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>Be warned: this is an experimental facility, with fewer checks than
841 usual. In particular, it is essential that the functions GHC finds in scope
842 must have the appropriate types, namely:
844 fromInteger :: forall a. (...) => Integer -> a
845 fromRational :: forall a. (...) => Rational -> a
846 negate :: forall a. (...) => a -> a
847 (-) :: forall a. (...) => a -> a -> a
848 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
849 (>>) :: forall m a. (...) => m a -> m b -> m b
850 return :: forall m a. (...) => a -> m a
851 fail :: forall m a. (...) => String -> m a
853 (The (...) part can be any context including the empty context; that part
855 If the functions don't have the right type, very peculiar things may
856 happen. Use <literal>-dcore-lint</literal> to
857 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
863 <!-- TYPE SYSTEM EXTENSIONS -->
864 <sect1 id="type-extensions">
865 <title>Type system extensions</title>
869 <title>Data types and type synonyms</title>
871 <sect3 id="nullary-types">
872 <title>Data types with no constructors</title>
874 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
875 a data type with no constructors. For example:</para>
879 data T a -- T :: * -> *
882 <para>Syntactically, the declaration lacks the "= constrs" part. The
883 type can be parameterised over types of any kind, but if the kind is
884 not <literal>*</literal> then an explicit kind annotation must be used
885 (see <xref linkend="sec-kinding"/>).</para>
887 <para>Such data types have only one value, namely bottom.
888 Nevertheless, they can be useful when defining "phantom types".</para>
891 <sect3 id="infix-tycons">
892 <title>Infix type constructors</title>
895 GHC allows type constructors to be operators, and to be written infix, very much
896 like expressions. More specifically:
899 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
900 The lexical syntax is the same as that for data constructors.
903 Types can be written infix. For example <literal>Int :*: Bool</literal>.
907 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
908 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
911 Fixities may be declared for type constructors just as for data constructors. However,
912 one cannot distinguish between the two in a fixity declaration; a fixity declaration
913 sets the fixity for a data constructor and the corresponding type constructor. For example:
917 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
918 and similarly for <literal>:*:</literal>.
919 <literal>Int `a` Bool</literal>.
922 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
925 Data type and type-synonym declarations can be written infix. E.g.
927 data a :*: b = Foo a b
928 type a :+: b = Either a b
932 The only thing that differs between operators in types and operators in expressions is that
933 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
934 are not allowed in types. Reason: the uniform thing to do would be to make them type
935 variables, but that's not very useful. A less uniform but more useful thing would be to
936 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
937 lists. So for now we just exclude them.
944 <sect3 id="type-synonyms">
945 <title>Liberalised type synonyms</title>
948 Type synonmys are like macros at the type level, and
949 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
950 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
952 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
953 in a type synonym, thus:
955 type Discard a = forall b. Show b => a -> b -> (a, String)
960 g :: Discard Int -> (Int,Bool) -- A rank-2 type
967 You can write an unboxed tuple in a type synonym:
969 type Pr = (# Int, Int #)
977 You can apply a type synonym to a forall type:
979 type Foo a = a -> a -> Bool
981 f :: Foo (forall b. b->b)
983 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
985 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
990 You can apply a type synonym to a partially applied type synonym:
992 type Generic i o = forall x. i x -> o x
997 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
999 foo :: forall x. x -> [x]
1007 GHC currently does kind checking before expanding synonyms (though even that
1011 After expanding type synonyms, GHC does validity checking on types, looking for
1012 the following mal-formedness which isn't detected simply by kind checking:
1015 Type constructor applied to a type involving for-alls.
1018 Unboxed tuple on left of an arrow.
1021 Partially-applied type synonym.
1025 this will be rejected:
1027 type Pr = (# Int, Int #)
1032 because GHC does not allow unboxed tuples on the left of a function arrow.
1037 <sect3 id="existential-quantification">
1038 <title>Existentially quantified data constructors
1042 The idea of using existential quantification in data type declarations
1043 was suggested by Laufer (I believe, thought doubtless someone will
1044 correct me), and implemented in Hope+. It's been in Lennart
1045 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1046 proved very useful. Here's the idea. Consider the declaration:
1052 data Foo = forall a. MkFoo a (a -> Bool)
1059 The data type <literal>Foo</literal> has two constructors with types:
1065 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1072 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1073 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1074 For example, the following expression is fine:
1080 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1086 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1087 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1088 isUpper</function> packages a character with a compatible function. These
1089 two things are each of type <literal>Foo</literal> and can be put in a list.
1093 What can we do with a value of type <literal>Foo</literal>?. In particular,
1094 what happens when we pattern-match on <function>MkFoo</function>?
1100 f (MkFoo val fn) = ???
1106 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1107 are compatible, the only (useful) thing we can do with them is to
1108 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1115 f (MkFoo val fn) = fn val
1121 What this allows us to do is to package heterogenous values
1122 together with a bunch of functions that manipulate them, and then treat
1123 that collection of packages in a uniform manner. You can express
1124 quite a bit of object-oriented-like programming this way.
1127 <sect4 id="existential">
1128 <title>Why existential?
1132 What has this to do with <emphasis>existential</emphasis> quantification?
1133 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1139 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1145 But Haskell programmers can safely think of the ordinary
1146 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1147 adding a new existential quantification construct.
1153 <title>Type classes</title>
1156 An easy extension (implemented in <command>hbc</command>) is to allow
1157 arbitrary contexts before the constructor. For example:
1163 data Baz = forall a. Eq a => Baz1 a a
1164 | forall b. Show b => Baz2 b (b -> b)
1170 The two constructors have the types you'd expect:
1176 Baz1 :: forall a. Eq a => a -> a -> Baz
1177 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1183 But when pattern matching on <function>Baz1</function> the matched values can be compared
1184 for equality, and when pattern matching on <function>Baz2</function> the first matched
1185 value can be converted to a string (as well as applying the function to it).
1186 So this program is legal:
1193 f (Baz1 p q) | p == q = "Yes"
1195 f (Baz2 v fn) = show (fn v)
1201 Operationally, in a dictionary-passing implementation, the
1202 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1203 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1204 extract it on pattern matching.
1208 Notice the way that the syntax fits smoothly with that used for
1209 universal quantification earlier.
1215 <title>Restrictions</title>
1218 There are several restrictions on the ways in which existentially-quantified
1219 constructors can be use.
1228 When pattern matching, each pattern match introduces a new,
1229 distinct, type for each existential type variable. These types cannot
1230 be unified with any other type, nor can they escape from the scope of
1231 the pattern match. For example, these fragments are incorrect:
1239 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1240 is the result of <function>f1</function>. One way to see why this is wrong is to
1241 ask what type <function>f1</function> has:
1245 f1 :: Foo -> a -- Weird!
1249 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1254 f1 :: forall a. Foo -> a -- Wrong!
1258 The original program is just plain wrong. Here's another sort of error
1262 f2 (Baz1 a b) (Baz1 p q) = a==q
1266 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1267 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1268 from the two <function>Baz1</function> constructors.
1276 You can't pattern-match on an existentially quantified
1277 constructor in a <literal>let</literal> or <literal>where</literal> group of
1278 bindings. So this is illegal:
1282 f3 x = a==b where { Baz1 a b = x }
1285 Instead, use a <literal>case</literal> expression:
1288 f3 x = case x of Baz1 a b -> a==b
1291 In general, you can only pattern-match
1292 on an existentially-quantified constructor in a <literal>case</literal> expression or
1293 in the patterns of a function definition.
1295 The reason for this restriction is really an implementation one.
1296 Type-checking binding groups is already a nightmare without
1297 existentials complicating the picture. Also an existential pattern
1298 binding at the top level of a module doesn't make sense, because it's
1299 not clear how to prevent the existentially-quantified type "escaping".
1300 So for now, there's a simple-to-state restriction. We'll see how
1308 You can't use existential quantification for <literal>newtype</literal>
1309 declarations. So this is illegal:
1313 newtype T = forall a. Ord a => MkT a
1317 Reason: a value of type <literal>T</literal> must be represented as a
1318 pair of a dictionary for <literal>Ord t</literal> and a value of type
1319 <literal>t</literal>. That contradicts the idea that
1320 <literal>newtype</literal> should have no concrete representation.
1321 You can get just the same efficiency and effect by using
1322 <literal>data</literal> instead of <literal>newtype</literal>. If
1323 there is no overloading involved, then there is more of a case for
1324 allowing an existentially-quantified <literal>newtype</literal>,
1325 because the <literal>data</literal> version does carry an
1326 implementation cost, but single-field existentially quantified
1327 constructors aren't much use. So the simple restriction (no
1328 existential stuff on <literal>newtype</literal>) stands, unless there
1329 are convincing reasons to change it.
1337 You can't use <literal>deriving</literal> to define instances of a
1338 data type with existentially quantified data constructors.
1340 Reason: in most cases it would not make sense. For example:#
1343 data T = forall a. MkT [a] deriving( Eq )
1346 To derive <literal>Eq</literal> in the standard way we would need to have equality
1347 between the single component of two <function>MkT</function> constructors:
1351 (MkT a) == (MkT b) = ???
1354 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1355 It's just about possible to imagine examples in which the derived instance
1356 would make sense, but it seems altogether simpler simply to prohibit such
1357 declarations. Define your own instances!
1372 <sect2 id="multi-param-type-classes">
1373 <title>Class declarations</title>
1376 This section documents GHC's implementation of multi-parameter type
1377 classes. There's lots of background in the paper <ulink
1378 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1379 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1380 Jones, Erik Meijer).
1383 There are the following constraints on class declarations:
1388 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1392 class Collection c a where
1393 union :: c a -> c a -> c a
1404 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1405 of "acyclic" involves only the superclass relationships. For example,
1411 op :: D b => a -> b -> b
1414 class C a => D a where { ... }
1418 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1419 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1420 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1427 <emphasis>There are no restrictions on the context in a class declaration
1428 (which introduces superclasses), except that the class hierarchy must
1429 be acyclic</emphasis>. So these class declarations are OK:
1433 class Functor (m k) => FiniteMap m k where
1436 class (Monad m, Monad (t m)) => Transform t m where
1437 lift :: m a -> (t m) a
1447 <emphasis>All of the class type variables must be reachable (in the sense
1448 mentioned in <xref linkend="type-restrictions"/>)
1449 from the free varibles of each method type
1450 </emphasis>. For example:
1454 class Coll s a where
1456 insert :: s -> a -> s
1460 is not OK, because the type of <literal>empty</literal> doesn't mention
1461 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1462 types, and has the same motivation.
1464 Sometimes, offending class declarations exhibit misunderstandings. For
1465 example, <literal>Coll</literal> might be rewritten
1469 class Coll s a where
1471 insert :: s a -> a -> s a
1475 which makes the connection between the type of a collection of
1476 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1477 Occasionally this really doesn't work, in which case you can split the
1485 class CollE s => Coll s a where
1486 insert :: s -> a -> s
1496 <sect3 id="class-method-types">
1497 <title>Class method types</title>
1499 Haskell 98 prohibits class method types to mention constraints on the
1500 class type variable, thus:
1503 fromList :: [a] -> s a
1504 elem :: Eq a => a -> s a -> Bool
1506 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1507 contains the constraint <literal>Eq a</literal>, constrains only the
1508 class type variable (in this case <literal>a</literal>).
1511 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1518 <sect2 id="type-restrictions">
1519 <title>Type signatures</title>
1521 <sect3><title>The context of a type signature</title>
1523 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1524 the form <emphasis>(class type-variable)</emphasis> or
1525 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1526 these type signatures are perfectly OK
1529 g :: Ord (T a ()) => ...
1533 GHC imposes the following restrictions on the constraints in a type signature.
1537 forall tv1..tvn (c1, ...,cn) => type
1540 (Here, we write the "foralls" explicitly, although the Haskell source
1541 language omits them; in Haskell 98, all the free type variables of an
1542 explicit source-language type signature are universally quantified,
1543 except for the class type variables in a class declaration. However,
1544 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1553 <emphasis>Each universally quantified type variable
1554 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1556 A type variable <literal>a</literal> is "reachable" if it it appears
1557 in the same constraint as either a type variable free in in
1558 <literal>type</literal>, or another reachable type variable.
1559 A value with a type that does not obey
1560 this reachability restriction cannot be used without introducing
1561 ambiguity; that is why the type is rejected.
1562 Here, for example, is an illegal type:
1566 forall a. Eq a => Int
1570 When a value with this type was used, the constraint <literal>Eq tv</literal>
1571 would be introduced where <literal>tv</literal> is a fresh type variable, and
1572 (in the dictionary-translation implementation) the value would be
1573 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1574 can never know which instance of <literal>Eq</literal> to use because we never
1575 get any more information about <literal>tv</literal>.
1579 that the reachability condition is weaker than saying that <literal>a</literal> is
1580 functionally dependendent on a type variable free in
1581 <literal>type</literal> (see <xref
1582 linkend="functional-dependencies"/>). The reason for this is there
1583 might be a "hidden" dependency, in a superclass perhaps. So
1584 "reachable" is a conservative approximation to "functionally dependent".
1585 For example, consider:
1587 class C a b | a -> b where ...
1588 class C a b => D a b where ...
1589 f :: forall a b. D a b => a -> a
1591 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1592 but that is not immediately apparent from <literal>f</literal>'s type.
1598 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1599 universally quantified type variables <literal>tvi</literal></emphasis>.
1601 For example, this type is OK because <literal>C a b</literal> mentions the
1602 universally quantified type variable <literal>b</literal>:
1606 forall a. C a b => burble
1610 The next type is illegal because the constraint <literal>Eq b</literal> does not
1611 mention <literal>a</literal>:
1615 forall a. Eq b => burble
1619 The reason for this restriction is milder than the other one. The
1620 excluded types are never useful or necessary (because the offending
1621 context doesn't need to be witnessed at this point; it can be floated
1622 out). Furthermore, floating them out increases sharing. Lastly,
1623 excluding them is a conservative choice; it leaves a patch of
1624 territory free in case we need it later.
1635 <title>For-all hoisting</title>
1637 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1638 end of an arrow, thus:
1640 type Discard a = forall b. a -> b -> a
1642 g :: Int -> Discard Int
1645 Simply expanding the type synonym would give
1647 g :: Int -> (forall b. Int -> b -> Int)
1649 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1651 g :: forall b. Int -> Int -> b -> Int
1653 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1654 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1655 performs the transformation:</emphasis>
1657 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1659 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1661 (In fact, GHC tries to retain as much synonym information as possible for use in
1662 error messages, but that is a usability issue.) This rule applies, of course, whether
1663 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1664 valid way to write <literal>g</literal>'s type signature:
1666 g :: Int -> Int -> forall b. b -> Int
1670 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1673 type Foo a = (?x::Int) => Bool -> a
1678 g :: (?x::Int) => Bool -> Bool -> Int
1686 <sect2 id="instance-decls">
1687 <title>Instance declarations</title>
1690 <title>Overlapping instances</title>
1692 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1697 instance context1 => C type1 where ...
1698 instance context2 => C type2 where ...
1701 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
1704 However, if you give the command line option
1705 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1706 option</primary></indexterm> then overlapping instance declarations are permitted.
1707 However, GHC arranges never to commit to using an instance declaration
1708 if another instance declaration also applies, either now or later.
1714 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1720 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1721 (but not identical to <literal>type1</literal>), or vice versa.
1725 Notice that these rules
1730 make it clear which instance decl to use
1731 (pick the most specific one that matches)
1738 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1739 Reason: you can pick which instance decl
1740 "matches" based on the type.
1745 However the rules are over-conservative. Two instance declarations can overlap,
1746 but it can still be clear in particular situations which to use. For example:
1748 instance C (Int,a) where ...
1749 instance C (a,Bool) where ...
1751 These are rejected by GHC's rules, but it is clear what to do when trying
1752 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1753 cannot apply. Yell if this restriction bites you.
1756 GHC is also conservative about committing to an overlapping instance. For example:
1758 class C a where { op :: a -> a }
1759 instance C [Int] where ...
1760 instance C a => C [a] where ...
1762 f :: C b => [b] -> [b]
1765 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1766 GHC does not commit to the second instance declaration, because in a paricular
1767 call of f, b might be instantiate to Int, so the first instance declaration
1768 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1769 GHC will instead silently pick the second instance, without complaining about
1770 the problem of subsequent instantiations.
1773 Regrettably, GHC doesn't guarantee to detect overlapping instance
1774 declarations if they appear in different modules. GHC can "see" the
1775 instance declarations in the transitive closure of all the modules
1776 imported by the one being compiled, so it can "see" all instance decls
1777 when it is compiling <literal>Main</literal>. However, it currently chooses not
1778 to look at ones that can't possibly be of use in the module currently
1779 being compiled, in the interests of efficiency. (Perhaps we should
1780 change that decision, at least for <literal>Main</literal>.)
1785 <title>Type synonyms in the instance head</title>
1788 <emphasis>Unlike Haskell 98, instance heads may use type
1789 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1790 As always, using a type synonym is just shorthand for
1791 writing the RHS of the type synonym definition. For example:
1795 type Point = (Int,Int)
1796 instance C Point where ...
1797 instance C [Point] where ...
1801 is legal. However, if you added
1805 instance C (Int,Int) where ...
1809 as well, then the compiler will complain about the overlapping
1810 (actually, identical) instance declarations. As always, type synonyms
1811 must be fully applied. You cannot, for example, write:
1816 instance Monad P where ...
1820 This design decision is independent of all the others, and easily
1821 reversed, but it makes sense to me.
1826 <sect3 id="undecidable-instances">
1827 <title>Undecidable instances</title>
1829 <para>An instance declaration must normally obey the following rules:
1831 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1832 an instance declaration <emphasis>must not</emphasis> be a type variable.
1833 For example, these are OK:
1836 instance C Int a where ...
1838 instance D (Int, Int) where ...
1840 instance E [[a]] where ...
1844 instance F a where ...
1846 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1847 For example, this is OK:
1849 instance Stateful (ST s) (MutVar s) where ...
1856 <para>All of the types in the <emphasis>context</emphasis> of
1857 an instance declaration <emphasis>must</emphasis> be type variables.
1860 instance C a b => Eq (a,b) where ...
1864 instance C Int b => Foo b where ...
1870 These restrictions ensure that
1871 context reduction terminates: each reduction step removes one type
1872 constructor. For example, the following would make the type checker
1873 loop if it wasn't excluded:
1875 instance C a => C a where ...
1877 There are two situations in which the rule is a bit of a pain. First,
1878 if one allows overlapping instance declarations then it's quite
1879 convenient to have a "default instance" declaration that applies if
1880 something more specific does not:
1889 Second, sometimes you might want to use the following to get the
1890 effect of a "class synonym":
1894 class (C1 a, C2 a, C3 a) => C a where { }
1896 instance (C1 a, C2 a, C3 a) => C a where { }
1900 This allows you to write shorter signatures:
1912 f :: (C1 a, C2 a, C3 a) => ...
1916 Voluminous correspondence on the Haskell mailing list has convinced me
1917 that it's worth experimenting with more liberal rules. If you use
1918 the experimental flag <option>-fallow-undecidable-instances</option>
1919 <indexterm><primary>-fallow-undecidable-instances
1920 option</primary></indexterm>, you can use arbitrary
1921 types in both an instance context and instance head. Termination is ensured by having a
1922 fixed-depth recursion stack. If you exceed the stack depth you get a
1923 sort of backtrace, and the opportunity to increase the stack depth
1924 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1927 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1928 allowing these idioms interesting idioms.
1935 <sect2 id="implicit-parameters">
1936 <title>Implicit parameters</title>
1938 <para> Implicit paramters are implemented as described in
1939 "Implicit parameters: dynamic scoping with static types",
1940 J Lewis, MB Shields, E Meijer, J Launchbury,
1941 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1945 <para>(Most of the following, stil rather incomplete, documentation is
1946 due to Jeff Lewis.)</para>
1948 <para>Implicit parameter support is enabled with the option
1949 <option>-fimplicit-params</option>.</para>
1952 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1953 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1954 context. In Haskell, all variables are statically bound. Dynamic
1955 binding of variables is a notion that goes back to Lisp, but was later
1956 discarded in more modern incarnations, such as Scheme. Dynamic binding
1957 can be very confusing in an untyped language, and unfortunately, typed
1958 languages, in particular Hindley-Milner typed languages like Haskell,
1959 only support static scoping of variables.
1962 However, by a simple extension to the type class system of Haskell, we
1963 can support dynamic binding. Basically, we express the use of a
1964 dynamically bound variable as a constraint on the type. These
1965 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1966 function uses a dynamically-bound variable <literal>?x</literal>
1967 of type <literal>t'</literal>". For
1968 example, the following expresses the type of a sort function,
1969 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1971 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1973 The dynamic binding constraints are just a new form of predicate in the type class system.
1976 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1977 where <literal>x</literal> is
1978 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1979 Use of this construct also introduces a new
1980 dynamic-binding constraint in the type of the expression.
1981 For example, the following definition
1982 shows how we can define an implicitly parameterized sort function in
1983 terms of an explicitly parameterized <literal>sortBy</literal> function:
1985 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1987 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1993 <title>Implicit-parameter type constraints</title>
1995 Dynamic binding constraints behave just like other type class
1996 constraints in that they are automatically propagated. Thus, when a
1997 function is used, its implicit parameters are inherited by the
1998 function that called it. For example, our <literal>sort</literal> function might be used
1999 to pick out the least value in a list:
2001 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2002 least xs = fst (sort xs)
2004 Without lifting a finger, the <literal>?cmp</literal> parameter is
2005 propagated to become a parameter of <literal>least</literal> as well. With explicit
2006 parameters, the default is that parameters must always be explicit
2007 propagated. With implicit parameters, the default is to always
2011 An implicit-parameter type constraint differs from other type class constraints in the
2012 following way: All uses of a particular implicit parameter must have
2013 the same type. This means that the type of <literal>(?x, ?x)</literal>
2014 is <literal>(?x::a) => (a,a)</literal>, and not
2015 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2019 <para> You can't have an implicit parameter in the context of a class or instance
2020 declaration. For example, both these declarations are illegal:
2022 class (?x::Int) => C a where ...
2023 instance (?x::a) => Foo [a] where ...
2025 Reason: exactly which implicit parameter you pick up depends on exactly where
2026 you invoke a function. But the ``invocation'' of instance declarations is done
2027 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2028 Easiest thing is to outlaw the offending types.</para>
2030 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2032 f :: (?x :: [a]) => Int -> Int
2035 g :: (Read a, Show a) => String -> String
2038 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2039 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2040 quite unambiguous, and fixes the type <literal>a</literal>.
2045 <title>Implicit-parameter bindings</title>
2048 An implicit parameter is <emphasis>bound</emphasis> using the standard
2049 <literal>let</literal> or <literal>where</literal> binding forms.
2050 For example, we define the <literal>min</literal> function by binding
2051 <literal>cmp</literal>.
2054 min = let ?cmp = (<=) in least
2058 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2059 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2060 (including in a list comprehension, or do-notation, or pattern guards),
2061 or a <literal>where</literal> clause.
2062 Note the following points:
2065 An implicit-parameter binding group must be a
2066 collection of simple bindings to implicit-style variables (no
2067 function-style bindings, and no type signatures); these bindings are
2068 neither polymorphic or recursive.
2071 You may not mix implicit-parameter bindings with ordinary bindings in a
2072 single <literal>let</literal>
2073 expression; use two nested <literal>let</literal>s instead.
2074 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2078 You may put multiple implicit-parameter bindings in a
2079 single binding group; but they are <emphasis>not</emphasis> treated
2080 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2081 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2082 parameter. The bindings are not nested, and may be re-ordered without changing
2083 the meaning of the program.
2084 For example, consider:
2086 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2088 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2089 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2091 f :: (?x::Int) => Int -> Int
2100 <sect2 id="linear-implicit-parameters">
2101 <title>Linear implicit parameters</title>
2103 Linear implicit parameters are an idea developed by Koen Claessen,
2104 Mark Shields, and Simon PJ. They address the long-standing
2105 problem that monads seem over-kill for certain sorts of problem, notably:
2108 <listitem> <para> distributing a supply of unique names </para> </listitem>
2109 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2110 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2114 Linear implicit parameters are just like ordinary implicit parameters,
2115 except that they are "linear" -- that is, they cannot be copied, and
2116 must be explicitly "split" instead. Linear implicit parameters are
2117 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2118 (The '/' in the '%' suggests the split!)
2123 import GHC.Exts( Splittable )
2125 data NameSupply = ...
2127 splitNS :: NameSupply -> (NameSupply, NameSupply)
2128 newName :: NameSupply -> Name
2130 instance Splittable NameSupply where
2134 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2135 f env (Lam x e) = Lam x' (f env e)
2138 env' = extend env x x'
2139 ...more equations for f...
2141 Notice that the implicit parameter %ns is consumed
2143 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2144 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2148 So the translation done by the type checker makes
2149 the parameter explicit:
2151 f :: NameSupply -> Env -> Expr -> Expr
2152 f ns env (Lam x e) = Lam x' (f ns1 env e)
2154 (ns1,ns2) = splitNS ns
2156 env = extend env x x'
2158 Notice the call to 'split' introduced by the type checker.
2159 How did it know to use 'splitNS'? Because what it really did
2160 was to introduce a call to the overloaded function 'split',
2161 defined by the class <literal>Splittable</literal>:
2163 class Splittable a where
2166 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2167 split for name supplies. But we can simply write
2173 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2175 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2176 <literal>GHC.Exts</literal>.
2181 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2182 are entirely distinct implicit parameters: you
2183 can use them together and they won't intefere with each other. </para>
2186 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2188 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2189 in the context of a class or instance declaration. </para></listitem>
2193 <sect3><title>Warnings</title>
2196 The monomorphism restriction is even more important than usual.
2197 Consider the example above:
2199 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2200 f env (Lam x e) = Lam x' (f env e)
2203 env' = extend env x x'
2205 If we replaced the two occurrences of x' by (newName %ns), which is
2206 usually a harmless thing to do, we get:
2208 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2209 f env (Lam x e) = Lam (newName %ns) (f env e)
2211 env' = extend env x (newName %ns)
2213 But now the name supply is consumed in <emphasis>three</emphasis> places
2214 (the two calls to newName,and the recursive call to f), so
2215 the result is utterly different. Urk! We don't even have
2219 Well, this is an experimental change. With implicit
2220 parameters we have already lost beta reduction anyway, and
2221 (as John Launchbury puts it) we can't sensibly reason about
2222 Haskell programs without knowing their typing.
2227 <sect3><title>Recursive functions</title>
2228 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2231 foo :: %x::T => Int -> [Int]
2233 foo n = %x : foo (n-1)
2235 where T is some type in class Splittable.</para>
2237 Do you get a list of all the same T's or all different T's
2238 (assuming that split gives two distinct T's back)?
2240 If you supply the type signature, taking advantage of polymorphic
2241 recursion, you get what you'd probably expect. Here's the
2242 translated term, where the implicit param is made explicit:
2245 foo x n = let (x1,x2) = split x
2246 in x1 : foo x2 (n-1)
2248 But if you don't supply a type signature, GHC uses the Hindley
2249 Milner trick of using a single monomorphic instance of the function
2250 for the recursive calls. That is what makes Hindley Milner type inference
2251 work. So the translation becomes
2255 foom n = x : foom (n-1)
2259 Result: 'x' is not split, and you get a list of identical T's. So the
2260 semantics of the program depends on whether or not foo has a type signature.
2263 You may say that this is a good reason to dislike linear implicit parameters
2264 and you'd be right. That is why they are an experimental feature.
2270 <sect2 id="functional-dependencies">
2271 <title>Functional dependencies
2274 <para> Functional dependencies are implemented as described by Mark Jones
2275 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2276 In Proceedings of the 9th European Symposium on Programming,
2277 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2281 Functional dependencies are introduced by a vertical bar in the syntax of a
2282 class declaration; e.g.
2284 class (Monad m) => MonadState s m | m -> s where ...
2286 class Foo a b c | a b -> c where ...
2288 There should be more documentation, but there isn't (yet). Yell if you need it.
2294 <sect2 id="sec-kinding">
2295 <title>Explicitly-kinded quantification</title>
2298 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2299 to give the kind explicitly as (machine-checked) documentation,
2300 just as it is nice to give a type signature for a function. On some occasions,
2301 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2302 John Hughes had to define the data type:
2304 data Set cxt a = Set [a]
2305 | Unused (cxt a -> ())
2307 The only use for the <literal>Unused</literal> constructor was to force the correct
2308 kind for the type variable <literal>cxt</literal>.
2311 GHC now instead allows you to specify the kind of a type variable directly, wherever
2312 a type variable is explicitly bound. Namely:
2314 <listitem><para><literal>data</literal> declarations:
2316 data Set (cxt :: * -> *) a = Set [a]
2317 </screen></para></listitem>
2318 <listitem><para><literal>type</literal> declarations:
2320 type T (f :: * -> *) = f Int
2321 </screen></para></listitem>
2322 <listitem><para><literal>class</literal> declarations:
2324 class (Eq a) => C (f :: * -> *) a where ...
2325 </screen></para></listitem>
2326 <listitem><para><literal>forall</literal>'s in type signatures:
2328 f :: forall (cxt :: * -> *). Set cxt Int
2329 </screen></para></listitem>
2334 The parentheses are required. Some of the spaces are required too, to
2335 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2336 will get a parse error, because "<literal>::*->*</literal>" is a
2337 single lexeme in Haskell.
2341 As part of the same extension, you can put kind annotations in types
2344 f :: (Int :: *) -> Int
2345 g :: forall a. a -> (a :: *)
2349 atype ::= '(' ctype '::' kind ')
2351 The parentheses are required.
2356 <sect2 id="universal-quantification">
2357 <title>Arbitrary-rank polymorphism
2361 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2362 allows us to say exactly what this means. For example:
2370 g :: forall b. (b -> b)
2372 The two are treated identically.
2376 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2377 explicit universal quantification in
2379 For example, all the following types are legal:
2381 f1 :: forall a b. a -> b -> a
2382 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2384 f2 :: (forall a. a->a) -> Int -> Int
2385 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2387 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2389 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2390 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2391 The <literal>forall</literal> makes explicit the universal quantification that
2392 is implicitly added by Haskell.
2395 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2396 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2397 shows, the polymorphic type on the left of the function arrow can be overloaded.
2400 The function <literal>f3</literal> has a rank-3 type;
2401 it has rank-2 types on the left of a function arrow.
2404 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2405 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2406 that restriction has now been lifted.)
2407 In particular, a forall-type (also called a "type scheme"),
2408 including an operational type class context, is legal:
2410 <listitem> <para> On the left of a function arrow </para> </listitem>
2411 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2412 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2413 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2414 field type signatures.</para> </listitem>
2415 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2416 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2418 There is one place you cannot put a <literal>forall</literal>:
2419 you cannot instantiate a type variable with a forall-type. So you cannot
2420 make a forall-type the argument of a type constructor. So these types are illegal:
2422 x1 :: [forall a. a->a]
2423 x2 :: (forall a. a->a, Int)
2424 x3 :: Maybe (forall a. a->a)
2426 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2427 a type variable any more!
2436 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2437 the types of the constructor arguments. Here are several examples:
2443 data T a = T1 (forall b. b -> b -> b) a
2445 data MonadT m = MkMonad { return :: forall a. a -> m a,
2446 bind :: forall a b. m a -> (a -> m b) -> m b
2449 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2455 The constructors have rank-2 types:
2461 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2462 MkMonad :: forall m. (forall a. a -> m a)
2463 -> (forall a b. m a -> (a -> m b) -> m b)
2465 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2471 Notice that you don't need to use a <literal>forall</literal> if there's an
2472 explicit context. For example in the first argument of the
2473 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2474 prefixed to the argument type. The implicit <literal>forall</literal>
2475 quantifies all type variables that are not already in scope, and are
2476 mentioned in the type quantified over.
2480 As for type signatures, implicit quantification happens for non-overloaded
2481 types too. So if you write this:
2484 data T a = MkT (Either a b) (b -> b)
2487 it's just as if you had written this:
2490 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2493 That is, since the type variable <literal>b</literal> isn't in scope, it's
2494 implicitly universally quantified. (Arguably, it would be better
2495 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2496 where that is what is wanted. Feedback welcomed.)
2500 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2501 the constructor to suitable values, just as usual. For example,
2512 a3 = MkSwizzle reverse
2515 a4 = let r x = Just x
2522 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2523 mkTs f x y = [T1 f x, T1 f y]
2529 The type of the argument can, as usual, be more general than the type
2530 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2531 does not need the <literal>Ord</literal> constraint.)
2535 When you use pattern matching, the bound variables may now have
2536 polymorphic types. For example:
2542 f :: T a -> a -> (a, Char)
2543 f (T1 w k) x = (w k x, w 'c' 'd')
2545 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2546 g (MkSwizzle s) xs f = s (map f (s xs))
2548 h :: MonadT m -> [m a] -> m [a]
2549 h m [] = return m []
2550 h m (x:xs) = bind m x $ \y ->
2551 bind m (h m xs) $ \ys ->
2558 In the function <function>h</function> we use the record selectors <literal>return</literal>
2559 and <literal>bind</literal> to extract the polymorphic bind and return functions
2560 from the <literal>MonadT</literal> data structure, rather than using pattern
2566 <title>Type inference</title>
2569 In general, type inference for arbitrary-rank types is undecideable.
2570 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2571 to get a decidable algorithm by requiring some help from the programmer.
2572 We do not yet have a formal specification of "some help" but the rule is this:
2575 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2576 provides an explicit polymorphic type for x, or GHC's type inference will assume
2577 that x's type has no foralls in it</emphasis>.
2580 What does it mean to "provide" an explicit type for x? You can do that by
2581 giving a type signature for x directly, using a pattern type signature
2582 (<xref linkend="scoped-type-variables"/>), thus:
2584 \ f :: (forall a. a->a) -> (f True, f 'c')
2586 Alternatively, you can give a type signature to the enclosing
2587 context, which GHC can "push down" to find the type for the variable:
2589 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2591 Here the type signature on the expression can be pushed inwards
2592 to give a type signature for f. Similarly, and more commonly,
2593 one can give a type signature for the function itself:
2595 h :: (forall a. a->a) -> (Bool,Char)
2596 h f = (f True, f 'c')
2598 You don't need to give a type signature if the lambda bound variable
2599 is a constructor argument. Here is an example we saw earlier:
2601 f :: T a -> a -> (a, Char)
2602 f (T1 w k) x = (w k x, w 'c' 'd')
2604 Here we do not need to give a type signature to <literal>w</literal>, because
2605 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2612 <sect3 id="implicit-quant">
2613 <title>Implicit quantification</title>
2616 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2617 user-written types, if and only if there is no explicit <literal>forall</literal>,
2618 GHC finds all the type variables mentioned in the type that are not already
2619 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2623 f :: forall a. a -> a
2630 h :: forall b. a -> b -> b
2636 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2639 f :: (a -> a) -> Int
2641 f :: forall a. (a -> a) -> Int
2643 f :: (forall a. a -> a) -> Int
2646 g :: (Ord a => a -> a) -> Int
2647 -- MEANS the illegal type
2648 g :: forall a. (Ord a => a -> a) -> Int
2650 g :: (forall a. Ord a => a -> a) -> Int
2652 The latter produces an illegal type, which you might think is silly,
2653 but at least the rule is simple. If you want the latter type, you
2654 can write your for-alls explicitly. Indeed, doing so is strongly advised
2663 <sect2 id="scoped-type-variables">
2664 <title>Scoped type variables
2668 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2669 variable</emphasis>. For example
2675 f (xs::[a]) = ys ++ ys
2684 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2685 This brings the type variable <literal>a</literal> into scope; it scopes over
2686 all the patterns and right hand sides for this equation for <function>f</function>.
2687 In particular, it is in scope at the type signature for <varname>y</varname>.
2691 Pattern type signatures are completely orthogonal to ordinary, separate
2692 type signatures. The two can be used independently or together.
2693 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2694 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2695 implicitly universally quantified. (If there are no type variables in
2696 scope, all type variables mentioned in the signature are universally
2697 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2698 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2699 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2700 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2701 it becomes possible to do so.
2705 Scoped type variables are implemented in both GHC and Hugs. Where the
2706 implementations differ from the specification below, those differences
2711 So much for the basic idea. Here are the details.
2715 <title>What a pattern type signature means</title>
2717 A type variable brought into scope by a pattern type signature is simply
2718 the name for a type. The restriction they express is that all occurrences
2719 of the same name mean the same type. For example:
2721 f :: [Int] -> Int -> Int
2722 f (xs::[a]) (y::a) = (head xs + y) :: a
2724 The pattern type signatures on the left hand side of
2725 <literal>f</literal> express the fact that <literal>xs</literal>
2726 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2727 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2728 specifies that this expression must have the same type <literal>a</literal>.
2729 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2730 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2731 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2732 rules, which specified that a pattern-bound type variable should be universally quantified.)
2733 For example, all of these are legal:</para>
2736 t (x::a) (y::a) = x+y*2
2738 f (x::a) (y::b) = [x,y] -- a unifies with b
2740 g (x::a) = x + 1::Int -- a unifies with Int
2742 h x = let k (y::a) = [x,y] -- a is free in the
2743 in k x -- environment
2745 k (x::a) True = ... -- a unifies with Int
2746 k (x::Int) False = ...
2749 w (x::a) = x -- a unifies with [b]
2755 <title>Scope and implicit quantification</title>
2763 All the type variables mentioned in a pattern,
2764 that are not already in scope,
2765 are brought into scope by the pattern. We describe this set as
2766 the <emphasis>type variables bound by the pattern</emphasis>.
2769 f (x::a) = let g (y::(a,b)) = fst y
2773 The pattern <literal>(x::a)</literal> brings the type variable
2774 <literal>a</literal> into scope, as well as the term
2775 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2776 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2777 and brings into scope the type variable <literal>b</literal>.
2783 The type variable(s) bound by the pattern have the same scope
2784 as the term variable(s) bound by the pattern. For example:
2787 f (x::a) = <...rhs of f...>
2788 (p::b, q::b) = (1,2)
2789 in <...body of let...>
2791 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2792 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2793 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2794 just like <literal>p</literal> and <literal>q</literal> do.
2795 Indeed, the newly bound type variables also scope over any ordinary, separate
2796 type signatures in the <literal>let</literal> group.
2803 The type variables bound by the pattern may be
2804 mentioned in ordinary type signatures or pattern
2805 type signatures anywhere within their scope.
2812 In ordinary type signatures, any type variable mentioned in the
2813 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2821 Ordinary type signatures do not bring any new type variables
2822 into scope (except in the type signature itself!). So this is illegal:
2829 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2830 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2831 and that is an incorrect typing.
2838 The pattern type signature is a monotype:
2843 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2847 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2848 not to type schemes.
2852 There is no implicit universal quantification on pattern type signatures (in contrast to
2853 ordinary type signatures).
2863 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2864 scope over the methods defined in the <literal>where</literal> part. For example:
2878 (Not implemented in Hugs yet, Dec 98).
2889 <title>Where a pattern type signature can occur</title>
2892 A pattern type signature can occur in any pattern. For example:
2897 A pattern type signature can be on an arbitrary sub-pattern, not
2902 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2911 Pattern type signatures, including the result part, can be used
2912 in lambda abstractions:
2915 (\ (x::a, y) :: a -> x)
2922 Pattern type signatures, including the result part, can be used
2923 in <literal>case</literal> expressions:
2926 case e of { ((x::a, y) :: (a,b)) -> x }
2929 Note that the <literal>-></literal> symbol in a case alternative
2930 leads to difficulties when parsing a type signature in the pattern: in
2931 the absence of the extra parentheses in the example above, the parser
2932 would try to interpret the <literal>-></literal> as a function
2933 arrow and give a parse error later.
2941 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2942 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2943 token or a parenthesised type of some sort). To see why,
2944 consider how one would parse this:
2958 Pattern type signatures can bind existential type variables.
2963 data T = forall a. MkT [a]
2966 f (MkT [t::a]) = MkT t3
2979 Pattern type signatures
2980 can be used in pattern bindings:
2983 f x = let (y, z::a) = x in ...
2984 f1 x = let (y, z::Int) = x in ...
2985 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2986 f3 :: (b->b) = \x -> x
2989 In all such cases, the binding is not generalised over the pattern-bound
2990 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2991 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2992 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2993 In contrast, the binding
2998 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2999 in <literal>f4</literal>'s scope.
3009 <title>Result type signatures</title>
3012 The result type of a function can be given a signature, thus:
3016 f (x::a) :: [a] = [x,x,x]
3020 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3021 result type. Sometimes this is the only way of naming the type variable
3026 f :: Int -> [a] -> [a]
3027 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3028 in \xs -> map g (reverse xs `zip` xs)
3033 The type variables bound in a result type signature scope over the right hand side
3034 of the definition. However, consider this corner-case:
3036 rev1 :: [a] -> [a] = \xs -> reverse xs
3038 foo ys = rev (ys::[a])
3040 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3041 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3042 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3043 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3044 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3047 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3048 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3052 rev1 :: [a] -> [a] = \xs -> reverse xs
3057 Result type signatures are not yet implemented in Hugs.
3064 <sect2 id="deriving-typeable">
3065 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3068 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3069 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3070 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3071 classes <literal>Eq</literal>, <literal>Ord</literal>,
3072 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3075 GHC extends this list with two more classes that may be automatically derived
3076 (provided the <option>-fglasgow-exts</option> flag is specified):
3077 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3078 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3079 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3083 <sect2 id="newtype-deriving">
3084 <title>Generalised derived instances for newtypes</title>
3087 When you define an abstract type using <literal>newtype</literal>, you may want
3088 the new type to inherit some instances from its representation. In
3089 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3090 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3091 other classes you have to write an explicit instance declaration. For
3092 example, if you define
3095 newtype Dollars = Dollars Int
3098 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3099 explicitly define an instance of <literal>Num</literal>:
3102 instance Num Dollars where
3103 Dollars a + Dollars b = Dollars (a+b)
3106 All the instance does is apply and remove the <literal>newtype</literal>
3107 constructor. It is particularly galling that, since the constructor
3108 doesn't appear at run-time, this instance declaration defines a
3109 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3110 dictionary, only slower!
3114 <sect3> <title> Generalising the deriving clause </title>
3116 GHC now permits such instances to be derived instead, so one can write
3118 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3121 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3122 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3123 derives an instance declaration of the form
3126 instance Num Int => Num Dollars
3129 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3133 We can also derive instances of constructor classes in a similar
3134 way. For example, suppose we have implemented state and failure monad
3135 transformers, such that
3138 instance Monad m => Monad (State s m)
3139 instance Monad m => Monad (Failure m)
3141 In Haskell 98, we can define a parsing monad by
3143 type Parser tok m a = State [tok] (Failure m) a
3146 which is automatically a monad thanks to the instance declarations
3147 above. With the extension, we can make the parser type abstract,
3148 without needing to write an instance of class <literal>Monad</literal>, via
3151 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3154 In this case the derived instance declaration is of the form
3156 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3159 Notice that, since <literal>Monad</literal> is a constructor class, the
3160 instance is a <emphasis>partial application</emphasis> of the new type, not the
3161 entire left hand side. We can imagine that the type declaration is
3162 ``eta-converted'' to generate the context of the instance
3167 We can even derive instances of multi-parameter classes, provided the
3168 newtype is the last class parameter. In this case, a ``partial
3169 application'' of the class appears in the <literal>deriving</literal>
3170 clause. For example, given the class
3173 class StateMonad s m | m -> s where ...
3174 instance Monad m => StateMonad s (State s m) where ...
3176 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3178 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3179 deriving (Monad, StateMonad [tok])
3182 The derived instance is obtained by completing the application of the
3183 class to the new type:
3186 instance StateMonad [tok] (State [tok] (Failure m)) =>
3187 StateMonad [tok] (Parser tok m)
3192 As a result of this extension, all derived instances in newtype
3193 declarations are treated uniformly (and implemented just by reusing
3194 the dictionary for the representation type), <emphasis>except</emphasis>
3195 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3196 the newtype and its representation.
3200 <sect3> <title> A more precise specification </title>
3202 Derived instance declarations are constructed as follows. Consider the
3203 declaration (after expansion of any type synonyms)
3206 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3212 <literal>S</literal> is a type constructor,
3215 The <literal>t1...tk</literal> are types,
3218 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3219 the <literal>ti</literal>, and
3222 The <literal>ci</literal> are partial applications of
3223 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3224 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3227 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3228 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3229 should not "look through" the type or its constructor. You can still
3230 derive these classes for a newtype, but it happens in the usual way, not
3231 via this new mechanism.
3234 Then, for each <literal>ci</literal>, the derived instance
3237 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3239 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3240 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3244 As an example which does <emphasis>not</emphasis> work, consider
3246 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3248 Here we cannot derive the instance
3250 instance Monad (State s m) => Monad (NonMonad m)
3253 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3254 and so cannot be "eta-converted" away. It is a good thing that this
3255 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3256 not, in fact, a monad --- for the same reason. Try defining
3257 <literal>>>=</literal> with the correct type: you won't be able to.
3261 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3262 important, since we can only derive instances for the last one. If the
3263 <literal>StateMonad</literal> class above were instead defined as
3266 class StateMonad m s | m -> s where ...
3269 then we would not have been able to derive an instance for the
3270 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3271 classes usually have one "main" parameter for which deriving new
3272 instances is most interesting.
3280 <!-- ==================== End of type system extensions ================= -->
3282 <!-- ====================== TEMPLATE HASKELL ======================= -->
3284 <sect1 id="template-haskell">
3285 <title>Template Haskell</title>
3287 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3288 Template Haskell at <ulink url="http://www.haskell.org/th/">
3289 http://www.haskell.org/th/</ulink>, while
3291 the main technical innovations is discussed in "<ulink
3292 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3293 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3294 The details of the Template Haskell design are still in flux. Make sure you
3295 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3296 (search for the type ExpQ).
3297 [Temporary: many changes to the original design are described in
3298 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3299 Not all of these changes are in GHC 6.2.]
3302 <para> The first example from that paper is set out below as a worked example to help get you started.
3306 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3307 Tim Sheard is going to expand it.)
3311 <title>Syntax</title>
3313 <para> Template Haskell has the following new syntactic
3314 constructions. You need to use the flag
3315 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3316 </indexterm>to switch these syntactic extensions on
3317 (<option>-fth</option> is currently implied by
3318 <option>-fglasgow-exts</option>, but you are encouraged to
3319 specify it explicitly).</para>
3323 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3324 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3325 There must be no space between the "$" and the identifier or parenthesis. This use
3326 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3327 of "." as an infix operator. If you want the infix operator, put spaces around it.
3329 <para> A splice can occur in place of
3331 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3332 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3333 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3335 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3336 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3342 A expression quotation is written in Oxford brackets, thus:
3344 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3345 the quotation has type <literal>Expr</literal>.</para></listitem>
3346 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3347 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3348 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3349 the quotation has type <literal>Type</literal>.</para></listitem>
3350 </itemizedlist></para></listitem>
3353 Reification is written thus:
3355 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3356 has type <literal>Dec</literal>. </para></listitem>
3357 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3358 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3359 <listitem><para> Still to come: fixities </para></listitem>
3361 </itemizedlist></para>
3368 <sect2> <title> Using Template Haskell </title>
3372 The data types and monadic constructor functions for Template Haskell are in the library
3373 <literal>Language.Haskell.THSyntax</literal>.
3377 You can only run a function at compile time if it is imported from another module. That is,
3378 you can't define a function in a module, and call it from within a splice in the same module.
3379 (It would make sense to do so, but it's hard to implement.)
3383 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3386 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3387 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3388 compiles and runs a program, and then looks at the result. So it's important that
3389 the program it compiles produces results whose representations are identical to
3390 those of the compiler itself.
3394 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3395 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3400 <sect2> <title> A Template Haskell Worked Example </title>
3401 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3402 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3409 -- Import our template "pr"
3410 import Printf ( pr )
3412 -- The splice operator $ takes the Haskell source code
3413 -- generated at compile time by "pr" and splices it into
3414 -- the argument of "putStrLn".
3415 main = putStrLn ( $(pr "Hello") )
3421 -- Skeletal printf from the paper.
3422 -- It needs to be in a separate module to the one where
3423 -- you intend to use it.
3425 -- Import some Template Haskell syntax
3426 import Language.Haskell.TH.Syntax
3428 -- Describe a format string
3429 data Format = D | S | L String
3431 -- Parse a format string. This is left largely to you
3432 -- as we are here interested in building our first ever
3433 -- Template Haskell program and not in building printf.
3434 parse :: String -> [Format]
3437 -- Generate Haskell source code from a parsed representation
3438 -- of the format string. This code will be spliced into
3439 -- the module which calls "pr", at compile time.
3440 gen :: [Format] -> ExpQ
3441 gen [D] = [| \n -> show n |]
3442 gen [S] = [| \s -> s |]
3443 gen [L s] = stringE s
3445 -- Here we generate the Haskell code for the splice
3446 -- from an input format string.
3447 pr :: String -> ExpQ
3448 pr s = gen (parse s)
3451 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3454 $ ghc --make -fth main.hs -o main.exe
3457 <para>Run "main.exe" and here is your output:</para>
3468 <!-- ===================== Arrow notation =================== -->
3470 <sect1 id="arrow-notation">
3471 <title>Arrow notation
3474 <para>Arrows are a generalization of monads introduced by John Hughes.
3475 For more details, see
3480 “Generalising Monads to Arrows”,
3481 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3482 pp67–111, May 2000.
3488 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3489 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3495 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3496 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3502 and the arrows web page at
3503 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3504 With the <option>-farrows</option> flag, GHC supports the arrow
3505 notation described in the second of these papers.
3506 What follows is a brief introduction to the notation;
3507 it won't make much sense unless you've read Hughes's paper.
3508 This notation is translated to ordinary Haskell,
3509 using combinators from the
3510 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3514 <para>The extension adds a new kind of expression for defining arrows:
3516 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3517 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3519 where <literal>proc</literal> is a new keyword.
3520 The variables of the pattern are bound in the body of the
3521 <literal>proc</literal>-expression,
3522 which is a new sort of thing called a <firstterm>command</firstterm>.
3523 The syntax of commands is as follows:
3525 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3526 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3527 | <replaceable>cmd</replaceable><superscript>0</superscript>
3529 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3530 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3531 infix operators as for expressions, and
3533 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3534 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3535 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3536 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3537 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3538 | <replaceable>fcmd</replaceable>
3540 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3541 | ( <replaceable>cmd</replaceable> )
3542 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3544 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3545 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3546 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3547 | <replaceable>cmd</replaceable>
3549 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3550 except that the bodies are commands instead of expressions.
3554 Commands produce values, but (like monadic computations)
3555 may yield more than one value,
3556 or none, and may do other things as well.
3557 For the most part, familiarity with monadic notation is a good guide to
3559 However the values of expressions, even monadic ones,
3560 are determined by the values of the variables they contain;
3561 this is not necessarily the case for commands.
3565 A simple example of the new notation is the expression
3567 proc x -> f -< x+1
3569 We call this a <firstterm>procedure</firstterm> or
3570 <firstterm>arrow abstraction</firstterm>.
3571 As with a lambda expression, the variable <literal>x</literal>
3572 is a new variable bound within the <literal>proc</literal>-expression.
3573 It refers to the input to the arrow.
3574 In the above example, <literal>-<</literal> is not an identifier but an
3575 new reserved symbol used for building commands from an expression of arrow
3576 type and an expression to be fed as input to that arrow.
3577 (The weird look will make more sense later.)
3578 It may be read as analogue of application for arrows.
3579 The above example is equivalent to the Haskell expression
3581 arr (\ x -> x+1) >>> f
3583 That would make no sense if the expression to the left of
3584 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3585 More generally, the expression to the left of <literal>-<</literal>
3586 may not involve any <firstterm>local variable</firstterm>,
3587 i.e. a variable bound in the current arrow abstraction.
3588 For such a situation there is a variant <literal>-<<</literal>, as in
3590 proc x -> f x -<< x+1
3592 which is equivalent to
3594 arr (\ x -> (f, x+1)) >>> app
3596 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3598 Such an arrow is equivalent to a monad, so if you're using this form
3599 you may find a monadic formulation more convenient.
3603 <title>do-notation for commands</title>
3606 Another form of command is a form of <literal>do</literal>-notation.
3607 For example, you can write
3616 You can read this much like ordinary <literal>do</literal>-notation,
3617 but with commands in place of monadic expressions.
3618 The first line sends the value of <literal>x+1</literal> as an input to
3619 the arrow <literal>f</literal>, and matches its output against
3620 <literal>y</literal>.
3621 In the next line, the output is discarded.
3622 The arrow <function>returnA</function> is defined in the
3623 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3624 module as <literal>arr id</literal>.
3625 The above example is treated as an abbreviation for
3627 arr (\ x -> (x, x)) >>>
3628 first (arr (\ x -> x+1) >>> f) >>>
3629 arr (\ (y, x) -> (y, (x, y))) >>>
3630 first (arr (\ y -> 2*y) >>> g) >>>
3632 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3633 first (arr (\ (x, z) -> x*z) >>> h) >>>
3634 arr (\ (t, z) -> t+z) >>>
3637 Note that variables not used later in the composition are projected out.
3638 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3640 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3641 module, this reduces to
3643 arr (\ x -> (x+1, x)) >>>
3645 arr (\ (y, x) -> (2*y, (x, y))) >>>
3647 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3649 arr (\ (t, z) -> t+z)
3651 which is what you might have written by hand.
3652 With arrow notation, GHC keeps track of all those tuples of variables for you.
3656 Note that although the above translation suggests that
3657 <literal>let</literal>-bound variables like <literal>z</literal> must be
3658 monomorphic, the actual translation produces Core,
3659 so polymorphic variables are allowed.
3663 It's also possible to have mutually recursive bindings,
3664 using the new <literal>rec</literal> keyword, as in the following example:
3666 counter :: ArrowCircuit a => a Bool Int
3667 counter = proc reset -> do
3668 rec output <- returnA -< if reset then 0 else next
3669 next <- delay 0 -< output+1
3670 returnA -< output
3672 The translation of such forms uses the <function>loop</function> combinator,
3673 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3679 <title>Conditional commands</title>
3682 In the previous example, we used a conditional expression to construct the
3684 Sometimes we want to conditionally execute different commands, as in
3691 which is translated to
3693 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3694 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3696 Since the translation uses <function>|||</function>,
3697 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3701 There are also <literal>case</literal> commands, like
3707 y <- h -< (x1, x2)
3711 The syntax is the same as for <literal>case</literal> expressions,
3712 except that the bodies of the alternatives are commands rather than expressions.
3713 The translation is similar to that of <literal>if</literal> commands.
3719 <title>Defining your own control structures</title>
3722 As we're seen, arrow notation provides constructs,
3723 modelled on those for expressions,
3724 for sequencing, value recursion and conditionals.
3725 But suitable combinators,
3726 which you can define in ordinary Haskell,
3727 may also be used to build new commands out of existing ones.
3728 The basic idea is that a command defines an arrow from environments to values.
3729 These environments assign values to the free local variables of the command.
3730 Thus combinators that produce arrows from arrows
3731 may also be used to build commands from commands.
3732 For example, the <literal>ArrowChoice</literal> class includes a combinator
3734 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3736 so we can use it to build commands:
3738 expr' = proc x -> do
3741 symbol Plus -< ()
3742 y <- term -< ()
3745 symbol Minus -< ()
3746 y <- term -< ()
3749 (The <literal>do</literal> on the first line is needed to prevent the first
3750 <literal><+> ...</literal> from being interpreted as part of the
3751 expression on the previous line.)
3752 This is equivalent to
3754 expr' = (proc x -> returnA -< x)
3755 <+> (proc x -> do
3756 symbol Plus -< ()
3757 y <- term -< ()
3759 <+> (proc x -> do
3760 symbol Minus -< ()
3761 y <- term -< ()
3764 It is essential that this operator be polymorphic in <literal>e</literal>
3765 (representing the environment input to the command
3766 and thence to its subcommands)
3767 and satisfy the corresponding naturality property
3769 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3771 at least for strict <literal>k</literal>.
3772 (This should be automatic if you're not using <function>seq</function>.)
3773 This ensures that environments seen by the subcommands are environments
3774 of the whole command,
3775 and also allows the translation to safely trim these environments.
3776 The operator must also not use any variable defined within the current
3781 We could define our own operator
3783 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3784 untilA body cond = proc x ->
3785 if cond x then returnA -< ()
3788 untilA body cond -< x
3790 and use it in the same way.
3791 Of course this infix syntax only makes sense for binary operators;
3792 there is also a more general syntax involving special brackets:
3796 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3803 <title>Primitive constructs</title>
3806 Some operators will need to pass additional inputs to their subcommands.
3807 For example, in an arrow type supporting exceptions,
3808 the operator that attaches an exception handler will wish to pass the
3809 exception that occurred to the handler.
3810 Such an operator might have a type
3812 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3814 where <literal>Ex</literal> is the type of exceptions handled.
3815 You could then use this with arrow notation by writing a command
3817 body `handleA` \ ex -> handler
3819 so that if an exception is raised in the command <literal>body</literal>,
3820 the variable <literal>ex</literal> is bound to the value of the exception
3821 and the command <literal>handler</literal>,
3822 which typically refers to <literal>ex</literal>, is entered.
3823 Though the syntax here looks like a functional lambda,
3824 we are talking about commands, and something different is going on.
3825 The input to the arrow represented by a command consists of values for
3826 the free local variables in the command, plus a stack of anonymous values.
3827 In all the prior examples, this stack was empty.
3828 In the second argument to <function>handleA</function>,
3829 this stack consists of one value, the value of the exception.
3830 The command form of lambda merely gives this value a name.
3835 the values on the stack are paired to the right of the environment.
3836 So operators like <function>handleA</function> that pass
3837 extra inputs to their subcommands can be designed for use with the notation
3838 by pairing the values with the environment in this way.
3839 More precisely, the type of each argument of the operator (and its result)
3840 should have the form
3842 a (...(e,t1), ... tn) t
3844 where <replaceable>e</replaceable> is a polymorphic variable
3845 (representing the environment)
3846 and <replaceable>ti</replaceable> are the types of the values on the stack,
3847 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3848 The polymorphic variable <replaceable>e</replaceable> must not occur in
3849 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3850 <replaceable>t</replaceable>.
3851 However the arrows involved need not be the same.
3852 Here are some more examples of suitable operators:
3854 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3855 runReader :: ... => a e c -> a' (e,State) c
3856 runState :: ... => a e c -> a' (e,State) (c,State)
3858 We can supply the extra input required by commands built with the last two
3859 by applying them to ordinary expressions, as in
3863 (|runReader (do { ... })|) s
3865 which adds <literal>s</literal> to the stack of inputs to the command
3866 built using <function>runReader</function>.
3870 The command versions of lambda abstraction and application are analogous to
3871 the expression versions.
3872 In particular, the beta and eta rules describe equivalences of commands.
3873 These three features (operators, lambda abstraction and application)
3874 are the core of the notation; everything else can be built using them,
3875 though the results would be somewhat clumsy.
3876 For example, we could simulate <literal>do</literal>-notation by defining
3878 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3879 u `bind` f = returnA &&& u >>> f
3881 bind_ :: Arrow a => a e b -> a e c -> a e c
3882 u `bind_` f = u `bind` (arr fst >>> f)
3884 We could simulate <literal>if</literal> by defining
3886 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3887 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3894 <title>Differences with the paper</title>
3899 <para>Instead of a single form of arrow application (arrow tail) with two
3900 translations, the implementation provides two forms
3901 <quote><literal>-<</literal></quote> (first-order)
3902 and <quote><literal>-<<</literal></quote> (higher-order).
3907 <para>User-defined operators are flagged with banana brackets instead of
3908 a new <literal>form</literal> keyword.
3917 <title>Portability</title>
3920 Although only GHC implements arrow notation directly,
3921 there is also a preprocessor
3923 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
3924 that translates arrow notation into Haskell 98
3925 for use with other Haskell systems.
3926 You would still want to check arrow programs with GHC;
3927 tracing type errors in the preprocessor output is not easy.
3928 Modules intended for both GHC and the preprocessor must observe some
3929 additional restrictions:
3934 The module must import
3935 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3941 The preprocessor cannot cope with other Haskell extensions.
3942 These would have to go in separate modules.
3948 Because the preprocessor targets Haskell (rather than Core),
3949 <literal>let</literal>-bound variables are monomorphic.
3960 <!-- ==================== ASSERTIONS ================= -->
3962 <sect1 id="sec-assertions">
3964 <indexterm><primary>Assertions</primary></indexterm>
3968 If you want to make use of assertions in your standard Haskell code, you
3969 could define a function like the following:
3975 assert :: Bool -> a -> a
3976 assert False x = error "assertion failed!"
3983 which works, but gives you back a less than useful error message --
3984 an assertion failed, but which and where?
3988 One way out is to define an extended <function>assert</function> function which also
3989 takes a descriptive string to include in the error message and
3990 perhaps combine this with the use of a pre-processor which inserts
3991 the source location where <function>assert</function> was used.
3995 Ghc offers a helping hand here, doing all of this for you. For every
3996 use of <function>assert</function> in the user's source:
4002 kelvinToC :: Double -> Double
4003 kelvinToC k = assert (k >= 0.0) (k+273.15)
4009 Ghc will rewrite this to also include the source location where the
4016 assert pred val ==> assertError "Main.hs|15" pred val
4022 The rewrite is only performed by the compiler when it spots
4023 applications of <function>Control.Exception.assert</function>, so you
4024 can still define and use your own versions of
4025 <function>assert</function>, should you so wish. If not, import
4026 <literal>Control.Exception</literal> to make use
4027 <function>assert</function> in your code.
4031 To have the compiler ignore uses of assert, use the compiler option
4032 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4033 option</primary></indexterm> That is, expressions of the form
4034 <literal>assert pred e</literal> will be rewritten to
4035 <literal>e</literal>.
4039 Assertion failures can be caught, see the documentation for the
4040 <literal>Control.Exception</literal> library for the details.
4046 <!-- =============================== PRAGMAS =========================== -->
4048 <sect1 id="pragmas">
4049 <title>Pragmas</title>
4051 <indexterm><primary>pragma</primary></indexterm>
4053 <para>GHC supports several pragmas, or instructions to the
4054 compiler placed in the source code. Pragmas don't normally affect
4055 the meaning of the program, but they might affect the efficiency
4056 of the generated code.</para>
4058 <para>Pragmas all take the form
4060 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4062 where <replaceable>word</replaceable> indicates the type of
4063 pragma, and is followed optionally by information specific to that
4064 type of pragma. Case is ignored in
4065 <replaceable>word</replaceable>. The various values for
4066 <replaceable>word</replaceable> that GHC understands are described
4067 in the following sections; any pragma encountered with an
4068 unrecognised <replaceable>word</replaceable> is (silently)
4071 <sect2 id="deprecated-pragma">
4072 <title>DEPRECATED pragma</title>
4073 <indexterm><primary>DEPRECATED</primary>
4076 <para>The DEPRECATED pragma lets you specify that a particular
4077 function, class, or type, is deprecated. There are two
4082 <para>You can deprecate an entire module thus:</para>
4084 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4087 <para>When you compile any module that import
4088 <literal>Wibble</literal>, GHC will print the specified
4093 <para>You can deprecate a function, class, or type, with the
4094 following top-level declaration:</para>
4096 {-# DEPRECATED f, C, T "Don't use these" #-}
4098 <para>When you compile any module that imports and uses any
4099 of the specifed entities, GHC will print the specified
4103 Any use of the deprecated item, or of anything from a deprecated
4104 module, will be flagged with an appropriate message. However,
4105 deprecations are not reported for
4106 (a) uses of a deprecated function within its defining module, and
4107 (b) uses of a deprecated function in an export list.
4108 The latter reduces spurious complaints within a library
4109 in which one module gathers together and re-exports
4110 the exports of several others.
4112 <para>You can suppress the warnings with the flag
4113 <option>-fno-warn-deprecations</option>.</para>
4116 <sect2 id="inline-noinline-pragma">
4117 <title>INLINE and NOINLINE pragmas</title>
4119 <para>These pragmas control the inlining of function
4122 <sect3 id="inline-pragma">
4123 <title>INLINE pragma</title>
4124 <indexterm><primary>INLINE</primary></indexterm>
4126 <para>GHC (with <option>-O</option>, as always) tries to
4127 inline (or “unfold”) functions/values that are
4128 “small enough,” thus avoiding the call overhead
4129 and possibly exposing other more-wonderful optimisations.
4130 Normally, if GHC decides a function is “too
4131 expensive” to inline, it will not do so, nor will it
4132 export that unfolding for other modules to use.</para>
4134 <para>The sledgehammer you can bring to bear is the
4135 <literal>INLINE</literal><indexterm><primary>INLINE
4136 pragma</primary></indexterm> pragma, used thusly:</para>
4139 key_function :: Int -> String -> (Bool, Double)
4141 #ifdef __GLASGOW_HASKELL__
4142 {-# INLINE key_function #-}
4146 <para>(You don't need to do the C pre-processor carry-on
4147 unless you're going to stick the code through HBC—it
4148 doesn't like <literal>INLINE</literal> pragmas.)</para>
4150 <para>The major effect of an <literal>INLINE</literal> pragma
4151 is to declare a function's “cost” to be very low.
4152 The normal unfolding machinery will then be very keen to
4155 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4156 function can be put anywhere its type signature could be
4159 <para><literal>INLINE</literal> pragmas are a particularly
4161 <literal>then</literal>/<literal>return</literal> (or
4162 <literal>bind</literal>/<literal>unit</literal>) functions in
4163 a monad. For example, in GHC's own
4164 <literal>UniqueSupply</literal> monad code, we have:</para>
4167 #ifdef __GLASGOW_HASKELL__
4168 {-# INLINE thenUs #-}
4169 {-# INLINE returnUs #-}
4173 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4174 linkend="noinline-pragma"/>).</para>
4177 <sect3 id="noinline-pragma">
4178 <title>NOINLINE pragma</title>
4180 <indexterm><primary>NOINLINE</primary></indexterm>
4181 <indexterm><primary>NOTINLINE</primary></indexterm>
4183 <para>The <literal>NOINLINE</literal> pragma does exactly what
4184 you'd expect: it stops the named function from being inlined
4185 by the compiler. You shouldn't ever need to do this, unless
4186 you're very cautious about code size.</para>
4188 <para><literal>NOTINLINE</literal> is a synonym for
4189 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4190 specified by Haskell 98 as the standard way to disable
4191 inlining, so it should be used if you want your code to be
4195 <sect3 id="phase-control">
4196 <title>Phase control</title>
4198 <para> Sometimes you want to control exactly when in GHC's
4199 pipeline the INLINE pragma is switched on. Inlining happens
4200 only during runs of the <emphasis>simplifier</emphasis>. Each
4201 run of the simplifier has a different <emphasis>phase
4202 number</emphasis>; the phase number decreases towards zero.
4203 If you use <option>-dverbose-core2core</option> you'll see the
4204 sequence of phase numbers for successive runs of the
4205 simpifier. In an INLINE pragma you can optionally specify a
4206 phase number, thus:</para>
4210 <para>You can say "inline <literal>f</literal> in Phase 2
4211 and all subsequent phases":
4213 {-# INLINE [2] f #-}
4219 <para>You can say "inline <literal>g</literal> in all
4220 phases up to, but not including, Phase 3":
4222 {-# INLINE [~3] g #-}
4228 <para>If you omit the phase indicator, you mean "inline in
4233 <para>You can use a phase number on a NOINLINE pragma too:</para>
4237 <para>You can say "do not inline <literal>f</literal>
4238 until Phase 2; in Phase 2 and subsequently behave as if
4239 there was no pragma at all":
4241 {-# NOINLINE [2] f #-}
4247 <para>You can say "do not inline <literal>g</literal> in
4248 Phase 3 or any subsequent phase; before that, behave as if
4249 there was no pragma":
4251 {-# NOINLINE [~3] g #-}
4257 <para>If you omit the phase indicator, you mean "never
4258 inline this function".</para>
4262 <para>The same phase-numbering control is available for RULES
4263 (<xref linkend="rewrite-rules"/>).</para>
4267 <sect2 id="line-pragma">
4268 <title>LINE pragma</title>
4270 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4271 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4272 <para>This pragma is similar to C's <literal>#line</literal>
4273 pragma, and is mainly for use in automatically generated Haskell
4274 code. It lets you specify the line number and filename of the
4275 original code; for example</para>
4278 {-# LINE 42 "Foo.vhs" #-}
4281 <para>if you'd generated the current file from something called
4282 <filename>Foo.vhs</filename> and this line corresponds to line
4283 42 in the original. GHC will adjust its error messages to refer
4284 to the line/file named in the <literal>LINE</literal>
4288 <sect2 id="options-pragma">
4289 <title>OPTIONS pragma</title>
4290 <indexterm><primary>OPTIONS</primary>
4292 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4295 <para>The <literal>OPTIONS</literal> pragma is used to specify
4296 additional options that are given to the compiler when compiling
4297 this source file. See <xref linkend="source-file-options"/> for
4302 <title>RULES pragma</title>
4304 <para>The RULES pragma lets you specify rewrite rules. It is
4305 described in <xref linkend="rewrite-rules"/>.</para>
4308 <sect2 id="specialize-pragma">
4309 <title>SPECIALIZE pragma</title>
4311 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4312 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4313 <indexterm><primary>overloading, death to</primary></indexterm>
4315 <para>(UK spelling also accepted.) For key overloaded
4316 functions, you can create extra versions (NB: more code space)
4317 specialised to particular types. Thus, if you have an
4318 overloaded function:</para>
4321 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4324 <para>If it is heavily used on lists with
4325 <literal>Widget</literal> keys, you could specialise it as
4329 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4332 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4333 be put anywhere its type signature could be put.</para>
4335 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4336 (a) a specialised version of the function and (b) a rewrite rule
4337 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4338 un-specialised function into a call to the specialised one.</para>
4340 <para>In earlier versions of GHC, it was possible to provide your own
4341 specialised function for a given type:
4344 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4347 This feature has been removed, as it is now subsumed by the
4348 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4352 <sect2 id="specialize-instance-pragma">
4353 <title>SPECIALIZE instance pragma
4357 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4358 <indexterm><primary>overloading, death to</primary></indexterm>
4359 Same idea, except for instance declarations. For example:
4362 instance (Eq a) => Eq (Foo a) where {
4363 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4367 The pragma must occur inside the <literal>where</literal> part
4368 of the instance declaration.
4371 Compatible with HBC, by the way, except perhaps in the placement
4377 <sect2 id="unpack-pragma">
4378 <title>UNPACK pragma</title>
4380 <indexterm><primary>UNPACK</primary></indexterm>
4382 <para>The <literal>UNPACK</literal> indicates to the compiler
4383 that it should unpack the contents of a constructor field into
4384 the constructor itself, removing a level of indirection. For
4388 data T = T {-# UNPACK #-} !Float
4389 {-# UNPACK #-} !Float
4392 <para>will create a constructor <literal>T</literal> containing
4393 two unboxed floats. This may not always be an optimisation: if
4394 the <function>T</function> constructor is scrutinised and the
4395 floats passed to a non-strict function for example, they will
4396 have to be reboxed (this is done automatically by the
4399 <para>Unpacking constructor fields should only be used in
4400 conjunction with <option>-O</option>, in order to expose
4401 unfoldings to the compiler so the reboxing can be removed as
4402 often as possible. For example:</para>
4406 f (T f1 f2) = f1 + f2
4409 <para>The compiler will avoid reboxing <function>f1</function>
4410 and <function>f2</function> by inlining <function>+</function>
4411 on floats, but only when <option>-O</option> is on.</para>
4413 <para>Any single-constructor data is eligible for unpacking; for
4417 data T = T {-# UNPACK #-} !(Int,Int)
4420 <para>will store the two <literal>Int</literal>s directly in the
4421 <function>T</function> constructor, by flattening the pair.
4422 Multi-level unpacking is also supported:</para>
4425 data T = T {-# UNPACK #-} !S
4426 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4429 <para>will store two unboxed <literal>Int#</literal>s
4430 directly in the <function>T</function> constructor. The
4431 unpacker can see through newtypes, too.</para>
4433 <para>If a field cannot be unpacked, you will not get a warning,
4434 so it might be an idea to check the generated code with
4435 <option>-ddump-simpl</option>.</para>
4437 <para>See also the <option>-funbox-strict-fields</option> flag,
4438 which essentially has the effect of adding
4439 <literal>{-# UNPACK #-}</literal> to every strict
4440 constructor field.</para>
4445 <!-- ======================= REWRITE RULES ======================== -->
4447 <sect1 id="rewrite-rules">
4448 <title>Rewrite rules
4450 <indexterm><primary>RULES pagma</primary></indexterm>
4451 <indexterm><primary>pragma, RULES</primary></indexterm>
4452 <indexterm><primary>rewrite rules</primary></indexterm></title>
4455 The programmer can specify rewrite rules as part of the source program
4456 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4457 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4458 and (b) the <option>-frules-off</option> flag
4459 (<xref linkend="options-f"/>) is not specified.
4467 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4474 <title>Syntax</title>
4477 From a syntactic point of view:
4483 There may be zero or more rules in a <literal>RULES</literal> pragma.
4490 Each rule has a name, enclosed in double quotes. The name itself has
4491 no significance at all. It is only used when reporting how many times the rule fired.
4497 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4498 immediately after the name of the rule. Thus:
4501 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4504 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4505 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4514 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4515 is set, so you must lay out your rules starting in the same column as the
4516 enclosing definitions.
4523 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4524 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4525 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4526 by spaces, just like in a type <literal>forall</literal>.
4532 A pattern variable may optionally have a type signature.
4533 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4534 For example, here is the <literal>foldr/build</literal> rule:
4537 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4538 foldr k z (build g) = g k z
4541 Since <function>g</function> has a polymorphic type, it must have a type signature.
4548 The left hand side of a rule must consist of a top-level variable applied
4549 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4552 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4553 "wrong2" forall f. f True = True
4556 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4563 A rule does not need to be in the same module as (any of) the
4564 variables it mentions, though of course they need to be in scope.
4570 Rules are automatically exported from a module, just as instance declarations are.
4581 <title>Semantics</title>
4584 From a semantic point of view:
4590 Rules are only applied if you use the <option>-O</option> flag.
4596 Rules are regarded as left-to-right rewrite rules.
4597 When GHC finds an expression that is a substitution instance of the LHS
4598 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4599 By "a substitution instance" we mean that the LHS can be made equal to the
4600 expression by substituting for the pattern variables.
4607 The LHS and RHS of a rule are typechecked, and must have the
4615 GHC makes absolutely no attempt to verify that the LHS and RHS
4616 of a rule have the same meaning. That is undecideable in general, and
4617 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4624 GHC makes no attempt to make sure that the rules are confluent or
4625 terminating. For example:
4628 "loop" forall x,y. f x y = f y x
4631 This rule will cause the compiler to go into an infinite loop.
4638 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4644 GHC currently uses a very simple, syntactic, matching algorithm
4645 for matching a rule LHS with an expression. It seeks a substitution
4646 which makes the LHS and expression syntactically equal modulo alpha
4647 conversion. The pattern (rule), but not the expression, is eta-expanded if
4648 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4649 But not beta conversion (that's called higher-order matching).
4653 Matching is carried out on GHC's intermediate language, which includes
4654 type abstractions and applications. So a rule only matches if the
4655 types match too. See <xref linkend="rule-spec"/> below.
4661 GHC keeps trying to apply the rules as it optimises the program.
4662 For example, consider:
4671 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4672 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4673 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4674 not be substituted, and the rule would not fire.
4681 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4682 that appears on the LHS of a rule</emphasis>, because once you have substituted
4683 for something you can't match against it (given the simple minded
4684 matching). So if you write the rule
4687 "map/map" forall f,g. map f . map g = map (f.g)
4690 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4691 It will only match something written with explicit use of ".".
4692 Well, not quite. It <emphasis>will</emphasis> match the expression
4698 where <function>wibble</function> is defined:
4701 wibble f g = map f . map g
4704 because <function>wibble</function> will be inlined (it's small).
4706 Later on in compilation, GHC starts inlining even things on the
4707 LHS of rules, but still leaves the rules enabled. This inlining
4708 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4715 All rules are implicitly exported from the module, and are therefore
4716 in force in any module that imports the module that defined the rule, directly
4717 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4718 in force when compiling A.) The situation is very similar to that for instance
4730 <title>List fusion</title>
4733 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4734 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4735 intermediate list should be eliminated entirely.
4739 The following are good producers:
4751 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4757 Explicit lists (e.g. <literal>[True, False]</literal>)
4763 The cons constructor (e.g <literal>3:4:[]</literal>)
4769 <function>++</function>
4775 <function>map</function>
4781 <function>filter</function>
4787 <function>iterate</function>, <function>repeat</function>
4793 <function>zip</function>, <function>zipWith</function>
4802 The following are good consumers:
4814 <function>array</function> (on its second argument)
4820 <function>length</function>
4826 <function>++</function> (on its first argument)
4832 <function>foldr</function>
4838 <function>map</function>
4844 <function>filter</function>
4850 <function>concat</function>
4856 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4862 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4863 will fuse with one but not the other)
4869 <function>partition</function>
4875 <function>head</function>
4881 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4887 <function>sequence_</function>
4893 <function>msum</function>
4899 <function>sortBy</function>
4908 So, for example, the following should generate no intermediate lists:
4911 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4917 This list could readily be extended; if there are Prelude functions that you use
4918 a lot which are not included, please tell us.
4922 If you want to write your own good consumers or producers, look at the
4923 Prelude definitions of the above functions to see how to do so.
4928 <sect2 id="rule-spec">
4929 <title>Specialisation
4933 Rewrite rules can be used to get the same effect as a feature
4934 present in earlier versions of GHC.
4935 For example, suppose that:
4938 genericLookup :: Ord a => Table a b -> a -> b
4939 intLookup :: Table Int b -> Int -> b
4942 where <function>intLookup</function> is an implementation of
4943 <function>genericLookup</function> that works very fast for
4944 keys of type <literal>Int</literal>. You might wish
4945 to tell GHC to use <function>intLookup</function> instead of
4946 <function>genericLookup</function> whenever the latter was called with
4947 type <literal>Table Int b -> Int -> b</literal>.
4948 It used to be possible to write
4951 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
4954 This feature is no longer in GHC, but rewrite rules let you do the same thing:
4957 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
4960 This slightly odd-looking rule instructs GHC to replace
4961 <function>genericLookup</function> by <function>intLookup</function>
4962 <emphasis>whenever the types match</emphasis>.
4963 What is more, this rule does not need to be in the same
4964 file as <function>genericLookup</function>, unlike the
4965 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
4966 have an original definition available to specialise).
4969 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
4970 <function>intLookup</function> really behaves as a specialised version
4971 of <function>genericLookup</function>!!!</para>
4973 <para>An example in which using <literal>RULES</literal> for
4974 specialisation will Win Big:
4977 toDouble :: Real a => a -> Double
4978 toDouble = fromRational . toRational
4980 {-# RULES "toDouble/Int" toDouble = i2d #-}
4981 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4984 The <function>i2d</function> function is virtually one machine
4985 instruction; the default conversion—via an intermediate
4986 <literal>Rational</literal>—is obscenely expensive by
4993 <title>Controlling what's going on</title>
5001 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5007 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5008 If you add <option>-dppr-debug</option> you get a more detailed listing.
5014 The defintion of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5017 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5018 {-# INLINE build #-}
5022 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5023 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5024 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5025 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5032 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5033 see how to write rules that will do fusion and yet give an efficient
5034 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5044 <sect2 id="core-pragma">
5045 <title>CORE pragma</title>
5047 <indexterm><primary>CORE pragma</primary></indexterm>
5048 <indexterm><primary>pragma, CORE</primary></indexterm>
5049 <indexterm><primary>core, annotation</primary></indexterm>
5052 The external core format supports <quote>Note</quote> annotations;
5053 the <literal>CORE</literal> pragma gives a way to specify what these
5054 should be in your Haskell source code. Syntactically, core
5055 annotations are attached to expressions and take a Haskell string
5056 literal as an argument. The following function definition shows an
5060 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5063 Sematically, this is equivalent to:
5071 However, when external for is generated (via
5072 <option>-fext-core</option>), there will be Notes attached to the
5073 expressions <function>show</function> and <varname>x</varname>.
5074 The core function declaration for <function>f</function> is:
5078 f :: %forall a . GHCziShow.ZCTShow a ->
5079 a -> GHCziBase.ZMZN GHCziBase.Char =
5080 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5082 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5084 (tpl1::GHCziBase.Int ->
5086 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5088 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5089 (tpl3::GHCziBase.ZMZN a ->
5090 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5098 Here, we can see that the function <function>show</function> (which
5099 has been expanded out to a case expression over the Show dictionary)
5100 has a <literal>%note</literal> attached to it, as does the
5101 expression <varname>eta</varname> (which used to be called
5102 <varname>x</varname>).
5109 <sect1 id="generic-classes">
5110 <title>Generic classes</title>
5112 <para>(Note: support for generic classes is currently broken in
5116 The ideas behind this extension are described in detail in "Derivable type classes",
5117 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5118 An example will give the idea:
5126 fromBin :: [Int] -> (a, [Int])
5128 toBin {| Unit |} Unit = []
5129 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5130 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5131 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5133 fromBin {| Unit |} bs = (Unit, bs)
5134 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5135 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5136 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5137 (y,bs'') = fromBin bs'
5140 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5141 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5142 which are defined thus in the library module <literal>Generics</literal>:
5146 data a :+: b = Inl a | Inr b
5147 data a :*: b = a :*: b
5150 Now you can make a data type into an instance of Bin like this:
5152 instance (Bin a, Bin b) => Bin (a,b)
5153 instance Bin a => Bin [a]
5155 That is, just leave off the "where" clause. Of course, you can put in the
5156 where clause and over-ride whichever methods you please.
5160 <title> Using generics </title>
5161 <para>To use generics you need to</para>
5164 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5165 <option>-fgenerics</option> (to generate extra per-data-type code),
5166 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5170 <para>Import the module <literal>Generics</literal> from the
5171 <literal>lang</literal> package. This import brings into
5172 scope the data types <literal>Unit</literal>,
5173 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5174 don't need this import if you don't mention these types
5175 explicitly; for example, if you are simply giving instance
5176 declarations.)</para>
5181 <sect2> <title> Changes wrt the paper </title>
5183 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5184 can be written infix (indeed, you can now use
5185 any operator starting in a colon as an infix type constructor). Also note that
5186 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5187 Finally, note that the syntax of the type patterns in the class declaration
5188 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5189 alone would ambiguous when they appear on right hand sides (an extension we
5190 anticipate wanting).
5194 <sect2> <title>Terminology and restrictions</title>
5196 Terminology. A "generic default method" in a class declaration
5197 is one that is defined using type patterns as above.
5198 A "polymorphic default method" is a default method defined as in Haskell 98.
5199 A "generic class declaration" is a class declaration with at least one
5200 generic default method.
5208 Alas, we do not yet implement the stuff about constructor names and
5215 A generic class can have only one parameter; you can't have a generic
5216 multi-parameter class.
5222 A default method must be defined entirely using type patterns, or entirely
5223 without. So this is illegal:
5226 op :: a -> (a, Bool)
5227 op {| Unit |} Unit = (Unit, True)
5230 However it is perfectly OK for some methods of a generic class to have
5231 generic default methods and others to have polymorphic default methods.
5237 The type variable(s) in the type pattern for a generic method declaration
5238 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:
5242 op {| p :*: q |} (x :*: y) = op (x :: p)
5250 The type patterns in a generic default method must take one of the forms:
5256 where "a" and "b" are type variables. Furthermore, all the type patterns for
5257 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5258 must use the same type variables. So this is illegal:
5262 op {| a :+: b |} (Inl x) = True
5263 op {| p :+: q |} (Inr y) = False
5265 The type patterns must be identical, even in equations for different methods of the class.
5266 So this too is illegal:
5270 op1 {| a :*: b |} (x :*: y) = True
5273 op2 {| p :*: q |} (x :*: y) = False
5275 (The reason for this restriction is that we gather all the equations for a particular type consructor
5276 into a single generic instance declaration.)
5282 A generic method declaration must give a case for each of the three type constructors.
5288 The type for a generic method can be built only from:
5290 <listitem> <para> Function arrows </para> </listitem>
5291 <listitem> <para> Type variables </para> </listitem>
5292 <listitem> <para> Tuples </para> </listitem>
5293 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5295 Here are some example type signatures for generic methods:
5298 op2 :: Bool -> (a,Bool)
5299 op3 :: [Int] -> a -> a
5302 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5306 This restriction is an implementation restriction: we just havn't got around to
5307 implementing the necessary bidirectional maps over arbitrary type constructors.
5308 It would be relatively easy to add specific type constructors, such as Maybe and list,
5309 to the ones that are allowed.</para>
5314 In an instance declaration for a generic class, the idea is that the compiler
5315 will fill in the methods for you, based on the generic templates. However it can only
5320 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5325 No constructor of the instance type has unboxed fields.
5329 (Of course, these things can only arise if you are already using GHC extensions.)
5330 However, you can still give an instance declarations for types which break these rules,
5331 provided you give explicit code to override any generic default methods.
5339 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5340 what the compiler does with generic declarations.
5345 <sect2> <title> Another example </title>
5347 Just to finish with, here's another example I rather like:
5351 nCons {| Unit |} _ = 1
5352 nCons {| a :*: b |} _ = 1
5353 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5356 tag {| Unit |} _ = 1
5357 tag {| a :*: b |} _ = 1
5358 tag {| a :+: b |} (Inl x) = tag x
5359 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5368 ;;; Local Variables: ***
5370 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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