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>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum plus deprecated
110 syntax of previous versions of the FFI for backwards
111 compatibility.</para>
113 <para>New reserved words: <literal>foreign</literal>.</para>
119 <option>-fno-monomorphism-restriction</option>:
120 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
123 <para> Switch off the Haskell 98 monomorphism restriction.
124 Independent of the <option>-fglasgow-exts</option>
131 <option>-fallow-overlapping-instances</option>
132 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
135 <option>-fallow-undecidable-instances</option>
136 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
139 <option>-fallow-incoherent-instances</option>
140 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
143 <option>-fcontext-stack</option>
144 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
147 <para> See <xref linkend="instance-decls"/>. Only relevant
148 if you also use <option>-fglasgow-exts</option>.</para>
154 <option>-finline-phase</option>
155 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
158 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
159 you also use <option>-fglasgow-exts</option>.</para>
165 <option>-farrows</option>
166 <indexterm><primary><option>-farrows</option></primary></indexterm>
169 <para>See <xref linkend="arrow-notation"/>. Independent of
170 <option>-fglasgow-exts</option>.</para>
172 <para>New reserved words/symbols: <literal>rec</literal>,
173 <literal>proc</literal>, <literal>-<</literal>,
174 <literal>>-</literal>, <literal>-<<</literal>,
175 <literal>>>-</literal>.</para>
177 <para>Other syntax stolen: <literal>(|</literal>,
178 <literal>|)</literal>.</para>
184 <option>-fgenerics</option>
185 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
188 <para>See <xref linkend="generic-classes"/>. Independent of
189 <option>-fglasgow-exts</option>.</para>
194 <term><option>-fno-implicit-prelude</option></term>
196 <para><indexterm><primary>-fno-implicit-prelude
197 option</primary></indexterm> GHC normally imports
198 <filename>Prelude.hi</filename> files for you. If you'd
199 rather it didn't, then give it a
200 <option>-fno-implicit-prelude</option> option. The idea is
201 that you can then import a Prelude of your own. (But don't
202 call it <literal>Prelude</literal>; the Haskell module
203 namespace is flat, and you must not conflict with any
204 Prelude module.)</para>
206 <para>Even though you have not imported the Prelude, most of
207 the built-in syntax still refers to the built-in Haskell
208 Prelude types and values, as specified by the Haskell
209 Report. For example, the type <literal>[Int]</literal>
210 still means <literal>Prelude.[] Int</literal>; tuples
211 continue to refer to the standard Prelude tuples; the
212 translation for list comprehensions continues to use
213 <literal>Prelude.map</literal> etc.</para>
215 <para>However, <option>-fno-implicit-prelude</option> does
216 change the handling of certain built-in syntax: see <xref
217 linkend="rebindable-syntax"/>.</para>
222 <term><option>-fth</option></term>
224 <para>Enables Template Haskell (see <xref
225 linkend="template-haskell"/>). Currently also implied by
226 <option>-fglasgow-exts</option>.</para>
228 <para>Syntax stolen: <literal>[|</literal>,
229 <literal>[e|</literal>, <literal>[p|</literal>,
230 <literal>[d|</literal>, <literal>[t|</literal>,
231 <literal>$(</literal>,
232 <literal>$<replaceable>varid</replaceable></literal>.</para>
237 <term><option>-fimplicit-params</option></term>
239 <para>Enables implicit parameters (see <xref
240 linkend="implicit-parameters"/>). Currently also implied by
241 <option>-fglasgow-exts</option>.</para>
244 <literal>?<replaceable>varid</replaceable></literal>,
245 <literal>%<replaceable>varid</replaceable></literal>.</para>
252 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
253 <!-- included from primitives.sgml -->
254 <!-- &primitives; -->
255 <sect1 id="primitives">
256 <title>Unboxed types and primitive operations</title>
258 <para>GHC is built on a raft of primitive data types and operations.
259 While you really can use this stuff to write fast code,
260 we generally find it a lot less painful, and more satisfying in the
261 long run, to use higher-level language features and libraries. With
262 any luck, the code you write will be optimised to the efficient
263 unboxed version in any case. And if it isn't, we'd like to know
266 <para>We do not currently have good, up-to-date documentation about the
267 primitives, perhaps because they are mainly intended for internal use.
268 There used to be a long section about them here in the User Guide, but it
269 became out of date, and wrong information is worse than none.</para>
271 <para>The Real Truth about what primitive types there are, and what operations
272 work over those types, is held in the file
273 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
274 This file is used directly to generate GHC's primitive-operation definitions, so
275 it is always correct! It is also intended for processing into text.</para>
278 the result of such processing is part of the description of the
280 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
281 Core language</ulink>.
282 So that document is a good place to look for a type-set version.
283 We would be very happy if someone wanted to volunteer to produce an SGML
284 back end to the program that processes <filename>primops.txt</filename> so that
285 we could include the results here in the User Guide.</para>
287 <para>What follows here is a brief summary of some main points.</para>
289 <sect2 id="glasgow-unboxed">
294 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
297 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
298 that values of that type are represented by a pointer to a heap
299 object. The representation of a Haskell <literal>Int</literal>, for
300 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
301 type, however, is represented by the value itself, no pointers or heap
302 allocation are involved.
306 Unboxed types correspond to the “raw machine” types you
307 would use in C: <literal>Int#</literal> (long int),
308 <literal>Double#</literal> (double), <literal>Addr#</literal>
309 (void *), etc. The <emphasis>primitive operations</emphasis>
310 (PrimOps) on these types are what you might expect; e.g.,
311 <literal>(+#)</literal> is addition on
312 <literal>Int#</literal>s, and is the machine-addition that we all
313 know and love—usually one instruction.
317 Primitive (unboxed) types cannot be defined in Haskell, and are
318 therefore built into the language and compiler. Primitive types are
319 always unlifted; that is, a value of a primitive type cannot be
320 bottom. We use the convention that primitive types, values, and
321 operations have a <literal>#</literal> suffix.
325 Primitive values are often represented by a simple bit-pattern, such
326 as <literal>Int#</literal>, <literal>Float#</literal>,
327 <literal>Double#</literal>. But this is not necessarily the case:
328 a primitive value might be represented by a pointer to a
329 heap-allocated object. Examples include
330 <literal>Array#</literal>, the type of primitive arrays. A
331 primitive array is heap-allocated because it is too big a value to fit
332 in a register, and would be too expensive to copy around; in a sense,
333 it is accidental that it is represented by a pointer. If a pointer
334 represents a primitive value, then it really does point to that value:
335 no unevaluated thunks, no indirections…nothing can be at the
336 other end of the pointer than the primitive value.
340 There are some restrictions on the use of primitive types, the main
341 one being that you can't pass a primitive value to a polymorphic
342 function or store one in a polymorphic data type. This rules out
343 things like <literal>[Int#]</literal> (i.e. lists of primitive
344 integers). The reason for this restriction is that polymorphic
345 arguments and constructor fields are assumed to be pointers: if an
346 unboxed integer is stored in one of these, the garbage collector would
347 attempt to follow it, leading to unpredictable space leaks. Or a
348 <function>seq</function> operation on the polymorphic component may
349 attempt to dereference the pointer, with disastrous results. Even
350 worse, the unboxed value might be larger than a pointer
351 (<literal>Double#</literal> for instance).
355 Nevertheless, A numerically-intensive program using unboxed types can
356 go a <emphasis>lot</emphasis> faster than its “standard”
357 counterpart—we saw a threefold speedup on one example.
362 <sect2 id="unboxed-tuples">
363 <title>Unboxed Tuples
367 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
368 they're available by default with <option>-fglasgow-exts</option>. An
369 unboxed tuple looks like this:
381 where <literal>e_1..e_n</literal> are expressions of any
382 type (primitive or non-primitive). The type of an unboxed tuple looks
387 Unboxed tuples are used for functions that need to return multiple
388 values, but they avoid the heap allocation normally associated with
389 using fully-fledged tuples. When an unboxed tuple is returned, the
390 components are put directly into registers or on the stack; the
391 unboxed tuple itself does not have a composite representation. Many
392 of the primitive operations listed in this section return unboxed
397 There are some pretty stringent restrictions on the use of unboxed tuples:
406 Unboxed tuple types are subject to the same restrictions as
407 other unboxed types; i.e. they may not be stored in polymorphic data
408 structures or passed to polymorphic functions.
415 Unboxed tuples may only be constructed as the direct result of
416 a function, and may only be deconstructed with a <literal>case</literal> expression.
417 eg. the following are valid:
421 f x y = (# x+1, y-1 #)
422 g x = case f x x of { (# a, b #) -> a + b }
426 but the following are invalid:
440 No variable can have an unboxed tuple type. This is illegal:
444 f :: (# Int, Int #) -> (# Int, Int #)
449 because <literal>x</literal> has an unboxed tuple type.
459 Note: we may relax some of these restrictions in the future.
463 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
464 tuples to avoid unnecessary allocation during sequences of operations.
471 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
473 <sect1 id="syntax-extns">
474 <title>Syntactic extensions</title>
476 <!-- ====================== HIERARCHICAL MODULES ======================= -->
478 <sect2 id="hierarchical-modules">
479 <title>Hierarchical Modules</title>
481 <para>GHC supports a small extension to the syntax of module
482 names: a module name is allowed to contain a dot
483 <literal>‘.’</literal>. This is also known as the
484 “hierarchical module namespace” extension, because
485 it extends the normally flat Haskell module namespace into a
486 more flexible hierarchy of modules.</para>
488 <para>This extension has very little impact on the language
489 itself; modules names are <emphasis>always</emphasis> fully
490 qualified, so you can just think of the fully qualified module
491 name as <quote>the module name</quote>. In particular, this
492 means that the full module name must be given after the
493 <literal>module</literal> keyword at the beginning of the
494 module; for example, the module <literal>A.B.C</literal> must
497 <programlisting>module A.B.C</programlisting>
500 <para>It is a common strategy to use the <literal>as</literal>
501 keyword to save some typing when using qualified names with
502 hierarchical modules. For example:</para>
505 import qualified Control.Monad.ST.Strict as ST
508 <para>For details on how GHC searches for source and interface
509 files in the presence of hierarchical modules, see <xref
510 linkend="search-path"/>.</para>
512 <para>GHC comes with a large collection of libraries arranged
513 hierarchically; see the accompanying library documentation.
514 There is an ongoing project to create and maintain a stable set
515 of <quote>core</quote> libraries used by several Haskell
516 compilers, and the libraries that GHC comes with represent the
517 current status of that project. For more details, see <ulink
518 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
519 Libraries</ulink>.</para>
523 <!-- ====================== PATTERN GUARDS ======================= -->
525 <sect2 id="pattern-guards">
526 <title>Pattern guards</title>
529 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
530 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.)
534 Suppose we have an abstract data type of finite maps, with a
538 lookup :: FiniteMap -> Int -> Maybe Int
541 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
542 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
546 clunky env var1 var2 | ok1 && ok2 = val1 + val2
547 | otherwise = var1 + var2
558 The auxiliary functions are
562 maybeToBool :: Maybe a -> Bool
563 maybeToBool (Just x) = True
564 maybeToBool Nothing = False
566 expectJust :: Maybe a -> a
567 expectJust (Just x) = x
568 expectJust Nothing = error "Unexpected Nothing"
572 What is <function>clunky</function> doing? The guard <literal>ok1 &&
573 ok2</literal> checks that both lookups succeed, using
574 <function>maybeToBool</function> to convert the <function>Maybe</function>
575 types to booleans. The (lazily evaluated) <function>expectJust</function>
576 calls extract the values from the results of the lookups, and binds the
577 returned values to <varname>val1</varname> and <varname>val2</varname>
578 respectively. If either lookup fails, then clunky takes the
579 <literal>otherwise</literal> case and returns the sum of its arguments.
583 This is certainly legal Haskell, but it is a tremendously verbose and
584 un-obvious way to achieve the desired effect. Arguably, a more direct way
585 to write clunky would be to use case expressions:
589 clunky env var1 var1 = case lookup env var1 of
591 Just val1 -> case lookup env var2 of
593 Just val2 -> val1 + val2
599 This is a bit shorter, but hardly better. Of course, we can rewrite any set
600 of pattern-matching, guarded equations as case expressions; that is
601 precisely what the compiler does when compiling equations! The reason that
602 Haskell provides guarded equations is because they allow us to write down
603 the cases we want to consider, one at a time, independently of each other.
604 This structure is hidden in the case version. Two of the right-hand sides
605 are really the same (<function>fail</function>), and the whole expression
606 tends to become more and more indented.
610 Here is how I would write clunky:
615 | Just val1 <- lookup env var1
616 , Just val2 <- lookup env var2
618 ...other equations for clunky...
622 The semantics should be clear enough. The qualifers are matched in order.
623 For a <literal><-</literal> qualifier, which I call a pattern guard, the
624 right hand side is evaluated and matched against the pattern on the left.
625 If the match fails then the whole guard fails and the next equation is
626 tried. If it succeeds, then the appropriate binding takes place, and the
627 next qualifier is matched, in the augmented environment. Unlike list
628 comprehensions, however, the type of the expression to the right of the
629 <literal><-</literal> is the same as the type of the pattern to its
630 left. The bindings introduced by pattern guards scope over all the
631 remaining guard qualifiers, and over the right hand side of the equation.
635 Just as with list comprehensions, boolean expressions can be freely mixed
636 with among the pattern guards. For example:
647 Haskell's current guards therefore emerge as a special case, in which the
648 qualifier list has just one element, a boolean expression.
652 <!-- ===================== Recursive do-notation =================== -->
654 <sect2 id="mdo-notation">
655 <title>The recursive do-notation
658 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
659 "A recursive do for Haskell",
660 Levent Erkok, John Launchbury",
661 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
664 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
665 that is, the variables bound in a do-expression are visible only in the textually following
666 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
667 group. It turns out that several applications can benefit from recursive bindings in
668 the do-notation, and this extension provides the necessary syntactic support.
671 Here is a simple (yet contrived) example:
674 import Control.Monad.Fix
676 justOnes = mdo xs <- Just (1:xs)
680 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
684 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
687 class Monad m => MonadFix m where
688 mfix :: (a -> m a) -> m a
691 The function <literal>mfix</literal>
692 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
693 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
694 For details, see the above mentioned reference.
697 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
698 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
699 for Haskell's internal state monad (strict and lazy, respectively).
702 There are three important points in using the recursive-do notation:
705 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
706 than <literal>do</literal>).
710 You should <literal>import Control.Monad.Fix</literal>.
711 (Note: Strictly speaking, this import is required only when you need to refer to the name
712 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
713 are encouraged to always import this module when using the mdo-notation.)
717 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
723 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
724 contains up to date information on recursive monadic bindings.
728 Historical note: The old implementation of the mdo-notation (and most
729 of the existing documents) used the name
730 <literal>MonadRec</literal> for the class and the corresponding library.
731 This name is not supported by GHC.
737 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
739 <sect2 id="parallel-list-comprehensions">
740 <title>Parallel List Comprehensions</title>
741 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
743 <indexterm><primary>parallel list comprehensions</primary>
746 <para>Parallel list comprehensions are a natural extension to list
747 comprehensions. List comprehensions can be thought of as a nice
748 syntax for writing maps and filters. Parallel comprehensions
749 extend this to include the zipWith family.</para>
751 <para>A parallel list comprehension has multiple independent
752 branches of qualifier lists, each separated by a `|' symbol. For
753 example, the following zips together two lists:</para>
756 [ (x, y) | x <- xs | y <- ys ]
759 <para>The behavior of parallel list comprehensions follows that of
760 zip, in that the resulting list will have the same length as the
761 shortest branch.</para>
763 <para>We can define parallel list comprehensions by translation to
764 regular comprehensions. Here's the basic idea:</para>
766 <para>Given a parallel comprehension of the form: </para>
769 [ e | p1 <- e11, p2 <- e12, ...
770 | q1 <- e21, q2 <- e22, ...
775 <para>This will be translated to: </para>
778 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
779 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
784 <para>where `zipN' is the appropriate zip for the given number of
789 <sect2 id="rebindable-syntax">
790 <title>Rebindable syntax</title>
793 <para>GHC allows most kinds of built-in syntax to be rebound by
794 the user, to facilitate replacing the <literal>Prelude</literal>
795 with a home-grown version, for example.</para>
797 <para>You may want to define your own numeric class
798 hierarchy. It completely defeats that purpose if the
799 literal "1" means "<literal>Prelude.fromInteger
800 1</literal>", which is what the Haskell Report specifies.
801 So the <option>-fno-implicit-prelude</option> flag causes
802 the following pieces of built-in syntax to refer to
803 <emphasis>whatever is in scope</emphasis>, not the Prelude
808 <para>Integer and fractional literals mean
809 "<literal>fromInteger 1</literal>" and
810 "<literal>fromRational 3.2</literal>", not the
811 Prelude-qualified versions; both in expressions and in
813 <para>However, the standard Prelude <literal>Eq</literal> class
814 is still used for the equality test necessary for literal patterns.</para>
818 <para>Negation (e.g. "<literal>- (f x)</literal>")
819 means "<literal>negate (f x)</literal>" (not
820 <literal>Prelude.negate</literal>).</para>
824 <para>In an n+k pattern, the standard Prelude
825 <literal>Ord</literal> class is still used for comparison,
826 but the necessary subtraction uses whatever
827 "<literal>(-)</literal>" is in scope (not
828 "<literal>Prelude.(-)</literal>").</para>
832 <para>"Do" notation is translated using whatever
833 functions <literal>(>>=)</literal>,
834 <literal>(>>)</literal>, <literal>fail</literal>, and
835 <literal>return</literal>, are in scope (not the Prelude
836 versions). List comprehensions, and parallel array
837 comprehensions, are unaffected. </para></listitem>
840 <para>Similarly recursive do notation (see
841 <xref linkend="mdo-notation"/>) uses whatever
842 <literal>mfix</literal> function is in scope, and arrow
843 notation (see <xref linkend="arrow-notation"/>)
844 uses whatever <literal>arr</literal>,
845 <literal>(>>>)</literal>, <literal>first</literal>,
846 <literal>app</literal>, <literal>(|||)</literal> and
847 <literal>loop</literal> functions are in scope.</para>
851 <para>The functions with these names that GHC finds in scope
852 must have types matching those of the originals, namely:
854 fromInteger :: Integer -> N
855 fromRational :: Rational -> N
858 (>>=) :: forall a b. M a -> (a -> M b) -> M b
859 (>>) :: forall a b. M a -> M b -> M b
860 return :: forall a. a -> M a
861 fail :: forall a. String -> M a
863 (Here <literal>N</literal> may be any type,
864 and <literal>M</literal> any type constructor.)</para>
866 <para>Be warned: this is an experimental facility, with
867 fewer checks than usual. Use <literal>-dcore-lint</literal>
868 to typecheck the desugared program. If Core Lint is happy
869 you should be all right.</para>
875 <!-- TYPE SYSTEM EXTENSIONS -->
876 <sect1 id="type-extensions">
877 <title>Type system extensions</title>
881 <title>Data types and type synonyms</title>
883 <sect3 id="nullary-types">
884 <title>Data types with no constructors</title>
886 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
887 a data type with no constructors. For example:</para>
891 data T a -- T :: * -> *
894 <para>Syntactically, the declaration lacks the "= constrs" part. The
895 type can be parameterised over types of any kind, but if the kind is
896 not <literal>*</literal> then an explicit kind annotation must be used
897 (see <xref linkend="sec-kinding"/>).</para>
899 <para>Such data types have only one value, namely bottom.
900 Nevertheless, they can be useful when defining "phantom types".</para>
903 <sect3 id="infix-tycons">
904 <title>Infix type constructors</title>
907 GHC allows type constructors to be operators, and to be written infix, very much
908 like expressions. More specifically:
911 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
912 The lexical syntax is the same as that for data constructors.
915 Types can be written infix. For example <literal>Int :*: Bool</literal>.
919 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
920 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
923 Fixities may be declared for type constructors just as for data constructors. However,
924 one cannot distinguish between the two in a fixity declaration; a fixity declaration
925 sets the fixity for a data constructor and the corresponding type constructor. For example:
929 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
930 and similarly for <literal>:*:</literal>.
931 <literal>Int `a` Bool</literal>.
934 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
937 Data type and type-synonym declarations can be written infix. E.g.
939 data a :*: b = Foo a b
940 type a :+: b = Either a b
944 The only thing that differs between operators in types and operators in expressions is that
945 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
946 are not allowed in types. Reason: the uniform thing to do would be to make them type
947 variables, but that's not very useful. A less uniform but more useful thing would be to
948 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
949 lists. So for now we just exclude them.
956 <sect3 id="type-synonyms">
957 <title>Liberalised type synonyms</title>
960 Type synonmys are like macros at the type level, and
961 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
962 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
964 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
965 in a type synonym, thus:
967 type Discard a = forall b. Show b => a -> b -> (a, String)
972 g :: Discard Int -> (Int,Bool) -- A rank-2 type
979 You can write an unboxed tuple in a type synonym:
981 type Pr = (# Int, Int #)
989 You can apply a type synonym to a forall type:
991 type Foo a = a -> a -> Bool
993 f :: Foo (forall b. b->b)
995 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
997 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1002 You can apply a type synonym to a partially applied type synonym:
1004 type Generic i o = forall x. i x -> o x
1007 foo :: Generic Id []
1009 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1011 foo :: forall x. x -> [x]
1019 GHC currently does kind checking before expanding synonyms (though even that
1023 After expanding type synonyms, GHC does validity checking on types, looking for
1024 the following mal-formedness which isn't detected simply by kind checking:
1027 Type constructor applied to a type involving for-alls.
1030 Unboxed tuple on left of an arrow.
1033 Partially-applied type synonym.
1037 this will be rejected:
1039 type Pr = (# Int, Int #)
1044 because GHC does not allow unboxed tuples on the left of a function arrow.
1049 <sect3 id="existential-quantification">
1050 <title>Existentially quantified data constructors
1054 The idea of using existential quantification in data type declarations
1055 was suggested by Laufer (I believe, thought doubtless someone will
1056 correct me), and implemented in Hope+. It's been in Lennart
1057 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1058 proved very useful. Here's the idea. Consider the declaration:
1064 data Foo = forall a. MkFoo a (a -> Bool)
1071 The data type <literal>Foo</literal> has two constructors with types:
1077 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1084 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1085 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1086 For example, the following expression is fine:
1092 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1098 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1099 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1100 isUpper</function> packages a character with a compatible function. These
1101 two things are each of type <literal>Foo</literal> and can be put in a list.
1105 What can we do with a value of type <literal>Foo</literal>?. In particular,
1106 what happens when we pattern-match on <function>MkFoo</function>?
1112 f (MkFoo val fn) = ???
1118 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1119 are compatible, the only (useful) thing we can do with them is to
1120 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1127 f (MkFoo val fn) = fn val
1133 What this allows us to do is to package heterogenous values
1134 together with a bunch of functions that manipulate them, and then treat
1135 that collection of packages in a uniform manner. You can express
1136 quite a bit of object-oriented-like programming this way.
1139 <sect4 id="existential">
1140 <title>Why existential?
1144 What has this to do with <emphasis>existential</emphasis> quantification?
1145 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1151 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1157 But Haskell programmers can safely think of the ordinary
1158 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1159 adding a new existential quantification construct.
1165 <title>Type classes</title>
1168 An easy extension (implemented in <command>hbc</command>) is to allow
1169 arbitrary contexts before the constructor. For example:
1175 data Baz = forall a. Eq a => Baz1 a a
1176 | forall b. Show b => Baz2 b (b -> b)
1182 The two constructors have the types you'd expect:
1188 Baz1 :: forall a. Eq a => a -> a -> Baz
1189 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1195 But when pattern matching on <function>Baz1</function> the matched values can be compared
1196 for equality, and when pattern matching on <function>Baz2</function> the first matched
1197 value can be converted to a string (as well as applying the function to it).
1198 So this program is legal:
1205 f (Baz1 p q) | p == q = "Yes"
1207 f (Baz2 v fn) = show (fn v)
1213 Operationally, in a dictionary-passing implementation, the
1214 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1215 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1216 extract it on pattern matching.
1220 Notice the way that the syntax fits smoothly with that used for
1221 universal quantification earlier.
1227 <title>Restrictions</title>
1230 There are several restrictions on the ways in which existentially-quantified
1231 constructors can be use.
1240 When pattern matching, each pattern match introduces a new,
1241 distinct, type for each existential type variable. These types cannot
1242 be unified with any other type, nor can they escape from the scope of
1243 the pattern match. For example, these fragments are incorrect:
1251 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1252 is the result of <function>f1</function>. One way to see why this is wrong is to
1253 ask what type <function>f1</function> has:
1257 f1 :: Foo -> a -- Weird!
1261 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1266 f1 :: forall a. Foo -> a -- Wrong!
1270 The original program is just plain wrong. Here's another sort of error
1274 f2 (Baz1 a b) (Baz1 p q) = a==q
1278 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1279 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1280 from the two <function>Baz1</function> constructors.
1288 You can't pattern-match on an existentially quantified
1289 constructor in a <literal>let</literal> or <literal>where</literal> group of
1290 bindings. So this is illegal:
1294 f3 x = a==b where { Baz1 a b = x }
1297 Instead, use a <literal>case</literal> expression:
1300 f3 x = case x of Baz1 a b -> a==b
1303 In general, you can only pattern-match
1304 on an existentially-quantified constructor in a <literal>case</literal> expression or
1305 in the patterns of a function definition.
1307 The reason for this restriction is really an implementation one.
1308 Type-checking binding groups is already a nightmare without
1309 existentials complicating the picture. Also an existential pattern
1310 binding at the top level of a module doesn't make sense, because it's
1311 not clear how to prevent the existentially-quantified type "escaping".
1312 So for now, there's a simple-to-state restriction. We'll see how
1320 You can't use existential quantification for <literal>newtype</literal>
1321 declarations. So this is illegal:
1325 newtype T = forall a. Ord a => MkT a
1329 Reason: a value of type <literal>T</literal> must be represented as a
1330 pair of a dictionary for <literal>Ord t</literal> and a value of type
1331 <literal>t</literal>. That contradicts the idea that
1332 <literal>newtype</literal> should have no concrete representation.
1333 You can get just the same efficiency and effect by using
1334 <literal>data</literal> instead of <literal>newtype</literal>. If
1335 there is no overloading involved, then there is more of a case for
1336 allowing an existentially-quantified <literal>newtype</literal>,
1337 because the <literal>data</literal> version does carry an
1338 implementation cost, but single-field existentially quantified
1339 constructors aren't much use. So the simple restriction (no
1340 existential stuff on <literal>newtype</literal>) stands, unless there
1341 are convincing reasons to change it.
1349 You can't use <literal>deriving</literal> to define instances of a
1350 data type with existentially quantified data constructors.
1352 Reason: in most cases it would not make sense. For example:#
1355 data T = forall a. MkT [a] deriving( Eq )
1358 To derive <literal>Eq</literal> in the standard way we would need to have equality
1359 between the single component of two <function>MkT</function> constructors:
1363 (MkT a) == (MkT b) = ???
1366 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1367 It's just about possible to imagine examples in which the derived instance
1368 would make sense, but it seems altogether simpler simply to prohibit such
1369 declarations. Define your own instances!
1384 <sect2 id="multi-param-type-classes">
1385 <title>Class declarations</title>
1388 This section documents GHC's implementation of multi-parameter type
1389 classes. There's lots of background in the paper <ulink
1390 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1391 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1392 Jones, Erik Meijer).
1395 There are the following constraints on class declarations:
1400 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1404 class Collection c a where
1405 union :: c a -> c a -> c a
1416 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1417 of "acyclic" involves only the superclass relationships. For example,
1423 op :: D b => a -> b -> b
1426 class C a => D a where { ... }
1430 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1431 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1432 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1439 <emphasis>There are no restrictions on the context in a class declaration
1440 (which introduces superclasses), except that the class hierarchy must
1441 be acyclic</emphasis>. So these class declarations are OK:
1445 class Functor (m k) => FiniteMap m k where
1448 class (Monad m, Monad (t m)) => Transform t m where
1449 lift :: m a -> (t m) a
1459 <emphasis>All of the class type variables must be reachable (in the sense
1460 mentioned in <xref linkend="type-restrictions"/>)
1461 from the free varibles of each method type
1462 </emphasis>. For example:
1466 class Coll s a where
1468 insert :: s -> a -> s
1472 is not OK, because the type of <literal>empty</literal> doesn't mention
1473 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1474 types, and has the same motivation.
1476 Sometimes, offending class declarations exhibit misunderstandings. For
1477 example, <literal>Coll</literal> might be rewritten
1481 class Coll s a where
1483 insert :: s a -> a -> s a
1487 which makes the connection between the type of a collection of
1488 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1489 Occasionally this really doesn't work, in which case you can split the
1497 class CollE s => Coll s a where
1498 insert :: s -> a -> s
1508 <sect3 id="class-method-types">
1509 <title>Class method types</title>
1511 Haskell 98 prohibits class method types to mention constraints on the
1512 class type variable, thus:
1515 fromList :: [a] -> s a
1516 elem :: Eq a => a -> s a -> Bool
1518 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1519 contains the constraint <literal>Eq a</literal>, constrains only the
1520 class type variable (in this case <literal>a</literal>).
1523 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1530 <sect2 id="type-restrictions">
1531 <title>Type signatures</title>
1533 <sect3><title>The context of a type signature</title>
1535 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1536 the form <emphasis>(class type-variable)</emphasis> or
1537 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1538 these type signatures are perfectly OK
1541 g :: Ord (T a ()) => ...
1545 GHC imposes the following restrictions on the constraints in a type signature.
1549 forall tv1..tvn (c1, ...,cn) => type
1552 (Here, we write the "foralls" explicitly, although the Haskell source
1553 language omits them; in Haskell 98, all the free type variables of an
1554 explicit source-language type signature are universally quantified,
1555 except for the class type variables in a class declaration. However,
1556 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1565 <emphasis>Each universally quantified type variable
1566 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1568 A type variable <literal>a</literal> is "reachable" if it it appears
1569 in the same constraint as either a type variable free in in
1570 <literal>type</literal>, or another reachable type variable.
1571 A value with a type that does not obey
1572 this reachability restriction cannot be used without introducing
1573 ambiguity; that is why the type is rejected.
1574 Here, for example, is an illegal type:
1578 forall a. Eq a => Int
1582 When a value with this type was used, the constraint <literal>Eq tv</literal>
1583 would be introduced where <literal>tv</literal> is a fresh type variable, and
1584 (in the dictionary-translation implementation) the value would be
1585 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1586 can never know which instance of <literal>Eq</literal> to use because we never
1587 get any more information about <literal>tv</literal>.
1591 that the reachability condition is weaker than saying that <literal>a</literal> is
1592 functionally dependendent on a type variable free in
1593 <literal>type</literal> (see <xref
1594 linkend="functional-dependencies"/>). The reason for this is there
1595 might be a "hidden" dependency, in a superclass perhaps. So
1596 "reachable" is a conservative approximation to "functionally dependent".
1597 For example, consider:
1599 class C a b | a -> b where ...
1600 class C a b => D a b where ...
1601 f :: forall a b. D a b => a -> a
1603 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1604 but that is not immediately apparent from <literal>f</literal>'s type.
1610 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1611 universally quantified type variables <literal>tvi</literal></emphasis>.
1613 For example, this type is OK because <literal>C a b</literal> mentions the
1614 universally quantified type variable <literal>b</literal>:
1618 forall a. C a b => burble
1622 The next type is illegal because the constraint <literal>Eq b</literal> does not
1623 mention <literal>a</literal>:
1627 forall a. Eq b => burble
1631 The reason for this restriction is milder than the other one. The
1632 excluded types are never useful or necessary (because the offending
1633 context doesn't need to be witnessed at this point; it can be floated
1634 out). Furthermore, floating them out increases sharing. Lastly,
1635 excluding them is a conservative choice; it leaves a patch of
1636 territory free in case we need it later.
1647 <title>For-all hoisting</title>
1649 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1650 end of an arrow, thus:
1652 type Discard a = forall b. a -> b -> a
1654 g :: Int -> Discard Int
1657 Simply expanding the type synonym would give
1659 g :: Int -> (forall b. Int -> b -> Int)
1661 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1663 g :: forall b. Int -> Int -> b -> Int
1665 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1666 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1667 performs the transformation:</emphasis>
1669 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1671 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1673 (In fact, GHC tries to retain as much synonym information as possible for use in
1674 error messages, but that is a usability issue.) This rule applies, of course, whether
1675 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1676 valid way to write <literal>g</literal>'s type signature:
1678 g :: Int -> Int -> forall b. b -> Int
1682 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1685 type Foo a = (?x::Int) => Bool -> a
1690 g :: (?x::Int) => Bool -> Bool -> Int
1698 <sect2 id="instance-decls">
1699 <title>Instance declarations</title>
1702 <title>Overlapping instances</title>
1704 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1709 instance context1 => C type1 where ...
1710 instance context2 => C type2 where ...
1713 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
1716 However, if you give the command line option
1717 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1718 option</primary></indexterm> then overlapping instance declarations are permitted.
1719 However, GHC arranges never to commit to using an instance declaration
1720 if another instance declaration also applies, either now or later.
1726 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1732 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1733 (but not identical to <literal>type1</literal>), or vice versa.
1737 Notice that these rules
1742 make it clear which instance decl to use
1743 (pick the most specific one that matches)
1750 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1751 Reason: you can pick which instance decl
1752 "matches" based on the type.
1757 However the rules are over-conservative. Two instance declarations can overlap,
1758 but it can still be clear in particular situations which to use. For example:
1760 instance C (Int,a) where ...
1761 instance C (a,Bool) where ...
1763 These are rejected by GHC's rules, but it is clear what to do when trying
1764 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1765 cannot apply. Yell if this restriction bites you.
1768 GHC is also conservative about committing to an overlapping instance. For example:
1770 class C a where { op :: a -> a }
1771 instance C [Int] where ...
1772 instance C a => C [a] where ...
1774 f :: C b => [b] -> [b]
1777 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1778 GHC does not commit to the second instance declaration, because in a paricular
1779 call of f, b might be instantiate to Int, so the first instance declaration
1780 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1781 GHC will instead silently pick the second instance, without complaining about
1782 the problem of subsequent instantiations.
1785 Regrettably, GHC doesn't guarantee to detect overlapping instance
1786 declarations if they appear in different modules. GHC can "see" the
1787 instance declarations in the transitive closure of all the modules
1788 imported by the one being compiled, so it can "see" all instance decls
1789 when it is compiling <literal>Main</literal>. However, it currently chooses not
1790 to look at ones that can't possibly be of use in the module currently
1791 being compiled, in the interests of efficiency. (Perhaps we should
1792 change that decision, at least for <literal>Main</literal>.)
1797 <title>Type synonyms in the instance head</title>
1800 <emphasis>Unlike Haskell 98, instance heads may use type
1801 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1802 As always, using a type synonym is just shorthand for
1803 writing the RHS of the type synonym definition. For example:
1807 type Point = (Int,Int)
1808 instance C Point where ...
1809 instance C [Point] where ...
1813 is legal. However, if you added
1817 instance C (Int,Int) where ...
1821 as well, then the compiler will complain about the overlapping
1822 (actually, identical) instance declarations. As always, type synonyms
1823 must be fully applied. You cannot, for example, write:
1828 instance Monad P where ...
1832 This design decision is independent of all the others, and easily
1833 reversed, but it makes sense to me.
1838 <sect3 id="undecidable-instances">
1839 <title>Undecidable instances</title>
1841 <para>An instance declaration must normally obey the following rules:
1843 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1844 an instance declaration <emphasis>must not</emphasis> be a type variable.
1845 For example, these are OK:
1848 instance C Int a where ...
1850 instance D (Int, Int) where ...
1852 instance E [[a]] where ...
1856 instance F a where ...
1858 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1859 For example, this is OK:
1861 instance Stateful (ST s) (MutVar s) where ...
1868 <para>All of the types in the <emphasis>context</emphasis> of
1869 an instance declaration <emphasis>must</emphasis> be type variables.
1872 instance C a b => Eq (a,b) where ...
1876 instance C Int b => Foo b where ...
1882 These restrictions ensure that
1883 context reduction terminates: each reduction step removes one type
1884 constructor. For example, the following would make the type checker
1885 loop if it wasn't excluded:
1887 instance C a => C a where ...
1889 There are two situations in which the rule is a bit of a pain. First,
1890 if one allows overlapping instance declarations then it's quite
1891 convenient to have a "default instance" declaration that applies if
1892 something more specific does not:
1901 Second, sometimes you might want to use the following to get the
1902 effect of a "class synonym":
1906 class (C1 a, C2 a, C3 a) => C a where { }
1908 instance (C1 a, C2 a, C3 a) => C a where { }
1912 This allows you to write shorter signatures:
1924 f :: (C1 a, C2 a, C3 a) => ...
1928 Voluminous correspondence on the Haskell mailing list has convinced me
1929 that it's worth experimenting with more liberal rules. If you use
1930 the experimental flag <option>-fallow-undecidable-instances</option>
1931 <indexterm><primary>-fallow-undecidable-instances
1932 option</primary></indexterm>, you can use arbitrary
1933 types in both an instance context and instance head. Termination is ensured by having a
1934 fixed-depth recursion stack. If you exceed the stack depth you get a
1935 sort of backtrace, and the opportunity to increase the stack depth
1936 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1939 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1940 allowing these idioms interesting idioms.
1947 <sect2 id="implicit-parameters">
1948 <title>Implicit parameters</title>
1950 <para> Implicit paramters are implemented as described in
1951 "Implicit parameters: dynamic scoping with static types",
1952 J Lewis, MB Shields, E Meijer, J Launchbury,
1953 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1957 <para>(Most of the following, stil rather incomplete, documentation is
1958 due to Jeff Lewis.)</para>
1960 <para>Implicit parameter support is enabled with the option
1961 <option>-fimplicit-params</option>.</para>
1964 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1965 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1966 context. In Haskell, all variables are statically bound. Dynamic
1967 binding of variables is a notion that goes back to Lisp, but was later
1968 discarded in more modern incarnations, such as Scheme. Dynamic binding
1969 can be very confusing in an untyped language, and unfortunately, typed
1970 languages, in particular Hindley-Milner typed languages like Haskell,
1971 only support static scoping of variables.
1974 However, by a simple extension to the type class system of Haskell, we
1975 can support dynamic binding. Basically, we express the use of a
1976 dynamically bound variable as a constraint on the type. These
1977 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1978 function uses a dynamically-bound variable <literal>?x</literal>
1979 of type <literal>t'</literal>". For
1980 example, the following expresses the type of a sort function,
1981 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1983 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1985 The dynamic binding constraints are just a new form of predicate in the type class system.
1988 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1989 where <literal>x</literal> is
1990 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1991 Use of this construct also introduces a new
1992 dynamic-binding constraint in the type of the expression.
1993 For example, the following definition
1994 shows how we can define an implicitly parameterized sort function in
1995 terms of an explicitly parameterized <literal>sortBy</literal> function:
1997 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1999 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2005 <title>Implicit-parameter type constraints</title>
2007 Dynamic binding constraints behave just like other type class
2008 constraints in that they are automatically propagated. Thus, when a
2009 function is used, its implicit parameters are inherited by the
2010 function that called it. For example, our <literal>sort</literal> function might be used
2011 to pick out the least value in a list:
2013 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2014 least xs = fst (sort xs)
2016 Without lifting a finger, the <literal>?cmp</literal> parameter is
2017 propagated to become a parameter of <literal>least</literal> as well. With explicit
2018 parameters, the default is that parameters must always be explicit
2019 propagated. With implicit parameters, the default is to always
2023 An implicit-parameter type constraint differs from other type class constraints in the
2024 following way: All uses of a particular implicit parameter must have
2025 the same type. This means that the type of <literal>(?x, ?x)</literal>
2026 is <literal>(?x::a) => (a,a)</literal>, and not
2027 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2031 <para> You can't have an implicit parameter in the context of a class or instance
2032 declaration. For example, both these declarations are illegal:
2034 class (?x::Int) => C a where ...
2035 instance (?x::a) => Foo [a] where ...
2037 Reason: exactly which implicit parameter you pick up depends on exactly where
2038 you invoke a function. But the ``invocation'' of instance declarations is done
2039 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2040 Easiest thing is to outlaw the offending types.</para>
2042 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2044 f :: (?x :: [a]) => Int -> Int
2047 g :: (Read a, Show a) => String -> String
2050 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2051 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2052 quite unambiguous, and fixes the type <literal>a</literal>.
2057 <title>Implicit-parameter bindings</title>
2060 An implicit parameter is <emphasis>bound</emphasis> using the standard
2061 <literal>let</literal> or <literal>where</literal> binding forms.
2062 For example, we define the <literal>min</literal> function by binding
2063 <literal>cmp</literal>.
2066 min = let ?cmp = (<=) in least
2070 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2071 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2072 (including in a list comprehension, or do-notation, or pattern guards),
2073 or a <literal>where</literal> clause.
2074 Note the following points:
2077 An implicit-parameter binding group must be a
2078 collection of simple bindings to implicit-style variables (no
2079 function-style bindings, and no type signatures); these bindings are
2080 neither polymorphic or recursive.
2083 You may not mix implicit-parameter bindings with ordinary bindings in a
2084 single <literal>let</literal>
2085 expression; use two nested <literal>let</literal>s instead.
2086 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2090 You may put multiple implicit-parameter bindings in a
2091 single binding group; but they are <emphasis>not</emphasis> treated
2092 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2093 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2094 parameter. The bindings are not nested, and may be re-ordered without changing
2095 the meaning of the program.
2096 For example, consider:
2098 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2100 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2101 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2103 f :: (?x::Int) => Int -> Int
2112 <sect2 id="linear-implicit-parameters">
2113 <title>Linear implicit parameters</title>
2115 Linear implicit parameters are an idea developed by Koen Claessen,
2116 Mark Shields, and Simon PJ. They address the long-standing
2117 problem that monads seem over-kill for certain sorts of problem, notably:
2120 <listitem> <para> distributing a supply of unique names </para> </listitem>
2121 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2122 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2126 Linear implicit parameters are just like ordinary implicit parameters,
2127 except that they are "linear" -- that is, they cannot be copied, and
2128 must be explicitly "split" instead. Linear implicit parameters are
2129 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2130 (The '/' in the '%' suggests the split!)
2135 import GHC.Exts( Splittable )
2137 data NameSupply = ...
2139 splitNS :: NameSupply -> (NameSupply, NameSupply)
2140 newName :: NameSupply -> Name
2142 instance Splittable NameSupply where
2146 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2147 f env (Lam x e) = Lam x' (f env e)
2150 env' = extend env x x'
2151 ...more equations for f...
2153 Notice that the implicit parameter %ns is consumed
2155 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2156 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2160 So the translation done by the type checker makes
2161 the parameter explicit:
2163 f :: NameSupply -> Env -> Expr -> Expr
2164 f ns env (Lam x e) = Lam x' (f ns1 env e)
2166 (ns1,ns2) = splitNS ns
2168 env = extend env x x'
2170 Notice the call to 'split' introduced by the type checker.
2171 How did it know to use 'splitNS'? Because what it really did
2172 was to introduce a call to the overloaded function 'split',
2173 defined by the class <literal>Splittable</literal>:
2175 class Splittable a where
2178 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2179 split for name supplies. But we can simply write
2185 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2187 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2188 <literal>GHC.Exts</literal>.
2193 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2194 are entirely distinct implicit parameters: you
2195 can use them together and they won't intefere with each other. </para>
2198 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2200 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2201 in the context of a class or instance declaration. </para></listitem>
2205 <sect3><title>Warnings</title>
2208 The monomorphism restriction is even more important than usual.
2209 Consider the example above:
2211 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2212 f env (Lam x e) = Lam x' (f env e)
2215 env' = extend env x x'
2217 If we replaced the two occurrences of x' by (newName %ns), which is
2218 usually a harmless thing to do, we get:
2220 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2221 f env (Lam x e) = Lam (newName %ns) (f env e)
2223 env' = extend env x (newName %ns)
2225 But now the name supply is consumed in <emphasis>three</emphasis> places
2226 (the two calls to newName,and the recursive call to f), so
2227 the result is utterly different. Urk! We don't even have
2231 Well, this is an experimental change. With implicit
2232 parameters we have already lost beta reduction anyway, and
2233 (as John Launchbury puts it) we can't sensibly reason about
2234 Haskell programs without knowing their typing.
2239 <sect3><title>Recursive functions</title>
2240 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2243 foo :: %x::T => Int -> [Int]
2245 foo n = %x : foo (n-1)
2247 where T is some type in class Splittable.</para>
2249 Do you get a list of all the same T's or all different T's
2250 (assuming that split gives two distinct T's back)?
2252 If you supply the type signature, taking advantage of polymorphic
2253 recursion, you get what you'd probably expect. Here's the
2254 translated term, where the implicit param is made explicit:
2257 foo x n = let (x1,x2) = split x
2258 in x1 : foo x2 (n-1)
2260 But if you don't supply a type signature, GHC uses the Hindley
2261 Milner trick of using a single monomorphic instance of the function
2262 for the recursive calls. That is what makes Hindley Milner type inference
2263 work. So the translation becomes
2267 foom n = x : foom (n-1)
2271 Result: 'x' is not split, and you get a list of identical T's. So the
2272 semantics of the program depends on whether or not foo has a type signature.
2275 You may say that this is a good reason to dislike linear implicit parameters
2276 and you'd be right. That is why they are an experimental feature.
2282 <sect2 id="functional-dependencies">
2283 <title>Functional dependencies
2286 <para> Functional dependencies are implemented as described by Mark Jones
2287 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2288 In Proceedings of the 9th European Symposium on Programming,
2289 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2293 Functional dependencies are introduced by a vertical bar in the syntax of a
2294 class declaration; e.g.
2296 class (Monad m) => MonadState s m | m -> s where ...
2298 class Foo a b c | a b -> c where ...
2300 There should be more documentation, but there isn't (yet). Yell if you need it.
2306 <sect2 id="sec-kinding">
2307 <title>Explicitly-kinded quantification</title>
2310 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2311 to give the kind explicitly as (machine-checked) documentation,
2312 just as it is nice to give a type signature for a function. On some occasions,
2313 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2314 John Hughes had to define the data type:
2316 data Set cxt a = Set [a]
2317 | Unused (cxt a -> ())
2319 The only use for the <literal>Unused</literal> constructor was to force the correct
2320 kind for the type variable <literal>cxt</literal>.
2323 GHC now instead allows you to specify the kind of a type variable directly, wherever
2324 a type variable is explicitly bound. Namely:
2326 <listitem><para><literal>data</literal> declarations:
2328 data Set (cxt :: * -> *) a = Set [a]
2329 </screen></para></listitem>
2330 <listitem><para><literal>type</literal> declarations:
2332 type T (f :: * -> *) = f Int
2333 </screen></para></listitem>
2334 <listitem><para><literal>class</literal> declarations:
2336 class (Eq a) => C (f :: * -> *) a where ...
2337 </screen></para></listitem>
2338 <listitem><para><literal>forall</literal>'s in type signatures:
2340 f :: forall (cxt :: * -> *). Set cxt Int
2341 </screen></para></listitem>
2346 The parentheses are required. Some of the spaces are required too, to
2347 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2348 will get a parse error, because "<literal>::*->*</literal>" is a
2349 single lexeme in Haskell.
2353 As part of the same extension, you can put kind annotations in types
2356 f :: (Int :: *) -> Int
2357 g :: forall a. a -> (a :: *)
2361 atype ::= '(' ctype '::' kind ')
2363 The parentheses are required.
2368 <sect2 id="universal-quantification">
2369 <title>Arbitrary-rank polymorphism
2373 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2374 allows us to say exactly what this means. For example:
2382 g :: forall b. (b -> b)
2384 The two are treated identically.
2388 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2389 explicit universal quantification in
2391 For example, all the following types are legal:
2393 f1 :: forall a b. a -> b -> a
2394 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2396 f2 :: (forall a. a->a) -> Int -> Int
2397 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2399 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2401 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2402 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2403 The <literal>forall</literal> makes explicit the universal quantification that
2404 is implicitly added by Haskell.
2407 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2408 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2409 shows, the polymorphic type on the left of the function arrow can be overloaded.
2412 The function <literal>f3</literal> has a rank-3 type;
2413 it has rank-2 types on the left of a function arrow.
2416 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2417 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2418 that restriction has now been lifted.)
2419 In particular, a forall-type (also called a "type scheme"),
2420 including an operational type class context, is legal:
2422 <listitem> <para> On the left of a function arrow </para> </listitem>
2423 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2424 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2425 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2426 field type signatures.</para> </listitem>
2427 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2428 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2430 There is one place you cannot put a <literal>forall</literal>:
2431 you cannot instantiate a type variable with a forall-type. So you cannot
2432 make a forall-type the argument of a type constructor. So these types are illegal:
2434 x1 :: [forall a. a->a]
2435 x2 :: (forall a. a->a, Int)
2436 x3 :: Maybe (forall a. a->a)
2438 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2439 a type variable any more!
2448 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2449 the types of the constructor arguments. Here are several examples:
2455 data T a = T1 (forall b. b -> b -> b) a
2457 data MonadT m = MkMonad { return :: forall a. a -> m a,
2458 bind :: forall a b. m a -> (a -> m b) -> m b
2461 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2467 The constructors have rank-2 types:
2473 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2474 MkMonad :: forall m. (forall a. a -> m a)
2475 -> (forall a b. m a -> (a -> m b) -> m b)
2477 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2483 Notice that you don't need to use a <literal>forall</literal> if there's an
2484 explicit context. For example in the first argument of the
2485 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2486 prefixed to the argument type. The implicit <literal>forall</literal>
2487 quantifies all type variables that are not already in scope, and are
2488 mentioned in the type quantified over.
2492 As for type signatures, implicit quantification happens for non-overloaded
2493 types too. So if you write this:
2496 data T a = MkT (Either a b) (b -> b)
2499 it's just as if you had written this:
2502 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2505 That is, since the type variable <literal>b</literal> isn't in scope, it's
2506 implicitly universally quantified. (Arguably, it would be better
2507 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2508 where that is what is wanted. Feedback welcomed.)
2512 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2513 the constructor to suitable values, just as usual. For example,
2524 a3 = MkSwizzle reverse
2527 a4 = let r x = Just x
2534 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2535 mkTs f x y = [T1 f x, T1 f y]
2541 The type of the argument can, as usual, be more general than the type
2542 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2543 does not need the <literal>Ord</literal> constraint.)
2547 When you use pattern matching, the bound variables may now have
2548 polymorphic types. For example:
2554 f :: T a -> a -> (a, Char)
2555 f (T1 w k) x = (w k x, w 'c' 'd')
2557 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2558 g (MkSwizzle s) xs f = s (map f (s xs))
2560 h :: MonadT m -> [m a] -> m [a]
2561 h m [] = return m []
2562 h m (x:xs) = bind m x $ \y ->
2563 bind m (h m xs) $ \ys ->
2570 In the function <function>h</function> we use the record selectors <literal>return</literal>
2571 and <literal>bind</literal> to extract the polymorphic bind and return functions
2572 from the <literal>MonadT</literal> data structure, rather than using pattern
2578 <title>Type inference</title>
2581 In general, type inference for arbitrary-rank types is undecideable.
2582 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2583 to get a decidable algorithm by requiring some help from the programmer.
2584 We do not yet have a formal specification of "some help" but the rule is this:
2587 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2588 provides an explicit polymorphic type for x, or GHC's type inference will assume
2589 that x's type has no foralls in it</emphasis>.
2592 What does it mean to "provide" an explicit type for x? You can do that by
2593 giving a type signature for x directly, using a pattern type signature
2594 (<xref linkend="scoped-type-variables"/>), thus:
2596 \ f :: (forall a. a->a) -> (f True, f 'c')
2598 Alternatively, you can give a type signature to the enclosing
2599 context, which GHC can "push down" to find the type for the variable:
2601 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2603 Here the type signature on the expression can be pushed inwards
2604 to give a type signature for f. Similarly, and more commonly,
2605 one can give a type signature for the function itself:
2607 h :: (forall a. a->a) -> (Bool,Char)
2608 h f = (f True, f 'c')
2610 You don't need to give a type signature if the lambda bound variable
2611 is a constructor argument. Here is an example we saw earlier:
2613 f :: T a -> a -> (a, Char)
2614 f (T1 w k) x = (w k x, w 'c' 'd')
2616 Here we do not need to give a type signature to <literal>w</literal>, because
2617 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2624 <sect3 id="implicit-quant">
2625 <title>Implicit quantification</title>
2628 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2629 user-written types, if and only if there is no explicit <literal>forall</literal>,
2630 GHC finds all the type variables mentioned in the type that are not already
2631 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2635 f :: forall a. a -> a
2642 h :: forall b. a -> b -> b
2648 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2651 f :: (a -> a) -> Int
2653 f :: forall a. (a -> a) -> Int
2655 f :: (forall a. a -> a) -> Int
2658 g :: (Ord a => a -> a) -> Int
2659 -- MEANS the illegal type
2660 g :: forall a. (Ord a => a -> a) -> Int
2662 g :: (forall a. Ord a => a -> a) -> Int
2664 The latter produces an illegal type, which you might think is silly,
2665 but at least the rule is simple. If you want the latter type, you
2666 can write your for-alls explicitly. Indeed, doing so is strongly advised
2675 <sect2 id="scoped-type-variables">
2676 <title>Scoped type variables
2680 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2681 variable</emphasis>. For example
2687 f (xs::[a]) = ys ++ ys
2696 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2697 This brings the type variable <literal>a</literal> into scope; it scopes over
2698 all the patterns and right hand sides for this equation for <function>f</function>.
2699 In particular, it is in scope at the type signature for <varname>y</varname>.
2703 Pattern type signatures are completely orthogonal to ordinary, separate
2704 type signatures. The two can be used independently or together.
2705 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2706 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2707 implicitly universally quantified. (If there are no type variables in
2708 scope, all type variables mentioned in the signature are universally
2709 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2710 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2711 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2712 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2713 it becomes possible to do so.
2717 Scoped type variables are implemented in both GHC and Hugs. Where the
2718 implementations differ from the specification below, those differences
2723 So much for the basic idea. Here are the details.
2727 <title>What a pattern type signature means</title>
2729 A type variable brought into scope by a pattern type signature is simply
2730 the name for a type. The restriction they express is that all occurrences
2731 of the same name mean the same type. For example:
2733 f :: [Int] -> Int -> Int
2734 f (xs::[a]) (y::a) = (head xs + y) :: a
2736 The pattern type signatures on the left hand side of
2737 <literal>f</literal> express the fact that <literal>xs</literal>
2738 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2739 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2740 specifies that this expression must have the same type <literal>a</literal>.
2741 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2742 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2743 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2744 rules, which specified that a pattern-bound type variable should be universally quantified.)
2745 For example, all of these are legal:</para>
2748 t (x::a) (y::a) = x+y*2
2750 f (x::a) (y::b) = [x,y] -- a unifies with b
2752 g (x::a) = x + 1::Int -- a unifies with Int
2754 h x = let k (y::a) = [x,y] -- a is free in the
2755 in k x -- environment
2757 k (x::a) True = ... -- a unifies with Int
2758 k (x::Int) False = ...
2761 w (x::a) = x -- a unifies with [b]
2767 <title>Scope and implicit quantification</title>
2775 All the type variables mentioned in a pattern,
2776 that are not already in scope,
2777 are brought into scope by the pattern. We describe this set as
2778 the <emphasis>type variables bound by the pattern</emphasis>.
2781 f (x::a) = let g (y::(a,b)) = fst y
2785 The pattern <literal>(x::a)</literal> brings the type variable
2786 <literal>a</literal> into scope, as well as the term
2787 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2788 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2789 and brings into scope the type variable <literal>b</literal>.
2795 The type variable(s) bound by the pattern have the same scope
2796 as the term variable(s) bound by the pattern. For example:
2799 f (x::a) = <...rhs of f...>
2800 (p::b, q::b) = (1,2)
2801 in <...body of let...>
2803 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2804 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2805 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2806 just like <literal>p</literal> and <literal>q</literal> do.
2807 Indeed, the newly bound type variables also scope over any ordinary, separate
2808 type signatures in the <literal>let</literal> group.
2815 The type variables bound by the pattern may be
2816 mentioned in ordinary type signatures or pattern
2817 type signatures anywhere within their scope.
2824 In ordinary type signatures, any type variable mentioned in the
2825 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2833 Ordinary type signatures do not bring any new type variables
2834 into scope (except in the type signature itself!). So this is illegal:
2841 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2842 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2843 and that is an incorrect typing.
2850 The pattern type signature is a monotype:
2855 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2859 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2860 not to type schemes.
2864 There is no implicit universal quantification on pattern type signatures (in contrast to
2865 ordinary type signatures).
2875 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2876 scope over the methods defined in the <literal>where</literal> part. For example:
2890 (Not implemented in Hugs yet, Dec 98).
2901 <title>Where a pattern type signature can occur</title>
2904 A pattern type signature can occur in any pattern. For example:
2909 A pattern type signature can be on an arbitrary sub-pattern, not
2914 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2923 Pattern type signatures, including the result part, can be used
2924 in lambda abstractions:
2927 (\ (x::a, y) :: a -> x)
2934 Pattern type signatures, including the result part, can be used
2935 in <literal>case</literal> expressions:
2938 case e of { ((x::a, y) :: (a,b)) -> x }
2941 Note that the <literal>-></literal> symbol in a case alternative
2942 leads to difficulties when parsing a type signature in the pattern: in
2943 the absence of the extra parentheses in the example above, the parser
2944 would try to interpret the <literal>-></literal> as a function
2945 arrow and give a parse error later.
2953 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2954 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2955 token or a parenthesised type of some sort). To see why,
2956 consider how one would parse this:
2970 Pattern type signatures can bind existential type variables.
2975 data T = forall a. MkT [a]
2978 f (MkT [t::a]) = MkT t3
2991 Pattern type signatures
2992 can be used in pattern bindings:
2995 f x = let (y, z::a) = x in ...
2996 f1 x = let (y, z::Int) = x in ...
2997 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2998 f3 :: (b->b) = \x -> x
3001 In all such cases, the binding is not generalised over the pattern-bound
3002 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3003 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3004 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3005 In contrast, the binding
3010 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3011 in <literal>f4</literal>'s scope.
3021 <title>Result type signatures</title>
3024 The result type of a function can be given a signature, thus:
3028 f (x::a) :: [a] = [x,x,x]
3032 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3033 result type. Sometimes this is the only way of naming the type variable
3038 f :: Int -> [a] -> [a]
3039 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3040 in \xs -> map g (reverse xs `zip` xs)
3045 The type variables bound in a result type signature scope over the right hand side
3046 of the definition. However, consider this corner-case:
3048 rev1 :: [a] -> [a] = \xs -> reverse xs
3050 foo ys = rev (ys::[a])
3052 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3053 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3054 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3055 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3056 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3059 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3060 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3064 rev1 :: [a] -> [a] = \xs -> reverse xs
3069 Result type signatures are not yet implemented in Hugs.
3076 <sect2 id="deriving-typeable">
3077 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3080 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3081 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3082 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3083 classes <literal>Eq</literal>, <literal>Ord</literal>,
3084 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3087 GHC extends this list with two more classes that may be automatically derived
3088 (provided the <option>-fglasgow-exts</option> flag is specified):
3089 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3090 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3091 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3095 <sect2 id="newtype-deriving">
3096 <title>Generalised derived instances for newtypes</title>
3099 When you define an abstract type using <literal>newtype</literal>, you may want
3100 the new type to inherit some instances from its representation. In
3101 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3102 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3103 other classes you have to write an explicit instance declaration. For
3104 example, if you define
3107 newtype Dollars = Dollars Int
3110 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3111 explicitly define an instance of <literal>Num</literal>:
3114 instance Num Dollars where
3115 Dollars a + Dollars b = Dollars (a+b)
3118 All the instance does is apply and remove the <literal>newtype</literal>
3119 constructor. It is particularly galling that, since the constructor
3120 doesn't appear at run-time, this instance declaration defines a
3121 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3122 dictionary, only slower!
3126 <sect3> <title> Generalising the deriving clause </title>
3128 GHC now permits such instances to be derived instead, so one can write
3130 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3133 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3134 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3135 derives an instance declaration of the form
3138 instance Num Int => Num Dollars
3141 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3145 We can also derive instances of constructor classes in a similar
3146 way. For example, suppose we have implemented state and failure monad
3147 transformers, such that
3150 instance Monad m => Monad (State s m)
3151 instance Monad m => Monad (Failure m)
3153 In Haskell 98, we can define a parsing monad by
3155 type Parser tok m a = State [tok] (Failure m) a
3158 which is automatically a monad thanks to the instance declarations
3159 above. With the extension, we can make the parser type abstract,
3160 without needing to write an instance of class <literal>Monad</literal>, via
3163 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3166 In this case the derived instance declaration is of the form
3168 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3171 Notice that, since <literal>Monad</literal> is a constructor class, the
3172 instance is a <emphasis>partial application</emphasis> of the new type, not the
3173 entire left hand side. We can imagine that the type declaration is
3174 ``eta-converted'' to generate the context of the instance
3179 We can even derive instances of multi-parameter classes, provided the
3180 newtype is the last class parameter. In this case, a ``partial
3181 application'' of the class appears in the <literal>deriving</literal>
3182 clause. For example, given the class
3185 class StateMonad s m | m -> s where ...
3186 instance Monad m => StateMonad s (State s m) where ...
3188 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3190 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3191 deriving (Monad, StateMonad [tok])
3194 The derived instance is obtained by completing the application of the
3195 class to the new type:
3198 instance StateMonad [tok] (State [tok] (Failure m)) =>
3199 StateMonad [tok] (Parser tok m)
3204 As a result of this extension, all derived instances in newtype
3205 declarations are treated uniformly (and implemented just by reusing
3206 the dictionary for the representation type), <emphasis>except</emphasis>
3207 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3208 the newtype and its representation.
3212 <sect3> <title> A more precise specification </title>
3214 Derived instance declarations are constructed as follows. Consider the
3215 declaration (after expansion of any type synonyms)
3218 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3224 <literal>S</literal> is a type constructor,
3227 The <literal>t1...tk</literal> are types,
3230 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3231 the <literal>ti</literal>, and
3234 The <literal>ci</literal> are partial applications of
3235 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3236 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3239 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3240 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3241 should not "look through" the type or its constructor. You can still
3242 derive these classes for a newtype, but it happens in the usual way, not
3243 via this new mechanism.
3246 Then, for each <literal>ci</literal>, the derived instance
3249 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3251 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3252 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3256 As an example which does <emphasis>not</emphasis> work, consider
3258 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3260 Here we cannot derive the instance
3262 instance Monad (State s m) => Monad (NonMonad m)
3265 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3266 and so cannot be "eta-converted" away. It is a good thing that this
3267 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3268 not, in fact, a monad --- for the same reason. Try defining
3269 <literal>>>=</literal> with the correct type: you won't be able to.
3273 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3274 important, since we can only derive instances for the last one. If the
3275 <literal>StateMonad</literal> class above were instead defined as
3278 class StateMonad m s | m -> s where ...
3281 then we would not have been able to derive an instance for the
3282 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3283 classes usually have one "main" parameter for which deriving new
3284 instances is most interesting.
3292 <!-- ==================== End of type system extensions ================= -->
3294 <!-- ====================== TEMPLATE HASKELL ======================= -->
3296 <sect1 id="template-haskell">
3297 <title>Template Haskell</title>
3299 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3300 Template Haskell at <ulink url="http://www.haskell.org/th/">
3301 http://www.haskell.org/th/</ulink>, while
3303 the main technical innovations is discussed in "<ulink
3304 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3305 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3306 The details of the Template Haskell design are still in flux. Make sure you
3307 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3308 (search for the type ExpQ).
3309 [Temporary: many changes to the original design are described in
3310 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3311 Not all of these changes are in GHC 6.2.]
3314 <para> The first example from that paper is set out below as a worked example to help get you started.
3318 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3319 Tim Sheard is going to expand it.)
3323 <title>Syntax</title>
3325 <para> Template Haskell has the following new syntactic
3326 constructions. You need to use the flag
3327 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3328 </indexterm>to switch these syntactic extensions on
3329 (<option>-fth</option> is currently implied by
3330 <option>-fglasgow-exts</option>, but you are encouraged to
3331 specify it explicitly).</para>
3335 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3336 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3337 There must be no space between the "$" and the identifier or parenthesis. This use
3338 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3339 of "." as an infix operator. If you want the infix operator, put spaces around it.
3341 <para> A splice can occur in place of
3343 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3344 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3345 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3347 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3348 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3354 A expression quotation is written in Oxford brackets, thus:
3356 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3357 the quotation has type <literal>Expr</literal>.</para></listitem>
3358 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3359 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3360 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3361 the quotation has type <literal>Type</literal>.</para></listitem>
3362 </itemizedlist></para></listitem>
3365 Reification is written thus:
3367 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3368 has type <literal>Dec</literal>. </para></listitem>
3369 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3370 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3371 <listitem><para> Still to come: fixities </para></listitem>
3373 </itemizedlist></para>
3380 <sect2> <title> Using Template Haskell </title>
3384 The data types and monadic constructor functions for Template Haskell are in the library
3385 <literal>Language.Haskell.THSyntax</literal>.
3389 You can only run a function at compile time if it is imported from another module. That is,
3390 you can't define a function in a module, and call it from within a splice in the same module.
3391 (It would make sense to do so, but it's hard to implement.)
3395 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3398 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3399 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3400 compiles and runs a program, and then looks at the result. So it's important that
3401 the program it compiles produces results whose representations are identical to
3402 those of the compiler itself.
3406 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3407 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3412 <sect2> <title> A Template Haskell Worked Example </title>
3413 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3414 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3421 -- Import our template "pr"
3422 import Printf ( pr )
3424 -- The splice operator $ takes the Haskell source code
3425 -- generated at compile time by "pr" and splices it into
3426 -- the argument of "putStrLn".
3427 main = putStrLn ( $(pr "Hello") )
3433 -- Skeletal printf from the paper.
3434 -- It needs to be in a separate module to the one where
3435 -- you intend to use it.
3437 -- Import some Template Haskell syntax
3438 import Language.Haskell.TH.Syntax
3440 -- Describe a format string
3441 data Format = D | S | L String
3443 -- Parse a format string. This is left largely to you
3444 -- as we are here interested in building our first ever
3445 -- Template Haskell program and not in building printf.
3446 parse :: String -> [Format]
3449 -- Generate Haskell source code from a parsed representation
3450 -- of the format string. This code will be spliced into
3451 -- the module which calls "pr", at compile time.
3452 gen :: [Format] -> ExpQ
3453 gen [D] = [| \n -> show n |]
3454 gen [S] = [| \s -> s |]
3455 gen [L s] = stringE s
3457 -- Here we generate the Haskell code for the splice
3458 -- from an input format string.
3459 pr :: String -> ExpQ
3460 pr s = gen (parse s)
3463 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3466 $ ghc --make -fth main.hs -o main.exe
3469 <para>Run "main.exe" and here is your output:</para>
3480 <!-- ===================== Arrow notation =================== -->
3482 <sect1 id="arrow-notation">
3483 <title>Arrow notation
3486 <para>Arrows are a generalization of monads introduced by John Hughes.
3487 For more details, see
3492 “Generalising Monads to Arrows”,
3493 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3494 pp67–111, May 2000.
3500 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3501 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3507 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3508 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3514 and the arrows web page at
3515 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3516 With the <option>-farrows</option> flag, GHC supports the arrow
3517 notation described in the second of these papers.
3518 What follows is a brief introduction to the notation;
3519 it won't make much sense unless you've read Hughes's paper.
3520 This notation is translated to ordinary Haskell,
3521 using combinators from the
3522 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3526 <para>The extension adds a new kind of expression for defining arrows:
3528 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3529 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3531 where <literal>proc</literal> is a new keyword.
3532 The variables of the pattern are bound in the body of the
3533 <literal>proc</literal>-expression,
3534 which is a new sort of thing called a <firstterm>command</firstterm>.
3535 The syntax of commands is as follows:
3537 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3538 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3539 | <replaceable>cmd</replaceable><superscript>0</superscript>
3541 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3542 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3543 infix operators as for expressions, and
3545 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3546 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3547 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3548 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3549 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3550 | <replaceable>fcmd</replaceable>
3552 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3553 | ( <replaceable>cmd</replaceable> )
3554 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3556 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3557 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3558 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3559 | <replaceable>cmd</replaceable>
3561 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3562 except that the bodies are commands instead of expressions.
3566 Commands produce values, but (like monadic computations)
3567 may yield more than one value,
3568 or none, and may do other things as well.
3569 For the most part, familiarity with monadic notation is a good guide to
3571 However the values of expressions, even monadic ones,
3572 are determined by the values of the variables they contain;
3573 this is not necessarily the case for commands.
3577 A simple example of the new notation is the expression
3579 proc x -> f -< x+1
3581 We call this a <firstterm>procedure</firstterm> or
3582 <firstterm>arrow abstraction</firstterm>.
3583 As with a lambda expression, the variable <literal>x</literal>
3584 is a new variable bound within the <literal>proc</literal>-expression.
3585 It refers to the input to the arrow.
3586 In the above example, <literal>-<</literal> is not an identifier but an
3587 new reserved symbol used for building commands from an expression of arrow
3588 type and an expression to be fed as input to that arrow.
3589 (The weird look will make more sense later.)
3590 It may be read as analogue of application for arrows.
3591 The above example is equivalent to the Haskell expression
3593 arr (\ x -> x+1) >>> f
3595 That would make no sense if the expression to the left of
3596 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3597 More generally, the expression to the left of <literal>-<</literal>
3598 may not involve any <firstterm>local variable</firstterm>,
3599 i.e. a variable bound in the current arrow abstraction.
3600 For such a situation there is a variant <literal>-<<</literal>, as in
3602 proc x -> f x -<< x+1
3604 which is equivalent to
3606 arr (\ x -> (f, x+1)) >>> app
3608 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3610 Such an arrow is equivalent to a monad, so if you're using this form
3611 you may find a monadic formulation more convenient.
3615 <title>do-notation for commands</title>
3618 Another form of command is a form of <literal>do</literal>-notation.
3619 For example, you can write
3628 You can read this much like ordinary <literal>do</literal>-notation,
3629 but with commands in place of monadic expressions.
3630 The first line sends the value of <literal>x+1</literal> as an input to
3631 the arrow <literal>f</literal>, and matches its output against
3632 <literal>y</literal>.
3633 In the next line, the output is discarded.
3634 The arrow <function>returnA</function> is defined in the
3635 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3636 module as <literal>arr id</literal>.
3637 The above example is treated as an abbreviation for
3639 arr (\ x -> (x, x)) >>>
3640 first (arr (\ x -> x+1) >>> f) >>>
3641 arr (\ (y, x) -> (y, (x, y))) >>>
3642 first (arr (\ y -> 2*y) >>> g) >>>
3644 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3645 first (arr (\ (x, z) -> x*z) >>> h) >>>
3646 arr (\ (t, z) -> t+z) >>>
3649 Note that variables not used later in the composition are projected out.
3650 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3652 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3653 module, this reduces to
3655 arr (\ x -> (x+1, x)) >>>
3657 arr (\ (y, x) -> (2*y, (x, y))) >>>
3659 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3661 arr (\ (t, z) -> t+z)
3663 which is what you might have written by hand.
3664 With arrow notation, GHC keeps track of all those tuples of variables for you.
3668 Note that although the above translation suggests that
3669 <literal>let</literal>-bound variables like <literal>z</literal> must be
3670 monomorphic, the actual translation produces Core,
3671 so polymorphic variables are allowed.
3675 It's also possible to have mutually recursive bindings,
3676 using the new <literal>rec</literal> keyword, as in the following example:
3678 counter :: ArrowCircuit a => a Bool Int
3679 counter = proc reset -> do
3680 rec output <- returnA -< if reset then 0 else next
3681 next <- delay 0 -< output+1
3682 returnA -< output
3684 The translation of such forms uses the <function>loop</function> combinator,
3685 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3691 <title>Conditional commands</title>
3694 In the previous example, we used a conditional expression to construct the
3696 Sometimes we want to conditionally execute different commands, as in
3703 which is translated to
3705 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3706 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3708 Since the translation uses <function>|||</function>,
3709 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3713 There are also <literal>case</literal> commands, like
3719 y <- h -< (x1, x2)
3723 The syntax is the same as for <literal>case</literal> expressions,
3724 except that the bodies of the alternatives are commands rather than expressions.
3725 The translation is similar to that of <literal>if</literal> commands.
3731 <title>Defining your own control structures</title>
3734 As we're seen, arrow notation provides constructs,
3735 modelled on those for expressions,
3736 for sequencing, value recursion and conditionals.
3737 But suitable combinators,
3738 which you can define in ordinary Haskell,
3739 may also be used to build new commands out of existing ones.
3740 The basic idea is that a command defines an arrow from environments to values.
3741 These environments assign values to the free local variables of the command.
3742 Thus combinators that produce arrows from arrows
3743 may also be used to build commands from commands.
3744 For example, the <literal>ArrowChoice</literal> class includes a combinator
3746 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3748 so we can use it to build commands:
3750 expr' = proc x -> do
3753 symbol Plus -< ()
3754 y <- term -< ()
3757 symbol Minus -< ()
3758 y <- term -< ()
3761 (The <literal>do</literal> on the first line is needed to prevent the first
3762 <literal><+> ...</literal> from being interpreted as part of the
3763 expression on the previous line.)
3764 This is equivalent to
3766 expr' = (proc x -> returnA -< x)
3767 <+> (proc x -> do
3768 symbol Plus -< ()
3769 y <- term -< ()
3771 <+> (proc x -> do
3772 symbol Minus -< ()
3773 y <- term -< ()
3776 It is essential that this operator be polymorphic in <literal>e</literal>
3777 (representing the environment input to the command
3778 and thence to its subcommands)
3779 and satisfy the corresponding naturality property
3781 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3783 at least for strict <literal>k</literal>.
3784 (This should be automatic if you're not using <function>seq</function>.)
3785 This ensures that environments seen by the subcommands are environments
3786 of the whole command,
3787 and also allows the translation to safely trim these environments.
3788 The operator must also not use any variable defined within the current
3793 We could define our own operator
3795 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3796 untilA body cond = proc x ->
3797 if cond x then returnA -< ()
3800 untilA body cond -< x
3802 and use it in the same way.
3803 Of course this infix syntax only makes sense for binary operators;
3804 there is also a more general syntax involving special brackets:
3808 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3815 <title>Primitive constructs</title>
3818 Some operators will need to pass additional inputs to their subcommands.
3819 For example, in an arrow type supporting exceptions,
3820 the operator that attaches an exception handler will wish to pass the
3821 exception that occurred to the handler.
3822 Such an operator might have a type
3824 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3826 where <literal>Ex</literal> is the type of exceptions handled.
3827 You could then use this with arrow notation by writing a command
3829 body `handleA` \ ex -> handler
3831 so that if an exception is raised in the command <literal>body</literal>,
3832 the variable <literal>ex</literal> is bound to the value of the exception
3833 and the command <literal>handler</literal>,
3834 which typically refers to <literal>ex</literal>, is entered.
3835 Though the syntax here looks like a functional lambda,
3836 we are talking about commands, and something different is going on.
3837 The input to the arrow represented by a command consists of values for
3838 the free local variables in the command, plus a stack of anonymous values.
3839 In all the prior examples, this stack was empty.
3840 In the second argument to <function>handleA</function>,
3841 this stack consists of one value, the value of the exception.
3842 The command form of lambda merely gives this value a name.
3847 the values on the stack are paired to the right of the environment.
3848 So operators like <function>handleA</function> that pass
3849 extra inputs to their subcommands can be designed for use with the notation
3850 by pairing the values with the environment in this way.
3851 More precisely, the type of each argument of the operator (and its result)
3852 should have the form
3854 a (...(e,t1), ... tn) t
3856 where <replaceable>e</replaceable> is a polymorphic variable
3857 (representing the environment)
3858 and <replaceable>ti</replaceable> are the types of the values on the stack,
3859 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3860 The polymorphic variable <replaceable>e</replaceable> must not occur in
3861 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3862 <replaceable>t</replaceable>.
3863 However the arrows involved need not be the same.
3864 Here are some more examples of suitable operators:
3866 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3867 runReader :: ... => a e c -> a' (e,State) c
3868 runState :: ... => a e c -> a' (e,State) (c,State)
3870 We can supply the extra input required by commands built with the last two
3871 by applying them to ordinary expressions, as in
3875 (|runReader (do { ... })|) s
3877 which adds <literal>s</literal> to the stack of inputs to the command
3878 built using <function>runReader</function>.
3882 The command versions of lambda abstraction and application are analogous to
3883 the expression versions.
3884 In particular, the beta and eta rules describe equivalences of commands.
3885 These three features (operators, lambda abstraction and application)
3886 are the core of the notation; everything else can be built using them,
3887 though the results would be somewhat clumsy.
3888 For example, we could simulate <literal>do</literal>-notation by defining
3890 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3891 u `bind` f = returnA &&& u >>> f
3893 bind_ :: Arrow a => a e b -> a e c -> a e c
3894 u `bind_` f = u `bind` (arr fst >>> f)
3896 We could simulate <literal>if</literal> by defining
3898 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3899 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3906 <title>Differences with the paper</title>
3911 <para>Instead of a single form of arrow application (arrow tail) with two
3912 translations, the implementation provides two forms
3913 <quote><literal>-<</literal></quote> (first-order)
3914 and <quote><literal>-<<</literal></quote> (higher-order).
3919 <para>User-defined operators are flagged with banana brackets instead of
3920 a new <literal>form</literal> keyword.
3929 <title>Portability</title>
3932 Although only GHC implements arrow notation directly,
3933 there is also a preprocessor
3935 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
3936 that translates arrow notation into Haskell 98
3937 for use with other Haskell systems.
3938 You would still want to check arrow programs with GHC;
3939 tracing type errors in the preprocessor output is not easy.
3940 Modules intended for both GHC and the preprocessor must observe some
3941 additional restrictions:
3946 The module must import
3947 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3953 The preprocessor cannot cope with other Haskell extensions.
3954 These would have to go in separate modules.
3960 Because the preprocessor targets Haskell (rather than Core),
3961 <literal>let</literal>-bound variables are monomorphic.
3972 <!-- ==================== ASSERTIONS ================= -->
3974 <sect1 id="sec-assertions">
3976 <indexterm><primary>Assertions</primary></indexterm>
3980 If you want to make use of assertions in your standard Haskell code, you
3981 could define a function like the following:
3987 assert :: Bool -> a -> a
3988 assert False x = error "assertion failed!"
3995 which works, but gives you back a less than useful error message --
3996 an assertion failed, but which and where?
4000 One way out is to define an extended <function>assert</function> function which also
4001 takes a descriptive string to include in the error message and
4002 perhaps combine this with the use of a pre-processor which inserts
4003 the source location where <function>assert</function> was used.
4007 Ghc offers a helping hand here, doing all of this for you. For every
4008 use of <function>assert</function> in the user's source:
4014 kelvinToC :: Double -> Double
4015 kelvinToC k = assert (k >= 0.0) (k+273.15)
4021 Ghc will rewrite this to also include the source location where the
4028 assert pred val ==> assertError "Main.hs|15" pred val
4034 The rewrite is only performed by the compiler when it spots
4035 applications of <function>Control.Exception.assert</function>, so you
4036 can still define and use your own versions of
4037 <function>assert</function>, should you so wish. If not, import
4038 <literal>Control.Exception</literal> to make use
4039 <function>assert</function> in your code.
4043 To have the compiler ignore uses of assert, use the compiler option
4044 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4045 option</primary></indexterm> That is, expressions of the form
4046 <literal>assert pred e</literal> will be rewritten to
4047 <literal>e</literal>.
4051 Assertion failures can be caught, see the documentation for the
4052 <literal>Control.Exception</literal> library for the details.
4058 <!-- =============================== PRAGMAS =========================== -->
4060 <sect1 id="pragmas">
4061 <title>Pragmas</title>
4063 <indexterm><primary>pragma</primary></indexterm>
4065 <para>GHC supports several pragmas, or instructions to the
4066 compiler placed in the source code. Pragmas don't normally affect
4067 the meaning of the program, but they might affect the efficiency
4068 of the generated code.</para>
4070 <para>Pragmas all take the form
4072 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4074 where <replaceable>word</replaceable> indicates the type of
4075 pragma, and is followed optionally by information specific to that
4076 type of pragma. Case is ignored in
4077 <replaceable>word</replaceable>. The various values for
4078 <replaceable>word</replaceable> that GHC understands are described
4079 in the following sections; any pragma encountered with an
4080 unrecognised <replaceable>word</replaceable> is (silently)
4083 <sect2 id="deprecated-pragma">
4084 <title>DEPRECATED pragma</title>
4085 <indexterm><primary>DEPRECATED</primary>
4088 <para>The DEPRECATED pragma lets you specify that a particular
4089 function, class, or type, is deprecated. There are two
4094 <para>You can deprecate an entire module thus:</para>
4096 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4099 <para>When you compile any module that import
4100 <literal>Wibble</literal>, GHC will print the specified
4105 <para>You can deprecate a function, class, or type, with the
4106 following top-level declaration:</para>
4108 {-# DEPRECATED f, C, T "Don't use these" #-}
4110 <para>When you compile any module that imports and uses any
4111 of the specifed entities, GHC will print the specified
4115 Any use of the deprecated item, or of anything from a deprecated
4116 module, will be flagged with an appropriate message. However,
4117 deprecations are not reported for
4118 (a) uses of a deprecated function within its defining module, and
4119 (b) uses of a deprecated function in an export list.
4120 The latter reduces spurious complaints within a library
4121 in which one module gathers together and re-exports
4122 the exports of several others.
4124 <para>You can suppress the warnings with the flag
4125 <option>-fno-warn-deprecations</option>.</para>
4128 <sect2 id="inline-noinline-pragma">
4129 <title>INLINE and NOINLINE pragmas</title>
4131 <para>These pragmas control the inlining of function
4134 <sect3 id="inline-pragma">
4135 <title>INLINE pragma</title>
4136 <indexterm><primary>INLINE</primary></indexterm>
4138 <para>GHC (with <option>-O</option>, as always) tries to
4139 inline (or “unfold”) functions/values that are
4140 “small enough,” thus avoiding the call overhead
4141 and possibly exposing other more-wonderful optimisations.
4142 Normally, if GHC decides a function is “too
4143 expensive” to inline, it will not do so, nor will it
4144 export that unfolding for other modules to use.</para>
4146 <para>The sledgehammer you can bring to bear is the
4147 <literal>INLINE</literal><indexterm><primary>INLINE
4148 pragma</primary></indexterm> pragma, used thusly:</para>
4151 key_function :: Int -> String -> (Bool, Double)
4153 #ifdef __GLASGOW_HASKELL__
4154 {-# INLINE key_function #-}
4158 <para>(You don't need to do the C pre-processor carry-on
4159 unless you're going to stick the code through HBC—it
4160 doesn't like <literal>INLINE</literal> pragmas.)</para>
4162 <para>The major effect of an <literal>INLINE</literal> pragma
4163 is to declare a function's “cost” to be very low.
4164 The normal unfolding machinery will then be very keen to
4167 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4168 function can be put anywhere its type signature could be
4171 <para><literal>INLINE</literal> pragmas are a particularly
4173 <literal>then</literal>/<literal>return</literal> (or
4174 <literal>bind</literal>/<literal>unit</literal>) functions in
4175 a monad. For example, in GHC's own
4176 <literal>UniqueSupply</literal> monad code, we have:</para>
4179 #ifdef __GLASGOW_HASKELL__
4180 {-# INLINE thenUs #-}
4181 {-# INLINE returnUs #-}
4185 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4186 linkend="noinline-pragma"/>).</para>
4189 <sect3 id="noinline-pragma">
4190 <title>NOINLINE pragma</title>
4192 <indexterm><primary>NOINLINE</primary></indexterm>
4193 <indexterm><primary>NOTINLINE</primary></indexterm>
4195 <para>The <literal>NOINLINE</literal> pragma does exactly what
4196 you'd expect: it stops the named function from being inlined
4197 by the compiler. You shouldn't ever need to do this, unless
4198 you're very cautious about code size.</para>
4200 <para><literal>NOTINLINE</literal> is a synonym for
4201 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4202 specified by Haskell 98 as the standard way to disable
4203 inlining, so it should be used if you want your code to be
4207 <sect3 id="phase-control">
4208 <title>Phase control</title>
4210 <para> Sometimes you want to control exactly when in GHC's
4211 pipeline the INLINE pragma is switched on. Inlining happens
4212 only during runs of the <emphasis>simplifier</emphasis>. Each
4213 run of the simplifier has a different <emphasis>phase
4214 number</emphasis>; the phase number decreases towards zero.
4215 If you use <option>-dverbose-core2core</option> you'll see the
4216 sequence of phase numbers for successive runs of the
4217 simpifier. In an INLINE pragma you can optionally specify a
4218 phase number, thus:</para>
4222 <para>You can say "inline <literal>f</literal> in Phase 2
4223 and all subsequent phases":
4225 {-# INLINE [2] f #-}
4231 <para>You can say "inline <literal>g</literal> in all
4232 phases up to, but not including, Phase 3":
4234 {-# INLINE [~3] g #-}
4240 <para>If you omit the phase indicator, you mean "inline in
4245 <para>You can use a phase number on a NOINLINE pragma too:</para>
4249 <para>You can say "do not inline <literal>f</literal>
4250 until Phase 2; in Phase 2 and subsequently behave as if
4251 there was no pragma at all":
4253 {-# NOINLINE [2] f #-}
4259 <para>You can say "do not inline <literal>g</literal> in
4260 Phase 3 or any subsequent phase; before that, behave as if
4261 there was no pragma":
4263 {-# NOINLINE [~3] g #-}
4269 <para>If you omit the phase indicator, you mean "never
4270 inline this function".</para>
4274 <para>The same phase-numbering control is available for RULES
4275 (<xref linkend="rewrite-rules"/>).</para>
4279 <sect2 id="line-pragma">
4280 <title>LINE pragma</title>
4282 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4283 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4284 <para>This pragma is similar to C's <literal>#line</literal>
4285 pragma, and is mainly for use in automatically generated Haskell
4286 code. It lets you specify the line number and filename of the
4287 original code; for example</para>
4290 {-# LINE 42 "Foo.vhs" #-}
4293 <para>if you'd generated the current file from something called
4294 <filename>Foo.vhs</filename> and this line corresponds to line
4295 42 in the original. GHC will adjust its error messages to refer
4296 to the line/file named in the <literal>LINE</literal>
4300 <sect2 id="options-pragma">
4301 <title>OPTIONS pragma</title>
4302 <indexterm><primary>OPTIONS</primary>
4304 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4307 <para>The <literal>OPTIONS</literal> pragma is used to specify
4308 additional options that are given to the compiler when compiling
4309 this source file. See <xref linkend="source-file-options"/> for
4314 <title>RULES pragma</title>
4316 <para>The RULES pragma lets you specify rewrite rules. It is
4317 described in <xref linkend="rewrite-rules"/>.</para>
4320 <sect2 id="specialize-pragma">
4321 <title>SPECIALIZE pragma</title>
4323 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4324 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4325 <indexterm><primary>overloading, death to</primary></indexterm>
4327 <para>(UK spelling also accepted.) For key overloaded
4328 functions, you can create extra versions (NB: more code space)
4329 specialised to particular types. Thus, if you have an
4330 overloaded function:</para>
4333 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4336 <para>If it is heavily used on lists with
4337 <literal>Widget</literal> keys, you could specialise it as
4341 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4344 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4345 be put anywhere its type signature could be put.</para>
4347 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4348 (a) a specialised version of the function and (b) a rewrite rule
4349 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4350 un-specialised function into a call to the specialised one.</para>
4352 <para>In earlier versions of GHC, it was possible to provide your own
4353 specialised function for a given type:
4356 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4359 This feature has been removed, as it is now subsumed by the
4360 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4364 <sect2 id="specialize-instance-pragma">
4365 <title>SPECIALIZE instance pragma
4369 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4370 <indexterm><primary>overloading, death to</primary></indexterm>
4371 Same idea, except for instance declarations. For example:
4374 instance (Eq a) => Eq (Foo a) where {
4375 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4379 The pragma must occur inside the <literal>where</literal> part
4380 of the instance declaration.
4383 Compatible with HBC, by the way, except perhaps in the placement
4389 <sect2 id="unpack-pragma">
4390 <title>UNPACK pragma</title>
4392 <indexterm><primary>UNPACK</primary></indexterm>
4394 <para>The <literal>UNPACK</literal> indicates to the compiler
4395 that it should unpack the contents of a constructor field into
4396 the constructor itself, removing a level of indirection. For
4400 data T = T {-# UNPACK #-} !Float
4401 {-# UNPACK #-} !Float
4404 <para>will create a constructor <literal>T</literal> containing
4405 two unboxed floats. This may not always be an optimisation: if
4406 the <function>T</function> constructor is scrutinised and the
4407 floats passed to a non-strict function for example, they will
4408 have to be reboxed (this is done automatically by the
4411 <para>Unpacking constructor fields should only be used in
4412 conjunction with <option>-O</option>, in order to expose
4413 unfoldings to the compiler so the reboxing can be removed as
4414 often as possible. For example:</para>
4418 f (T f1 f2) = f1 + f2
4421 <para>The compiler will avoid reboxing <function>f1</function>
4422 and <function>f2</function> by inlining <function>+</function>
4423 on floats, but only when <option>-O</option> is on.</para>
4425 <para>Any single-constructor data is eligible for unpacking; for
4429 data T = T {-# UNPACK #-} !(Int,Int)
4432 <para>will store the two <literal>Int</literal>s directly in the
4433 <function>T</function> constructor, by flattening the pair.
4434 Multi-level unpacking is also supported:</para>
4437 data T = T {-# UNPACK #-} !S
4438 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4441 <para>will store two unboxed <literal>Int#</literal>s
4442 directly in the <function>T</function> constructor. The
4443 unpacker can see through newtypes, too.</para>
4445 <para>If a field cannot be unpacked, you will not get a warning,
4446 so it might be an idea to check the generated code with
4447 <option>-ddump-simpl</option>.</para>
4449 <para>See also the <option>-funbox-strict-fields</option> flag,
4450 which essentially has the effect of adding
4451 <literal>{-# UNPACK #-}</literal> to every strict
4452 constructor field.</para>
4457 <!-- ======================= REWRITE RULES ======================== -->
4459 <sect1 id="rewrite-rules">
4460 <title>Rewrite rules
4462 <indexterm><primary>RULES pagma</primary></indexterm>
4463 <indexterm><primary>pragma, RULES</primary></indexterm>
4464 <indexterm><primary>rewrite rules</primary></indexterm></title>
4467 The programmer can specify rewrite rules as part of the source program
4468 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4469 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4470 and (b) the <option>-frules-off</option> flag
4471 (<xref linkend="options-f"/>) is not specified.
4479 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4486 <title>Syntax</title>
4489 From a syntactic point of view:
4495 There may be zero or more rules in a <literal>RULES</literal> pragma.
4502 Each rule has a name, enclosed in double quotes. The name itself has
4503 no significance at all. It is only used when reporting how many times the rule fired.
4509 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4510 immediately after the name of the rule. Thus:
4513 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4516 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4517 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4526 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4527 is set, so you must lay out your rules starting in the same column as the
4528 enclosing definitions.
4535 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4536 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4537 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4538 by spaces, just like in a type <literal>forall</literal>.
4544 A pattern variable may optionally have a type signature.
4545 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4546 For example, here is the <literal>foldr/build</literal> rule:
4549 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4550 foldr k z (build g) = g k z
4553 Since <function>g</function> has a polymorphic type, it must have a type signature.
4560 The left hand side of a rule must consist of a top-level variable applied
4561 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4564 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4565 "wrong2" forall f. f True = True
4568 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4575 A rule does not need to be in the same module as (any of) the
4576 variables it mentions, though of course they need to be in scope.
4582 Rules are automatically exported from a module, just as instance declarations are.
4593 <title>Semantics</title>
4596 From a semantic point of view:
4602 Rules are only applied if you use the <option>-O</option> flag.
4608 Rules are regarded as left-to-right rewrite rules.
4609 When GHC finds an expression that is a substitution instance of the LHS
4610 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4611 By "a substitution instance" we mean that the LHS can be made equal to the
4612 expression by substituting for the pattern variables.
4619 The LHS and RHS of a rule are typechecked, and must have the
4627 GHC makes absolutely no attempt to verify that the LHS and RHS
4628 of a rule have the same meaning. That is undecideable in general, and
4629 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4636 GHC makes no attempt to make sure that the rules are confluent or
4637 terminating. For example:
4640 "loop" forall x,y. f x y = f y x
4643 This rule will cause the compiler to go into an infinite loop.
4650 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4656 GHC currently uses a very simple, syntactic, matching algorithm
4657 for matching a rule LHS with an expression. It seeks a substitution
4658 which makes the LHS and expression syntactically equal modulo alpha
4659 conversion. The pattern (rule), but not the expression, is eta-expanded if
4660 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4661 But not beta conversion (that's called higher-order matching).
4665 Matching is carried out on GHC's intermediate language, which includes
4666 type abstractions and applications. So a rule only matches if the
4667 types match too. See <xref linkend="rule-spec"/> below.
4673 GHC keeps trying to apply the rules as it optimises the program.
4674 For example, consider:
4683 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4684 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4685 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4686 not be substituted, and the rule would not fire.
4693 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4694 that appears on the LHS of a rule</emphasis>, because once you have substituted
4695 for something you can't match against it (given the simple minded
4696 matching). So if you write the rule
4699 "map/map" forall f,g. map f . map g = map (f.g)
4702 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4703 It will only match something written with explicit use of ".".
4704 Well, not quite. It <emphasis>will</emphasis> match the expression
4710 where <function>wibble</function> is defined:
4713 wibble f g = map f . map g
4716 because <function>wibble</function> will be inlined (it's small).
4718 Later on in compilation, GHC starts inlining even things on the
4719 LHS of rules, but still leaves the rules enabled. This inlining
4720 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4727 All rules are implicitly exported from the module, and are therefore
4728 in force in any module that imports the module that defined the rule, directly
4729 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4730 in force when compiling A.) The situation is very similar to that for instance
4742 <title>List fusion</title>
4745 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4746 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4747 intermediate list should be eliminated entirely.
4751 The following are good producers:
4763 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4769 Explicit lists (e.g. <literal>[True, False]</literal>)
4775 The cons constructor (e.g <literal>3:4:[]</literal>)
4781 <function>++</function>
4787 <function>map</function>
4793 <function>filter</function>
4799 <function>iterate</function>, <function>repeat</function>
4805 <function>zip</function>, <function>zipWith</function>
4814 The following are good consumers:
4826 <function>array</function> (on its second argument)
4832 <function>length</function>
4838 <function>++</function> (on its first argument)
4844 <function>foldr</function>
4850 <function>map</function>
4856 <function>filter</function>
4862 <function>concat</function>
4868 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4874 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4875 will fuse with one but not the other)
4881 <function>partition</function>
4887 <function>head</function>
4893 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4899 <function>sequence_</function>
4905 <function>msum</function>
4911 <function>sortBy</function>
4920 So, for example, the following should generate no intermediate lists:
4923 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4929 This list could readily be extended; if there are Prelude functions that you use
4930 a lot which are not included, please tell us.
4934 If you want to write your own good consumers or producers, look at the
4935 Prelude definitions of the above functions to see how to do so.
4940 <sect2 id="rule-spec">
4941 <title>Specialisation
4945 Rewrite rules can be used to get the same effect as a feature
4946 present in earlier versions of GHC.
4947 For example, suppose that:
4950 genericLookup :: Ord a => Table a b -> a -> b
4951 intLookup :: Table Int b -> Int -> b
4954 where <function>intLookup</function> is an implementation of
4955 <function>genericLookup</function> that works very fast for
4956 keys of type <literal>Int</literal>. You might wish
4957 to tell GHC to use <function>intLookup</function> instead of
4958 <function>genericLookup</function> whenever the latter was called with
4959 type <literal>Table Int b -> Int -> b</literal>.
4960 It used to be possible to write
4963 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
4966 This feature is no longer in GHC, but rewrite rules let you do the same thing:
4969 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
4972 This slightly odd-looking rule instructs GHC to replace
4973 <function>genericLookup</function> by <function>intLookup</function>
4974 <emphasis>whenever the types match</emphasis>.
4975 What is more, this rule does not need to be in the same
4976 file as <function>genericLookup</function>, unlike the
4977 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
4978 have an original definition available to specialise).
4981 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
4982 <function>intLookup</function> really behaves as a specialised version
4983 of <function>genericLookup</function>!!!</para>
4985 <para>An example in which using <literal>RULES</literal> for
4986 specialisation will Win Big:
4989 toDouble :: Real a => a -> Double
4990 toDouble = fromRational . toRational
4992 {-# RULES "toDouble/Int" toDouble = i2d #-}
4993 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4996 The <function>i2d</function> function is virtually one machine
4997 instruction; the default conversion—via an intermediate
4998 <literal>Rational</literal>—is obscenely expensive by
5005 <title>Controlling what's going on</title>
5013 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5019 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5020 If you add <option>-dppr-debug</option> you get a more detailed listing.
5026 The defintion of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5029 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5030 {-# INLINE build #-}
5034 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5035 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5036 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5037 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5044 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5045 see how to write rules that will do fusion and yet give an efficient
5046 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5056 <sect2 id="core-pragma">
5057 <title>CORE pragma</title>
5059 <indexterm><primary>CORE pragma</primary></indexterm>
5060 <indexterm><primary>pragma, CORE</primary></indexterm>
5061 <indexterm><primary>core, annotation</primary></indexterm>
5064 The external core format supports <quote>Note</quote> annotations;
5065 the <literal>CORE</literal> pragma gives a way to specify what these
5066 should be in your Haskell source code. Syntactically, core
5067 annotations are attached to expressions and take a Haskell string
5068 literal as an argument. The following function definition shows an
5072 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5075 Sematically, this is equivalent to:
5083 However, when external for is generated (via
5084 <option>-fext-core</option>), there will be Notes attached to the
5085 expressions <function>show</function> and <varname>x</varname>.
5086 The core function declaration for <function>f</function> is:
5090 f :: %forall a . GHCziShow.ZCTShow a ->
5091 a -> GHCziBase.ZMZN GHCziBase.Char =
5092 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5094 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5096 (tpl1::GHCziBase.Int ->
5098 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5100 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5101 (tpl3::GHCziBase.ZMZN a ->
5102 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5110 Here, we can see that the function <function>show</function> (which
5111 has been expanded out to a case expression over the Show dictionary)
5112 has a <literal>%note</literal> attached to it, as does the
5113 expression <varname>eta</varname> (which used to be called
5114 <varname>x</varname>).
5121 <sect1 id="generic-classes">
5122 <title>Generic classes</title>
5124 <para>(Note: support for generic classes is currently broken in
5128 The ideas behind this extension are described in detail in "Derivable type classes",
5129 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5130 An example will give the idea:
5138 fromBin :: [Int] -> (a, [Int])
5140 toBin {| Unit |} Unit = []
5141 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5142 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5143 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5145 fromBin {| Unit |} bs = (Unit, bs)
5146 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5147 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5148 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5149 (y,bs'') = fromBin bs'
5152 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5153 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5154 which are defined thus in the library module <literal>Generics</literal>:
5158 data a :+: b = Inl a | Inr b
5159 data a :*: b = a :*: b
5162 Now you can make a data type into an instance of Bin like this:
5164 instance (Bin a, Bin b) => Bin (a,b)
5165 instance Bin a => Bin [a]
5167 That is, just leave off the "where" clause. Of course, you can put in the
5168 where clause and over-ride whichever methods you please.
5172 <title> Using generics </title>
5173 <para>To use generics you need to</para>
5176 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5177 <option>-fgenerics</option> (to generate extra per-data-type code),
5178 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5182 <para>Import the module <literal>Generics</literal> from the
5183 <literal>lang</literal> package. This import brings into
5184 scope the data types <literal>Unit</literal>,
5185 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5186 don't need this import if you don't mention these types
5187 explicitly; for example, if you are simply giving instance
5188 declarations.)</para>
5193 <sect2> <title> Changes wrt the paper </title>
5195 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5196 can be written infix (indeed, you can now use
5197 any operator starting in a colon as an infix type constructor). Also note that
5198 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5199 Finally, note that the syntax of the type patterns in the class declaration
5200 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5201 alone would ambiguous when they appear on right hand sides (an extension we
5202 anticipate wanting).
5206 <sect2> <title>Terminology and restrictions</title>
5208 Terminology. A "generic default method" in a class declaration
5209 is one that is defined using type patterns as above.
5210 A "polymorphic default method" is a default method defined as in Haskell 98.
5211 A "generic class declaration" is a class declaration with at least one
5212 generic default method.
5220 Alas, we do not yet implement the stuff about constructor names and
5227 A generic class can have only one parameter; you can't have a generic
5228 multi-parameter class.
5234 A default method must be defined entirely using type patterns, or entirely
5235 without. So this is illegal:
5238 op :: a -> (a, Bool)
5239 op {| Unit |} Unit = (Unit, True)
5242 However it is perfectly OK for some methods of a generic class to have
5243 generic default methods and others to have polymorphic default methods.
5249 The type variable(s) in the type pattern for a generic method declaration
5250 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:
5254 op {| p :*: q |} (x :*: y) = op (x :: p)
5262 The type patterns in a generic default method must take one of the forms:
5268 where "a" and "b" are type variables. Furthermore, all the type patterns for
5269 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5270 must use the same type variables. So this is illegal:
5274 op {| a :+: b |} (Inl x) = True
5275 op {| p :+: q |} (Inr y) = False
5277 The type patterns must be identical, even in equations for different methods of the class.
5278 So this too is illegal:
5282 op1 {| a :*: b |} (x :*: y) = True
5285 op2 {| p :*: q |} (x :*: y) = False
5287 (The reason for this restriction is that we gather all the equations for a particular type consructor
5288 into a single generic instance declaration.)
5294 A generic method declaration must give a case for each of the three type constructors.
5300 The type for a generic method can be built only from:
5302 <listitem> <para> Function arrows </para> </listitem>
5303 <listitem> <para> Type variables </para> </listitem>
5304 <listitem> <para> Tuples </para> </listitem>
5305 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5307 Here are some example type signatures for generic methods:
5310 op2 :: Bool -> (a,Bool)
5311 op3 :: [Int] -> a -> a
5314 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5318 This restriction is an implementation restriction: we just havn't got around to
5319 implementing the necessary bidirectional maps over arbitrary type constructors.
5320 It would be relatively easy to add specific type constructors, such as Maybe and list,
5321 to the ones that are allowed.</para>
5326 In an instance declaration for a generic class, the idea is that the compiler
5327 will fill in the methods for you, based on the generic templates. However it can only
5332 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5337 No constructor of the instance type has unboxed fields.
5341 (Of course, these things can only arise if you are already using GHC extensions.)
5342 However, you can still give an instance declarations for types which break these rules,
5343 provided you give explicit code to override any generic default methods.
5351 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5352 what the compiler does with generic declarations.
5357 <sect2> <title> Another example </title>
5359 Just to finish with, here's another example I rather like:
5363 nCons {| Unit |} _ = 1
5364 nCons {| a :*: b |} _ = 1
5365 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5368 tag {| Unit |} _ = 1
5369 tag {| a :*: b |} _ = 1
5370 tag {| a :+: b |} (Inl x) = tag x
5371 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5380 ;;; Local Variables: ***
5382 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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