertions">
5131 <indexterm><primary>Assertions</primary></indexterm>
5135 If you want to make use of assertions in your standard Haskell code, you
5136 could define a function like the following:
5142 assert :: Bool -> a -> a
5143 assert False x = error "assertion failed!"
5150 which works, but gives you back a less than useful error message --
5151 an assertion failed, but which and where?
5155 One way out is to define an extended <function>assert</function> function which also
5156 takes a descriptive string to include in the error message and
5157 perhaps combine this with the use of a pre-processor which inserts
5158 the source location where <function>assert</function> was used.
5162 Ghc offers a helping hand here, doing all of this for you. For every
5163 use of <function>assert</function> in the user's source:
5169 kelvinToC :: Double -> Double
5170 kelvinToC k = assert (k >= 0.0) (k+273.15)
5176 Ghc will rewrite this to also include the source location where the
5183 assert pred val ==> assertError "Main.hs|15" pred val
5189 The rewrite is only performed by the compiler when it spots
5190 applications of <function>Control.Exception.assert</function>, so you
5191 can still define and use your own versions of
5192 <function>assert</function>, should you so wish. If not, import
5193 <literal>Control.Exception</literal> to make use
5194 <function>assert</function> in your code.
5198 GHC ignores assertions when optimisation is turned on with the
5199 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5200 <literal>assert pred e</literal> will be rewritten to
5201 <literal>e</literal>. You can also disable assertions using the
5202 <option>-fignore-asserts</option>
5203 option<indexterm><primary><option>-fignore-asserts</option></primary>
5204 </indexterm>.</para>
5207 Assertion failures can be caught, see the documentation for the
5208 <literal>Control.Exception</literal> library for the details.
5214 <!-- =============================== PRAGMAS =========================== -->
5216 <sect1 id="pragmas">
5217 <title>Pragmas</title>
5219 <indexterm><primary>pragma</primary></indexterm>
5221 <para>GHC supports several pragmas, or instructions to the
5222 compiler placed in the source code. Pragmas don't normally affect
5223 the meaning of the program, but they might affect the efficiency
5224 of the generated code.</para>
5226 <para>Pragmas all take the form
5228 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5230 where <replaceable>word</replaceable> indicates the type of
5231 pragma, and is followed optionally by information specific to that
5232 type of pragma. Case is ignored in
5233 <replaceable>word</replaceable>. The various values for
5234 <replaceable>word</replaceable> that GHC understands are described
5235 in the following sections; any pragma encountered with an
5236 unrecognised <replaceable>word</replaceable> is (silently)
5239 <sect2 id="deprecated-pragma">
5240 <title>DEPRECATED pragma</title>
5241 <indexterm><primary>DEPRECATED</primary>
5244 <para>The DEPRECATED pragma lets you specify that a particular
5245 function, class, or type, is deprecated. There are two
5250 <para>You can deprecate an entire module thus:</para>
5252 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5255 <para>When you compile any module that import
5256 <literal>Wibble</literal>, GHC will print the specified
5261 <para>You can deprecate a function, class, type, or data constructor, with the
5262 following top-level declaration:</para>
5264 {-# DEPRECATED f, C, T "Don't use these" #-}
5266 <para>When you compile any module that imports and uses any
5267 of the specified entities, GHC will print the specified
5269 <para> You can only depecate entities declared at top level in the module
5270 being compiled, and you can only use unqualified names in the list of
5271 entities being deprecated. A capitalised name, such as <literal>T</literal>
5272 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5273 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5274 both are in scope. If both are in scope, there is currently no way to deprecate
5275 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5278 Any use of the deprecated item, or of anything from a deprecated
5279 module, will be flagged with an appropriate message. However,
5280 deprecations are not reported for
5281 (a) uses of a deprecated function within its defining module, and
5282 (b) uses of a deprecated function in an export list.
5283 The latter reduces spurious complaints within a library
5284 in which one module gathers together and re-exports
5285 the exports of several others.
5287 <para>You can suppress the warnings with the flag
5288 <option>-fno-warn-deprecations</option>.</para>
5291 <sect2 id="include-pragma">
5292 <title>INCLUDE pragma</title>
5294 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5295 of C header files that should be <literal>#include</literal>'d into
5296 the C source code generated by the compiler for the current module (if
5297 compiling via C). For example:</para>
5300 {-# INCLUDE "foo.h" #-}
5301 {-# INCLUDE <stdio.h> #-}</programlisting>
5303 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5304 your source file with any <literal>OPTIONS_GHC</literal>
5307 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5308 to the <option>-#include</option> option (<xref
5309 linkend="options-C-compiler" />), because the
5310 <literal>INCLUDE</literal> pragma is understood by other
5311 compilers. Yet another alternative is to add the include file to each
5312 <literal>foreign import</literal> declaration in your code, but we
5313 don't recommend using this approach with GHC.</para>
5316 <sect2 id="inline-noinline-pragma">
5317 <title>INLINE and NOINLINE pragmas</title>
5319 <para>These pragmas control the inlining of function
5322 <sect3 id="inline-pragma">
5323 <title>INLINE pragma</title>
5324 <indexterm><primary>INLINE</primary></indexterm>
5326 <para>GHC (with <option>-O</option>, as always) tries to
5327 inline (or “unfold”) functions/values that are
5328 “small enough,” thus avoiding the call overhead
5329 and possibly exposing other more-wonderful optimisations.
5330 Normally, if GHC decides a function is “too
5331 expensive” to inline, it will not do so, nor will it
5332 export that unfolding for other modules to use.</para>
5334 <para>The sledgehammer you can bring to bear is the
5335 <literal>INLINE</literal><indexterm><primary>INLINE
5336 pragma</primary></indexterm> pragma, used thusly:</para>
5339 key_function :: Int -> String -> (Bool, Double)
5341 #ifdef __GLASGOW_HASKELL__
5342 {-# INLINE key_function #-}
5346 <para>(You don't need to do the C pre-processor carry-on
5347 unless you're going to stick the code through HBC—it
5348 doesn't like <literal>INLINE</literal> pragmas.)</para>
5350 <para>The major effect of an <literal>INLINE</literal> pragma
5351 is to declare a function's “cost” to be very low.
5352 The normal unfolding machinery will then be very keen to
5355 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5356 function can be put anywhere its type signature could be
5359 <para><literal>INLINE</literal> pragmas are a particularly
5361 <literal>then</literal>/<literal>return</literal> (or
5362 <literal>bind</literal>/<literal>unit</literal>) functions in
5363 a monad. For example, in GHC's own
5364 <literal>UniqueSupply</literal> monad code, we have:</para>
5367 #ifdef __GLASGOW_HASKELL__
5368 {-# INLINE thenUs #-}
5369 {-# INLINE returnUs #-}
5373 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5374 linkend="noinline-pragma"/>).</para>
5377 <sect3 id="noinline-pragma">
5378 <title>NOINLINE pragma</title>
5380 <indexterm><primary>NOINLINE</primary></indexterm>
5381 <indexterm><primary>NOTINLINE</primary></indexterm>
5383 <para>The <literal>NOINLINE</literal> pragma does exactly what
5384 you'd expect: it stops the named function from being inlined
5385 by the compiler. You shouldn't ever need to do this, unless
5386 you're very cautious about code size.</para>
5388 <para><literal>NOTINLINE</literal> is a synonym for
5389 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5390 specified by Haskell 98 as the standard way to disable
5391 inlining, so it should be used if you want your code to be
5395 <sect3 id="phase-control">
5396 <title>Phase control</title>
5398 <para> Sometimes you want to control exactly when in GHC's
5399 pipeline the INLINE pragma is switched on. Inlining happens
5400 only during runs of the <emphasis>simplifier</emphasis>. Each
5401 run of the simplifier has a different <emphasis>phase
5402 number</emphasis>; the phase number decreases towards zero.
5403 If you use <option>-dverbose-core2core</option> you'll see the
5404 sequence of phase numbers for successive runs of the
5405 simplifier. In an INLINE pragma you can optionally specify a
5409 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5410 <literal>f</literal>
5411 until phase <literal>k</literal>, but from phase
5412 <literal>k</literal> onwards be very keen to inline it.
5415 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5416 <literal>f</literal>
5417 until phase <literal>k</literal>, but from phase
5418 <literal>k</literal> onwards do not inline it.
5421 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5422 <literal>f</literal>
5423 until phase <literal>k</literal>, but from phase
5424 <literal>k</literal> onwards be willing to inline it (as if
5425 there was no pragma).
5428 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5429 <literal>f</literal>
5430 until phase <literal>k</literal>, but from phase
5431 <literal>k</literal> onwards do not inline it.
5434 The same information is summarised here:
5436 -- Before phase 2 Phase 2 and later
5437 {-# INLINE [2] f #-} -- No Yes
5438 {-# INLINE [~2] f #-} -- Yes No
5439 {-# NOINLINE [2] f #-} -- No Maybe
5440 {-# NOINLINE [~2] f #-} -- Maybe No
5442 {-# INLINE f #-} -- Yes Yes
5443 {-# NOINLINE f #-} -- No No
5445 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5446 function body is small, or it is applied to interesting-looking arguments etc).
5447 Another way to understand the semantics is this:
5449 <listitem><para>For both INLINE and NOINLINE, the phase number says
5450 when inlining is allowed at all.</para></listitem>
5451 <listitem><para>The INLINE pragma has the additional effect of making the
5452 function body look small, so that when inlining is allowed it is very likely to
5457 <para>The same phase-numbering control is available for RULES
5458 (<xref linkend="rewrite-rules"/>).</para>
5462 <sect2 id="language-pragma">
5463 <title>LANGUAGE pragma</title>
5465 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5466 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5468 <para>This allows language extensions to be enabled in a portable way.
5469 It is the intention that all Haskell compilers support the
5470 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5471 all extensions are supported by all compilers, of
5472 course. The <literal>LANGUAGE</literal> pragma should be used instead
5473 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5475 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5477 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5479 <para>Any extension from the <literal>Extension</literal> type defined in
5481 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>
5485 <sect2 id="line-pragma">
5486 <title>LINE pragma</title>
5488 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5489 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5490 <para>This pragma is similar to C's <literal>#line</literal>
5491 pragma, and is mainly for use in automatically generated Haskell
5492 code. It lets you specify the line number and filename of the
5493 original code; for example</para>
5495 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5497 <para>if you'd generated the current file from something called
5498 <filename>Foo.vhs</filename> and this line corresponds to line
5499 42 in the original. GHC will adjust its error messages to refer
5500 to the line/file named in the <literal>LINE</literal>
5504 <sect2 id="options-pragma">
5505 <title>OPTIONS_GHC pragma</title>
5506 <indexterm><primary>OPTIONS_GHC</primary>
5508 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5511 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5512 additional options that are given to the compiler when compiling
5513 this source file. See <xref linkend="source-file-options"/> for
5516 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5517 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5521 <title>RULES pragma</title>
5523 <para>The RULES pragma lets you specify rewrite rules. It is
5524 described in <xref linkend="rewrite-rules"/>.</para>
5527 <sect2 id="specialize-pragma">
5528 <title>SPECIALIZE pragma</title>
5530 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5531 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5532 <indexterm><primary>overloading, death to</primary></indexterm>
5534 <para>(UK spelling also accepted.) For key overloaded
5535 functions, you can create extra versions (NB: more code space)
5536 specialised to particular types. Thus, if you have an
5537 overloaded function:</para>
5540 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5543 <para>If it is heavily used on lists with
5544 <literal>Widget</literal> keys, you could specialise it as
5548 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5551 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5552 be put anywhere its type signature could be put.</para>
5554 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5555 (a) a specialised version of the function and (b) a rewrite rule
5556 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5557 un-specialised function into a call to the specialised one.</para>
5559 <para>The type in a SPECIALIZE pragma can be any type that is less
5560 polymorphic than the type of the original function. In concrete terms,
5561 if the original function is <literal>f</literal> then the pragma
5563 {-# SPECIALIZE f :: <type> #-}
5565 is valid if and only if the defintion
5567 f_spec :: <type>
5570 is valid. Here are some examples (where we only give the type signature
5571 for the original function, not its code):
5573 f :: Eq a => a -> b -> b
5574 {-# SPECIALISE f :: Int -> b -> b #-}
5576 g :: (Eq a, Ix b) => a -> b -> b
5577 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5579 h :: Eq a => a -> a -> a
5580 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5582 The last of these examples will generate a
5583 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5584 well. If you use this kind of specialisation, let us know how well it works.
5587 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5588 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5589 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5590 The <literal>INLINE</literal> pragma affects the specialised verison of the
5591 function (only), and applies even if the function is recursive. The motivating
5594 -- A GADT for arrays with type-indexed representation
5596 ArrInt :: !Int -> ByteArray# -> Arr Int
5597 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5599 (!:) :: Arr e -> Int -> e
5600 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5601 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5602 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5603 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5605 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5606 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5607 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5608 the specialised function will be inlined. It has two calls to
5609 <literal>(!:)</literal>,
5610 both at type <literal>Int</literal>. Both these calls fire the first
5611 specialisation, whose body is also inlined. The result is a type-based
5612 unrolling of the indexing function.</para>
5613 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5614 on an ordinarily-recursive function.</para>
5616 <para>Note: In earlier versions of GHC, it was possible to provide your own
5617 specialised function for a given type:
5620 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5623 This feature has been removed, as it is now subsumed by the
5624 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5628 <sect2 id="specialize-instance-pragma">
5629 <title>SPECIALIZE instance pragma
5633 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5634 <indexterm><primary>overloading, death to</primary></indexterm>
5635 Same idea, except for instance declarations. For example:
5638 instance (Eq a) => Eq (Foo a) where {
5639 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5643 The pragma must occur inside the <literal>where</literal> part
5644 of the instance declaration.
5647 Compatible with HBC, by the way, except perhaps in the placement
5653 <sect2 id="unpack-pragma">
5654 <title>UNPACK pragma</title>
5656 <indexterm><primary>UNPACK</primary></indexterm>
5658 <para>The <literal>UNPACK</literal> indicates to the compiler
5659 that it should unpack the contents of a constructor field into
5660 the constructor itself, removing a level of indirection. For
5664 data T = T {-# UNPACK #-} !Float
5665 {-# UNPACK #-} !Float
5668 <para>will create a constructor <literal>T</literal> containing
5669 two unboxed floats. This may not always be an optimisation: if
5670 the <function>T</function> constructor is scrutinised and the
5671 floats passed to a non-strict function for example, they will
5672 have to be reboxed (this is done automatically by the
5675 <para>Unpacking constructor fields should only be used in
5676 conjunction with <option>-O</option>, in order to expose
5677 unfoldings to the compiler so the reboxing can be removed as
5678 often as possible. For example:</para>
5682 f (T f1 f2) = f1 + f2
5685 <para>The compiler will avoid reboxing <function>f1</function>
5686 and <function>f2</function> by inlining <function>+</function>
5687 on floats, but only when <option>-O</option> is on.</para>
5689 <para>Any single-constructor data is eligible for unpacking; for
5693 data T = T {-# UNPACK #-} !(Int,Int)
5696 <para>will store the two <literal>Int</literal>s directly in the
5697 <function>T</function> constructor, by flattening the pair.
5698 Multi-level unpacking is also supported:</para>
5701 data T = T {-# UNPACK #-} !S
5702 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5705 <para>will store two unboxed <literal>Int#</literal>s
5706 directly in the <function>T</function> constructor. The
5707 unpacker can see through newtypes, too.</para>
5709 <para>If a field cannot be unpacked, you will not get a warning,
5710 so it might be an idea to check the generated code with
5711 <option>-ddump-simpl</option>.</para>
5713 <para>See also the <option>-funbox-strict-fields</option> flag,
5714 which essentially has the effect of adding
5715 <literal>{-# UNPACK #-}</literal> to every strict
5716 constructor field.</para>
5721 <!-- ======================= REWRITE RULES ======================== -->
5723 <sect1 id="rewrite-rules">
5724 <title>Rewrite rules
5726 <indexterm><primary>RULES pragma</primary></indexterm>
5727 <indexterm><primary>pragma, RULES</primary></indexterm>
5728 <indexterm><primary>rewrite rules</primary></indexterm></title>
5731 The programmer can specify rewrite rules as part of the source program
5732 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5733 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5734 and (b) the <option>-frules-off</option> flag
5735 (<xref linkend="options-f"/>) is not specified, and (c) the
5736 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5745 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5752 <title>Syntax</title>
5755 From a syntactic point of view:
5761 There may be zero or more rules in a <literal>RULES</literal> pragma.
5768 Each rule has a name, enclosed in double quotes. The name itself has
5769 no significance at all. It is only used when reporting how many times the rule fired.
5775 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5776 immediately after the name of the rule. Thus:
5779 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5782 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5783 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5792 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5793 is set, so you must lay out your rules starting in the same column as the
5794 enclosing definitions.
5801 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5802 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5803 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5804 by spaces, just like in a type <literal>forall</literal>.
5810 A pattern variable may optionally have a type signature.
5811 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5812 For example, here is the <literal>foldr/build</literal> rule:
5815 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5816 foldr k z (build g) = g k z
5819 Since <function>g</function> has a polymorphic type, it must have a type signature.
5826 The left hand side of a rule must consist of a top-level variable applied
5827 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5830 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5831 "wrong2" forall f. f True = True
5834 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5841 A rule does not need to be in the same module as (any of) the
5842 variables it mentions, though of course they need to be in scope.
5848 Rules are automatically exported from a module, just as instance declarations are.
5859 <title>Semantics</title>
5862 From a semantic point of view:
5868 Rules are only applied if you use the <option>-O</option> flag.
5874 Rules are regarded as left-to-right rewrite rules.
5875 When GHC finds an expression that is a substitution instance of the LHS
5876 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5877 By "a substitution instance" we mean that the LHS can be made equal to the
5878 expression by substituting for the pattern variables.
5885 The LHS and RHS of a rule are typechecked, and must have the
5893 GHC makes absolutely no attempt to verify that the LHS and RHS
5894 of a rule have the same meaning. That is undecidable in general, and
5895 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5902 GHC makes no attempt to make sure that the rules are confluent or
5903 terminating. For example:
5906 "loop" forall x,y. f x y = f y x
5909 This rule will cause the compiler to go into an infinite loop.
5916 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5922 GHC currently uses a very simple, syntactic, matching algorithm
5923 for matching a rule LHS with an expression. It seeks a substitution
5924 which makes the LHS and expression syntactically equal modulo alpha
5925 conversion. The pattern (rule), but not the expression, is eta-expanded if
5926 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5927 But not beta conversion (that's called higher-order matching).
5931 Matching is carried out on GHC's intermediate language, which includes
5932 type abstractions and applications. So a rule only matches if the
5933 types match too. See <xref linkend="rule-spec"/> below.
5939 GHC keeps trying to apply the rules as it optimises the program.
5940 For example, consider:
5949 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5950 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5951 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5952 not be substituted, and the rule would not fire.
5959 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5960 that appears on the LHS of a rule</emphasis>, because once you have substituted
5961 for something you can't match against it (given the simple minded
5962 matching). So if you write the rule
5965 "map/map" forall f,g. map f . map g = map (f.g)
5968 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5969 It will only match something written with explicit use of ".".
5970 Well, not quite. It <emphasis>will</emphasis> match the expression
5976 where <function>wibble</function> is defined:
5979 wibble f g = map f . map g
5982 because <function>wibble</function> will be inlined (it's small).
5984 Later on in compilation, GHC starts inlining even things on the
5985 LHS of rules, but still leaves the rules enabled. This inlining
5986 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5993 All rules are implicitly exported from the module, and are therefore
5994 in force in any module that imports the module that defined the rule, directly
5995 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5996 in force when compiling A.) The situation is very similar to that for instance
6008 <title>List fusion</title>
6011 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6012 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6013 intermediate list should be eliminated entirely.
6017 The following are good producers:
6029 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6035 Explicit lists (e.g. <literal>[True, False]</literal>)
6041 The cons constructor (e.g <literal>3:4:[]</literal>)
6047 <function>++</function>
6053 <function>map</function>
6059 <function>take</function>, <function>filter</function>
6065 <function>iterate</function>, <function>repeat</function>
6071 <function>zip</function>, <function>zipWith</function>
6080 The following are good consumers:
6092 <function>array</function> (on its second argument)
6098 <function>++</function> (on its first argument)
6104 <function>foldr</function>
6110 <function>map</function>
6116 <function>take</function>, <function>filter</function>
6122 <function>concat</function>
6128 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6134 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6135 will fuse with one but not the other)
6141 <function>partition</function>
6147 <function>head</function>
6153 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6159 <function>sequence_</function>
6165 <function>msum</function>
6171 <function>sortBy</function>
6180 So, for example, the following should generate no intermediate lists:
6183 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6189 This list could readily be extended; if there are Prelude functions that you use
6190 a lot which are not included, please tell us.
6194 If you want to write your own good consumers or producers, look at the
6195 Prelude definitions of the above functions to see how to do so.
6200 <sect2 id="rule-spec">
6201 <title>Specialisation
6205 Rewrite rules can be used to get the same effect as a feature
6206 present in earlier versions of GHC.
6207 For example, suppose that:
6210 genericLookup :: Ord a => Table a b -> a -> b
6211 intLookup :: Table Int b -> Int -> b
6214 where <function>intLookup</function> is an implementation of
6215 <function>genericLookup</function> that works very fast for
6216 keys of type <literal>Int</literal>. You might wish
6217 to tell GHC to use <function>intLookup</function> instead of
6218 <function>genericLookup</function> whenever the latter was called with
6219 type <literal>Table Int b -> Int -> b</literal>.
6220 It used to be possible to write
6223 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6226 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6229 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6232 This slightly odd-looking rule instructs GHC to replace
6233 <function>genericLookup</function> by <function>intLookup</function>
6234 <emphasis>whenever the types match</emphasis>.
6235 What is more, this rule does not need to be in the same
6236 file as <function>genericLookup</function>, unlike the
6237 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6238 have an original definition available to specialise).
6241 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6242 <function>intLookup</function> really behaves as a specialised version
6243 of <function>genericLookup</function>!!!</para>
6245 <para>An example in which using <literal>RULES</literal> for
6246 specialisation will Win Big:
6249 toDouble :: Real a => a -> Double
6250 toDouble = fromRational . toRational
6252 {-# RULES "toDouble/Int" toDouble = i2d #-}
6253 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6256 The <function>i2d</function> function is virtually one machine
6257 instruction; the default conversion—via an intermediate
6258 <literal>Rational</literal>—is obscenely expensive by
6265 <title>Controlling what's going on</title>
6273 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6279 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6280 If you add <option>-dppr-debug</option> you get a more detailed listing.
6286 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6289 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6290 {-# INLINE build #-}
6294 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6295 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6296 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6297 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6304 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6305 see how to write rules that will do fusion and yet give an efficient
6306 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6316 <sect2 id="core-pragma">
6317 <title>CORE pragma</title>
6319 <indexterm><primary>CORE pragma</primary></indexterm>
6320 <indexterm><primary>pragma, CORE</primary></indexterm>
6321 <indexterm><primary>core, annotation</primary></indexterm>
6324 The external core format supports <quote>Note</quote> annotations;
6325 the <literal>CORE</literal> pragma gives a way to specify what these
6326 should be in your Haskell source code. Syntactically, core
6327 annotations are attached to expressions and take a Haskell string
6328 literal as an argument. The following function definition shows an
6332 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6335 Semantically, this is equivalent to:
6343 However, when external for is generated (via
6344 <option>-fext-core</option>), there will be Notes attached to the
6345 expressions <function>show</function> and <varname>x</varname>.
6346 The core function declaration for <function>f</function> is:
6350 f :: %forall a . GHCziShow.ZCTShow a ->
6351 a -> GHCziBase.ZMZN GHCziBase.Char =
6352 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6354 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6356 (tpl1::GHCziBase.Int ->
6358 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6360 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6361 (tpl3::GHCziBase.ZMZN a ->
6362 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6370 Here, we can see that the function <function>show</function> (which
6371 has been expanded out to a case expression over the Show dictionary)
6372 has a <literal>%note</literal> attached to it, as does the
6373 expression <varname>eta</varname> (which used to be called
6374 <varname>x</varname>).
6381 <sect1 id="special-ids">
6382 <title>Special built-in functions</title>
6383 <para>GHC has a few built-in funcions with special behaviour. These
6384 are now described in the module <ulink
6385 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
6386 in the library documentation.</para>
6390 <sect1 id="generic-classes">
6391 <title>Generic classes</title>
6394 The ideas behind this extension are described in detail in "Derivable type classes",
6395 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6396 An example will give the idea:
6404 fromBin :: [Int] -> (a, [Int])
6406 toBin {| Unit |} Unit = []
6407 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6408 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6409 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6411 fromBin {| Unit |} bs = (Unit, bs)
6412 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6413 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6414 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6415 (y,bs'') = fromBin bs'
6418 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6419 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6420 which are defined thus in the library module <literal>Generics</literal>:
6424 data a :+: b = Inl a | Inr b
6425 data a :*: b = a :*: b
6428 Now you can make a data type into an instance of Bin like this:
6430 instance (Bin a, Bin b) => Bin (a,b)
6431 instance Bin a => Bin [a]
6433 That is, just leave off the "where" clause. Of course, you can put in the
6434 where clause and over-ride whichever methods you please.
6438 <title> Using generics </title>
6439 <para>To use generics you need to</para>
6442 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6443 <option>-XGenerics</option> (to generate extra per-data-type code),
6444 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6448 <para>Import the module <literal>Generics</literal> from the
6449 <literal>lang</literal> package. This import brings into
6450 scope the data types <literal>Unit</literal>,
6451 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6452 don't need this import if you don't mention these types
6453 explicitly; for example, if you are simply giving instance
6454 declarations.)</para>
6459 <sect2> <title> Changes wrt the paper </title>
6461 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6462 can be written infix (indeed, you can now use
6463 any operator starting in a colon as an infix type constructor). Also note that
6464 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6465 Finally, note that the syntax of the type patterns in the class declaration
6466 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6467 alone would ambiguous when they appear on right hand sides (an extension we
6468 anticipate wanting).
6472 <sect2> <title>Terminology and restrictions</title>
6474 Terminology. A "generic default method" in a class declaration
6475 is one that is defined using type patterns as above.
6476 A "polymorphic default method" is a default method defined as in Haskell 98.
6477 A "generic class declaration" is a class declaration with at least one
6478 generic default method.
6486 Alas, we do not yet implement the stuff about constructor names and
6493 A generic class can have only one parameter; you can't have a generic
6494 multi-parameter class.
6500 A default method must be defined entirely using type patterns, or entirely
6501 without. So this is illegal:
6504 op :: a -> (a, Bool)
6505 op {| Unit |} Unit = (Unit, True)
6508 However it is perfectly OK for some methods of a generic class to have
6509 generic default methods and others to have polymorphic default methods.
6515 The type variable(s) in the type pattern for a generic method declaration
6516 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:
6520 op {| p :*: q |} (x :*: y) = op (x :: p)
6528 The type patterns in a generic default method must take one of the forms:
6534 where "a" and "b" are type variables. Furthermore, all the type patterns for
6535 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6536 must use the same type variables. So this is illegal:
6540 op {| a :+: b |} (Inl x) = True
6541 op {| p :+: q |} (Inr y) = False
6543 The type patterns must be identical, even in equations for different methods of the class.
6544 So this too is illegal:
6548 op1 {| a :*: b |} (x :*: y) = True
6551 op2 {| p :*: q |} (x :*: y) = False
6553 (The reason for this restriction is that we gather all the equations for a particular type consructor
6554 into a single generic instance declaration.)
6560 A generic method declaration must give a case for each of the three type constructors.
6566 The type for a generic method can be built only from:
6568 <listitem> <para> Function arrows </para> </listitem>
6569 <listitem> <para> Type variables </para> </listitem>
6570 <listitem> <para> Tuples </para> </listitem>
6571 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6573 Here are some example type signatures for generic methods:
6576 op2 :: Bool -> (a,Bool)
6577 op3 :: [Int] -> a -> a
6580 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6584 This restriction is an implementation restriction: we just havn't got around to
6585 implementing the necessary bidirectional maps over arbitrary type constructors.
6586 It would be relatively easy to add specific type constructors, such as Maybe and list,
6587 to the ones that are allowed.</para>
6592 In an instance declaration for a generic class, the idea is that the compiler
6593 will fill in the methods for you, based on the generic templates. However it can only
6598 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6603 No constructor of the instance type has unboxed fields.
6607 (Of course, these things can only arise if you are already using GHC extensions.)
6608 However, you can still give an instance declarations for types which break these rules,
6609 provided you give explicit code to override any generic default methods.
6617 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6618 what the compiler does with generic declarations.
6623 <sect2> <title> Another example </title>
6625 Just to finish with, here's another example I rather like:
6629 nCons {| Unit |} _ = 1
6630 nCons {| a :*: b |} _ = 1
6631 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6634 tag {| Unit |} _ = 1
6635 tag {| a :*: b |} _ = 1
6636 tag {| a :+: b |} (Inl x) = tag x
6637 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6643 <sect1 id="monomorphism">
6644 <title>Control over monomorphism</title>
6646 <para>GHC supports two flags that control the way in which generalisation is
6647 carried out at let and where bindings.
6651 <title>Switching off the dreaded Monomorphism Restriction</title>
6652 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
6654 <para>Haskell's monomorphism restriction (see
6655 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6657 of the Haskell Report)
6658 can be completely switched off by
6659 <option>-XNoMonomorphismRestriction</option>.
6664 <title>Monomorphic pattern bindings</title>
6665 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
6666 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
6668 <para> As an experimental change, we are exploring the possibility of
6669 making pattern bindings monomorphic; that is, not generalised at all.
6670 A pattern binding is a binding whose LHS has no function arguments,
6671 and is not a simple variable. For example:
6673 f x = x -- Not a pattern binding
6674 f = \x -> x -- Not a pattern binding
6675 f :: Int -> Int = \x -> x -- Not a pattern binding
6677 (g,h) = e -- A pattern binding
6678 (f) = e -- A pattern binding
6679 [x] = e -- A pattern binding
6681 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6682 default</emphasis>. Use <option>-XMonoPatBinds</option> to recover the
6691 ;;; Local Variables: ***
6693 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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