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 Here are some 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 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
781 <literal>-fglasgow-exts</literal>.
785 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
786 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
787 be distinct (Section 3.3 of the paper).
791 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
792 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
793 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
794 and improve termination (Section 3.2 of the paper).
800 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
801 contains up to date information on recursive monadic bindings.
805 Historical note: The old implementation of the mdo-notation (and most
806 of the existing documents) used the name
807 <literal>MonadRec</literal> for the class and the corresponding library.
808 This name is not supported by GHC.
814 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
816 <sect2 id="parallel-list-comprehensions">
817 <title>Parallel List Comprehensions</title>
818 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
820 <indexterm><primary>parallel list comprehensions</primary>
823 <para>Parallel list comprehensions are a natural extension to list
824 comprehensions. List comprehensions can be thought of as a nice
825 syntax for writing maps and filters. Parallel comprehensions
826 extend this to include the zipWith family.</para>
828 <para>A parallel list comprehension has multiple independent
829 branches of qualifier lists, each separated by a `|' symbol. For
830 example, the following zips together two lists:</para>
833 [ (x, y) | x <- xs | y <- ys ]
836 <para>The behavior of parallel list comprehensions follows that of
837 zip, in that the resulting list will have the same length as the
838 shortest branch.</para>
840 <para>We can define parallel list comprehensions by translation to
841 regular comprehensions. Here's the basic idea:</para>
843 <para>Given a parallel comprehension of the form: </para>
846 [ e | p1 <- e11, p2 <- e12, ...
847 | q1 <- e21, q2 <- e22, ...
852 <para>This will be translated to: </para>
855 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
856 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
861 <para>where `zipN' is the appropriate zip for the given number of
866 <sect2 id="rebindable-syntax">
867 <title>Rebindable syntax</title>
870 <para>GHC allows most kinds of built-in syntax to be rebound by
871 the user, to facilitate replacing the <literal>Prelude</literal>
872 with a home-grown version, for example.</para>
874 <para>You may want to define your own numeric class
875 hierarchy. It completely defeats that purpose if the
876 literal "1" means "<literal>Prelude.fromInteger
877 1</literal>", which is what the Haskell Report specifies.
878 So the <option>-XNoImplicitPrelude</option> flag causes
879 the following pieces of built-in syntax to refer to
880 <emphasis>whatever is in scope</emphasis>, not the Prelude
885 <para>An integer literal <literal>368</literal> means
886 "<literal>fromInteger (368::Integer)</literal>", rather than
887 "<literal>Prelude.fromInteger (368::Integer)</literal>".
890 <listitem><para>Fractional literals are handed in just the same way,
891 except that the translation is
892 <literal>fromRational (3.68::Rational)</literal>.
895 <listitem><para>The equality test in an overloaded numeric pattern
896 uses whatever <literal>(==)</literal> is in scope.
899 <listitem><para>The subtraction operation, and the
900 greater-than-or-equal test, in <literal>n+k</literal> patterns
901 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
905 <para>Negation (e.g. "<literal>- (f x)</literal>")
906 means "<literal>negate (f x)</literal>", both in numeric
907 patterns, and expressions.
911 <para>"Do" notation is translated using whatever
912 functions <literal>(>>=)</literal>,
913 <literal>(>>)</literal>, and <literal>fail</literal>,
914 are in scope (not the Prelude
915 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
916 comprehensions, are unaffected. </para></listitem>
920 notation (see <xref linkend="arrow-notation"/>)
921 uses whatever <literal>arr</literal>,
922 <literal>(>>>)</literal>, <literal>first</literal>,
923 <literal>app</literal>, <literal>(|||)</literal> and
924 <literal>loop</literal> functions are in scope. But unlike the
925 other constructs, the types of these functions must match the
926 Prelude types very closely. Details are in flux; if you want
930 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
931 even if that is a little unexpected. For emample, the
932 static semantics of the literal <literal>368</literal>
933 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
934 <literal>fromInteger</literal> to have any of the types:
936 fromInteger :: Integer -> Integer
937 fromInteger :: forall a. Foo a => Integer -> a
938 fromInteger :: Num a => a -> Integer
939 fromInteger :: Integer -> Bool -> Bool
943 <para>Be warned: this is an experimental facility, with
944 fewer checks than usual. Use <literal>-dcore-lint</literal>
945 to typecheck the desugared program. If Core Lint is happy
946 you should be all right.</para>
950 <sect2 id="postfix-operators">
951 <title>Postfix operators</title>
954 GHC allows a small extension to the syntax of left operator sections, which
955 allows you to define postfix operators. The extension is this: the left section
959 is equivalent (from the point of view of both type checking and execution) to the expression
963 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
964 The strict Haskell 98 interpretation is that the section is equivalent to
968 That is, the operator must be a function of two arguments. GHC allows it to
969 take only one argument, and that in turn allows you to write the function
972 <para>Since this extension goes beyond Haskell 98, it should really be enabled
973 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
974 change their behaviour, of course.)
976 <para>The extension does not extend to the left-hand side of function
977 definitions; you must define such a function in prefix form.</para>
981 <sect2 id="disambiguate-fields">
982 <title>Record field disambiguation</title>
984 In record construction and record pattern matching
985 it is entirely unambiguous which field is referred to, even if there are two different
986 data types in scope with a common field name. For example:
989 data S = MkS { x :: Int, y :: Bool }
994 data T = MkT { x :: Int }
996 ok1 (MkS { x = n }) = n+1 -- Unambiguous
998 ok2 n = MkT { x = n+1 } -- Unambiguous
1000 bad1 k = k { x = 3 } -- Ambiguous
1001 bad2 k = x k -- Ambiguous
1003 Even though there are two <literal>x</literal>'s in scope,
1004 it is clear that the <literal>x</literal> in the pattern in the
1005 definition of <literal>ok1</literal> can only mean the field
1006 <literal>x</literal> from type <literal>S</literal>. Similarly for
1007 the function <literal>ok2</literal>. However, in the record update
1008 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1009 it is not clear which of the two types is intended.
1012 Haskell 98 regards all four as ambiguous, but with the
1013 <option>-fdisambiguate-record-fields</option> flag, GHC will accept
1014 the former two. The rules are precisely the same as those for instance
1015 declarations in Haskell 98, where the method names on the left-hand side
1016 of the method bindings in an instance declaration refer unambiguously
1017 to the method of that class (provided they are in scope at all), even
1018 if there are other variables in scope with the same name.
1019 This reduces the clutter of qualified names when you import two
1020 records from different modules that use the same field name.
1026 <!-- TYPE SYSTEM EXTENSIONS -->
1027 <sect1 id="data-type-extensions">
1028 <title>Extensions to data types and type synonyms</title>
1030 <sect2 id="nullary-types">
1031 <title>Data types with no constructors</title>
1033 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1034 a data type with no constructors. For example:</para>
1038 data T a -- T :: * -> *
1041 <para>Syntactically, the declaration lacks the "= constrs" part. The
1042 type can be parameterised over types of any kind, but if the kind is
1043 not <literal>*</literal> then an explicit kind annotation must be used
1044 (see <xref linkend="kinding"/>).</para>
1046 <para>Such data types have only one value, namely bottom.
1047 Nevertheless, they can be useful when defining "phantom types".</para>
1050 <sect2 id="infix-tycons">
1051 <title>Infix type constructors, classes, and type variables</title>
1054 GHC allows type constructors, classes, and type variables to be operators, and
1055 to be written infix, very much like expressions. More specifically:
1058 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1059 The lexical syntax is the same as that for data constructors.
1062 Data type and type-synonym declarations can be written infix, parenthesised
1063 if you want further arguments. E.g.
1065 data a :*: b = Foo a b
1066 type a :+: b = Either a b
1067 class a :=: b where ...
1069 data (a :**: b) x = Baz a b x
1070 type (a :++: b) y = Either (a,b) y
1074 Types, and class constraints, can be written infix. For example
1077 f :: (a :=: b) => a -> b
1081 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1082 The lexical syntax is the same as that for variable operators, excluding "(.)",
1083 "(!)", and "(*)". In a binding position, the operator must be
1084 parenthesised. For example:
1086 type T (+) = Int + Int
1090 liftA2 :: Arrow (~>)
1091 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1097 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1098 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1101 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1102 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1103 sets the fixity for a data constructor and the corresponding type constructor. For example:
1107 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1108 and similarly for <literal>:*:</literal>.
1109 <literal>Int `a` Bool</literal>.
1112 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1119 <sect2 id="type-synonyms">
1120 <title>Liberalised type synonyms</title>
1123 Type synonyms are like macros at the type level, and
1124 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1125 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1127 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1128 in a type synonym, thus:
1130 type Discard a = forall b. Show b => a -> b -> (a, String)
1135 g :: Discard Int -> (Int,String) -- A rank-2 type
1142 You can write an unboxed tuple in a type synonym:
1144 type Pr = (# Int, Int #)
1152 You can apply a type synonym to a forall type:
1154 type Foo a = a -> a -> Bool
1156 f :: Foo (forall b. b->b)
1158 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1160 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1165 You can apply a type synonym to a partially applied type synonym:
1167 type Generic i o = forall x. i x -> o x
1170 foo :: Generic Id []
1172 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1174 foo :: forall x. x -> [x]
1182 GHC currently does kind checking before expanding synonyms (though even that
1186 After expanding type synonyms, GHC does validity checking on types, looking for
1187 the following mal-formedness which isn't detected simply by kind checking:
1190 Type constructor applied to a type involving for-alls.
1193 Unboxed tuple on left of an arrow.
1196 Partially-applied type synonym.
1200 this will be rejected:
1202 type Pr = (# Int, Int #)
1207 because GHC does not allow unboxed tuples on the left of a function arrow.
1212 <sect2 id="existential-quantification">
1213 <title>Existentially quantified data constructors
1217 The idea of using existential quantification in data type declarations
1218 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1219 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1220 London, 1991). It was later formalised by Laufer and Odersky
1221 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1222 TOPLAS, 16(5), pp1411-1430, 1994).
1223 It's been in Lennart
1224 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1225 proved very useful. Here's the idea. Consider the declaration:
1231 data Foo = forall a. MkFoo a (a -> Bool)
1238 The data type <literal>Foo</literal> has two constructors with types:
1244 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1251 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1252 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1253 For example, the following expression is fine:
1259 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1265 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1266 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1267 isUpper</function> packages a character with a compatible function. These
1268 two things are each of type <literal>Foo</literal> and can be put in a list.
1272 What can we do with a value of type <literal>Foo</literal>?. In particular,
1273 what happens when we pattern-match on <function>MkFoo</function>?
1279 f (MkFoo val fn) = ???
1285 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1286 are compatible, the only (useful) thing we can do with them is to
1287 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1294 f (MkFoo val fn) = fn val
1300 What this allows us to do is to package heterogenous values
1301 together with a bunch of functions that manipulate them, and then treat
1302 that collection of packages in a uniform manner. You can express
1303 quite a bit of object-oriented-like programming this way.
1306 <sect3 id="existential">
1307 <title>Why existential?
1311 What has this to do with <emphasis>existential</emphasis> quantification?
1312 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1318 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1324 But Haskell programmers can safely think of the ordinary
1325 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1326 adding a new existential quantification construct.
1332 <title>Type classes</title>
1335 An easy extension is to allow
1336 arbitrary contexts before the constructor. For example:
1342 data Baz = forall a. Eq a => Baz1 a a
1343 | forall b. Show b => Baz2 b (b -> b)
1349 The two constructors have the types you'd expect:
1355 Baz1 :: forall a. Eq a => a -> a -> Baz
1356 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1362 But when pattern matching on <function>Baz1</function> the matched values can be compared
1363 for equality, and when pattern matching on <function>Baz2</function> the first matched
1364 value can be converted to a string (as well as applying the function to it).
1365 So this program is legal:
1372 f (Baz1 p q) | p == q = "Yes"
1374 f (Baz2 v fn) = show (fn v)
1380 Operationally, in a dictionary-passing implementation, the
1381 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1382 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1383 extract it on pattern matching.
1387 Notice the way that the syntax fits smoothly with that used for
1388 universal quantification earlier.
1393 <sect3 id="existential-records">
1394 <title>Record Constructors</title>
1397 GHC allows existentials to be used with records syntax as well. For example:
1400 data Counter a = forall self. NewCounter
1402 , _inc :: self -> self
1403 , _display :: self -> IO ()
1407 Here <literal>tag</literal> is a public field, with a well-typed selector
1408 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1409 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1410 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1411 compile-time error. In other words, <emphasis>GHC defines a record selector function
1412 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1413 (This example used an underscore in the fields for which record selectors
1414 will not be defined, but that is only programming style; GHC ignores them.)
1418 To make use of these hidden fields, we need to create some helper functions:
1421 inc :: Counter a -> Counter a
1422 inc (NewCounter x i d t) = NewCounter
1423 { _this = i x, _inc = i, _display = d, tag = t }
1425 display :: Counter a -> IO ()
1426 display NewCounter{ _this = x, _display = d } = d x
1429 Now we can define counters with different underlying implementations:
1432 counterA :: Counter String
1433 counterA = NewCounter
1434 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1436 counterB :: Counter String
1437 counterB = NewCounter
1438 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1441 display (inc counterA) -- prints "1"
1442 display (inc (inc counterB)) -- prints "##"
1445 At the moment, record update syntax is only supported for Haskell 98 data types,
1446 so the following function does <emphasis>not</emphasis> work:
1449 -- This is invalid; use explicit NewCounter instead for now
1450 setTag :: Counter a -> a -> Counter a
1451 setTag obj t = obj{ tag = t }
1460 <title>Restrictions</title>
1463 There are several restrictions on the ways in which existentially-quantified
1464 constructors can be use.
1473 When pattern matching, each pattern match introduces a new,
1474 distinct, type for each existential type variable. These types cannot
1475 be unified with any other type, nor can they escape from the scope of
1476 the pattern match. For example, these fragments are incorrect:
1484 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1485 is the result of <function>f1</function>. One way to see why this is wrong is to
1486 ask what type <function>f1</function> has:
1490 f1 :: Foo -> a -- Weird!
1494 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1499 f1 :: forall a. Foo -> a -- Wrong!
1503 The original program is just plain wrong. Here's another sort of error
1507 f2 (Baz1 a b) (Baz1 p q) = a==q
1511 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1512 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1513 from the two <function>Baz1</function> constructors.
1521 You can't pattern-match on an existentially quantified
1522 constructor in a <literal>let</literal> or <literal>where</literal> group of
1523 bindings. So this is illegal:
1527 f3 x = a==b where { Baz1 a b = x }
1530 Instead, use a <literal>case</literal> expression:
1533 f3 x = case x of Baz1 a b -> a==b
1536 In general, you can only pattern-match
1537 on an existentially-quantified constructor in a <literal>case</literal> expression or
1538 in the patterns of a function definition.
1540 The reason for this restriction is really an implementation one.
1541 Type-checking binding groups is already a nightmare without
1542 existentials complicating the picture. Also an existential pattern
1543 binding at the top level of a module doesn't make sense, because it's
1544 not clear how to prevent the existentially-quantified type "escaping".
1545 So for now, there's a simple-to-state restriction. We'll see how
1553 You can't use existential quantification for <literal>newtype</literal>
1554 declarations. So this is illegal:
1558 newtype T = forall a. Ord a => MkT a
1562 Reason: a value of type <literal>T</literal> must be represented as a
1563 pair of a dictionary for <literal>Ord t</literal> and a value of type
1564 <literal>t</literal>. That contradicts the idea that
1565 <literal>newtype</literal> should have no concrete representation.
1566 You can get just the same efficiency and effect by using
1567 <literal>data</literal> instead of <literal>newtype</literal>. If
1568 there is no overloading involved, then there is more of a case for
1569 allowing an existentially-quantified <literal>newtype</literal>,
1570 because the <literal>data</literal> version does carry an
1571 implementation cost, but single-field existentially quantified
1572 constructors aren't much use. So the simple restriction (no
1573 existential stuff on <literal>newtype</literal>) stands, unless there
1574 are convincing reasons to change it.
1582 You can't use <literal>deriving</literal> to define instances of a
1583 data type with existentially quantified data constructors.
1585 Reason: in most cases it would not make sense. For example:;
1588 data T = forall a. MkT [a] deriving( Eq )
1591 To derive <literal>Eq</literal> in the standard way we would need to have equality
1592 between the single component of two <function>MkT</function> constructors:
1596 (MkT a) == (MkT b) = ???
1599 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1600 It's just about possible to imagine examples in which the derived instance
1601 would make sense, but it seems altogether simpler simply to prohibit such
1602 declarations. Define your own instances!
1613 <!-- ====================== Generalised algebraic data types ======================= -->
1615 <sect2 id="gadt-style">
1616 <title>Declaring data types with explicit constructor signatures</title>
1618 <para>GHC allows you to declare an algebraic data type by
1619 giving the type signatures of constructors explicitly. For example:
1623 Just :: a -> Maybe a
1625 The form is called a "GADT-style declaration"
1626 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1627 can only be declared using this form.</para>
1628 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1629 For example, these two declarations are equivalent:
1631 data Foo = forall a. MkFoo a (a -> Bool)
1632 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1635 <para>Any data type that can be declared in standard Haskell-98 syntax
1636 can also be declared using GADT-style syntax.
1637 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1638 they treat class constraints on the data constructors differently.
1639 Specifically, if the constructor is given a type-class context, that
1640 context is made available by pattern matching. For example:
1643 MkSet :: Eq a => [a] -> Set a
1645 makeSet :: Eq a => [a] -> Set a
1646 makeSet xs = MkSet (nub xs)
1648 insert :: a -> Set a -> Set a
1649 insert a (MkSet as) | a `elem` as = MkSet as
1650 | otherwise = MkSet (a:as)
1652 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1653 gives rise to a <literal>(Eq a)</literal>
1654 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1655 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1656 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1657 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1658 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1659 In the example, the equality dictionary is used to satisfy the equality constraint
1660 generated by the call to <literal>elem</literal>, so that the type of
1661 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1663 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1664 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1665 In Haskell 98 the defintion
1667 data Eq a => Set' a = MkSet' [a]
1669 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1670 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1671 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1672 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1673 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1675 For example, a possible application of GHC's behaviour is to reify dictionaries:
1677 data NumInst a where
1678 MkNumInst :: Num a => NumInst a
1680 intInst :: NumInst Int
1683 plus :: NumInst a -> a -> a -> a
1684 plus MkNumInst p q = p + q
1686 Here, a value of type <literal>NumInst a</literal> is equivalent
1687 to an explicit <literal>(Num a)</literal> dictionary.
1691 The rest of this section gives further details about GADT-style data
1696 The result type of each data constructor must begin with the type constructor being defined.
1697 If the result type of all constructors
1698 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1699 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1700 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1704 The type signature of
1705 each constructor is independent, and is implicitly universally quantified as usual.
1706 Different constructors may have different universally-quantified type variables
1707 and different type-class constraints.
1708 For example, this is fine:
1711 T1 :: Eq b => b -> T b
1712 T2 :: (Show c, Ix c) => c -> [c] -> T c
1717 Unlike a Haskell-98-style
1718 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1719 have no scope. Indeed, one can write a kind signature instead:
1721 data Set :: * -> * where ...
1723 or even a mixture of the two:
1725 data Foo a :: (* -> *) -> * where ...
1727 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1730 data Foo a (b :: * -> *) where ...
1736 You can use strictness annotations, in the obvious places
1737 in the constructor type:
1740 Lit :: !Int -> Term Int
1741 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1742 Pair :: Term a -> Term b -> Term (a,b)
1747 You can use a <literal>deriving</literal> clause on a GADT-style data type
1748 declaration. For example, these two declarations are equivalent
1750 data Maybe1 a where {
1751 Nothing1 :: Maybe1 a ;
1752 Just1 :: a -> Maybe1 a
1753 } deriving( Eq, Ord )
1755 data Maybe2 a = Nothing2 | Just2 a
1761 You can use record syntax on a GADT-style data type declaration:
1765 Adult { name :: String, children :: [Person] } :: Person
1766 Child { name :: String } :: Person
1768 As usual, for every constructor that has a field <literal>f</literal>, the type of
1769 field <literal>f</literal> must be the same (modulo alpha conversion).
1772 At the moment, record updates are not yet possible with GADT-style declarations,
1773 so support is limited to record construction, selection and pattern matching.
1776 aPerson = Adult { name = "Fred", children = [] }
1778 shortName :: Person -> Bool
1779 hasChildren (Adult { children = kids }) = not (null kids)
1780 hasChildren (Child {}) = False
1785 As in the case of existentials declared using the Haskell-98-like record syntax
1786 (<xref linkend="existential-records"/>),
1787 record-selector functions are generated only for those fields that have well-typed
1789 Here is the example of that section, in GADT-style syntax:
1791 data Counter a where
1792 NewCounter { _this :: self
1793 , _inc :: self -> self
1794 , _display :: self -> IO ()
1799 As before, only one selector function is generated here, that for <literal>tag</literal>.
1800 Nevertheless, you can still use all the field names in pattern matching and record construction.
1802 </itemizedlist></para>
1806 <title>Generalised Algebraic Data Types (GADTs)</title>
1808 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1809 by allowing constructors to have richer return types. Here is an example:
1812 Lit :: Int -> Term Int
1813 Succ :: Term Int -> Term Int
1814 IsZero :: Term Int -> Term Bool
1815 If :: Term Bool -> Term a -> Term a -> Term a
1816 Pair :: Term a -> Term b -> Term (a,b)
1818 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1819 case with ordinary data types. This generality allows us to
1820 write a well-typed <literal>eval</literal> function
1821 for these <literal>Terms</literal>:
1825 eval (Succ t) = 1 + eval t
1826 eval (IsZero t) = eval t == 0
1827 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1828 eval (Pair e1 e2) = (eval e1, eval e2)
1830 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1831 For example, in the right hand side of the equation
1836 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1837 A precise specification of the type rules is beyond what this user manual aspires to,
1838 but the design closely follows that described in
1840 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1841 unification-based type inference for GADTs</ulink>,
1843 The general principle is this: <emphasis>type refinement is only carried out
1844 based on user-supplied type annotations</emphasis>.
1845 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1846 and lots of obscure error messages will
1847 occur. However, the refinement is quite general. For example, if we had:
1849 eval :: Term a -> a -> a
1850 eval (Lit i) j = i+j
1852 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1853 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1854 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1857 These and many other examples are given in papers by Hongwei Xi, and
1858 Tim Sheard. There is a longer introduction
1859 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1861 <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
1862 may use different notation to that implemented in GHC.
1865 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
1866 <option>-XGADTs</option>.
1869 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1870 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1871 The result type of each constructor must begin with the type constructor being defined,
1872 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1873 For example, in the <literal>Term</literal> data
1874 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1875 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1880 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1881 an ordianary data type.
1885 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1889 Lit { val :: Int } :: Term Int
1890 Succ { num :: Term Int } :: Term Int
1891 Pred { num :: Term Int } :: Term Int
1892 IsZero { arg :: Term Int } :: Term Bool
1893 Pair { arg1 :: Term a
1896 If { cnd :: Term Bool
1901 However, for GADTs there is the following additional constraint:
1902 every constructor that has a field <literal>f</literal> must have
1903 the same result type (modulo alpha conversion)
1904 Hence, in the above example, we cannot merge the <literal>num</literal>
1905 and <literal>arg</literal> fields above into a
1906 single name. Although their field types are both <literal>Term Int</literal>,
1907 their selector functions actually have different types:
1910 num :: Term Int -> Term Int
1911 arg :: Term Bool -> Term Int
1920 <!-- ====================== End of Generalised algebraic data types ======================= -->
1923 <sect2 id="deriving-typeable">
1924 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1927 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1928 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1929 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1930 classes <literal>Eq</literal>, <literal>Ord</literal>,
1931 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1934 GHC extends this list with two more classes that may be automatically derived
1935 (provided the <option>-fglasgow-exts</option> flag is specified):
1936 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1937 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1938 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1940 <para>An instance of <literal>Typeable</literal> can only be derived if the
1941 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1942 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1944 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1945 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1947 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1948 are used, and only <literal>Typeable1</literal> up to
1949 <literal>Typeable7</literal> are provided in the library.)
1950 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1951 class, whose kind suits that of the data type constructor, and
1952 then writing the data type instance by hand.
1956 <sect2 id="newtype-deriving">
1957 <title>Generalised derived instances for newtypes</title>
1960 When you define an abstract type using <literal>newtype</literal>, you may want
1961 the new type to inherit some instances from its representation. In
1962 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1963 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1964 other classes you have to write an explicit instance declaration. For
1965 example, if you define
1968 newtype Dollars = Dollars Int
1971 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1972 explicitly define an instance of <literal>Num</literal>:
1975 instance Num Dollars where
1976 Dollars a + Dollars b = Dollars (a+b)
1979 All the instance does is apply and remove the <literal>newtype</literal>
1980 constructor. It is particularly galling that, since the constructor
1981 doesn't appear at run-time, this instance declaration defines a
1982 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1983 dictionary, only slower!
1987 <sect3> <title> Generalising the deriving clause </title>
1989 GHC now permits such instances to be derived instead, so one can write
1991 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1994 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1995 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1996 derives an instance declaration of the form
1999 instance Num Int => Num Dollars
2002 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2006 We can also derive instances of constructor classes in a similar
2007 way. For example, suppose we have implemented state and failure monad
2008 transformers, such that
2011 instance Monad m => Monad (State s m)
2012 instance Monad m => Monad (Failure m)
2014 In Haskell 98, we can define a parsing monad by
2016 type Parser tok m a = State [tok] (Failure m) a
2019 which is automatically a monad thanks to the instance declarations
2020 above. With the extension, we can make the parser type abstract,
2021 without needing to write an instance of class <literal>Monad</literal>, via
2024 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2027 In this case the derived instance declaration is of the form
2029 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2032 Notice that, since <literal>Monad</literal> is a constructor class, the
2033 instance is a <emphasis>partial application</emphasis> of the new type, not the
2034 entire left hand side. We can imagine that the type declaration is
2035 ``eta-converted'' to generate the context of the instance
2040 We can even derive instances of multi-parameter classes, provided the
2041 newtype is the last class parameter. In this case, a ``partial
2042 application'' of the class appears in the <literal>deriving</literal>
2043 clause. For example, given the class
2046 class StateMonad s m | m -> s where ...
2047 instance Monad m => StateMonad s (State s m) where ...
2049 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2051 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2052 deriving (Monad, StateMonad [tok])
2055 The derived instance is obtained by completing the application of the
2056 class to the new type:
2059 instance StateMonad [tok] (State [tok] (Failure m)) =>
2060 StateMonad [tok] (Parser tok m)
2065 As a result of this extension, all derived instances in newtype
2066 declarations are treated uniformly (and implemented just by reusing
2067 the dictionary for the representation type), <emphasis>except</emphasis>
2068 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2069 the newtype and its representation.
2073 <sect3> <title> A more precise specification </title>
2075 Derived instance declarations are constructed as follows. Consider the
2076 declaration (after expansion of any type synonyms)
2079 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2085 The <literal>ci</literal> are partial applications of
2086 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2087 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2090 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2093 The type <literal>t</literal> is an arbitrary type.
2096 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2097 nor in the <literal>ci</literal>, and
2100 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2101 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2102 should not "look through" the type or its constructor. You can still
2103 derive these classes for a newtype, but it happens in the usual way, not
2104 via this new mechanism.
2107 Then, for each <literal>ci</literal>, the derived instance
2110 instance ci t => ci (T v1...vk)
2112 As an example which does <emphasis>not</emphasis> work, consider
2114 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2116 Here we cannot derive the instance
2118 instance Monad (State s m) => Monad (NonMonad m)
2121 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2122 and so cannot be "eta-converted" away. It is a good thing that this
2123 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2124 not, in fact, a monad --- for the same reason. Try defining
2125 <literal>>>=</literal> with the correct type: you won't be able to.
2129 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2130 important, since we can only derive instances for the last one. If the
2131 <literal>StateMonad</literal> class above were instead defined as
2134 class StateMonad m s | m -> s where ...
2137 then we would not have been able to derive an instance for the
2138 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2139 classes usually have one "main" parameter for which deriving new
2140 instances is most interesting.
2142 <para>Lastly, all of this applies only for classes other than
2143 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2144 and <literal>Data</literal>, for which the built-in derivation applies (section
2145 4.3.3. of the Haskell Report).
2146 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2147 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2148 the standard method is used or the one described here.)
2154 <sect2 id="stand-alone-deriving">
2155 <title>Stand-alone deriving declarations</title>
2158 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2160 data Foo a = Bar a | Baz String
2162 derive instance Eq (Foo a)
2164 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2165 you can use it as a variable name elsewhere.</para>
2166 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2167 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2170 newtype Foo a = MkFoo (State Int a)
2172 derive instance MonadState Int Foo
2174 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2175 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2183 <!-- TYPE SYSTEM EXTENSIONS -->
2184 <sect1 id="other-type-extensions">
2185 <title>Other type system extensions</title>
2187 <sect2 id="multi-param-type-classes">
2188 <title>Class declarations</title>
2191 This section, and the next one, documents GHC's type-class extensions.
2192 There's lots of background in the paper <ulink
2193 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2194 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2195 Jones, Erik Meijer).
2198 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2202 <title>Multi-parameter type classes</title>
2204 Multi-parameter type classes are permitted. For example:
2208 class Collection c a where
2209 union :: c a -> c a -> c a
2217 <title>The superclasses of a class declaration</title>
2220 There are no restrictions on the context in a class declaration
2221 (which introduces superclasses), except that the class hierarchy must
2222 be acyclic. So these class declarations are OK:
2226 class Functor (m k) => FiniteMap m k where
2229 class (Monad m, Monad (t m)) => Transform t m where
2230 lift :: m a -> (t m) a
2236 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2237 of "acyclic" involves only the superclass relationships. For example,
2243 op :: D b => a -> b -> b
2246 class C a => D a where { ... }
2250 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2251 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2252 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2259 <sect3 id="class-method-types">
2260 <title>Class method types</title>
2263 Haskell 98 prohibits class method types to mention constraints on the
2264 class type variable, thus:
2267 fromList :: [a] -> s a
2268 elem :: Eq a => a -> s a -> Bool
2270 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2271 contains the constraint <literal>Eq a</literal>, constrains only the
2272 class type variable (in this case <literal>a</literal>).
2273 GHC lifts this restriction.
2280 <sect2 id="functional-dependencies">
2281 <title>Functional dependencies
2284 <para> Functional dependencies are implemented as described by Mark Jones
2285 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2286 In Proceedings of the 9th European Symposium on Programming,
2287 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2291 Functional dependencies are introduced by a vertical bar in the syntax of a
2292 class declaration; e.g.
2294 class (Monad m) => MonadState s m | m -> s where ...
2296 class Foo a b c | a b -> c where ...
2298 There should be more documentation, but there isn't (yet). Yell if you need it.
2301 <sect3><title>Rules for functional dependencies </title>
2303 In a class declaration, all of the class type variables must be reachable (in the sense
2304 mentioned in <xref linkend="type-restrictions"/>)
2305 from the free variables of each method type.
2309 class Coll s a where
2311 insert :: s -> a -> s
2314 is not OK, because the type of <literal>empty</literal> doesn't mention
2315 <literal>a</literal>. Functional dependencies can make the type variable
2318 class Coll s a | s -> a where
2320 insert :: s -> a -> s
2323 Alternatively <literal>Coll</literal> might be rewritten
2326 class Coll s a where
2328 insert :: s a -> a -> s a
2332 which makes the connection between the type of a collection of
2333 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2334 Occasionally this really doesn't work, in which case you can split the
2342 class CollE s => Coll s a where
2343 insert :: s -> a -> s
2350 <title>Background on functional dependencies</title>
2352 <para>The following description of the motivation and use of functional dependencies is taken
2353 from the Hugs user manual, reproduced here (with minor changes) by kind
2354 permission of Mark Jones.
2357 Consider the following class, intended as part of a
2358 library for collection types:
2360 class Collects e ce where
2362 insert :: e -> ce -> ce
2363 member :: e -> ce -> Bool
2365 The type variable e used here represents the element type, while ce is the type
2366 of the container itself. Within this framework, we might want to define
2367 instances of this class for lists or characteristic functions (both of which
2368 can be used to represent collections of any equality type), bit sets (which can
2369 be used to represent collections of characters), or hash tables (which can be
2370 used to represent any collection whose elements have a hash function). Omitting
2371 standard implementation details, this would lead to the following declarations:
2373 instance Eq e => Collects e [e] where ...
2374 instance Eq e => Collects e (e -> Bool) where ...
2375 instance Collects Char BitSet where ...
2376 instance (Hashable e, Collects a ce)
2377 => Collects e (Array Int ce) where ...
2379 All this looks quite promising; we have a class and a range of interesting
2380 implementations. Unfortunately, there are some serious problems with the class
2381 declaration. First, the empty function has an ambiguous type:
2383 empty :: Collects e ce => ce
2385 By "ambiguous" we mean that there is a type variable e that appears on the left
2386 of the <literal>=></literal> symbol, but not on the right. The problem with
2387 this is that, according to the theoretical foundations of Haskell overloading,
2388 we cannot guarantee a well-defined semantics for any term with an ambiguous
2392 We can sidestep this specific problem by removing the empty member from the
2393 class declaration. However, although the remaining members, insert and member,
2394 do not have ambiguous types, we still run into problems when we try to use
2395 them. For example, consider the following two functions:
2397 f x y = insert x . insert y
2400 for which GHC infers the following types:
2402 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2403 g :: (Collects Bool c, Collects Char c) => c -> c
2405 Notice that the type for f allows the two parameters x and y to be assigned
2406 different types, even though it attempts to insert each of the two values, one
2407 after the other, into the same collection. If we're trying to model collections
2408 that contain only one type of value, then this is clearly an inaccurate
2409 type. Worse still, the definition for g is accepted, without causing a type
2410 error. As a result, the error in this code will not be flagged at the point
2411 where it appears. Instead, it will show up only when we try to use g, which
2412 might even be in a different module.
2415 <sect4><title>An attempt to use constructor classes</title>
2418 Faced with the problems described above, some Haskell programmers might be
2419 tempted to use something like the following version of the class declaration:
2421 class Collects e c where
2423 insert :: e -> c e -> c e
2424 member :: e -> c e -> Bool
2426 The key difference here is that we abstract over the type constructor c that is
2427 used to form the collection type c e, and not over that collection type itself,
2428 represented by ce in the original class declaration. This avoids the immediate
2429 problems that we mentioned above: empty has type <literal>Collects e c => c
2430 e</literal>, which is not ambiguous.
2433 The function f from the previous section has a more accurate type:
2435 f :: (Collects e c) => e -> e -> c e -> c e
2437 The function g from the previous section is now rejected with a type error as
2438 we would hope because the type of f does not allow the two arguments to have
2440 This, then, is an example of a multiple parameter class that does actually work
2441 quite well in practice, without ambiguity problems.
2442 There is, however, a catch. This version of the Collects class is nowhere near
2443 as general as the original class seemed to be: only one of the four instances
2444 for <literal>Collects</literal>
2445 given above can be used with this version of Collects because only one of
2446 them---the instance for lists---has a collection type that can be written in
2447 the form c e, for some type constructor c, and element type e.
2451 <sect4><title>Adding functional dependencies</title>
2454 To get a more useful version of the Collects class, Hugs provides a mechanism
2455 that allows programmers to specify dependencies between the parameters of a
2456 multiple parameter class (For readers with an interest in theoretical
2457 foundations and previous work: The use of dependency information can be seen
2458 both as a generalization of the proposal for `parametric type classes' that was
2459 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2460 later framework for "improvement" of qualified types. The
2461 underlying ideas are also discussed in a more theoretical and abstract setting
2462 in a manuscript [implparam], where they are identified as one point in a
2463 general design space for systems of implicit parameterization.).
2465 To start with an abstract example, consider a declaration such as:
2467 class C a b where ...
2469 which tells us simply that C can be thought of as a binary relation on types
2470 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2471 included in the definition of classes to add information about dependencies
2472 between parameters, as in the following examples:
2474 class D a b | a -> b where ...
2475 class E a b | a -> b, b -> a where ...
2477 The notation <literal>a -> b</literal> used here between the | and where
2478 symbols --- not to be
2479 confused with a function type --- indicates that the a parameter uniquely
2480 determines the b parameter, and might be read as "a determines b." Thus D is
2481 not just a relation, but actually a (partial) function. Similarly, from the two
2482 dependencies that are included in the definition of E, we can see that E
2483 represents a (partial) one-one mapping between types.
2486 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2487 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2488 m>=0, meaning that the y parameters are uniquely determined by the x
2489 parameters. Spaces can be used as separators if more than one variable appears
2490 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2491 annotated with multiple dependencies using commas as separators, as in the
2492 definition of E above. Some dependencies that we can write in this notation are
2493 redundant, and will be rejected because they don't serve any useful
2494 purpose, and may instead indicate an error in the program. Examples of
2495 dependencies like this include <literal>a -> a </literal>,
2496 <literal>a -> a a </literal>,
2497 <literal>a -> </literal>, etc. There can also be
2498 some redundancy if multiple dependencies are given, as in
2499 <literal>a->b</literal>,
2500 <literal>b->c </literal>, <literal>a->c </literal>, and
2501 in which some subset implies the remaining dependencies. Examples like this are
2502 not treated as errors. Note that dependencies appear only in class
2503 declarations, and not in any other part of the language. In particular, the
2504 syntax for instance declarations, class constraints, and types is completely
2508 By including dependencies in a class declaration, we provide a mechanism for
2509 the programmer to specify each multiple parameter class more precisely. The
2510 compiler, on the other hand, is responsible for ensuring that the set of
2511 instances that are in scope at any given point in the program is consistent
2512 with any declared dependencies. For example, the following pair of instance
2513 declarations cannot appear together in the same scope because they violate the
2514 dependency for D, even though either one on its own would be acceptable:
2516 instance D Bool Int where ...
2517 instance D Bool Char where ...
2519 Note also that the following declaration is not allowed, even by itself:
2521 instance D [a] b where ...
2523 The problem here is that this instance would allow one particular choice of [a]
2524 to be associated with more than one choice for b, which contradicts the
2525 dependency specified in the definition of D. More generally, this means that,
2526 in any instance of the form:
2528 instance D t s where ...
2530 for some particular types t and s, the only variables that can appear in s are
2531 the ones that appear in t, and hence, if the type t is known, then s will be
2532 uniquely determined.
2535 The benefit of including dependency information is that it allows us to define
2536 more general multiple parameter classes, without ambiguity problems, and with
2537 the benefit of more accurate types. To illustrate this, we return to the
2538 collection class example, and annotate the original definition of <literal>Collects</literal>
2539 with a simple dependency:
2541 class Collects e ce | ce -> e where
2543 insert :: e -> ce -> ce
2544 member :: e -> ce -> Bool
2546 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2547 determined by the type of the collection ce. Note that both parameters of
2548 Collects are of kind *; there are no constructor classes here. Note too that
2549 all of the instances of Collects that we gave earlier can be used
2550 together with this new definition.
2553 What about the ambiguity problems that we encountered with the original
2554 definition? The empty function still has type Collects e ce => ce, but it is no
2555 longer necessary to regard that as an ambiguous type: Although the variable e
2556 does not appear on the right of the => symbol, the dependency for class
2557 Collects tells us that it is uniquely determined by ce, which does appear on
2558 the right of the => symbol. Hence the context in which empty is used can still
2559 give enough information to determine types for both ce and e, without
2560 ambiguity. More generally, we need only regard a type as ambiguous if it
2561 contains a variable on the left of the => that is not uniquely determined
2562 (either directly or indirectly) by the variables on the right.
2565 Dependencies also help to produce more accurate types for user defined
2566 functions, and hence to provide earlier detection of errors, and less cluttered
2567 types for programmers to work with. Recall the previous definition for a
2570 f x y = insert x y = insert x . insert y
2572 for which we originally obtained a type:
2574 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2576 Given the dependency information that we have for Collects, however, we can
2577 deduce that a and b must be equal because they both appear as the second
2578 parameter in a Collects constraint with the same first parameter c. Hence we
2579 can infer a shorter and more accurate type for f:
2581 f :: (Collects a c) => a -> a -> c -> c
2583 In a similar way, the earlier definition of g will now be flagged as a type error.
2586 Although we have given only a few examples here, it should be clear that the
2587 addition of dependency information can help to make multiple parameter classes
2588 more useful in practice, avoiding ambiguity problems, and allowing more general
2589 sets of instance declarations.
2595 <sect2 id="instance-decls">
2596 <title>Instance declarations</title>
2598 <sect3 id="instance-rules">
2599 <title>Relaxed rules for instance declarations</title>
2601 <para>An instance declaration has the form
2603 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 ...
2605 The part before the "<literal>=></literal>" is the
2606 <emphasis>context</emphasis>, while the part after the
2607 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2611 In Haskell 98 the head of an instance declaration
2612 must be of the form <literal>C (T a1 ... an)</literal>, where
2613 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2614 and the <literal>a1 ... an</literal> are distinct type variables.
2615 Furthermore, the assertions in the context of the instance declaration
2616 must be of the form <literal>C a</literal> where <literal>a</literal>
2617 is a type variable that occurs in the head.
2620 The <option>-fglasgow-exts</option> flag loosens these restrictions
2621 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2622 the context and head of the instance declaration can each consist of arbitrary
2623 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2627 The Paterson Conditions: for each assertion in the context
2629 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2630 <listitem><para>The assertion has fewer constructors and variables (taken together
2631 and counting repetitions) than the head</para></listitem>
2635 <listitem><para>The Coverage Condition. For each functional dependency,
2636 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2637 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2638 every type variable in
2639 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2640 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2641 substitution mapping each type variable in the class declaration to the
2642 corresponding type in the instance declaration.
2645 These restrictions ensure that context reduction terminates: each reduction
2646 step makes the problem smaller by at least one
2647 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2648 if you give the <option>-fallow-undecidable-instances</option>
2649 flag (<xref linkend="undecidable-instances"/>).
2650 You can find lots of background material about the reason for these
2651 restrictions in the paper <ulink
2652 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2653 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2656 For example, these are OK:
2658 instance C Int [a] -- Multiple parameters
2659 instance Eq (S [a]) -- Structured type in head
2661 -- Repeated type variable in head
2662 instance C4 a a => C4 [a] [a]
2663 instance Stateful (ST s) (MutVar s)
2665 -- Head can consist of type variables only
2667 instance (Eq a, Show b) => C2 a b
2669 -- Non-type variables in context
2670 instance Show (s a) => Show (Sized s a)
2671 instance C2 Int a => C3 Bool [a]
2672 instance C2 Int a => C3 [a] b
2676 -- Context assertion no smaller than head
2677 instance C a => C a where ...
2678 -- (C b b) has more more occurrences of b than the head
2679 instance C b b => Foo [b] where ...
2684 The same restrictions apply to instances generated by
2685 <literal>deriving</literal> clauses. Thus the following is accepted:
2687 data MinHeap h a = H a (h a)
2690 because the derived instance
2692 instance (Show a, Show (h a)) => Show (MinHeap h a)
2694 conforms to the above rules.
2698 A useful idiom permitted by the above rules is as follows.
2699 If one allows overlapping instance declarations then it's quite
2700 convenient to have a "default instance" declaration that applies if
2701 something more specific does not:
2709 <sect3 id="undecidable-instances">
2710 <title>Undecidable instances</title>
2713 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2714 For example, sometimes you might want to use the following to get the
2715 effect of a "class synonym":
2717 class (C1 a, C2 a, C3 a) => C a where { }
2719 instance (C1 a, C2 a, C3 a) => C a where { }
2721 This allows you to write shorter signatures:
2727 f :: (C1 a, C2 a, C3 a) => ...
2729 The restrictions on functional dependencies (<xref
2730 linkend="functional-dependencies"/>) are particularly troublesome.
2731 It is tempting to introduce type variables in the context that do not appear in
2732 the head, something that is excluded by the normal rules. For example:
2734 class HasConverter a b | a -> b where
2737 data Foo a = MkFoo a
2739 instance (HasConverter a b,Show b) => Show (Foo a) where
2740 show (MkFoo value) = show (convert value)
2742 This is dangerous territory, however. Here, for example, is a program that would make the
2747 instance F [a] [[a]]
2748 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2750 Similarly, it can be tempting to lift the coverage condition:
2752 class Mul a b c | a b -> c where
2753 (.*.) :: a -> b -> c
2755 instance Mul Int Int Int where (.*.) = (*)
2756 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2757 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2759 The third instance declaration does not obey the coverage condition;
2760 and indeed the (somewhat strange) definition:
2762 f = \ b x y -> if b then x .*. [y] else y
2764 makes instance inference go into a loop, because it requires the constraint
2765 <literal>(Mul a [b] b)</literal>.
2768 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2769 the experimental flag <option>-XUndecidableInstances</option>
2770 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
2771 both the Paterson Conditions and the Coverage Condition
2772 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2773 fixed-depth recursion stack. If you exceed the stack depth you get a
2774 sort of backtrace, and the opportunity to increase the stack depth
2775 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2781 <sect3 id="instance-overlap">
2782 <title>Overlapping instances</title>
2784 In general, <emphasis>GHC requires that that it be unambiguous which instance
2786 should be used to resolve a type-class constraint</emphasis>. This behaviour
2787 can be modified by two flags: <option>-XOverlappingInstances</option>
2788 <indexterm><primary>-XOverlappingInstances
2789 </primary></indexterm>
2790 and <option>-XIncoherentInstances</option>
2791 <indexterm><primary>-XIncoherentInstances
2792 </primary></indexterm>, as this section discusses. Both these
2793 flags are dynamic flags, and can be set on a per-module basis, using
2794 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2796 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2797 it tries to match every instance declaration against the
2799 by instantiating the head of the instance declaration. For example, consider
2802 instance context1 => C Int a where ... -- (A)
2803 instance context2 => C a Bool where ... -- (B)
2804 instance context3 => C Int [a] where ... -- (C)
2805 instance context4 => C Int [Int] where ... -- (D)
2807 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2808 but (C) and (D) do not. When matching, GHC takes
2809 no account of the context of the instance declaration
2810 (<literal>context1</literal> etc).
2811 GHC's default behaviour is that <emphasis>exactly one instance must match the
2812 constraint it is trying to resolve</emphasis>.
2813 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2814 including both declarations (A) and (B), say); an error is only reported if a
2815 particular constraint matches more than one.
2819 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
2820 more than one instance to match, provided there is a most specific one. For
2821 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2822 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2823 most-specific match, the program is rejected.
2826 However, GHC is conservative about committing to an overlapping instance. For example:
2831 Suppose that from the RHS of <literal>f</literal> we get the constraint
2832 <literal>C Int [b]</literal>. But
2833 GHC does not commit to instance (C), because in a particular
2834 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2835 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2836 So GHC rejects the program.
2837 (If you add the flag <option>-XIncoherentInstances</option>,
2838 GHC will instead pick (C), without complaining about
2839 the problem of subsequent instantiations.)
2842 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
2843 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
2844 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
2845 it instead. In this case, GHC will refrain from
2846 simplifying the constraint <literal>C Int [Int]</literal> (for the same reason
2847 as before) but, rather than rejecting the program, it will infer the type
2849 f :: C Int b => [b] -> [b]
2851 That postpones the question of which instance to pick to the
2852 call site for <literal>f</literal>
2853 by which time more is known about the type <literal>b</literal>.
2856 The willingness to be overlapped or incoherent is a property of
2857 the <emphasis>instance declaration</emphasis> itself, controlled by the
2858 presence or otherwise of the <option>-XOverlappingInstances</option>
2859 and <option>-XIncoherentInstances</option> flags when that mdodule is
2860 being defined. Neither flag is required in a module that imports and uses the
2861 instance declaration. Specifically, during the lookup process:
2864 An instance declaration is ignored during the lookup process if (a) a more specific
2865 match is found, and (b) the instance declaration was compiled with
2866 <option>-XOverlappingInstances</option>. The flag setting for the
2867 more-specific instance does not matter.
2870 Suppose an instance declaration does not match the constraint being looked up, but
2871 does unify with it, so that it might match when the constraint is further
2872 instantiated. Usually GHC will regard this as a reason for not committing to
2873 some other constraint. But if the instance declaration was compiled with
2874 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
2875 check for that declaration.
2878 These rules make it possible for a library author to design a library that relies on
2879 overlapping instances without the library client having to know.
2882 If an instance declaration is compiled without
2883 <option>-XOverlappingInstances</option>,
2884 then that instance can never be overlapped. This could perhaps be
2885 inconvenient. Perhaps the rule should instead say that the
2886 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2887 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2888 at a usage site should be permitted regardless of how the instance declarations
2889 are compiled, if the <option>-XOverlappingInstances</option> flag is
2890 used at the usage site. (Mind you, the exact usage site can occasionally be
2891 hard to pin down.) We are interested to receive feedback on these points.
2893 <para>The <option>-XIncoherentInstances</option> flag implies the
2894 <option>-XOverlappingInstances</option> flag, but not vice versa.
2899 <title>Type synonyms in the instance head</title>
2902 <emphasis>Unlike Haskell 98, instance heads may use type
2903 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2904 As always, using a type synonym is just shorthand for
2905 writing the RHS of the type synonym definition. For example:
2909 type Point = (Int,Int)
2910 instance C Point where ...
2911 instance C [Point] where ...
2915 is legal. However, if you added
2919 instance C (Int,Int) where ...
2923 as well, then the compiler will complain about the overlapping
2924 (actually, identical) instance declarations. As always, type synonyms
2925 must be fully applied. You cannot, for example, write:
2930 instance Monad P where ...
2934 This design decision is independent of all the others, and easily
2935 reversed, but it makes sense to me.
2943 <sect2 id="type-restrictions">
2944 <title>Type signatures</title>
2946 <sect3><title>The context of a type signature</title>
2948 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2949 the form <emphasis>(class type-variable)</emphasis> or
2950 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2951 these type signatures are perfectly OK
2954 g :: Ord (T a ()) => ...
2958 GHC imposes the following restrictions on the constraints in a type signature.
2962 forall tv1..tvn (c1, ...,cn) => type
2965 (Here, we write the "foralls" explicitly, although the Haskell source
2966 language omits them; in Haskell 98, all the free type variables of an
2967 explicit source-language type signature are universally quantified,
2968 except for the class type variables in a class declaration. However,
2969 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2978 <emphasis>Each universally quantified type variable
2979 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2981 A type variable <literal>a</literal> is "reachable" if it it appears
2982 in the same constraint as either a type variable free in in
2983 <literal>type</literal>, or another reachable type variable.
2984 A value with a type that does not obey
2985 this reachability restriction cannot be used without introducing
2986 ambiguity; that is why the type is rejected.
2987 Here, for example, is an illegal type:
2991 forall a. Eq a => Int
2995 When a value with this type was used, the constraint <literal>Eq tv</literal>
2996 would be introduced where <literal>tv</literal> is a fresh type variable, and
2997 (in the dictionary-translation implementation) the value would be
2998 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2999 can never know which instance of <literal>Eq</literal> to use because we never
3000 get any more information about <literal>tv</literal>.
3004 that the reachability condition is weaker than saying that <literal>a</literal> is
3005 functionally dependent on a type variable free in
3006 <literal>type</literal> (see <xref
3007 linkend="functional-dependencies"/>). The reason for this is there
3008 might be a "hidden" dependency, in a superclass perhaps. So
3009 "reachable" is a conservative approximation to "functionally dependent".
3010 For example, consider:
3012 class C a b | a -> b where ...
3013 class C a b => D a b where ...
3014 f :: forall a b. D a b => a -> a
3016 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
3017 but that is not immediately apparent from <literal>f</literal>'s type.
3023 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
3024 universally quantified type variables <literal>tvi</literal></emphasis>.
3026 For example, this type is OK because <literal>C a b</literal> mentions the
3027 universally quantified type variable <literal>b</literal>:
3031 forall a. C a b => burble
3035 The next type is illegal because the constraint <literal>Eq b</literal> does not
3036 mention <literal>a</literal>:
3040 forall a. Eq b => burble
3044 The reason for this restriction is milder than the other one. The
3045 excluded types are never useful or necessary (because the offending
3046 context doesn't need to be witnessed at this point; it can be floated
3047 out). Furthermore, floating them out increases sharing. Lastly,
3048 excluding them is a conservative choice; it leaves a patch of
3049 territory free in case we need it later.
3063 <sect2 id="implicit-parameters">
3064 <title>Implicit parameters</title>
3066 <para> Implicit parameters are implemented as described in
3067 "Implicit parameters: dynamic scoping with static types",
3068 J Lewis, MB Shields, E Meijer, J Launchbury,
3069 27th ACM Symposium on Principles of Programming Languages (POPL'00),
3073 <para>(Most of the following, stil rather incomplete, documentation is
3074 due to Jeff Lewis.)</para>
3076 <para>Implicit parameter support is enabled with the option
3077 <option>-XImplicitParams</option>.</para>
3080 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
3081 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
3082 context. In Haskell, all variables are statically bound. Dynamic
3083 binding of variables is a notion that goes back to Lisp, but was later
3084 discarded in more modern incarnations, such as Scheme. Dynamic binding
3085 can be very confusing in an untyped language, and unfortunately, typed
3086 languages, in particular Hindley-Milner typed languages like Haskell,
3087 only support static scoping of variables.
3090 However, by a simple extension to the type class system of Haskell, we
3091 can support dynamic binding. Basically, we express the use of a
3092 dynamically bound variable as a constraint on the type. These
3093 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3094 function uses a dynamically-bound variable <literal>?x</literal>
3095 of type <literal>t'</literal>". For
3096 example, the following expresses the type of a sort function,
3097 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3099 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3101 The dynamic binding constraints are just a new form of predicate in the type class system.
3104 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3105 where <literal>x</literal> is
3106 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3107 Use of this construct also introduces a new
3108 dynamic-binding constraint in the type of the expression.
3109 For example, the following definition
3110 shows how we can define an implicitly parameterized sort function in
3111 terms of an explicitly parameterized <literal>sortBy</literal> function:
3113 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3115 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3121 <title>Implicit-parameter type constraints</title>
3123 Dynamic binding constraints behave just like other type class
3124 constraints in that they are automatically propagated. Thus, when a
3125 function is used, its implicit parameters are inherited by the
3126 function that called it. For example, our <literal>sort</literal> function might be used
3127 to pick out the least value in a list:
3129 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3130 least xs = head (sort xs)
3132 Without lifting a finger, the <literal>?cmp</literal> parameter is
3133 propagated to become a parameter of <literal>least</literal> as well. With explicit
3134 parameters, the default is that parameters must always be explicit
3135 propagated. With implicit parameters, the default is to always
3139 An implicit-parameter type constraint differs from other type class constraints in the
3140 following way: All uses of a particular implicit parameter must have
3141 the same type. This means that the type of <literal>(?x, ?x)</literal>
3142 is <literal>(?x::a) => (a,a)</literal>, and not
3143 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3147 <para> You can't have an implicit parameter in the context of a class or instance
3148 declaration. For example, both these declarations are illegal:
3150 class (?x::Int) => C a where ...
3151 instance (?x::a) => Foo [a] where ...
3153 Reason: exactly which implicit parameter you pick up depends on exactly where
3154 you invoke a function. But the ``invocation'' of instance declarations is done
3155 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3156 Easiest thing is to outlaw the offending types.</para>
3158 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3160 f :: (?x :: [a]) => Int -> Int
3163 g :: (Read a, Show a) => String -> String
3166 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3167 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3168 quite unambiguous, and fixes the type <literal>a</literal>.
3173 <title>Implicit-parameter bindings</title>
3176 An implicit parameter is <emphasis>bound</emphasis> using the standard
3177 <literal>let</literal> or <literal>where</literal> binding forms.
3178 For example, we define the <literal>min</literal> function by binding
3179 <literal>cmp</literal>.
3182 min = let ?cmp = (<=) in least
3186 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3187 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3188 (including in a list comprehension, or do-notation, or pattern guards),
3189 or a <literal>where</literal> clause.
3190 Note the following points:
3193 An implicit-parameter binding group must be a
3194 collection of simple bindings to implicit-style variables (no
3195 function-style bindings, and no type signatures); these bindings are
3196 neither polymorphic or recursive.
3199 You may not mix implicit-parameter bindings with ordinary bindings in a
3200 single <literal>let</literal>
3201 expression; use two nested <literal>let</literal>s instead.
3202 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3206 You may put multiple implicit-parameter bindings in a
3207 single binding group; but they are <emphasis>not</emphasis> treated
3208 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3209 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3210 parameter. The bindings are not nested, and may be re-ordered without changing
3211 the meaning of the program.
3212 For example, consider:
3214 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3216 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3217 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3219 f :: (?x::Int) => Int -> Int
3227 <sect3><title>Implicit parameters and polymorphic recursion</title>
3230 Consider these two definitions:
3233 len1 xs = let ?acc = 0 in len_acc1 xs
3236 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3241 len2 xs = let ?acc = 0 in len_acc2 xs
3243 len_acc2 :: (?acc :: Int) => [a] -> Int
3245 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3247 The only difference between the two groups is that in the second group
3248 <literal>len_acc</literal> is given a type signature.
3249 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3250 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3251 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3252 has a type signature, the recursive call is made to the
3253 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3254 as an implicit parameter. So we get the following results in GHCi:
3261 Adding a type signature dramatically changes the result! This is a rather
3262 counter-intuitive phenomenon, worth watching out for.
3266 <sect3><title>Implicit parameters and monomorphism</title>
3268 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3269 Haskell Report) to implicit parameters. For example, consider:
3277 Since the binding for <literal>y</literal> falls under the Monomorphism
3278 Restriction it is not generalised, so the type of <literal>y</literal> is
3279 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3280 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3281 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3282 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3283 <literal>y</literal> in the body of the <literal>let</literal> will see the
3284 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3285 <literal>14</literal>.
3290 <!-- ======================= COMMENTED OUT ========================
3292 We intend to remove linear implicit parameters, so I'm at least removing
3293 them from the 6.6 user manual
3295 <sect2 id="linear-implicit-parameters">
3296 <title>Linear implicit parameters</title>
3298 Linear implicit parameters are an idea developed by Koen Claessen,
3299 Mark Shields, and Simon PJ. They address the long-standing
3300 problem that monads seem over-kill for certain sorts of problem, notably:
3303 <listitem> <para> distributing a supply of unique names </para> </listitem>
3304 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3305 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3309 Linear implicit parameters are just like ordinary implicit parameters,
3310 except that they are "linear"; that is, they cannot be copied, and
3311 must be explicitly "split" instead. Linear implicit parameters are
3312 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3313 (The '/' in the '%' suggests the split!)
3318 import GHC.Exts( Splittable )
3320 data NameSupply = ...
3322 splitNS :: NameSupply -> (NameSupply, NameSupply)
3323 newName :: NameSupply -> Name
3325 instance Splittable NameSupply where
3329 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3330 f env (Lam x e) = Lam x' (f env e)
3333 env' = extend env x x'
3334 ...more equations for f...
3336 Notice that the implicit parameter %ns is consumed
3338 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3339 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3343 So the translation done by the type checker makes
3344 the parameter explicit:
3346 f :: NameSupply -> Env -> Expr -> Expr
3347 f ns env (Lam x e) = Lam x' (f ns1 env e)
3349 (ns1,ns2) = splitNS ns
3351 env = extend env x x'
3353 Notice the call to 'split' introduced by the type checker.
3354 How did it know to use 'splitNS'? Because what it really did
3355 was to introduce a call to the overloaded function 'split',
3356 defined by the class <literal>Splittable</literal>:
3358 class Splittable a where
3361 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3362 split for name supplies. But we can simply write
3368 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3370 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3371 <literal>GHC.Exts</literal>.
3376 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3377 are entirely distinct implicit parameters: you
3378 can use them together and they won't intefere with each other. </para>
3381 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3383 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3384 in the context of a class or instance declaration. </para></listitem>
3388 <sect3><title>Warnings</title>
3391 The monomorphism restriction is even more important than usual.
3392 Consider the example above:
3394 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3395 f env (Lam x e) = Lam x' (f env e)
3398 env' = extend env x x'
3400 If we replaced the two occurrences of x' by (newName %ns), which is
3401 usually a harmless thing to do, we get:
3403 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3404 f env (Lam x e) = Lam (newName %ns) (f env e)
3406 env' = extend env x (newName %ns)
3408 But now the name supply is consumed in <emphasis>three</emphasis> places
3409 (the two calls to newName,and the recursive call to f), so
3410 the result is utterly different. Urk! We don't even have
3414 Well, this is an experimental change. With implicit
3415 parameters we have already lost beta reduction anyway, and
3416 (as John Launchbury puts it) we can't sensibly reason about
3417 Haskell programs without knowing their typing.
3422 <sect3><title>Recursive functions</title>
3423 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3426 foo :: %x::T => Int -> [Int]
3428 foo n = %x : foo (n-1)
3430 where T is some type in class Splittable.</para>
3432 Do you get a list of all the same T's or all different T's
3433 (assuming that split gives two distinct T's back)?
3435 If you supply the type signature, taking advantage of polymorphic
3436 recursion, you get what you'd probably expect. Here's the
3437 translated term, where the implicit param is made explicit:
3440 foo x n = let (x1,x2) = split x
3441 in x1 : foo x2 (n-1)
3443 But if you don't supply a type signature, GHC uses the Hindley
3444 Milner trick of using a single monomorphic instance of the function
3445 for the recursive calls. That is what makes Hindley Milner type inference
3446 work. So the translation becomes
3450 foom n = x : foom (n-1)
3454 Result: 'x' is not split, and you get a list of identical T's. So the
3455 semantics of the program depends on whether or not foo has a type signature.
3458 You may say that this is a good reason to dislike linear implicit parameters
3459 and you'd be right. That is why they are an experimental feature.
3465 ================ END OF Linear Implicit Parameters commented out -->
3467 <sect2 id="kinding">
3468 <title>Explicitly-kinded quantification</title>
3471 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3472 to give the kind explicitly as (machine-checked) documentation,
3473 just as it is nice to give a type signature for a function. On some occasions,
3474 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3475 John Hughes had to define the data type:
3477 data Set cxt a = Set [a]
3478 | Unused (cxt a -> ())
3480 The only use for the <literal>Unused</literal> constructor was to force the correct
3481 kind for the type variable <literal>cxt</literal>.
3484 GHC now instead allows you to specify the kind of a type variable directly, wherever
3485 a type variable is explicitly bound. Namely:
3487 <listitem><para><literal>data</literal> declarations:
3489 data Set (cxt :: * -> *) a = Set [a]
3490 </screen></para></listitem>
3491 <listitem><para><literal>type</literal> declarations:
3493 type T (f :: * -> *) = f Int
3494 </screen></para></listitem>
3495 <listitem><para><literal>class</literal> declarations:
3497 class (Eq a) => C (f :: * -> *) a where ...
3498 </screen></para></listitem>
3499 <listitem><para><literal>forall</literal>'s in type signatures:
3501 f :: forall (cxt :: * -> *). Set cxt Int
3502 </screen></para></listitem>
3507 The parentheses are required. Some of the spaces are required too, to
3508 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3509 will get a parse error, because "<literal>::*->*</literal>" is a
3510 single lexeme in Haskell.
3514 As part of the same extension, you can put kind annotations in types
3517 f :: (Int :: *) -> Int
3518 g :: forall a. a -> (a :: *)
3522 atype ::= '(' ctype '::' kind ')
3524 The parentheses are required.
3529 <sect2 id="universal-quantification">
3530 <title>Arbitrary-rank polymorphism
3534 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3535 allows us to say exactly what this means. For example:
3543 g :: forall b. (b -> b)
3545 The two are treated identically.
3549 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3550 explicit universal quantification in
3552 For example, all the following types are legal:
3554 f1 :: forall a b. a -> b -> a
3555 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3557 f2 :: (forall a. a->a) -> Int -> Int
3558 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3560 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3562 f4 :: Int -> (forall a. a -> a)
3564 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3565 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3566 The <literal>forall</literal> makes explicit the universal quantification that
3567 is implicitly added by Haskell.
3570 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3571 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3572 shows, the polymorphic type on the left of the function arrow can be overloaded.
3575 The function <literal>f3</literal> has a rank-3 type;
3576 it has rank-2 types on the left of a function arrow.
3579 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3580 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3581 that restriction has now been lifted.)
3582 In particular, a forall-type (also called a "type scheme"),
3583 including an operational type class context, is legal:
3585 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3586 of a function arrow </para> </listitem>
3587 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3588 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3589 field type signatures.</para> </listitem>
3590 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3591 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3593 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3594 a type variable any more!
3603 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3604 the types of the constructor arguments. Here are several examples:
3610 data T a = T1 (forall b. b -> b -> b) a
3612 data MonadT m = MkMonad { return :: forall a. a -> m a,
3613 bind :: forall a b. m a -> (a -> m b) -> m b
3616 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3622 The constructors have rank-2 types:
3628 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3629 MkMonad :: forall m. (forall a. a -> m a)
3630 -> (forall a b. m a -> (a -> m b) -> m b)
3632 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3638 Notice that you don't need to use a <literal>forall</literal> if there's an
3639 explicit context. For example in the first argument of the
3640 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3641 prefixed to the argument type. The implicit <literal>forall</literal>
3642 quantifies all type variables that are not already in scope, and are
3643 mentioned in the type quantified over.
3647 As for type signatures, implicit quantification happens for non-overloaded
3648 types too. So if you write this:
3651 data T a = MkT (Either a b) (b -> b)
3654 it's just as if you had written this:
3657 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3660 That is, since the type variable <literal>b</literal> isn't in scope, it's
3661 implicitly universally quantified. (Arguably, it would be better
3662 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3663 where that is what is wanted. Feedback welcomed.)
3667 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3668 the constructor to suitable values, just as usual. For example,
3679 a3 = MkSwizzle reverse
3682 a4 = let r x = Just x
3689 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3690 mkTs f x y = [T1 f x, T1 f y]
3696 The type of the argument can, as usual, be more general than the type
3697 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3698 does not need the <literal>Ord</literal> constraint.)
3702 When you use pattern matching, the bound variables may now have
3703 polymorphic types. For example:
3709 f :: T a -> a -> (a, Char)
3710 f (T1 w k) x = (w k x, w 'c' 'd')
3712 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3713 g (MkSwizzle s) xs f = s (map f (s xs))
3715 h :: MonadT m -> [m a] -> m [a]
3716 h m [] = return m []
3717 h m (x:xs) = bind m x $ \y ->
3718 bind m (h m xs) $ \ys ->
3725 In the function <function>h</function> we use the record selectors <literal>return</literal>
3726 and <literal>bind</literal> to extract the polymorphic bind and return functions
3727 from the <literal>MonadT</literal> data structure, rather than using pattern
3733 <title>Type inference</title>
3736 In general, type inference for arbitrary-rank types is undecidable.
3737 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3738 to get a decidable algorithm by requiring some help from the programmer.
3739 We do not yet have a formal specification of "some help" but the rule is this:
3742 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3743 provides an explicit polymorphic type for x, or GHC's type inference will assume
3744 that x's type has no foralls in it</emphasis>.
3747 What does it mean to "provide" an explicit type for x? You can do that by
3748 giving a type signature for x directly, using a pattern type signature
3749 (<xref linkend="scoped-type-variables"/>), thus:
3751 \ f :: (forall a. a->a) -> (f True, f 'c')
3753 Alternatively, you can give a type signature to the enclosing
3754 context, which GHC can "push down" to find the type for the variable:
3756 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3758 Here the type signature on the expression can be pushed inwards
3759 to give a type signature for f. Similarly, and more commonly,
3760 one can give a type signature for the function itself:
3762 h :: (forall a. a->a) -> (Bool,Char)
3763 h f = (f True, f 'c')
3765 You don't need to give a type signature if the lambda bound variable
3766 is a constructor argument. Here is an example we saw earlier:
3768 f :: T a -> a -> (a, Char)
3769 f (T1 w k) x = (w k x, w 'c' 'd')
3771 Here we do not need to give a type signature to <literal>w</literal>, because
3772 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3779 <sect3 id="implicit-quant">
3780 <title>Implicit quantification</title>
3783 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3784 user-written types, if and only if there is no explicit <literal>forall</literal>,
3785 GHC finds all the type variables mentioned in the type that are not already
3786 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3790 f :: forall a. a -> a
3797 h :: forall b. a -> b -> b
3803 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3806 f :: (a -> a) -> Int
3808 f :: forall a. (a -> a) -> Int
3810 f :: (forall a. a -> a) -> Int
3813 g :: (Ord a => a -> a) -> Int
3814 -- MEANS the illegal type
3815 g :: forall a. (Ord a => a -> a) -> Int
3817 g :: (forall a. Ord a => a -> a) -> Int
3819 The latter produces an illegal type, which you might think is silly,
3820 but at least the rule is simple. If you want the latter type, you
3821 can write your for-alls explicitly. Indeed, doing so is strongly advised
3828 <sect2 id="impredicative-polymorphism">
3829 <title>Impredicative polymorphism
3831 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3832 that you can call a polymorphic function at a polymorphic type, and
3833 parameterise data structures over polymorphic types. For example:
3835 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3836 f (Just g) = Just (g [3], g "hello")
3839 Notice here that the <literal>Maybe</literal> type is parameterised by the
3840 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3843 <para>The technical details of this extension are described in the paper
3844 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3845 type inference for higher-rank types and impredicativity</ulink>,
3846 which appeared at ICFP 2006.
3850 <sect2 id="scoped-type-variables">
3851 <title>Lexically scoped type variables
3855 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3856 which some type signatures are simply impossible to write. For example:
3858 f :: forall a. [a] -> [a]
3864 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3865 the entire definition of <literal>f</literal>.
3866 In particular, it is in scope at the type signature for <varname>ys</varname>.
3867 In Haskell 98 it is not possible to declare
3868 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3869 it becomes possible to do so.
3871 <para>Lexically-scoped type variables are enabled by
3872 <option>-fglasgow-exts</option>.
3874 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3875 variables work, compared to earlier releases. Read this section
3879 <title>Overview</title>
3881 <para>The design follows the following principles
3883 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3884 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3885 design.)</para></listitem>
3886 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3887 type variables. This means that every programmer-written type signature
3888 (includin one that contains free scoped type variables) denotes a
3889 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3890 checker, and no inference is involved.</para></listitem>
3891 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3892 changing the program.</para></listitem>
3896 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3898 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3899 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3900 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3901 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3905 In Haskell, a programmer-written type signature is implicitly quantifed over
3906 its free type variables (<ulink
3907 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3909 of the Haskel Report).
3910 Lexically scoped type variables affect this implicit quantification rules
3911 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3912 quantified. For example, if type variable <literal>a</literal> is in scope,
3915 (e :: a -> a) means (e :: a -> a)
3916 (e :: b -> b) means (e :: forall b. b->b)
3917 (e :: a -> b) means (e :: forall b. a->b)
3925 <sect3 id="decl-type-sigs">
3926 <title>Declaration type signatures</title>
3927 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3928 quantification (using <literal>forall</literal>) brings into scope the
3929 explicitly-quantified
3930 type variables, in the definition of the named function(s). For example:
3932 f :: forall a. [a] -> [a]
3933 f (x:xs) = xs ++ [ x :: a ]
3935 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3936 the definition of "<literal>f</literal>".
3938 <para>This only happens if the quantification in <literal>f</literal>'s type
3939 signature is explicit. For example:
3942 g (x:xs) = xs ++ [ x :: a ]
3944 This program will be rejected, because "<literal>a</literal>" does not scope
3945 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3946 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3947 quantification rules.
3951 <sect3 id="exp-type-sigs">
3952 <title>Expression type signatures</title>
3954 <para>An expression type signature that has <emphasis>explicit</emphasis>
3955 quantification (using <literal>forall</literal>) brings into scope the
3956 explicitly-quantified
3957 type variables, in the annotated expression. For example:
3959 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3961 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3962 type variable <literal>s</literal> into scope, in the annotated expression
3963 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3968 <sect3 id="pattern-type-sigs">
3969 <title>Pattern type signatures</title>
3971 A type signature may occur in any pattern; this is a <emphasis>pattern type
3972 signature</emphasis>.
3975 -- f and g assume that 'a' is already in scope
3976 f = \(x::Int, y::a) -> x
3978 h ((x,y) :: (Int,Bool)) = (y,x)
3980 In the case where all the type variables in the pattern type sigature are
3981 already in scope (i.e. bound by the enclosing context), matters are simple: the
3982 signature simply constrains the type of the pattern in the obvious way.
3985 There is only one situation in which you can write a pattern type signature that
3986 mentions a type variable that is not already in scope, namely in pattern match
3987 of an existential data constructor. For example:
3989 data T = forall a. MkT [a]
3992 k (MkT [t::a]) = MkT t3
3996 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3997 variable that is not already in scope. Indeed, it cannot already be in scope,
3998 because it is bound by the pattern match. GHC's rule is that in this situation
3999 (and only then), a pattern type signature can mention a type variable that is
4000 not already in scope; the effect is to bring it into scope, standing for the
4001 existentially-bound type variable.
4004 If this seems a little odd, we think so too. But we must have
4005 <emphasis>some</emphasis> way to bring such type variables into scope, else we
4006 could not name existentially-bound type variables in subequent type signatures.
4009 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
4010 signature is allowed to mention a lexical variable that is not already in
4012 For example, both <literal>f</literal> and <literal>g</literal> would be
4013 illegal if <literal>a</literal> was not already in scope.
4019 <!-- ==================== Commented out part about result type signatures
4021 <sect3 id="result-type-sigs">
4022 <title>Result type signatures</title>
4025 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
4028 {- f assumes that 'a' is already in scope -}
4029 f x y :: [a] = [x,y,x]
4031 g = \ x :: [Int] -> [3,4]
4033 h :: forall a. [a] -> a
4037 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
4038 the result of the function. Similarly, the body of the lambda in the RHS of
4039 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
4040 alternative in <literal>h</literal> is <literal>a</literal>.
4042 <para> A result type signature never brings new type variables into scope.</para>
4044 There are a couple of syntactic wrinkles. First, notice that all three
4045 examples would parse quite differently with parentheses:
4047 {- f assumes that 'a' is already in scope -}
4048 f x (y :: [a]) = [x,y,x]
4050 g = \ (x :: [Int]) -> [3,4]
4052 h :: forall a. [a] -> a
4056 Now the signature is on the <emphasis>pattern</emphasis>; and
4057 <literal>h</literal> would certainly be ill-typed (since the pattern
4058 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
4060 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
4061 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
4062 token or a parenthesised type of some sort). To see why,
4063 consider how one would parse this:
4072 <sect3 id="cls-inst-scoped-tyvars">
4073 <title>Class and instance declarations</title>
4076 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
4077 scope over the methods defined in the <literal>where</literal> part. For example:
4095 <sect2 id="typing-binds">
4096 <title>Generalised typing of mutually recursive bindings</title>
4099 The Haskell Report specifies that a group of bindings (at top level, or in a
4100 <literal>let</literal> or <literal>where</literal>) should be sorted into
4101 strongly-connected components, and then type-checked in dependency order
4102 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4103 Report, Section 4.5.1</ulink>).
4104 As each group is type-checked, any binders of the group that
4106 an explicit type signature are put in the type environment with the specified
4108 and all others are monomorphic until the group is generalised
4109 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4112 <para>Following a suggestion of Mark Jones, in his paper
4113 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4115 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
4117 <emphasis>the dependency analysis ignores references to variables that have an explicit
4118 type signature</emphasis>.
4119 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4120 typecheck. For example, consider:
4122 f :: Eq a => a -> Bool
4123 f x = (x == x) || g True || g "Yes"
4125 g y = (y <= y) || f True
4127 This is rejected by Haskell 98, but under Jones's scheme the definition for
4128 <literal>g</literal> is typechecked first, separately from that for
4129 <literal>f</literal>,
4130 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4131 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4132 type is generalised, to get
4134 g :: Ord a => a -> Bool
4136 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4137 <literal>g</literal> in the type environment.
4141 The same refined dependency analysis also allows the type signatures of
4142 mutually-recursive functions to have different contexts, something that is illegal in
4143 Haskell 98 (Section 4.5.2, last sentence). With
4144 <option>-XRelaxedPolyRec</option>
4145 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4146 type signatures; in practice this means that only variables bound by the same
4147 pattern binding must have the same context. For example, this is fine:
4149 f :: Eq a => a -> Bool
4150 f x = (x == x) || g True
4152 g :: Ord a => a -> Bool
4153 g y = (y <= y) || f True
4158 <sect2 id="overloaded-strings">
4159 <title>Overloaded string literals
4163 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4164 string literal has type <literal>String</literal>, but with overloaded string
4165 literals enabled (with <literal>-XOverloadedStrings</literal>)
4166 a string literal has type <literal>(IsString a) => a</literal>.
4169 This means that the usual string syntax can be used, e.g., for packed strings
4170 and other variations of string like types. String literals behave very much
4171 like integer literals, i.e., they can be used in both expressions and patterns.
4172 If used in a pattern the literal with be replaced by an equality test, in the same
4173 way as an integer literal is.
4176 The class <literal>IsString</literal> is defined as:
4178 class IsString a where
4179 fromString :: String -> a
4181 The only predefined instance is the obvious one to make strings work as usual:
4183 instance IsString [Char] where
4186 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4187 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4188 from module <literal>GHC.Exts</literal>.
4191 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4195 Each type in a default declaration must be an
4196 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4200 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4201 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4202 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4203 <emphasis>or</emphasis> <literal>IsString</literal>.
4212 import GHC.Exts( IsString(..) )
4214 newtype MyString = MyString String deriving (Eq, Show)
4215 instance IsString MyString where
4216 fromString = MyString
4218 greet :: MyString -> MyString
4219 greet "hello" = "world"
4223 print $ greet "hello"
4224 print $ greet "fool"
4228 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4229 to work since it gets translated into an equality comparison.
4233 <sect2 id="type-families">
4234 <title>Type families
4238 GHC supports the definition of type families indexed by types. They may be
4239 seen as an extension of Haskell 98's class-based overloading of values to
4240 types. When type families are declared in classes, they are also known as
4244 There are two forms of type families: data families and type synonym families.
4245 Currently, only the former are fully implemented, while we are still working
4246 on the latter. As a result, the specification of the language extension is
4247 also still to some degree in flux. Hence, a more detailed description of
4248 the language extension and its use is currently available
4249 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4250 wiki page on type families</ulink>. The material will be moved to this user's
4251 guide when it has stabilised.
4254 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4261 <!-- ==================== End of type system extensions ================= -->
4263 <!-- ====================== TEMPLATE HASKELL ======================= -->
4265 <sect1 id="template-haskell">
4266 <title>Template Haskell</title>
4268 <para>Template Haskell allows you to do compile-time meta-programming in
4271 the main technical innovations is discussed in "<ulink
4272 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4273 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4276 There is a Wiki page about
4277 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4278 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4282 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4283 Haskell library reference material</ulink>
4284 (search for the type ExpQ).
4285 [Temporary: many changes to the original design are described in
4286 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4287 Not all of these changes are in GHC 6.6.]
4290 <para> The first example from that paper is set out below as a worked example to help get you started.
4294 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4295 Tim Sheard is going to expand it.)
4299 <title>Syntax</title>
4301 <para> Template Haskell has the following new syntactic
4302 constructions. You need to use the flag
4303 <option>-XTemplateHaskell</option>
4304 <indexterm><primary><option>-XTemplateHaskell</option></primary>
4305 </indexterm>to switch these syntactic extensions on
4306 (<option>-XTemplateHaskell</option> is no longer implied by
4307 <option>-fglasgow-exts</option>).</para>
4311 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4312 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4313 There must be no space between the "$" and the identifier or parenthesis. This use
4314 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4315 of "." as an infix operator. If you want the infix operator, put spaces around it.
4317 <para> A splice can occur in place of
4319 <listitem><para> an expression; the spliced expression must
4320 have type <literal>Q Exp</literal></para></listitem>
4321 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4322 <listitem><para> [Planned, but not implemented yet.] a
4323 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4325 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4326 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4332 A expression quotation is written in Oxford brackets, thus:
4334 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4335 the quotation has type <literal>Expr</literal>.</para></listitem>
4336 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4337 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4338 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
4339 the quotation has type <literal>Type</literal>.</para></listitem>
4340 </itemizedlist></para></listitem>
4343 Reification is written thus:
4345 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4346 has type <literal>Dec</literal>. </para></listitem>
4347 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4348 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4349 <listitem><para> Still to come: fixities </para></listitem>
4351 </itemizedlist></para>
4358 <sect2> <title> Using Template Haskell </title>
4362 The data types and monadic constructor functions for Template Haskell are in the library
4363 <literal>Language.Haskell.THSyntax</literal>.
4367 You can only run a function at compile time if it is imported from another module. That is,
4368 you can't define a function in a module, and call it from within a splice in the same module.
4369 (It would make sense to do so, but it's hard to implement.)
4373 Furthermore, you can only run a function at compile time if it is imported
4374 from another module <emphasis>that is not part of a mutually-recursive group of modules
4375 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4376 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4377 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4381 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4384 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4385 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4386 compiles and runs a program, and then looks at the result. So it's important that
4387 the program it compiles produces results whose representations are identical to
4388 those of the compiler itself.
4392 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4393 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4398 <sect2> <title> A Template Haskell Worked Example </title>
4399 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4400 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4407 -- Import our template "pr"
4408 import Printf ( pr )
4410 -- The splice operator $ takes the Haskell source code
4411 -- generated at compile time by "pr" and splices it into
4412 -- the argument of "putStrLn".
4413 main = putStrLn ( $(pr "Hello") )
4419 -- Skeletal printf from the paper.
4420 -- It needs to be in a separate module to the one where
4421 -- you intend to use it.
4423 -- Import some Template Haskell syntax
4424 import Language.Haskell.TH
4426 -- Describe a format string
4427 data Format = D | S | L String
4429 -- Parse a format string. This is left largely to you
4430 -- as we are here interested in building our first ever
4431 -- Template Haskell program and not in building printf.
4432 parse :: String -> [Format]
4435 -- Generate Haskell source code from a parsed representation
4436 -- of the format string. This code will be spliced into
4437 -- the module which calls "pr", at compile time.
4438 gen :: [Format] -> ExpQ
4439 gen [D] = [| \n -> show n |]
4440 gen [S] = [| \s -> s |]
4441 gen [L s] = stringE s
4443 -- Here we generate the Haskell code for the splice
4444 -- from an input format string.
4445 pr :: String -> ExpQ
4446 pr s = gen (parse s)
4449 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4452 $ ghc --make -XTemplateHaskell main.hs -o main.exe
4455 <para>Run "main.exe" and here is your output:</para>
4465 <title>Using Template Haskell with Profiling</title>
4466 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4468 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4469 interpreter to run the splice expressions. The bytecode interpreter
4470 runs the compiled expression on top of the same runtime on which GHC
4471 itself is running; this means that the compiled code referred to by
4472 the interpreted expression must be compatible with this runtime, and
4473 in particular this means that object code that is compiled for
4474 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4475 expression, because profiled object code is only compatible with the
4476 profiling version of the runtime.</para>
4478 <para>This causes difficulties if you have a multi-module program
4479 containing Template Haskell code and you need to compile it for
4480 profiling, because GHC cannot load the profiled object code and use it
4481 when executing the splices. Fortunately GHC provides a workaround.
4482 The basic idea is to compile the program twice:</para>
4486 <para>Compile the program or library first the normal way, without
4487 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4490 <para>Then compile it again with <option>-prof</option>, and
4491 additionally use <option>-osuf
4492 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4493 to name the object files differentliy (you can choose any suffix
4494 that isn't the normal object suffix here). GHC will automatically
4495 load the object files built in the first step when executing splice
4496 expressions. If you omit the <option>-osuf</option> flag when
4497 building with <option>-prof</option> and Template Haskell is used,
4498 GHC will emit an error message. </para>
4505 <!-- ===================== Arrow notation =================== -->
4507 <sect1 id="arrow-notation">
4508 <title>Arrow notation
4511 <para>Arrows are a generalization of monads introduced by John Hughes.
4512 For more details, see
4517 “Generalising Monads to Arrows”,
4518 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4519 pp67–111, May 2000.
4525 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4526 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4532 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4533 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4539 and the arrows web page at
4540 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4541 With the <option>-XArrows</option> flag, GHC supports the arrow
4542 notation described in the second of these papers.
4543 What follows is a brief introduction to the notation;
4544 it won't make much sense unless you've read Hughes's paper.
4545 This notation is translated to ordinary Haskell,
4546 using combinators from the
4547 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4551 <para>The extension adds a new kind of expression for defining arrows:
4553 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4554 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4556 where <literal>proc</literal> is a new keyword.
4557 The variables of the pattern are bound in the body of the
4558 <literal>proc</literal>-expression,
4559 which is a new sort of thing called a <firstterm>command</firstterm>.
4560 The syntax of commands is as follows:
4562 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4563 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4564 | <replaceable>cmd</replaceable><superscript>0</superscript>
4566 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4567 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4568 infix operators as for expressions, and
4570 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4571 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4572 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4573 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4574 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4575 | <replaceable>fcmd</replaceable>
4577 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4578 | ( <replaceable>cmd</replaceable> )
4579 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4581 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4582 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4583 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4584 | <replaceable>cmd</replaceable>
4586 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4587 except that the bodies are commands instead of expressions.
4591 Commands produce values, but (like monadic computations)
4592 may yield more than one value,
4593 or none, and may do other things as well.
4594 For the most part, familiarity with monadic notation is a good guide to
4596 However the values of expressions, even monadic ones,
4597 are determined by the values of the variables they contain;
4598 this is not necessarily the case for commands.
4602 A simple example of the new notation is the expression
4604 proc x -> f -< x+1
4606 We call this a <firstterm>procedure</firstterm> or
4607 <firstterm>arrow abstraction</firstterm>.
4608 As with a lambda expression, the variable <literal>x</literal>
4609 is a new variable bound within the <literal>proc</literal>-expression.
4610 It refers to the input to the arrow.
4611 In the above example, <literal>-<</literal> is not an identifier but an
4612 new reserved symbol used for building commands from an expression of arrow
4613 type and an expression to be fed as input to that arrow.
4614 (The weird look will make more sense later.)
4615 It may be read as analogue of application for arrows.
4616 The above example is equivalent to the Haskell expression
4618 arr (\ x -> x+1) >>> f
4620 That would make no sense if the expression to the left of
4621 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4622 More generally, the expression to the left of <literal>-<</literal>
4623 may not involve any <firstterm>local variable</firstterm>,
4624 i.e. a variable bound in the current arrow abstraction.
4625 For such a situation there is a variant <literal>-<<</literal>, as in
4627 proc x -> f x -<< x+1
4629 which is equivalent to
4631 arr (\ x -> (f x, x+1)) >>> app
4633 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4635 Such an arrow is equivalent to a monad, so if you're using this form
4636 you may find a monadic formulation more convenient.
4640 <title>do-notation for commands</title>
4643 Another form of command is a form of <literal>do</literal>-notation.
4644 For example, you can write
4653 You can read this much like ordinary <literal>do</literal>-notation,
4654 but with commands in place of monadic expressions.
4655 The first line sends the value of <literal>x+1</literal> as an input to
4656 the arrow <literal>f</literal>, and matches its output against
4657 <literal>y</literal>.
4658 In the next line, the output is discarded.
4659 The arrow <function>returnA</function> is defined in the
4660 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4661 module as <literal>arr id</literal>.
4662 The above example is treated as an abbreviation for
4664 arr (\ x -> (x, x)) >>>
4665 first (arr (\ x -> x+1) >>> f) >>>
4666 arr (\ (y, x) -> (y, (x, y))) >>>
4667 first (arr (\ y -> 2*y) >>> g) >>>
4669 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4670 first (arr (\ (x, z) -> x*z) >>> h) >>>
4671 arr (\ (t, z) -> t+z) >>>
4674 Note that variables not used later in the composition are projected out.
4675 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4677 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4678 module, this reduces to
4680 arr (\ x -> (x+1, x)) >>>
4682 arr (\ (y, x) -> (2*y, (x, y))) >>>
4684 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4686 arr (\ (t, z) -> t+z)
4688 which is what you might have written by hand.
4689 With arrow notation, GHC keeps track of all those tuples of variables for you.
4693 Note that although the above translation suggests that
4694 <literal>let</literal>-bound variables like <literal>z</literal> must be
4695 monomorphic, the actual translation produces Core,
4696 so polymorphic variables are allowed.
4700 It's also possible to have mutually recursive bindings,
4701 using the new <literal>rec</literal> keyword, as in the following example:
4703 counter :: ArrowCircuit a => a Bool Int
4704 counter = proc reset -> do
4705 rec output <- returnA -< if reset then 0 else next
4706 next <- delay 0 -< output+1
4707 returnA -< output
4709 The translation of such forms uses the <function>loop</function> combinator,
4710 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4716 <title>Conditional commands</title>
4719 In the previous example, we used a conditional expression to construct the
4721 Sometimes we want to conditionally execute different commands, as in
4728 which is translated to
4730 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4731 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4733 Since the translation uses <function>|||</function>,
4734 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4738 There are also <literal>case</literal> commands, like
4744 y <- h -< (x1, x2)
4748 The syntax is the same as for <literal>case</literal> expressions,
4749 except that the bodies of the alternatives are commands rather than expressions.
4750 The translation is similar to that of <literal>if</literal> commands.
4756 <title>Defining your own control structures</title>
4759 As we're seen, arrow notation provides constructs,
4760 modelled on those for expressions,
4761 for sequencing, value recursion and conditionals.
4762 But suitable combinators,
4763 which you can define in ordinary Haskell,
4764 may also be used to build new commands out of existing ones.
4765 The basic idea is that a command defines an arrow from environments to values.
4766 These environments assign values to the free local variables of the command.
4767 Thus combinators that produce arrows from arrows
4768 may also be used to build commands from commands.
4769 For example, the <literal>ArrowChoice</literal> class includes a combinator
4771 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4773 so we can use it to build commands:
4775 expr' = proc x -> do
4778 symbol Plus -< ()
4779 y <- term -< ()
4782 symbol Minus -< ()
4783 y <- term -< ()
4786 (The <literal>do</literal> on the first line is needed to prevent the first
4787 <literal><+> ...</literal> from being interpreted as part of the
4788 expression on the previous line.)
4789 This is equivalent to
4791 expr' = (proc x -> returnA -< x)
4792 <+> (proc x -> do
4793 symbol Plus -< ()
4794 y <- term -< ()
4796 <+> (proc x -> do
4797 symbol Minus -< ()
4798 y <- term -< ()
4801 It is essential that this operator be polymorphic in <literal>e</literal>
4802 (representing the environment input to the command
4803 and thence to its subcommands)
4804 and satisfy the corresponding naturality property
4806 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4808 at least for strict <literal>k</literal>.
4809 (This should be automatic if you're not using <function>seq</function>.)
4810 This ensures that environments seen by the subcommands are environments
4811 of the whole command,
4812 and also allows the translation to safely trim these environments.
4813 The operator must also not use any variable defined within the current
4818 We could define our own operator
4820 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4821 untilA body cond = proc x ->
4822 if cond x then returnA -< ()
4825 untilA body cond -< x
4827 and use it in the same way.
4828 Of course this infix syntax only makes sense for binary operators;
4829 there is also a more general syntax involving special brackets:
4833 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4840 <title>Primitive constructs</title>
4843 Some operators will need to pass additional inputs to their subcommands.
4844 For example, in an arrow type supporting exceptions,
4845 the operator that attaches an exception handler will wish to pass the
4846 exception that occurred to the handler.
4847 Such an operator might have a type
4849 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4851 where <literal>Ex</literal> is the type of exceptions handled.
4852 You could then use this with arrow notation by writing a command
4854 body `handleA` \ ex -> handler
4856 so that if an exception is raised in the command <literal>body</literal>,
4857 the variable <literal>ex</literal> is bound to the value of the exception
4858 and the command <literal>handler</literal>,
4859 which typically refers to <literal>ex</literal>, is entered.
4860 Though the syntax here looks like a functional lambda,
4861 we are talking about commands, and something different is going on.
4862 The input to the arrow represented by a command consists of values for
4863 the free local variables in the command, plus a stack of anonymous values.
4864 In all the prior examples, this stack was empty.
4865 In the second argument to <function>handleA</function>,
4866 this stack consists of one value, the value of the exception.
4867 The command form of lambda merely gives this value a name.
4872 the values on the stack are paired to the right of the environment.
4873 So operators like <function>handleA</function> that pass
4874 extra inputs to their subcommands can be designed for use with the notation
4875 by pairing the values with the environment in this way.
4876 More precisely, the type of each argument of the operator (and its result)
4877 should have the form
4879 a (...(e,t1), ... tn) t
4881 where <replaceable>e</replaceable> is a polymorphic variable
4882 (representing the environment)
4883 and <replaceable>ti</replaceable> are the types of the values on the stack,
4884 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4885 The polymorphic variable <replaceable>e</replaceable> must not occur in
4886 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4887 <replaceable>t</replaceable>.
4888 However the arrows involved need not be the same.
4889 Here are some more examples of suitable operators:
4891 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4892 runReader :: ... => a e c -> a' (e,State) c
4893 runState :: ... => a e c -> a' (e,State) (c,State)
4895 We can supply the extra input required by commands built with the last two
4896 by applying them to ordinary expressions, as in
4900 (|runReader (do { ... })|) s
4902 which adds <literal>s</literal> to the stack of inputs to the command
4903 built using <function>runReader</function>.
4907 The command versions of lambda abstraction and application are analogous to
4908 the expression versions.
4909 In particular, the beta and eta rules describe equivalences of commands.
4910 These three features (operators, lambda abstraction and application)
4911 are the core of the notation; everything else can be built using them,
4912 though the results would be somewhat clumsy.
4913 For example, we could simulate <literal>do</literal>-notation by defining
4915 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4916 u `bind` f = returnA &&& u >>> f
4918 bind_ :: Arrow a => a e b -> a e c -> a e c
4919 u `bind_` f = u `bind` (arr fst >>> f)
4921 We could simulate <literal>if</literal> by defining
4923 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4924 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4931 <title>Differences with the paper</title>
4936 <para>Instead of a single form of arrow application (arrow tail) with two
4937 translations, the implementation provides two forms
4938 <quote><literal>-<</literal></quote> (first-order)
4939 and <quote><literal>-<<</literal></quote> (higher-order).
4944 <para>User-defined operators are flagged with banana brackets instead of
4945 a new <literal>form</literal> keyword.
4954 <title>Portability</title>
4957 Although only GHC implements arrow notation directly,
4958 there is also a preprocessor
4960 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4961 that translates arrow notation into Haskell 98
4962 for use with other Haskell systems.
4963 You would still want to check arrow programs with GHC;
4964 tracing type errors in the preprocessor output is not easy.
4965 Modules intended for both GHC and the preprocessor must observe some
4966 additional restrictions:
4971 The module must import
4972 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4978 The preprocessor cannot cope with other Haskell extensions.
4979 These would have to go in separate modules.
4985 Because the preprocessor targets Haskell (rather than Core),
4986 <literal>let</literal>-bound variables are monomorphic.
4997 <!-- ==================== BANG PATTERNS ================= -->
4999 <sect1 id="bang-patterns">
5000 <title>Bang patterns
5001 <indexterm><primary>Bang patterns</primary></indexterm>
5003 <para>GHC supports an extension of pattern matching called <emphasis>bang
5004 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
5006 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
5007 prime feature description</ulink> contains more discussion and examples
5008 than the material below.
5011 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
5014 <sect2 id="bang-patterns-informal">
5015 <title>Informal description of bang patterns
5018 The main idea is to add a single new production to the syntax of patterns:
5022 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
5023 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
5028 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
5029 whereas without the bang it would be lazy.
5030 Bang patterns can be nested of course:
5034 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
5035 <literal>y</literal>.
5036 A bang only really has an effect if it precedes a variable or wild-card pattern:
5041 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
5042 forces evaluation anyway does nothing.
5044 Bang patterns work in <literal>case</literal> expressions too, of course:
5046 g5 x = let y = f x in body
5047 g6 x = case f x of { y -> body }
5048 g7 x = case f x of { !y -> body }
5050 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
5051 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
5052 result, and then evaluates <literal>body</literal>.
5054 Bang patterns work in <literal>let</literal> and <literal>where</literal>
5055 definitions too. For example:
5059 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
5060 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
5061 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
5062 in a function argument <literal>![x,y]</literal> means the
5063 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
5064 is part of the syntax of <literal>let</literal> bindings.
5069 <sect2 id="bang-patterns-sem">
5070 <title>Syntax and semantics
5074 We add a single new production to the syntax of patterns:
5078 There is one problem with syntactic ambiguity. Consider:
5082 Is this a definition of the infix function "<literal>(!)</literal>",
5083 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
5084 ambiguity in favour of the latter. If you want to define
5085 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
5090 The semantics of Haskell pattern matching is described in <ulink
5091 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5092 Section 3.17.2</ulink> of the Haskell Report. To this description add
5093 one extra item 10, saying:
5094 <itemizedlist><listitem><para>Matching
5095 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5096 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5097 <listitem><para>otherwise, <literal>pat</literal> is matched against
5098 <literal>v</literal></para></listitem>
5100 </para></listitem></itemizedlist>
5101 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5102 Section 3.17.3</ulink>, add a new case (t):
5104 case v of { !pat -> e; _ -> e' }
5105 = v `seq` case v of { pat -> e; _ -> e' }
5108 That leaves let expressions, whose translation is given in
5109 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5111 of the Haskell Report.
5112 In the translation box, first apply
5113 the following transformation: for each pattern <literal>pi</literal> that is of
5114 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5115 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5116 have a bang at the top, apply the rules in the existing box.
5118 <para>The effect of the let rule is to force complete matching of the pattern
5119 <literal>qi</literal> before evaluation of the body is begun. The bang is
5120 retained in the translated form in case <literal>qi</literal> is a variable,
5128 The let-binding can be recursive. However, it is much more common for
5129 the let-binding to be non-recursive, in which case the following law holds:
5130 <literal>(let !p = rhs in body)</literal>
5132 <literal>(case rhs of !p -> body)</literal>
5135 A pattern with a bang at the outermost level is not allowed at the top level of
5141 <!-- ==================== ASSERTIONS ================= -->
5143 <sect1 id="assertions">
5145 <indexterm><primary>Assertions</primary></indexterm>
5149 If you want to make use of assertions in your standard Haskell code, you
5150 could define a function like the following:
5156 assert :: Bool -> a -> a
5157 assert False x = error "assertion failed!"
5164 which works, but gives you back a less than useful error message --
5165 an assertion failed, but which and where?
5169 One way out is to define an extended <function>assert</function> function which also
5170 takes a descriptive string to include in the error message and
5171 perhaps combine this with the use of a pre-processor which inserts
5172 the source location where <function>assert</function> was used.
5176 Ghc offers a helping hand here, doing all of this for you. For every
5177 use of <function>assert</function> in the user's source:
5183 kelvinToC :: Double -> Double
5184 kelvinToC k = assert (k >= 0.0) (k+273.15)
5190 Ghc will rewrite this to also include the source location where the
5197 assert pred val ==> assertError "Main.hs|15" pred val
5203 The rewrite is only performed by the compiler when it spots
5204 applications of <function>Control.Exception.assert</function>, so you
5205 can still define and use your own versions of
5206 <function>assert</function>, should you so wish. If not, import
5207 <literal>Control.Exception</literal> to make use
5208 <function>assert</function> in your code.
5212 GHC ignores assertions when optimisation is turned on with the
5213 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5214 <literal>assert pred e</literal> will be rewritten to
5215 <literal>e</literal>. You can also disable assertions using the
5216 <option>-fignore-asserts</option>
5217 option<indexterm><primary><option>-fignore-asserts</option></primary>
5218 </indexterm>.</para>
5221 Assertion failures can be caught, see the documentation for the
5222 <literal>Control.Exception</literal> library for the details.
5228 <!-- =============================== PRAGMAS =========================== -->
5230 <sect1 id="pragmas">
5231 <title>Pragmas</title>
5233 <indexterm><primary>pragma</primary></indexterm>
5235 <para>GHC supports several pragmas, or instructions to the
5236 compiler placed in the source code. Pragmas don't normally affect
5237 the meaning of the program, but they might affect the efficiency
5238 of the generated code.</para>
5240 <para>Pragmas all take the form
5242 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5244 where <replaceable>word</replaceable> indicates the type of
5245 pragma, and is followed optionally by information specific to that
5246 type of pragma. Case is ignored in
5247 <replaceable>word</replaceable>. The various values for
5248 <replaceable>word</replaceable> that GHC understands are described
5249 in the following sections; any pragma encountered with an
5250 unrecognised <replaceable>word</replaceable> is (silently)
5253 <sect2 id="deprecated-pragma">
5254 <title>DEPRECATED pragma</title>
5255 <indexterm><primary>DEPRECATED</primary>
5258 <para>The DEPRECATED pragma lets you specify that a particular
5259 function, class, or type, is deprecated. There are two
5264 <para>You can deprecate an entire module thus:</para>
5266 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5269 <para>When you compile any module that import
5270 <literal>Wibble</literal>, GHC will print the specified
5275 <para>You can deprecate a function, class, type, or data constructor, with the
5276 following top-level declaration:</para>
5278 {-# DEPRECATED f, C, T "Don't use these" #-}
5280 <para>When you compile any module that imports and uses any
5281 of the specified entities, GHC will print the specified
5283 <para> You can only depecate entities declared at top level in the module
5284 being compiled, and you can only use unqualified names in the list of
5285 entities being deprecated. A capitalised name, such as <literal>T</literal>
5286 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5287 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5288 both are in scope. If both are in scope, there is currently no way to deprecate
5289 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5292 Any use of the deprecated item, or of anything from a deprecated
5293 module, will be flagged with an appropriate message. However,
5294 deprecations are not reported for
5295 (a) uses of a deprecated function within its defining module, and
5296 (b) uses of a deprecated function in an export list.
5297 The latter reduces spurious complaints within a library
5298 in which one module gathers together and re-exports
5299 the exports of several others.
5301 <para>You can suppress the warnings with the flag
5302 <option>-fno-warn-deprecations</option>.</para>
5305 <sect2 id="include-pragma">
5306 <title>INCLUDE pragma</title>
5308 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5309 of C header files that should be <literal>#include</literal>'d into
5310 the C source code generated by the compiler for the current module (if
5311 compiling via C). For example:</para>
5314 {-# INCLUDE "foo.h" #-}
5315 {-# INCLUDE <stdio.h> #-}</programlisting>
5317 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5318 your source file with any <literal>OPTIONS_GHC</literal>
5321 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5322 to the <option>-#include</option> option (<xref
5323 linkend="options-C-compiler" />), because the
5324 <literal>INCLUDE</literal> pragma is understood by other
5325 compilers. Yet another alternative is to add the include file to each
5326 <literal>foreign import</literal> declaration in your code, but we
5327 don't recommend using this approach with GHC.</para>
5330 <sect2 id="inline-noinline-pragma">
5331 <title>INLINE and NOINLINE pragmas</title>
5333 <para>These pragmas control the inlining of function
5336 <sect3 id="inline-pragma">
5337 <title>INLINE pragma</title>
5338 <indexterm><primary>INLINE</primary></indexterm>
5340 <para>GHC (with <option>-O</option>, as always) tries to
5341 inline (or “unfold”) functions/values that are
5342 “small enough,” thus avoiding the call overhead
5343 and possibly exposing other more-wonderful optimisations.
5344 Normally, if GHC decides a function is “too
5345 expensive” to inline, it will not do so, nor will it
5346 export that unfolding for other modules to use.</para>
5348 <para>The sledgehammer you can bring to bear is the
5349 <literal>INLINE</literal><indexterm><primary>INLINE
5350 pragma</primary></indexterm> pragma, used thusly:</para>
5353 key_function :: Int -> String -> (Bool, Double)
5355 #ifdef __GLASGOW_HASKELL__
5356 {-# INLINE key_function #-}
5360 <para>(You don't need to do the C pre-processor carry-on
5361 unless you're going to stick the code through HBC—it
5362 doesn't like <literal>INLINE</literal> pragmas.)</para>
5364 <para>The major effect of an <literal>INLINE</literal> pragma
5365 is to declare a function's “cost” to be very low.
5366 The normal unfolding machinery will then be very keen to
5369 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5370 function can be put anywhere its type signature could be
5373 <para><literal>INLINE</literal> pragmas are a particularly
5375 <literal>then</literal>/<literal>return</literal> (or
5376 <literal>bind</literal>/<literal>unit</literal>) functions in
5377 a monad. For example, in GHC's own
5378 <literal>UniqueSupply</literal> monad code, we have:</para>
5381 #ifdef __GLASGOW_HASKELL__
5382 {-# INLINE thenUs #-}
5383 {-# INLINE returnUs #-}
5387 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5388 linkend="noinline-pragma"/>).</para>
5391 <sect3 id="noinline-pragma">
5392 <title>NOINLINE pragma</title>
5394 <indexterm><primary>NOINLINE</primary></indexterm>
5395 <indexterm><primary>NOTINLINE</primary></indexterm>
5397 <para>The <literal>NOINLINE</literal> pragma does exactly what
5398 you'd expect: it stops the named function from being inlined
5399 by the compiler. You shouldn't ever need to do this, unless
5400 you're very cautious about code size.</para>
5402 <para><literal>NOTINLINE</literal> is a synonym for
5403 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5404 specified by Haskell 98 as the standard way to disable
5405 inlining, so it should be used if you want your code to be
5409 <sect3 id="phase-control">
5410 <title>Phase control</title>
5412 <para> Sometimes you want to control exactly when in GHC's
5413 pipeline the INLINE pragma is switched on. Inlining happens
5414 only during runs of the <emphasis>simplifier</emphasis>. Each
5415 run of the simplifier has a different <emphasis>phase
5416 number</emphasis>; the phase number decreases towards zero.
5417 If you use <option>-dverbose-core2core</option> you'll see the
5418 sequence of phase numbers for successive runs of the
5419 simplifier. In an INLINE pragma you can optionally specify a
5423 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5424 <literal>f</literal>
5425 until phase <literal>k</literal>, but from phase
5426 <literal>k</literal> onwards be very keen to inline it.
5429 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5430 <literal>f</literal>
5431 until phase <literal>k</literal>, but from phase
5432 <literal>k</literal> onwards do not inline it.
5435 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5436 <literal>f</literal>
5437 until phase <literal>k</literal>, but from phase
5438 <literal>k</literal> onwards be willing to inline it (as if
5439 there was no pragma).
5442 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5443 <literal>f</literal>
5444 until phase <literal>k</literal>, but from phase
5445 <literal>k</literal> onwards do not inline it.
5448 The same information is summarised here:
5450 -- Before phase 2 Phase 2 and later
5451 {-# INLINE [2] f #-} -- No Yes
5452 {-# INLINE [~2] f #-} -- Yes No
5453 {-# NOINLINE [2] f #-} -- No Maybe
5454 {-# NOINLINE [~2] f #-} -- Maybe No
5456 {-# INLINE f #-} -- Yes Yes
5457 {-# NOINLINE f #-} -- No No
5459 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5460 function body is small, or it is applied to interesting-looking arguments etc).
5461 Another way to understand the semantics is this:
5463 <listitem><para>For both INLINE and NOINLINE, the phase number says
5464 when inlining is allowed at all.</para></listitem>
5465 <listitem><para>The INLINE pragma has the additional effect of making the
5466 function body look small, so that when inlining is allowed it is very likely to
5471 <para>The same phase-numbering control is available for RULES
5472 (<xref linkend="rewrite-rules"/>).</para>
5476 <sect2 id="language-pragma">
5477 <title>LANGUAGE pragma</title>
5479 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5480 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5482 <para>This allows language extensions to be enabled in a portable way.
5483 It is the intention that all Haskell compilers support the
5484 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5485 all extensions are supported by all compilers, of
5486 course. The <literal>LANGUAGE</literal> pragma should be used instead
5487 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5489 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5491 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5493 <para>Any extension from the <literal>Extension</literal> type defined in
5495 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>
5499 <sect2 id="line-pragma">
5500 <title>LINE pragma</title>
5502 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5503 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5504 <para>This pragma is similar to C's <literal>#line</literal>
5505 pragma, and is mainly for use in automatically generated Haskell
5506 code. It lets you specify the line number and filename of the
5507 original code; for example</para>
5509 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5511 <para>if you'd generated the current file from something called
5512 <filename>Foo.vhs</filename> and this line corresponds to line
5513 42 in the original. GHC will adjust its error messages to refer
5514 to the line/file named in the <literal>LINE</literal>
5518 <sect2 id="options-pragma">
5519 <title>OPTIONS_GHC pragma</title>
5520 <indexterm><primary>OPTIONS_GHC</primary>
5522 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5525 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5526 additional options that are given to the compiler when compiling
5527 this source file. See <xref linkend="source-file-options"/> for
5530 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5531 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5535 <title>RULES pragma</title>
5537 <para>The RULES pragma lets you specify rewrite rules. It is
5538 described in <xref linkend="rewrite-rules"/>.</para>
5541 <sect2 id="specialize-pragma">
5542 <title>SPECIALIZE pragma</title>
5544 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5545 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5546 <indexterm><primary>overloading, death to</primary></indexterm>
5548 <para>(UK spelling also accepted.) For key overloaded
5549 functions, you can create extra versions (NB: more code space)
5550 specialised to particular types. Thus, if you have an
5551 overloaded function:</para>
5554 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5557 <para>If it is heavily used on lists with
5558 <literal>Widget</literal> keys, you could specialise it as
5562 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5565 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5566 be put anywhere its type signature could be put.</para>
5568 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5569 (a) a specialised version of the function and (b) a rewrite rule
5570 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5571 un-specialised function into a call to the specialised one.</para>
5573 <para>The type in a SPECIALIZE pragma can be any type that is less
5574 polymorphic than the type of the original function. In concrete terms,
5575 if the original function is <literal>f</literal> then the pragma
5577 {-# SPECIALIZE f :: <type> #-}
5579 is valid if and only if the defintion
5581 f_spec :: <type>
5584 is valid. Here are some examples (where we only give the type signature
5585 for the original function, not its code):
5587 f :: Eq a => a -> b -> b
5588 {-# SPECIALISE f :: Int -> b -> b #-}
5590 g :: (Eq a, Ix b) => a -> b -> b
5591 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5593 h :: Eq a => a -> a -> a
5594 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5596 The last of these examples will generate a
5597 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5598 well. If you use this kind of specialisation, let us know how well it works.
5601 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5602 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5603 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5604 The <literal>INLINE</literal> pragma affects the specialised verison of the
5605 function (only), and applies even if the function is recursive. The motivating
5608 -- A GADT for arrays with type-indexed representation
5610 ArrInt :: !Int -> ByteArray# -> Arr Int
5611 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5613 (!:) :: Arr e -> Int -> e
5614 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5615 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5616 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5617 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5619 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5620 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5621 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5622 the specialised function will be inlined. It has two calls to
5623 <literal>(!:)</literal>,
5624 both at type <literal>Int</literal>. Both these calls fire the first
5625 specialisation, whose body is also inlined. The result is a type-based
5626 unrolling of the indexing function.</para>
5627 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5628 on an ordinarily-recursive function.</para>
5630 <para>Note: In earlier versions of GHC, it was possible to provide your own
5631 specialised function for a given type:
5634 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5637 This feature has been removed, as it is now subsumed by the
5638 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5642 <sect2 id="specialize-instance-pragma">
5643 <title>SPECIALIZE instance pragma
5647 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5648 <indexterm><primary>overloading, death to</primary></indexterm>
5649 Same idea, except for instance declarations. For example:
5652 instance (Eq a) => Eq (Foo a) where {
5653 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5657 The pragma must occur inside the <literal>where</literal> part
5658 of the instance declaration.
5661 Compatible with HBC, by the way, except perhaps in the placement
5667 <sect2 id="unpack-pragma">
5668 <title>UNPACK pragma</title>
5670 <indexterm><primary>UNPACK</primary></indexterm>
5672 <para>The <literal>UNPACK</literal> indicates to the compiler
5673 that it should unpack the contents of a constructor field into
5674 the constructor itself, removing a level of indirection. For
5678 data T = T {-# UNPACK #-} !Float
5679 {-# UNPACK #-} !Float
5682 <para>will create a constructor <literal>T</literal> containing
5683 two unboxed floats. This may not always be an optimisation: if
5684 the <function>T</function> constructor is scrutinised and the
5685 floats passed to a non-strict function for example, they will
5686 have to be reboxed (this is done automatically by the
5689 <para>Unpacking constructor fields should only be used in
5690 conjunction with <option>-O</option>, in order to expose
5691 unfoldings to the compiler so the reboxing can be removed as
5692 often as possible. For example:</para>
5696 f (T f1 f2) = f1 + f2
5699 <para>The compiler will avoid reboxing <function>f1</function>
5700 and <function>f2</function> by inlining <function>+</function>
5701 on floats, but only when <option>-O</option> is on.</para>
5703 <para>Any single-constructor data is eligible for unpacking; for
5707 data T = T {-# UNPACK #-} !(Int,Int)
5710 <para>will store the two <literal>Int</literal>s directly in the
5711 <function>T</function> constructor, by flattening the pair.
5712 Multi-level unpacking is also supported:</para>
5715 data T = T {-# UNPACK #-} !S
5716 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5719 <para>will store two unboxed <literal>Int#</literal>s
5720 directly in the <function>T</function> constructor. The
5721 unpacker can see through newtypes, too.</para>
5723 <para>If a field cannot be unpacked, you will not get a warning,
5724 so it might be an idea to check the generated code with
5725 <option>-ddump-simpl</option>.</para>
5727 <para>See also the <option>-funbox-strict-fields</option> flag,
5728 which essentially has the effect of adding
5729 <literal>{-# UNPACK #-}</literal> to every strict
5730 constructor field.</para>
5735 <!-- ======================= REWRITE RULES ======================== -->
5737 <sect1 id="rewrite-rules">
5738 <title>Rewrite rules
5740 <indexterm><primary>RULES pragma</primary></indexterm>
5741 <indexterm><primary>pragma, RULES</primary></indexterm>
5742 <indexterm><primary>rewrite rules</primary></indexterm></title>
5745 The programmer can specify rewrite rules as part of the source program
5746 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5747 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5748 and (b) the <option>-frules-off</option> flag
5749 (<xref linkend="options-f"/>) is not specified, and (c) the
5750 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5759 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5766 <title>Syntax</title>
5769 From a syntactic point of view:
5775 There may be zero or more rules in a <literal>RULES</literal> pragma.
5782 Each rule has a name, enclosed in double quotes. The name itself has
5783 no significance at all. It is only used when reporting how many times the rule fired.
5789 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5790 immediately after the name of the rule. Thus:
5793 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5796 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5797 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5806 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5807 is set, so you must lay out your rules starting in the same column as the
5808 enclosing definitions.
5815 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5816 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5817 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5818 by spaces, just like in a type <literal>forall</literal>.
5824 A pattern variable may optionally have a type signature.
5825 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5826 For example, here is the <literal>foldr/build</literal> rule:
5829 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5830 foldr k z (build g) = g k z
5833 Since <function>g</function> has a polymorphic type, it must have a type signature.
5840 The left hand side of a rule must consist of a top-level variable applied
5841 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5844 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5845 "wrong2" forall f. f True = True
5848 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5855 A rule does not need to be in the same module as (any of) the
5856 variables it mentions, though of course they need to be in scope.
5862 Rules are automatically exported from a module, just as instance declarations are.
5873 <title>Semantics</title>
5876 From a semantic point of view:
5882 Rules are only applied if you use the <option>-O</option> flag.
5888 Rules are regarded as left-to-right rewrite rules.
5889 When GHC finds an expression that is a substitution instance of the LHS
5890 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5891 By "a substitution instance" we mean that the LHS can be made equal to the
5892 expression by substituting for the pattern variables.
5899 The LHS and RHS of a rule are typechecked, and must have the
5907 GHC makes absolutely no attempt to verify that the LHS and RHS
5908 of a rule have the same meaning. That is undecidable in general, and
5909 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5916 GHC makes no attempt to make sure that the rules are confluent or
5917 terminating. For example:
5920 "loop" forall x,y. f x y = f y x
5923 This rule will cause the compiler to go into an infinite loop.
5930 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5936 GHC currently uses a very simple, syntactic, matching algorithm
5937 for matching a rule LHS with an expression. It seeks a substitution
5938 which makes the LHS and expression syntactically equal modulo alpha
5939 conversion. The pattern (rule), but not the expression, is eta-expanded if
5940 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5941 But not beta conversion (that's called higher-order matching).
5945 Matching is carried out on GHC's intermediate language, which includes
5946 type abstractions and applications. So a rule only matches if the
5947 types match too. See <xref linkend="rule-spec"/> below.
5953 GHC keeps trying to apply the rules as it optimises the program.
5954 For example, consider:
5963 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5964 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5965 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5966 not be substituted, and the rule would not fire.
5973 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5974 that appears on the LHS of a rule</emphasis>, because once you have substituted
5975 for something you can't match against it (given the simple minded
5976 matching). So if you write the rule
5979 "map/map" forall f,g. map f . map g = map (f.g)
5982 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5983 It will only match something written with explicit use of ".".
5984 Well, not quite. It <emphasis>will</emphasis> match the expression
5990 where <function>wibble</function> is defined:
5993 wibble f g = map f . map g
5996 because <function>wibble</function> will be inlined (it's small).
5998 Later on in compilation, GHC starts inlining even things on the
5999 LHS of rules, but still leaves the rules enabled. This inlining
6000 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
6007 All rules are implicitly exported from the module, and are therefore
6008 in force in any module that imports the module that defined the rule, directly
6009 or indirectly. (That is, if A imports B, which imports C, then C's rules are
6010 in force when compiling A.) The situation is very similar to that for instance
6022 <title>List fusion</title>
6025 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
6026 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
6027 intermediate list should be eliminated entirely.
6031 The following are good producers:
6043 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
6049 Explicit lists (e.g. <literal>[True, False]</literal>)
6055 The cons constructor (e.g <literal>3:4:[]</literal>)
6061 <function>++</function>
6067 <function>map</function>
6073 <function>take</function>, <function>filter</function>
6079 <function>iterate</function>, <function>repeat</function>
6085 <function>zip</function>, <function>zipWith</function>
6094 The following are good consumers:
6106 <function>array</function> (on its second argument)
6112 <function>++</function> (on its first argument)
6118 <function>foldr</function>
6124 <function>map</function>
6130 <function>take</function>, <function>filter</function>
6136 <function>concat</function>
6142 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6148 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6149 will fuse with one but not the other)
6155 <function>partition</function>
6161 <function>head</function>
6167 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6173 <function>sequence_</function>
6179 <function>msum</function>
6185 <function>sortBy</function>
6194 So, for example, the following should generate no intermediate lists:
6197 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6203 This list could readily be extended; if there are Prelude functions that you use
6204 a lot which are not included, please tell us.
6208 If you want to write your own good consumers or producers, look at the
6209 Prelude definitions of the above functions to see how to do so.
6214 <sect2 id="rule-spec">
6215 <title>Specialisation
6219 Rewrite rules can be used to get the same effect as a feature
6220 present in earlier versions of GHC.
6221 For example, suppose that:
6224 genericLookup :: Ord a => Table a b -> a -> b
6225 intLookup :: Table Int b -> Int -> b
6228 where <function>intLookup</function> is an implementation of
6229 <function>genericLookup</function> that works very fast for
6230 keys of type <literal>Int</literal>. You might wish
6231 to tell GHC to use <function>intLookup</function> instead of
6232 <function>genericLookup</function> whenever the latter was called with
6233 type <literal>Table Int b -> Int -> b</literal>.
6234 It used to be possible to write
6237 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6240 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6243 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6246 This slightly odd-looking rule instructs GHC to replace
6247 <function>genericLookup</function> by <function>intLookup</function>
6248 <emphasis>whenever the types match</emphasis>.
6249 What is more, this rule does not need to be in the same
6250 file as <function>genericLookup</function>, unlike the
6251 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6252 have an original definition available to specialise).
6255 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6256 <function>intLookup</function> really behaves as a specialised version
6257 of <function>genericLookup</function>!!!</para>
6259 <para>An example in which using <literal>RULES</literal> for
6260 specialisation will Win Big:
6263 toDouble :: Real a => a -> Double
6264 toDouble = fromRational . toRational
6266 {-# RULES "toDouble/Int" toDouble = i2d #-}
6267 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6270 The <function>i2d</function> function is virtually one machine
6271 instruction; the default conversion—via an intermediate
6272 <literal>Rational</literal>—is obscenely expensive by
6279 <title>Controlling what's going on</title>
6287 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6293 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6294 If you add <option>-dppr-debug</option> you get a more detailed listing.
6300 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6303 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6304 {-# INLINE build #-}
6308 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6309 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6310 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6311 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6318 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6319 see how to write rules that will do fusion and yet give an efficient
6320 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6330 <sect2 id="core-pragma">
6331 <title>CORE pragma</title>
6333 <indexterm><primary>CORE pragma</primary></indexterm>
6334 <indexterm><primary>pragma, CORE</primary></indexterm>
6335 <indexterm><primary>core, annotation</primary></indexterm>
6338 The external core format supports <quote>Note</quote> annotations;
6339 the <literal>CORE</literal> pragma gives a way to specify what these
6340 should be in your Haskell source code. Syntactically, core
6341 annotations are attached to expressions and take a Haskell string
6342 literal as an argument. The following function definition shows an
6346 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6349 Semantically, this is equivalent to:
6357 However, when external for is generated (via
6358 <option>-fext-core</option>), there will be Notes attached to the
6359 expressions <function>show</function> and <varname>x</varname>.
6360 The core function declaration for <function>f</function> is:
6364 f :: %forall a . GHCziShow.ZCTShow a ->
6365 a -> GHCziBase.ZMZN GHCziBase.Char =
6366 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6368 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6370 (tpl1::GHCziBase.Int ->
6372 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6374 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6375 (tpl3::GHCziBase.ZMZN a ->
6376 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6384 Here, we can see that the function <function>show</function> (which
6385 has been expanded out to a case expression over the Show dictionary)
6386 has a <literal>%note</literal> attached to it, as does the
6387 expression <varname>eta</varname> (which used to be called
6388 <varname>x</varname>).
6395 <sect1 id="special-ids">
6396 <title>Special built-in functions</title>
6397 <para>GHC has a few built-in funcions with special behaviour. These
6398 are now described in the module <ulink
6399 url="../libraries/base/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
6400 in the library documentation.</para>
6404 <sect1 id="generic-classes">
6405 <title>Generic classes</title>
6408 The ideas behind this extension are described in detail in "Derivable type classes",
6409 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6410 An example will give the idea:
6418 fromBin :: [Int] -> (a, [Int])
6420 toBin {| Unit |} Unit = []
6421 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6422 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6423 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6425 fromBin {| Unit |} bs = (Unit, bs)
6426 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6427 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6428 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6429 (y,bs'') = fromBin bs'
6432 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6433 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6434 which are defined thus in the library module <literal>Generics</literal>:
6438 data a :+: b = Inl a | Inr b
6439 data a :*: b = a :*: b
6442 Now you can make a data type into an instance of Bin like this:
6444 instance (Bin a, Bin b) => Bin (a,b)
6445 instance Bin a => Bin [a]
6447 That is, just leave off the "where" clause. Of course, you can put in the
6448 where clause and over-ride whichever methods you please.
6452 <title> Using generics </title>
6453 <para>To use generics you need to</para>
6456 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6457 <option>-XGenerics</option> (to generate extra per-data-type code),
6458 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6462 <para>Import the module <literal>Generics</literal> from the
6463 <literal>lang</literal> package. This import brings into
6464 scope the data types <literal>Unit</literal>,
6465 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6466 don't need this import if you don't mention these types
6467 explicitly; for example, if you are simply giving instance
6468 declarations.)</para>
6473 <sect2> <title> Changes wrt the paper </title>
6475 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6476 can be written infix (indeed, you can now use
6477 any operator starting in a colon as an infix type constructor). Also note that
6478 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6479 Finally, note that the syntax of the type patterns in the class declaration
6480 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6481 alone would ambiguous when they appear on right hand sides (an extension we
6482 anticipate wanting).
6486 <sect2> <title>Terminology and restrictions</title>
6488 Terminology. A "generic default method" in a class declaration
6489 is one that is defined using type patterns as above.
6490 A "polymorphic default method" is a default method defined as in Haskell 98.
6491 A "generic class declaration" is a class declaration with at least one
6492 generic default method.
6500 Alas, we do not yet implement the stuff about constructor names and
6507 A generic class can have only one parameter; you can't have a generic
6508 multi-parameter class.
6514 A default method must be defined entirely using type patterns, or entirely
6515 without. So this is illegal:
6518 op :: a -> (a, Bool)
6519 op {| Unit |} Unit = (Unit, True)
6522 However it is perfectly OK for some methods of a generic class to have
6523 generic default methods and others to have polymorphic default methods.
6529 The type variable(s) in the type pattern for a generic method declaration
6530 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:
6534 op {| p :*: q |} (x :*: y) = op (x :: p)
6542 The type patterns in a generic default method must take one of the forms:
6548 where "a" and "b" are type variables. Furthermore, all the type patterns for
6549 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6550 must use the same type variables. So this is illegal:
6554 op {| a :+: b |} (Inl x) = True
6555 op {| p :+: q |} (Inr y) = False
6557 The type patterns must be identical, even in equations for different methods of the class.
6558 So this too is illegal:
6562 op1 {| a :*: b |} (x :*: y) = True
6565 op2 {| p :*: q |} (x :*: y) = False
6567 (The reason for this restriction is that we gather all the equations for a particular type consructor
6568 into a single generic instance declaration.)
6574 A generic method declaration must give a case for each of the three type constructors.
6580 The type for a generic method can be built only from:
6582 <listitem> <para> Function arrows </para> </listitem>
6583 <listitem> <para> Type variables </para> </listitem>
6584 <listitem> <para> Tuples </para> </listitem>
6585 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6587 Here are some example type signatures for generic methods:
6590 op2 :: Bool -> (a,Bool)
6591 op3 :: [Int] -> a -> a
6594 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6598 This restriction is an implementation restriction: we just havn't got around to
6599 implementing the necessary bidirectional maps over arbitrary type constructors.
6600 It would be relatively easy to add specific type constructors, such as Maybe and list,
6601 to the ones that are allowed.</para>
6606 In an instance declaration for a generic class, the idea is that the compiler
6607 will fill in the methods for you, based on the generic templates. However it can only
6612 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6617 No constructor of the instance type has unboxed fields.
6621 (Of course, these things can only arise if you are already using GHC extensions.)
6622 However, you can still give an instance declarations for types which break these rules,
6623 provided you give explicit code to override any generic default methods.
6631 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6632 what the compiler does with generic declarations.
6637 <sect2> <title> Another example </title>
6639 Just to finish with, here's another example I rather like:
6643 nCons {| Unit |} _ = 1
6644 nCons {| a :*: b |} _ = 1
6645 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6648 tag {| Unit |} _ = 1
6649 tag {| a :*: b |} _ = 1
6650 tag {| a :+: b |} (Inl x) = tag x
6651 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6657 <sect1 id="monomorphism">
6658 <title>Control over monomorphism</title>
6660 <para>GHC supports two flags that control the way in which generalisation is
6661 carried out at let and where bindings.
6665 <title>Switching off the dreaded Monomorphism Restriction</title>
6666 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
6668 <para>Haskell's monomorphism restriction (see
6669 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6671 of the Haskell Report)
6672 can be completely switched off by
6673 <option>-XNoMonomorphismRestriction</option>.
6678 <title>Monomorphic pattern bindings</title>
6679 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
6680 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
6682 <para> As an experimental change, we are exploring the possibility of
6683 making pattern bindings monomorphic; that is, not generalised at all.
6684 A pattern binding is a binding whose LHS has no function arguments,
6685 and is not a simple variable. For example:
6687 f x = x -- Not a pattern binding
6688 f = \x -> x -- Not a pattern binding
6689 f :: Int -> Int = \x -> x -- Not a pattern binding
6691 (g,h) = e -- A pattern binding
6692 (f) = e -- A pattern binding
6693 [x] = e -- A pattern binding
6695 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6696 default</emphasis>. Use <option>-XMonoPatBinds</option> to recover the
6705 ;;; Local Variables: ***
6707 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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