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>-fimplicit-params</option></term>
224 <para>Enables implicit parameters (see <xref
225 linkend="implicit-parameters"/>). Currently also implied by
226 <option>-fglasgow-exts</option>.</para>
229 <literal>?<replaceable>varid</replaceable></literal>,
230 <literal>%<replaceable>varid</replaceable></literal>.</para>
235 <term><option>-fscoped-type-variables</option></term>
237 <para>Enables lexically-scoped type variables (see <xref
238 linkend="scoped-type-variables"/>). Implied by
239 <option>-fglasgow-exts</option>.</para>
244 <term><option>-fth</option></term>
246 <para>Enables Template Haskell (see <xref
247 linkend="template-haskell"/>). Currently also implied by
248 <option>-fglasgow-exts</option>.</para>
250 <para>Syntax stolen: <literal>[|</literal>,
251 <literal>[e|</literal>, <literal>[p|</literal>,
252 <literal>[d|</literal>, <literal>[t|</literal>,
253 <literal>$(</literal>,
254 <literal>$<replaceable>varid</replaceable></literal>.</para>
261 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
262 <!-- included from primitives.sgml -->
263 <!-- &primitives; -->
264 <sect1 id="primitives">
265 <title>Unboxed types and primitive operations</title>
267 <para>GHC is built on a raft of primitive data types and operations.
268 While you really can use this stuff to write fast code,
269 we generally find it a lot less painful, and more satisfying in the
270 long run, to use higher-level language features and libraries. With
271 any luck, the code you write will be optimised to the efficient
272 unboxed version in any case. And if it isn't, we'd like to know
275 <para>We do not currently have good, up-to-date documentation about the
276 primitives, perhaps because they are mainly intended for internal use.
277 There used to be a long section about them here in the User Guide, but it
278 became out of date, and wrong information is worse than none.</para>
280 <para>The Real Truth about what primitive types there are, and what operations
281 work over those types, is held in the file
282 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
283 This file is used directly to generate GHC's primitive-operation definitions, so
284 it is always correct! It is also intended for processing into text.</para>
287 the result of such processing is part of the description of the
289 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
290 Core language</ulink>.
291 So that document is a good place to look for a type-set version.
292 We would be very happy if someone wanted to volunteer to produce an SGML
293 back end to the program that processes <filename>primops.txt</filename> so that
294 we could include the results here in the User Guide.</para>
296 <para>What follows here is a brief summary of some main points.</para>
298 <sect2 id="glasgow-unboxed">
303 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
306 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
307 that values of that type are represented by a pointer to a heap
308 object. The representation of a Haskell <literal>Int</literal>, for
309 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
310 type, however, is represented by the value itself, no pointers or heap
311 allocation are involved.
315 Unboxed types correspond to the “raw machine” types you
316 would use in C: <literal>Int#</literal> (long int),
317 <literal>Double#</literal> (double), <literal>Addr#</literal>
318 (void *), etc. The <emphasis>primitive operations</emphasis>
319 (PrimOps) on these types are what you might expect; e.g.,
320 <literal>(+#)</literal> is addition on
321 <literal>Int#</literal>s, and is the machine-addition that we all
322 know and love—usually one instruction.
326 Primitive (unboxed) types cannot be defined in Haskell, and are
327 therefore built into the language and compiler. Primitive types are
328 always unlifted; that is, a value of a primitive type cannot be
329 bottom. We use the convention that primitive types, values, and
330 operations have a <literal>#</literal> suffix.
334 Primitive values are often represented by a simple bit-pattern, such
335 as <literal>Int#</literal>, <literal>Float#</literal>,
336 <literal>Double#</literal>. But this is not necessarily the case:
337 a primitive value might be represented by a pointer to a
338 heap-allocated object. Examples include
339 <literal>Array#</literal>, the type of primitive arrays. A
340 primitive array is heap-allocated because it is too big a value to fit
341 in a register, and would be too expensive to copy around; in a sense,
342 it is accidental that it is represented by a pointer. If a pointer
343 represents a primitive value, then it really does point to that value:
344 no unevaluated thunks, no indirections…nothing can be at the
345 other end of the pointer than the primitive value.
349 There are some restrictions on the use of primitive types, the main
350 one being that you can't pass a primitive value to a polymorphic
351 function or store one in a polymorphic data type. This rules out
352 things like <literal>[Int#]</literal> (i.e. lists of primitive
353 integers). The reason for this restriction is that polymorphic
354 arguments and constructor fields are assumed to be pointers: if an
355 unboxed integer is stored in one of these, the garbage collector would
356 attempt to follow it, leading to unpredictable space leaks. Or a
357 <function>seq</function> operation on the polymorphic component may
358 attempt to dereference the pointer, with disastrous results. Even
359 worse, the unboxed value might be larger than a pointer
360 (<literal>Double#</literal> for instance).
364 Nevertheless, A numerically-intensive program using unboxed types can
365 go a <emphasis>lot</emphasis> faster than its “standard”
366 counterpart—we saw a threefold speedup on one example.
371 <sect2 id="unboxed-tuples">
372 <title>Unboxed Tuples
376 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
377 they're available by default with <option>-fglasgow-exts</option>. An
378 unboxed tuple looks like this:
390 where <literal>e_1..e_n</literal> are expressions of any
391 type (primitive or non-primitive). The type of an unboxed tuple looks
396 Unboxed tuples are used for functions that need to return multiple
397 values, but they avoid the heap allocation normally associated with
398 using fully-fledged tuples. When an unboxed tuple is returned, the
399 components are put directly into registers or on the stack; the
400 unboxed tuple itself does not have a composite representation. Many
401 of the primitive operations listed in this section return unboxed
406 There are some pretty stringent restrictions on the use of unboxed tuples:
415 Unboxed tuple types are subject to the same restrictions as
416 other unboxed types; i.e. they may not be stored in polymorphic data
417 structures or passed to polymorphic functions.
424 Unboxed tuples may only be constructed as the direct result of
425 a function, and may only be deconstructed with a <literal>case</literal> expression.
426 eg. the following are valid:
430 f x y = (# x+1, y-1 #)
431 g x = case f x x of { (# a, b #) -> a + b }
435 but the following are invalid:
449 No variable can have an unboxed tuple type. This is illegal:
453 f :: (# Int, Int #) -> (# Int, Int #)
458 because <literal>x</literal> has an unboxed tuple type.
468 Note: we may relax some of these restrictions in the future.
472 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
473 tuples to avoid unnecessary allocation during sequences of operations.
480 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
482 <sect1 id="syntax-extns">
483 <title>Syntactic extensions</title>
485 <!-- ====================== HIERARCHICAL MODULES ======================= -->
487 <sect2 id="hierarchical-modules">
488 <title>Hierarchical Modules</title>
490 <para>GHC supports a small extension to the syntax of module
491 names: a module name is allowed to contain a dot
492 <literal>‘.’</literal>. This is also known as the
493 “hierarchical module namespace” extension, because
494 it extends the normally flat Haskell module namespace into a
495 more flexible hierarchy of modules.</para>
497 <para>This extension has very little impact on the language
498 itself; modules names are <emphasis>always</emphasis> fully
499 qualified, so you can just think of the fully qualified module
500 name as <quote>the module name</quote>. In particular, this
501 means that the full module name must be given after the
502 <literal>module</literal> keyword at the beginning of the
503 module; for example, the module <literal>A.B.C</literal> must
506 <programlisting>module A.B.C</programlisting>
509 <para>It is a common strategy to use the <literal>as</literal>
510 keyword to save some typing when using qualified names with
511 hierarchical modules. For example:</para>
514 import qualified Control.Monad.ST.Strict as ST
517 <para>For details on how GHC searches for source and interface
518 files in the presence of hierarchical modules, see <xref
519 linkend="search-path"/>.</para>
521 <para>GHC comes with a large collection of libraries arranged
522 hierarchically; see the accompanying library documentation.
523 There is an ongoing project to create and maintain a stable set
524 of <quote>core</quote> libraries used by several Haskell
525 compilers, and the libraries that GHC comes with represent the
526 current status of that project. For more details, see <ulink
527 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
528 Libraries</ulink>.</para>
532 <!-- ====================== PATTERN GUARDS ======================= -->
534 <sect2 id="pattern-guards">
535 <title>Pattern guards</title>
538 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
539 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.)
543 Suppose we have an abstract data type of finite maps, with a
547 lookup :: FiniteMap -> Int -> Maybe Int
550 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
551 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
555 clunky env var1 var2 | ok1 && ok2 = val1 + val2
556 | otherwise = var1 + var2
567 The auxiliary functions are
571 maybeToBool :: Maybe a -> Bool
572 maybeToBool (Just x) = True
573 maybeToBool Nothing = False
575 expectJust :: Maybe a -> a
576 expectJust (Just x) = x
577 expectJust Nothing = error "Unexpected Nothing"
581 What is <function>clunky</function> doing? The guard <literal>ok1 &&
582 ok2</literal> checks that both lookups succeed, using
583 <function>maybeToBool</function> to convert the <function>Maybe</function>
584 types to booleans. The (lazily evaluated) <function>expectJust</function>
585 calls extract the values from the results of the lookups, and binds the
586 returned values to <varname>val1</varname> and <varname>val2</varname>
587 respectively. If either lookup fails, then clunky takes the
588 <literal>otherwise</literal> case and returns the sum of its arguments.
592 This is certainly legal Haskell, but it is a tremendously verbose and
593 un-obvious way to achieve the desired effect. Arguably, a more direct way
594 to write clunky would be to use case expressions:
598 clunky env var1 var1 = case lookup env var1 of
600 Just val1 -> case lookup env var2 of
602 Just val2 -> val1 + val2
608 This is a bit shorter, but hardly better. Of course, we can rewrite any set
609 of pattern-matching, guarded equations as case expressions; that is
610 precisely what the compiler does when compiling equations! The reason that
611 Haskell provides guarded equations is because they allow us to write down
612 the cases we want to consider, one at a time, independently of each other.
613 This structure is hidden in the case version. Two of the right-hand sides
614 are really the same (<function>fail</function>), and the whole expression
615 tends to become more and more indented.
619 Here is how I would write clunky:
624 | Just val1 <- lookup env var1
625 , Just val2 <- lookup env var2
627 ...other equations for clunky...
631 The semantics should be clear enough. The qualifiers are matched in order.
632 For a <literal><-</literal> qualifier, which I call a pattern guard, the
633 right hand side is evaluated and matched against the pattern on the left.
634 If the match fails then the whole guard fails and the next equation is
635 tried. If it succeeds, then the appropriate binding takes place, and the
636 next qualifier is matched, in the augmented environment. Unlike list
637 comprehensions, however, the type of the expression to the right of the
638 <literal><-</literal> is the same as the type of the pattern to its
639 left. The bindings introduced by pattern guards scope over all the
640 remaining guard qualifiers, and over the right hand side of the equation.
644 Just as with list comprehensions, boolean expressions can be freely mixed
645 with among the pattern guards. For example:
656 Haskell's current guards therefore emerge as a special case, in which the
657 qualifier list has just one element, a boolean expression.
661 <!-- ===================== Recursive do-notation =================== -->
663 <sect2 id="mdo-notation">
664 <title>The recursive do-notation
667 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
668 "A recursive do for Haskell",
669 Levent Erkok, John Launchbury",
670 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
673 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
674 that is, the variables bound in a do-expression are visible only in the textually following
675 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
676 group. It turns out that several applications can benefit from recursive bindings in
677 the do-notation, and this extension provides the necessary syntactic support.
680 Here is a simple (yet contrived) example:
683 import Control.Monad.Fix
685 justOnes = mdo xs <- Just (1:xs)
689 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
693 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
696 class Monad m => MonadFix m where
697 mfix :: (a -> m a) -> m a
700 The function <literal>mfix</literal>
701 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
702 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
703 For details, see the above mentioned reference.
706 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
707 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
708 for Haskell's internal state monad (strict and lazy, respectively).
711 There are three important points in using the recursive-do notation:
714 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
715 than <literal>do</literal>).
719 You should <literal>import Control.Monad.Fix</literal>.
720 (Note: Strictly speaking, this import is required only when you need to refer to the name
721 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
722 are encouraged to always import this module when using the mdo-notation.)
726 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
732 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
733 contains up to date information on recursive monadic bindings.
737 Historical note: The old implementation of the mdo-notation (and most
738 of the existing documents) used the name
739 <literal>MonadRec</literal> for the class and the corresponding library.
740 This name is not supported by GHC.
746 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
748 <sect2 id="parallel-list-comprehensions">
749 <title>Parallel List Comprehensions</title>
750 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
752 <indexterm><primary>parallel list comprehensions</primary>
755 <para>Parallel list comprehensions are a natural extension to list
756 comprehensions. List comprehensions can be thought of as a nice
757 syntax for writing maps and filters. Parallel comprehensions
758 extend this to include the zipWith family.</para>
760 <para>A parallel list comprehension has multiple independent
761 branches of qualifier lists, each separated by a `|' symbol. For
762 example, the following zips together two lists:</para>
765 [ (x, y) | x <- xs | y <- ys ]
768 <para>The behavior of parallel list comprehensions follows that of
769 zip, in that the resulting list will have the same length as the
770 shortest branch.</para>
772 <para>We can define parallel list comprehensions by translation to
773 regular comprehensions. Here's the basic idea:</para>
775 <para>Given a parallel comprehension of the form: </para>
778 [ e | p1 <- e11, p2 <- e12, ...
779 | q1 <- e21, q2 <- e22, ...
784 <para>This will be translated to: </para>
787 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
788 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
793 <para>where `zipN' is the appropriate zip for the given number of
798 <sect2 id="rebindable-syntax">
799 <title>Rebindable syntax</title>
802 <para>GHC allows most kinds of built-in syntax to be rebound by
803 the user, to facilitate replacing the <literal>Prelude</literal>
804 with a home-grown version, for example.</para>
806 <para>You may want to define your own numeric class
807 hierarchy. It completely defeats that purpose if the
808 literal "1" means "<literal>Prelude.fromInteger
809 1</literal>", which is what the Haskell Report specifies.
810 So the <option>-fno-implicit-prelude</option> flag causes
811 the following pieces of built-in syntax to refer to
812 <emphasis>whatever is in scope</emphasis>, not the Prelude
817 <para>Integer and fractional literals mean
818 "<literal>fromInteger 1</literal>" and
819 "<literal>fromRational 3.2</literal>", not the
820 Prelude-qualified versions; both in expressions and in
822 <para>However, the standard Prelude <literal>Eq</literal> class
823 is still used for the equality test necessary for literal patterns.</para>
827 <para>Negation (e.g. "<literal>- (f x)</literal>")
828 means "<literal>negate (f x)</literal>" (not
829 <literal>Prelude.negate</literal>).</para>
833 <para>In an n+k pattern, the standard Prelude
834 <literal>Ord</literal> class is still used for comparison,
835 but the necessary subtraction uses whatever
836 "<literal>(-)</literal>" is in scope (not
837 "<literal>Prelude.(-)</literal>").</para>
841 <para>"Do" notation is translated using whatever
842 functions <literal>(>>=)</literal>,
843 <literal>(>>)</literal>, <literal>fail</literal>, and
844 <literal>return</literal>, are in scope (not the Prelude
845 versions). List comprehensions, and parallel array
846 comprehensions, are unaffected. </para></listitem>
849 <para>Similarly recursive do notation (see
850 <xref linkend="mdo-notation"/>) uses whatever
851 <literal>mfix</literal> function is in scope, and arrow
852 notation (see <xref linkend="arrow-notation"/>)
853 uses whatever <literal>arr</literal>,
854 <literal>(>>>)</literal>, <literal>first</literal>,
855 <literal>app</literal>, <literal>(|||)</literal> and
856 <literal>loop</literal> functions are in scope.</para>
860 <para>The functions with these names that GHC finds in scope
861 must have types matching those of the originals, namely:
863 fromInteger :: Integer -> N
864 fromRational :: Rational -> N
867 (>>=) :: forall a b. M a -> (a -> M b) -> M b
868 (>>) :: forall a b. M a -> M b -> M b
869 return :: forall a. a -> M a
870 fail :: forall a. String -> M a
872 (Here <literal>N</literal> may be any type,
873 and <literal>M</literal> any type constructor.)</para>
875 <para>Be warned: this is an experimental facility, with
876 fewer checks than usual. Use <literal>-dcore-lint</literal>
877 to typecheck the desugared program. If Core Lint is happy
878 you should be all right.</para>
884 <!-- TYPE SYSTEM EXTENSIONS -->
885 <sect1 id="type-extensions">
886 <title>Type system extensions</title>
890 <title>Data types and type synonyms</title>
892 <sect3 id="nullary-types">
893 <title>Data types with no constructors</title>
895 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
896 a data type with no constructors. For example:</para>
900 data T a -- T :: * -> *
903 <para>Syntactically, the declaration lacks the "= constrs" part. The
904 type can be parameterised over types of any kind, but if the kind is
905 not <literal>*</literal> then an explicit kind annotation must be used
906 (see <xref linkend="sec-kinding"/>).</para>
908 <para>Such data types have only one value, namely bottom.
909 Nevertheless, they can be useful when defining "phantom types".</para>
912 <sect3 id="infix-tycons">
913 <title>Infix type constructors</title>
916 GHC allows type constructors to be operators, and to be written infix, very much
917 like expressions. More specifically:
920 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
921 The lexical syntax is the same as that for data constructors.
924 Types can be written infix. For example <literal>Int :*: Bool</literal>.
928 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
929 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
932 Fixities may be declared for type constructors just as for data constructors. However,
933 one cannot distinguish between the two in a fixity declaration; a fixity declaration
934 sets the fixity for a data constructor and the corresponding type constructor. For example:
938 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
939 and similarly for <literal>:*:</literal>.
940 <literal>Int `a` Bool</literal>.
943 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
946 Data type and type-synonym declarations can be written infix. E.g.
948 data a :*: b = Foo a b
949 type a :+: b = Either a b
953 The only thing that differs between operators in types and operators in expressions is that
954 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
955 are not allowed in types. Reason: the uniform thing to do would be to make them type
956 variables, but that's not very useful. A less uniform but more useful thing would be to
957 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
958 lists. So for now we just exclude them.
965 <sect3 id="type-synonyms">
966 <title>Liberalised type synonyms</title>
969 Type synonyms are like macros at the type level, and
970 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
971 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
973 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
974 in a type synonym, thus:
976 type Discard a = forall b. Show b => a -> b -> (a, String)
981 g :: Discard Int -> (Int,Bool) -- A rank-2 type
988 You can write an unboxed tuple in a type synonym:
990 type Pr = (# Int, Int #)
998 You can apply a type synonym to a forall type:
1000 type Foo a = a -> a -> Bool
1002 f :: Foo (forall b. b->b)
1004 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1006 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1011 You can apply a type synonym to a partially applied type synonym:
1013 type Generic i o = forall x. i x -> o x
1016 foo :: Generic Id []
1018 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1020 foo :: forall x. x -> [x]
1028 GHC currently does kind checking before expanding synonyms (though even that
1032 After expanding type synonyms, GHC does validity checking on types, looking for
1033 the following mal-formedness which isn't detected simply by kind checking:
1036 Type constructor applied to a type involving for-alls.
1039 Unboxed tuple on left of an arrow.
1042 Partially-applied type synonym.
1046 this will be rejected:
1048 type Pr = (# Int, Int #)
1053 because GHC does not allow unboxed tuples on the left of a function arrow.
1058 <sect3 id="existential-quantification">
1059 <title>Existentially quantified data constructors
1063 The idea of using existential quantification in data type declarations
1064 was suggested by Laufer (I believe, thought doubtless someone will
1065 correct me), and implemented in Hope+. It's been in Lennart
1066 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1067 proved very useful. Here's the idea. Consider the declaration:
1073 data Foo = forall a. MkFoo a (a -> Bool)
1080 The data type <literal>Foo</literal> has two constructors with types:
1086 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1093 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1094 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1095 For example, the following expression is fine:
1101 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1107 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1108 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1109 isUpper</function> packages a character with a compatible function. These
1110 two things are each of type <literal>Foo</literal> and can be put in a list.
1114 What can we do with a value of type <literal>Foo</literal>?. In particular,
1115 what happens when we pattern-match on <function>MkFoo</function>?
1121 f (MkFoo val fn) = ???
1127 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1128 are compatible, the only (useful) thing we can do with them is to
1129 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1136 f (MkFoo val fn) = fn val
1142 What this allows us to do is to package heterogenous values
1143 together with a bunch of functions that manipulate them, and then treat
1144 that collection of packages in a uniform manner. You can express
1145 quite a bit of object-oriented-like programming this way.
1148 <sect4 id="existential">
1149 <title>Why existential?
1153 What has this to do with <emphasis>existential</emphasis> quantification?
1154 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1160 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1166 But Haskell programmers can safely think of the ordinary
1167 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1168 adding a new existential quantification construct.
1174 <title>Type classes</title>
1177 An easy extension (implemented in <command>hbc</command>) is to allow
1178 arbitrary contexts before the constructor. For example:
1184 data Baz = forall a. Eq a => Baz1 a a
1185 | forall b. Show b => Baz2 b (b -> b)
1191 The two constructors have the types you'd expect:
1197 Baz1 :: forall a. Eq a => a -> a -> Baz
1198 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1204 But when pattern matching on <function>Baz1</function> the matched values can be compared
1205 for equality, and when pattern matching on <function>Baz2</function> the first matched
1206 value can be converted to a string (as well as applying the function to it).
1207 So this program is legal:
1214 f (Baz1 p q) | p == q = "Yes"
1216 f (Baz2 v fn) = show (fn v)
1222 Operationally, in a dictionary-passing implementation, the
1223 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1224 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1225 extract it on pattern matching.
1229 Notice the way that the syntax fits smoothly with that used for
1230 universal quantification earlier.
1236 <title>Restrictions</title>
1239 There are several restrictions on the ways in which existentially-quantified
1240 constructors can be use.
1249 When pattern matching, each pattern match introduces a new,
1250 distinct, type for each existential type variable. These types cannot
1251 be unified with any other type, nor can they escape from the scope of
1252 the pattern match. For example, these fragments are incorrect:
1260 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1261 is the result of <function>f1</function>. One way to see why this is wrong is to
1262 ask what type <function>f1</function> has:
1266 f1 :: Foo -> a -- Weird!
1270 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1275 f1 :: forall a. Foo -> a -- Wrong!
1279 The original program is just plain wrong. Here's another sort of error
1283 f2 (Baz1 a b) (Baz1 p q) = a==q
1287 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1288 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1289 from the two <function>Baz1</function> constructors.
1297 You can't pattern-match on an existentially quantified
1298 constructor in a <literal>let</literal> or <literal>where</literal> group of
1299 bindings. So this is illegal:
1303 f3 x = a==b where { Baz1 a b = x }
1306 Instead, use a <literal>case</literal> expression:
1309 f3 x = case x of Baz1 a b -> a==b
1312 In general, you can only pattern-match
1313 on an existentially-quantified constructor in a <literal>case</literal> expression or
1314 in the patterns of a function definition.
1316 The reason for this restriction is really an implementation one.
1317 Type-checking binding groups is already a nightmare without
1318 existentials complicating the picture. Also an existential pattern
1319 binding at the top level of a module doesn't make sense, because it's
1320 not clear how to prevent the existentially-quantified type "escaping".
1321 So for now, there's a simple-to-state restriction. We'll see how
1329 You can't use existential quantification for <literal>newtype</literal>
1330 declarations. So this is illegal:
1334 newtype T = forall a. Ord a => MkT a
1338 Reason: a value of type <literal>T</literal> must be represented as a
1339 pair of a dictionary for <literal>Ord t</literal> and a value of type
1340 <literal>t</literal>. That contradicts the idea that
1341 <literal>newtype</literal> should have no concrete representation.
1342 You can get just the same efficiency and effect by using
1343 <literal>data</literal> instead of <literal>newtype</literal>. If
1344 there is no overloading involved, then there is more of a case for
1345 allowing an existentially-quantified <literal>newtype</literal>,
1346 because the <literal>data</literal> version does carry an
1347 implementation cost, but single-field existentially quantified
1348 constructors aren't much use. So the simple restriction (no
1349 existential stuff on <literal>newtype</literal>) stands, unless there
1350 are convincing reasons to change it.
1358 You can't use <literal>deriving</literal> to define instances of a
1359 data type with existentially quantified data constructors.
1361 Reason: in most cases it would not make sense. For example:#
1364 data T = forall a. MkT [a] deriving( Eq )
1367 To derive <literal>Eq</literal> in the standard way we would need to have equality
1368 between the single component of two <function>MkT</function> constructors:
1372 (MkT a) == (MkT b) = ???
1375 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1376 It's just about possible to imagine examples in which the derived instance
1377 would make sense, but it seems altogether simpler simply to prohibit such
1378 declarations. Define your own instances!
1393 <sect2 id="multi-param-type-classes">
1394 <title>Class declarations</title>
1397 This section documents GHC's implementation of multi-parameter type
1398 classes. There's lots of background in the paper <ulink
1399 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1400 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1401 Jones, Erik Meijer).
1404 There are the following constraints on class declarations:
1409 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1413 class Collection c a where
1414 union :: c a -> c a -> c a
1425 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1426 of "acyclic" involves only the superclass relationships. For example,
1432 op :: D b => a -> b -> b
1435 class C a => D a where { ... }
1439 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1440 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1441 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1448 <emphasis>There are no restrictions on the context in a class declaration
1449 (which introduces superclasses), except that the class hierarchy must
1450 be acyclic</emphasis>. So these class declarations are OK:
1454 class Functor (m k) => FiniteMap m k where
1457 class (Monad m, Monad (t m)) => Transform t m where
1458 lift :: m a -> (t m) a
1468 <emphasis>All of the class type variables must be reachable (in the sense
1469 mentioned in <xref linkend="type-restrictions"/>)
1470 from the free variables of each method type
1471 </emphasis>. For example:
1475 class Coll s a where
1477 insert :: s -> a -> s
1481 is not OK, because the type of <literal>empty</literal> doesn't mention
1482 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1483 types, and has the same motivation.
1485 Sometimes, offending class declarations exhibit misunderstandings. For
1486 example, <literal>Coll</literal> might be rewritten
1490 class Coll s a where
1492 insert :: s a -> a -> s a
1496 which makes the connection between the type of a collection of
1497 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1498 Occasionally this really doesn't work, in which case you can split the
1506 class CollE s => Coll s a where
1507 insert :: s -> a -> s
1517 <sect3 id="class-method-types">
1518 <title>Class method types</title>
1520 Haskell 98 prohibits class method types to mention constraints on the
1521 class type variable, thus:
1524 fromList :: [a] -> s a
1525 elem :: Eq a => a -> s a -> Bool
1527 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1528 contains the constraint <literal>Eq a</literal>, constrains only the
1529 class type variable (in this case <literal>a</literal>).
1532 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1539 <sect2 id="type-restrictions">
1540 <title>Type signatures</title>
1542 <sect3><title>The context of a type signature</title>
1544 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1545 the form <emphasis>(class type-variable)</emphasis> or
1546 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1547 these type signatures are perfectly OK
1550 g :: Ord (T a ()) => ...
1554 GHC imposes the following restrictions on the constraints in a type signature.
1558 forall tv1..tvn (c1, ...,cn) => type
1561 (Here, we write the "foralls" explicitly, although the Haskell source
1562 language omits them; in Haskell 98, all the free type variables of an
1563 explicit source-language type signature are universally quantified,
1564 except for the class type variables in a class declaration. However,
1565 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1574 <emphasis>Each universally quantified type variable
1575 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1577 A type variable <literal>a</literal> is "reachable" if it it appears
1578 in the same constraint as either a type variable free in in
1579 <literal>type</literal>, or another reachable type variable.
1580 A value with a type that does not obey
1581 this reachability restriction cannot be used without introducing
1582 ambiguity; that is why the type is rejected.
1583 Here, for example, is an illegal type:
1587 forall a. Eq a => Int
1591 When a value with this type was used, the constraint <literal>Eq tv</literal>
1592 would be introduced where <literal>tv</literal> is a fresh type variable, and
1593 (in the dictionary-translation implementation) the value would be
1594 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1595 can never know which instance of <literal>Eq</literal> to use because we never
1596 get any more information about <literal>tv</literal>.
1600 that the reachability condition is weaker than saying that <literal>a</literal> is
1601 functionally dependent on a type variable free in
1602 <literal>type</literal> (see <xref
1603 linkend="functional-dependencies"/>). The reason for this is there
1604 might be a "hidden" dependency, in a superclass perhaps. So
1605 "reachable" is a conservative approximation to "functionally dependent".
1606 For example, consider:
1608 class C a b | a -> b where ...
1609 class C a b => D a b where ...
1610 f :: forall a b. D a b => a -> a
1612 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1613 but that is not immediately apparent from <literal>f</literal>'s type.
1619 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1620 universally quantified type variables <literal>tvi</literal></emphasis>.
1622 For example, this type is OK because <literal>C a b</literal> mentions the
1623 universally quantified type variable <literal>b</literal>:
1627 forall a. C a b => burble
1631 The next type is illegal because the constraint <literal>Eq b</literal> does not
1632 mention <literal>a</literal>:
1636 forall a. Eq b => burble
1640 The reason for this restriction is milder than the other one. The
1641 excluded types are never useful or necessary (because the offending
1642 context doesn't need to be witnessed at this point; it can be floated
1643 out). Furthermore, floating them out increases sharing. Lastly,
1644 excluding them is a conservative choice; it leaves a patch of
1645 territory free in case we need it later.
1656 <title>For-all hoisting</title>
1658 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1659 end of an arrow, thus:
1661 type Discard a = forall b. a -> b -> a
1663 g :: Int -> Discard Int
1666 Simply expanding the type synonym would give
1668 g :: Int -> (forall b. Int -> b -> Int)
1670 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1672 g :: forall b. Int -> Int -> b -> Int
1674 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1675 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1676 performs the transformation:</emphasis>
1678 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1680 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1682 (In fact, GHC tries to retain as much synonym information as possible for use in
1683 error messages, but that is a usability issue.) This rule applies, of course, whether
1684 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1685 valid way to write <literal>g</literal>'s type signature:
1687 g :: Int -> Int -> forall b. b -> Int
1691 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1694 type Foo a = (?x::Int) => Bool -> a
1699 g :: (?x::Int) => Bool -> Bool -> Int
1707 <sect2 id="instance-decls">
1708 <title>Instance declarations</title>
1711 <title>Overlapping instances</title>
1713 In general, <emphasis>GHC requires that that it be unambiguous which instance
1715 should be used to resolve a type-class constraint</emphasis>. This behaviour
1716 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1717 <indexterm><primary>-fallow-overlapping-instances
1718 </primary></indexterm>
1719 and <option>-fallow-incoherent-instances</option>
1720 <indexterm><primary>-fallow-incoherent-instances
1721 </primary></indexterm>, as this section discusses.</para>
1723 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1724 it tries to match every instance declaration against the
1726 by instantiating the head of the instance declaration. For example, consider
1729 instance context1 => C Int a where ... -- (A)
1730 instance context2 => C a Bool where ... -- (B)
1731 instance context3 => C Int [a] where ... -- (C)
1732 instance context4 => C Int [Int] where ... -- (D)
1734 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>, but (C) and (D) do not. When matching, GHC takes
1735 no account of the context of the instance declaration
1736 (<literal>context1</literal> etc).
1737 GHC's default behaviour is that <emphasis>exactly one instance must match the
1738 constraint it is trying to resolve</emphasis>.
1739 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1740 including both declarations (A) and (B), say); an error is only reported if a
1741 particular constraint matches more than one.
1745 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1746 more than one instance to match, provided there is a most specific one. For
1747 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1748 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1749 most-specific match, the program is rejected.
1752 However, GHC is conservative about committing to an overlapping instance. For example:
1757 Suppose that from the RHS of <literal>f</literal> we get the constraint
1758 <literal>C Int [b]</literal>. But
1759 GHC does not commit to instance (C), because in a particular
1760 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1761 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1762 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1763 GHC will instead pick (C), without complaining about
1764 the problem of subsequent instantiations.
1769 <title>Type synonyms in the instance head</title>
1772 <emphasis>Unlike Haskell 98, instance heads may use type
1773 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1774 As always, using a type synonym is just shorthand for
1775 writing the RHS of the type synonym definition. For example:
1779 type Point = (Int,Int)
1780 instance C Point where ...
1781 instance C [Point] where ...
1785 is legal. However, if you added
1789 instance C (Int,Int) where ...
1793 as well, then the compiler will complain about the overlapping
1794 (actually, identical) instance declarations. As always, type synonyms
1795 must be fully applied. You cannot, for example, write:
1800 instance Monad P where ...
1804 This design decision is independent of all the others, and easily
1805 reversed, but it makes sense to me.
1810 <sect3 id="undecidable-instances">
1811 <title>Undecidable instances</title>
1813 <para>An instance declaration must normally obey the following rules:
1815 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1816 an instance declaration <emphasis>must not</emphasis> be a type variable.
1817 For example, these are OK:
1820 instance C Int a where ...
1822 instance D (Int, Int) where ...
1824 instance E [[a]] where ...
1828 instance F a where ...
1830 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1831 For example, this is OK:
1833 instance Stateful (ST s) (MutVar s) where ...
1840 <para>All of the types in the <emphasis>context</emphasis> of
1841 an instance declaration <emphasis>must</emphasis> be type variables.
1844 instance C a b => Eq (a,b) where ...
1848 instance C Int b => Foo b where ...
1854 These restrictions ensure that
1855 context reduction terminates: each reduction step removes one type
1856 constructor. For example, the following would make the type checker
1857 loop if it wasn't excluded:
1859 instance C a => C a where ...
1861 There are two situations in which the rule is a bit of a pain. First,
1862 if one allows overlapping instance declarations then it's quite
1863 convenient to have a "default instance" declaration that applies if
1864 something more specific does not:
1873 Second, sometimes you might want to use the following to get the
1874 effect of a "class synonym":
1878 class (C1 a, C2 a, C3 a) => C a where { }
1880 instance (C1 a, C2 a, C3 a) => C a where { }
1884 This allows you to write shorter signatures:
1896 f :: (C1 a, C2 a, C3 a) => ...
1900 Voluminous correspondence on the Haskell mailing list has convinced me
1901 that it's worth experimenting with more liberal rules. If you use
1902 the experimental flag <option>-fallow-undecidable-instances</option>
1903 <indexterm><primary>-fallow-undecidable-instances
1904 option</primary></indexterm>, you can use arbitrary
1905 types in both an instance context and instance head. Termination is ensured by having a
1906 fixed-depth recursion stack. If you exceed the stack depth you get a
1907 sort of backtrace, and the opportunity to increase the stack depth
1908 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1911 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1912 allowing these idioms interesting idioms.
1919 <sect2 id="implicit-parameters">
1920 <title>Implicit parameters</title>
1922 <para> Implicit parameters are implemented as described in
1923 "Implicit parameters: dynamic scoping with static types",
1924 J Lewis, MB Shields, E Meijer, J Launchbury,
1925 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1929 <para>(Most of the following, stil rather incomplete, documentation is
1930 due to Jeff Lewis.)</para>
1932 <para>Implicit parameter support is enabled with the option
1933 <option>-fimplicit-params</option>.</para>
1936 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1937 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1938 context. In Haskell, all variables are statically bound. Dynamic
1939 binding of variables is a notion that goes back to Lisp, but was later
1940 discarded in more modern incarnations, such as Scheme. Dynamic binding
1941 can be very confusing in an untyped language, and unfortunately, typed
1942 languages, in particular Hindley-Milner typed languages like Haskell,
1943 only support static scoping of variables.
1946 However, by a simple extension to the type class system of Haskell, we
1947 can support dynamic binding. Basically, we express the use of a
1948 dynamically bound variable as a constraint on the type. These
1949 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1950 function uses a dynamically-bound variable <literal>?x</literal>
1951 of type <literal>t'</literal>". For
1952 example, the following expresses the type of a sort function,
1953 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1955 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1957 The dynamic binding constraints are just a new form of predicate in the type class system.
1960 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1961 where <literal>x</literal> is
1962 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1963 Use of this construct also introduces a new
1964 dynamic-binding constraint in the type of the expression.
1965 For example, the following definition
1966 shows how we can define an implicitly parameterized sort function in
1967 terms of an explicitly parameterized <literal>sortBy</literal> function:
1969 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1971 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1977 <title>Implicit-parameter type constraints</title>
1979 Dynamic binding constraints behave just like other type class
1980 constraints in that they are automatically propagated. Thus, when a
1981 function is used, its implicit parameters are inherited by the
1982 function that called it. For example, our <literal>sort</literal> function might be used
1983 to pick out the least value in a list:
1985 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1986 least xs = fst (sort xs)
1988 Without lifting a finger, the <literal>?cmp</literal> parameter is
1989 propagated to become a parameter of <literal>least</literal> as well. With explicit
1990 parameters, the default is that parameters must always be explicit
1991 propagated. With implicit parameters, the default is to always
1995 An implicit-parameter type constraint differs from other type class constraints in the
1996 following way: All uses of a particular implicit parameter must have
1997 the same type. This means that the type of <literal>(?x, ?x)</literal>
1998 is <literal>(?x::a) => (a,a)</literal>, and not
1999 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2003 <para> You can't have an implicit parameter in the context of a class or instance
2004 declaration. For example, both these declarations are illegal:
2006 class (?x::Int) => C a where ...
2007 instance (?x::a) => Foo [a] where ...
2009 Reason: exactly which implicit parameter you pick up depends on exactly where
2010 you invoke a function. But the ``invocation'' of instance declarations is done
2011 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2012 Easiest thing is to outlaw the offending types.</para>
2014 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2016 f :: (?x :: [a]) => Int -> Int
2019 g :: (Read a, Show a) => String -> String
2022 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2023 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2024 quite unambiguous, and fixes the type <literal>a</literal>.
2029 <title>Implicit-parameter bindings</title>
2032 An implicit parameter is <emphasis>bound</emphasis> using the standard
2033 <literal>let</literal> or <literal>where</literal> binding forms.
2034 For example, we define the <literal>min</literal> function by binding
2035 <literal>cmp</literal>.
2038 min = let ?cmp = (<=) in least
2042 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2043 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2044 (including in a list comprehension, or do-notation, or pattern guards),
2045 or a <literal>where</literal> clause.
2046 Note the following points:
2049 An implicit-parameter binding group must be a
2050 collection of simple bindings to implicit-style variables (no
2051 function-style bindings, and no type signatures); these bindings are
2052 neither polymorphic or recursive.
2055 You may not mix implicit-parameter bindings with ordinary bindings in a
2056 single <literal>let</literal>
2057 expression; use two nested <literal>let</literal>s instead.
2058 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2062 You may put multiple implicit-parameter bindings in a
2063 single binding group; but they are <emphasis>not</emphasis> treated
2064 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2065 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2066 parameter. The bindings are not nested, and may be re-ordered without changing
2067 the meaning of the program.
2068 For example, consider:
2070 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2072 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2073 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2075 f :: (?x::Int) => Int -> Int
2084 <sect2 id="linear-implicit-parameters">
2085 <title>Linear implicit parameters</title>
2087 Linear implicit parameters are an idea developed by Koen Claessen,
2088 Mark Shields, and Simon PJ. They address the long-standing
2089 problem that monads seem over-kill for certain sorts of problem, notably:
2092 <listitem> <para> distributing a supply of unique names </para> </listitem>
2093 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2094 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2098 Linear implicit parameters are just like ordinary implicit parameters,
2099 except that they are "linear" -- that is, they cannot be copied, and
2100 must be explicitly "split" instead. Linear implicit parameters are
2101 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2102 (The '/' in the '%' suggests the split!)
2107 import GHC.Exts( Splittable )
2109 data NameSupply = ...
2111 splitNS :: NameSupply -> (NameSupply, NameSupply)
2112 newName :: NameSupply -> Name
2114 instance Splittable NameSupply where
2118 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2119 f env (Lam x e) = Lam x' (f env e)
2122 env' = extend env x x'
2123 ...more equations for f...
2125 Notice that the implicit parameter %ns is consumed
2127 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2128 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2132 So the translation done by the type checker makes
2133 the parameter explicit:
2135 f :: NameSupply -> Env -> Expr -> Expr
2136 f ns env (Lam x e) = Lam x' (f ns1 env e)
2138 (ns1,ns2) = splitNS ns
2140 env = extend env x x'
2142 Notice the call to 'split' introduced by the type checker.
2143 How did it know to use 'splitNS'? Because what it really did
2144 was to introduce a call to the overloaded function 'split',
2145 defined by the class <literal>Splittable</literal>:
2147 class Splittable a where
2150 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2151 split for name supplies. But we can simply write
2157 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2159 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2160 <literal>GHC.Exts</literal>.
2165 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2166 are entirely distinct implicit parameters: you
2167 can use them together and they won't intefere with each other. </para>
2170 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2172 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2173 in the context of a class or instance declaration. </para></listitem>
2177 <sect3><title>Warnings</title>
2180 The monomorphism restriction is even more important than usual.
2181 Consider the example above:
2183 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2184 f env (Lam x e) = Lam x' (f env e)
2187 env' = extend env x x'
2189 If we replaced the two occurrences of x' by (newName %ns), which is
2190 usually a harmless thing to do, we get:
2192 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2193 f env (Lam x e) = Lam (newName %ns) (f env e)
2195 env' = extend env x (newName %ns)
2197 But now the name supply is consumed in <emphasis>three</emphasis> places
2198 (the two calls to newName,and the recursive call to f), so
2199 the result is utterly different. Urk! We don't even have
2203 Well, this is an experimental change. With implicit
2204 parameters we have already lost beta reduction anyway, and
2205 (as John Launchbury puts it) we can't sensibly reason about
2206 Haskell programs without knowing their typing.
2211 <sect3><title>Recursive functions</title>
2212 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2215 foo :: %x::T => Int -> [Int]
2217 foo n = %x : foo (n-1)
2219 where T is some type in class Splittable.</para>
2221 Do you get a list of all the same T's or all different T's
2222 (assuming that split gives two distinct T's back)?
2224 If you supply the type signature, taking advantage of polymorphic
2225 recursion, you get what you'd probably expect. Here's the
2226 translated term, where the implicit param is made explicit:
2229 foo x n = let (x1,x2) = split x
2230 in x1 : foo x2 (n-1)
2232 But if you don't supply a type signature, GHC uses the Hindley
2233 Milner trick of using a single monomorphic instance of the function
2234 for the recursive calls. That is what makes Hindley Milner type inference
2235 work. So the translation becomes
2239 foom n = x : foom (n-1)
2243 Result: 'x' is not split, and you get a list of identical T's. So the
2244 semantics of the program depends on whether or not foo has a type signature.
2247 You may say that this is a good reason to dislike linear implicit parameters
2248 and you'd be right. That is why they are an experimental feature.
2254 <sect2 id="functional-dependencies">
2255 <title>Functional dependencies
2258 <para> Functional dependencies are implemented as described by Mark Jones
2259 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2260 In Proceedings of the 9th European Symposium on Programming,
2261 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2265 Functional dependencies are introduced by a vertical bar in the syntax of a
2266 class declaration; e.g.
2268 class (Monad m) => MonadState s m | m -> s where ...
2270 class Foo a b c | a b -> c where ...
2272 There should be more documentation, but there isn't (yet). Yell if you need it.
2278 <sect2 id="sec-kinding">
2279 <title>Explicitly-kinded quantification</title>
2282 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2283 to give the kind explicitly as (machine-checked) documentation,
2284 just as it is nice to give a type signature for a function. On some occasions,
2285 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2286 John Hughes had to define the data type:
2288 data Set cxt a = Set [a]
2289 | Unused (cxt a -> ())
2291 The only use for the <literal>Unused</literal> constructor was to force the correct
2292 kind for the type variable <literal>cxt</literal>.
2295 GHC now instead allows you to specify the kind of a type variable directly, wherever
2296 a type variable is explicitly bound. Namely:
2298 <listitem><para><literal>data</literal> declarations:
2300 data Set (cxt :: * -> *) a = Set [a]
2301 </screen></para></listitem>
2302 <listitem><para><literal>type</literal> declarations:
2304 type T (f :: * -> *) = f Int
2305 </screen></para></listitem>
2306 <listitem><para><literal>class</literal> declarations:
2308 class (Eq a) => C (f :: * -> *) a where ...
2309 </screen></para></listitem>
2310 <listitem><para><literal>forall</literal>'s in type signatures:
2312 f :: forall (cxt :: * -> *). Set cxt Int
2313 </screen></para></listitem>
2318 The parentheses are required. Some of the spaces are required too, to
2319 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2320 will get a parse error, because "<literal>::*->*</literal>" is a
2321 single lexeme in Haskell.
2325 As part of the same extension, you can put kind annotations in types
2328 f :: (Int :: *) -> Int
2329 g :: forall a. a -> (a :: *)
2333 atype ::= '(' ctype '::' kind ')
2335 The parentheses are required.
2340 <sect2 id="universal-quantification">
2341 <title>Arbitrary-rank polymorphism
2345 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2346 allows us to say exactly what this means. For example:
2354 g :: forall b. (b -> b)
2356 The two are treated identically.
2360 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2361 explicit universal quantification in
2363 For example, all the following types are legal:
2365 f1 :: forall a b. a -> b -> a
2366 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2368 f2 :: (forall a. a->a) -> Int -> Int
2369 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2371 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2373 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2374 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2375 The <literal>forall</literal> makes explicit the universal quantification that
2376 is implicitly added by Haskell.
2379 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2380 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2381 shows, the polymorphic type on the left of the function arrow can be overloaded.
2384 The function <literal>f3</literal> has a rank-3 type;
2385 it has rank-2 types on the left of a function arrow.
2388 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2389 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2390 that restriction has now been lifted.)
2391 In particular, a forall-type (also called a "type scheme"),
2392 including an operational type class context, is legal:
2394 <listitem> <para> On the left of a function arrow </para> </listitem>
2395 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2396 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2397 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2398 field type signatures.</para> </listitem>
2399 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2400 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2402 There is one place you cannot put a <literal>forall</literal>:
2403 you cannot instantiate a type variable with a forall-type. So you cannot
2404 make a forall-type the argument of a type constructor. So these types are illegal:
2406 x1 :: [forall a. a->a]
2407 x2 :: (forall a. a->a, Int)
2408 x3 :: Maybe (forall a. a->a)
2410 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2411 a type variable any more!
2420 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2421 the types of the constructor arguments. Here are several examples:
2427 data T a = T1 (forall b. b -> b -> b) a
2429 data MonadT m = MkMonad { return :: forall a. a -> m a,
2430 bind :: forall a b. m a -> (a -> m b) -> m b
2433 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2439 The constructors have rank-2 types:
2445 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2446 MkMonad :: forall m. (forall a. a -> m a)
2447 -> (forall a b. m a -> (a -> m b) -> m b)
2449 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2455 Notice that you don't need to use a <literal>forall</literal> if there's an
2456 explicit context. For example in the first argument of the
2457 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2458 prefixed to the argument type. The implicit <literal>forall</literal>
2459 quantifies all type variables that are not already in scope, and are
2460 mentioned in the type quantified over.
2464 As for type signatures, implicit quantification happens for non-overloaded
2465 types too. So if you write this:
2468 data T a = MkT (Either a b) (b -> b)
2471 it's just as if you had written this:
2474 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2477 That is, since the type variable <literal>b</literal> isn't in scope, it's
2478 implicitly universally quantified. (Arguably, it would be better
2479 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2480 where that is what is wanted. Feedback welcomed.)
2484 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2485 the constructor to suitable values, just as usual. For example,
2496 a3 = MkSwizzle reverse
2499 a4 = let r x = Just x
2506 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2507 mkTs f x y = [T1 f x, T1 f y]
2513 The type of the argument can, as usual, be more general than the type
2514 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2515 does not need the <literal>Ord</literal> constraint.)
2519 When you use pattern matching, the bound variables may now have
2520 polymorphic types. For example:
2526 f :: T a -> a -> (a, Char)
2527 f (T1 w k) x = (w k x, w 'c' 'd')
2529 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2530 g (MkSwizzle s) xs f = s (map f (s xs))
2532 h :: MonadT m -> [m a] -> m [a]
2533 h m [] = return m []
2534 h m (x:xs) = bind m x $ \y ->
2535 bind m (h m xs) $ \ys ->
2542 In the function <function>h</function> we use the record selectors <literal>return</literal>
2543 and <literal>bind</literal> to extract the polymorphic bind and return functions
2544 from the <literal>MonadT</literal> data structure, rather than using pattern
2550 <title>Type inference</title>
2553 In general, type inference for arbitrary-rank types is undecidable.
2554 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2555 to get a decidable algorithm by requiring some help from the programmer.
2556 We do not yet have a formal specification of "some help" but the rule is this:
2559 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2560 provides an explicit polymorphic type for x, or GHC's type inference will assume
2561 that x's type has no foralls in it</emphasis>.
2564 What does it mean to "provide" an explicit type for x? You can do that by
2565 giving a type signature for x directly, using a pattern type signature
2566 (<xref linkend="scoped-type-variables"/>), thus:
2568 \ f :: (forall a. a->a) -> (f True, f 'c')
2570 Alternatively, you can give a type signature to the enclosing
2571 context, which GHC can "push down" to find the type for the variable:
2573 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2575 Here the type signature on the expression can be pushed inwards
2576 to give a type signature for f. Similarly, and more commonly,
2577 one can give a type signature for the function itself:
2579 h :: (forall a. a->a) -> (Bool,Char)
2580 h f = (f True, f 'c')
2582 You don't need to give a type signature if the lambda bound variable
2583 is a constructor argument. Here is an example we saw earlier:
2585 f :: T a -> a -> (a, Char)
2586 f (T1 w k) x = (w k x, w 'c' 'd')
2588 Here we do not need to give a type signature to <literal>w</literal>, because
2589 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2596 <sect3 id="implicit-quant">
2597 <title>Implicit quantification</title>
2600 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2601 user-written types, if and only if there is no explicit <literal>forall</literal>,
2602 GHC finds all the type variables mentioned in the type that are not already
2603 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2607 f :: forall a. a -> a
2614 h :: forall b. a -> b -> b
2620 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2623 f :: (a -> a) -> Int
2625 f :: forall a. (a -> a) -> Int
2627 f :: (forall a. a -> a) -> Int
2630 g :: (Ord a => a -> a) -> Int
2631 -- MEANS the illegal type
2632 g :: forall a. (Ord a => a -> a) -> Int
2634 g :: (forall a. Ord a => a -> a) -> Int
2636 The latter produces an illegal type, which you might think is silly,
2637 but at least the rule is simple. If you want the latter type, you
2638 can write your for-alls explicitly. Indeed, doing so is strongly advised
2647 <sect2 id="scoped-type-variables">
2648 <title>Scoped type variables
2652 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2653 variable</emphasis>. For example
2659 f (xs::[a]) = ys ++ ys
2668 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2669 This brings the type variable <literal>a</literal> into scope; it scopes over
2670 all the patterns and right hand sides for this equation for <function>f</function>.
2671 In particular, it is in scope at the type signature for <varname>y</varname>.
2675 Pattern type signatures are completely orthogonal to ordinary, separate
2676 type signatures. The two can be used independently or together.
2677 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2678 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2679 implicitly universally quantified. (If there are no type variables in
2680 scope, all type variables mentioned in the signature are universally
2681 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2682 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2683 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2684 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2685 it becomes possible to do so.
2689 Scoped type variables are implemented in both GHC and Hugs. Where the
2690 implementations differ from the specification below, those differences
2695 So much for the basic idea. Here are the details.
2699 <title>What a pattern type signature means</title>
2701 A type variable brought into scope by a pattern type signature is simply
2702 the name for a type. The restriction they express is that all occurrences
2703 of the same name mean the same type. For example:
2705 f :: [Int] -> Int -> Int
2706 f (xs::[a]) (y::a) = (head xs + y) :: a
2708 The pattern type signatures on the left hand side of
2709 <literal>f</literal> express the fact that <literal>xs</literal>
2710 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2711 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2712 specifies that this expression must have the same type <literal>a</literal>.
2713 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2714 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2715 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2716 rules, which specified that a pattern-bound type variable should be universally quantified.)
2717 For example, all of these are legal:</para>
2720 t (x::a) (y::a) = x+y*2
2722 f (x::a) (y::b) = [x,y] -- a unifies with b
2724 g (x::a) = x + 1::Int -- a unifies with Int
2726 h x = let k (y::a) = [x,y] -- a is free in the
2727 in k x -- environment
2729 k (x::a) True = ... -- a unifies with Int
2730 k (x::Int) False = ...
2733 w (x::a) = x -- a unifies with [b]
2739 <title>Scope and implicit quantification</title>
2747 All the type variables mentioned in a pattern,
2748 that are not already in scope,
2749 are brought into scope by the pattern. We describe this set as
2750 the <emphasis>type variables bound by the pattern</emphasis>.
2753 f (x::a) = let g (y::(a,b)) = fst y
2757 The pattern <literal>(x::a)</literal> brings the type variable
2758 <literal>a</literal> into scope, as well as the term
2759 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2760 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2761 and brings into scope the type variable <literal>b</literal>.
2767 The type variable(s) bound by the pattern have the same scope
2768 as the term variable(s) bound by the pattern. For example:
2771 f (x::a) = <...rhs of f...>
2772 (p::b, q::b) = (1,2)
2773 in <...body of let...>
2775 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2776 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2777 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2778 just like <literal>p</literal> and <literal>q</literal> do.
2779 Indeed, the newly bound type variables also scope over any ordinary, separate
2780 type signatures in the <literal>let</literal> group.
2787 The type variables bound by the pattern may be
2788 mentioned in ordinary type signatures or pattern
2789 type signatures anywhere within their scope.
2796 In ordinary type signatures, any type variable mentioned in the
2797 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2805 Ordinary type signatures do not bring any new type variables
2806 into scope (except in the type signature itself!). So this is illegal:
2813 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2814 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2815 and that is an incorrect typing.
2822 The pattern type signature is a monotype:
2827 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2831 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2832 not to type schemes.
2836 There is no implicit universal quantification on pattern type signatures (in contrast to
2837 ordinary type signatures).
2847 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2848 scope over the methods defined in the <literal>where</literal> part. For example:
2862 (Not implemented in Hugs yet, Dec 98).
2873 <title>Where a pattern type signature can occur</title>
2876 A pattern type signature can occur in any pattern. For example:
2881 A pattern type signature can be on an arbitrary sub-pattern, not
2886 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2895 Pattern type signatures, including the result part, can be used
2896 in lambda abstractions:
2899 (\ (x::a, y) :: a -> x)
2906 Pattern type signatures, including the result part, can be used
2907 in <literal>case</literal> expressions:
2910 case e of { ((x::a, y) :: (a,b)) -> x }
2913 Note that the <literal>-></literal> symbol in a case alternative
2914 leads to difficulties when parsing a type signature in the pattern: in
2915 the absence of the extra parentheses in the example above, the parser
2916 would try to interpret the <literal>-></literal> as a function
2917 arrow and give a parse error later.
2925 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2926 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2927 token or a parenthesised type of some sort). To see why,
2928 consider how one would parse this:
2942 Pattern type signatures can bind existential type variables.
2947 data T = forall a. MkT [a]
2950 f (MkT [t::a]) = MkT t3
2963 Pattern type signatures
2964 can be used in pattern bindings:
2967 f x = let (y, z::a) = x in ...
2968 f1 x = let (y, z::Int) = x in ...
2969 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2970 f3 :: (b->b) = \x -> x
2973 In all such cases, the binding is not generalised over the pattern-bound
2974 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2975 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2976 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2977 In contrast, the binding
2982 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2983 in <literal>f4</literal>'s scope.
2993 <title>Result type signatures</title>
2996 The result type of a function can be given a signature, thus:
3000 f (x::a) :: [a] = [x,x,x]
3004 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3005 result type. Sometimes this is the only way of naming the type variable
3010 f :: Int -> [a] -> [a]
3011 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3012 in \xs -> map g (reverse xs `zip` xs)
3017 The type variables bound in a result type signature scope over the right hand side
3018 of the definition. However, consider this corner-case:
3020 rev1 :: [a] -> [a] = \xs -> reverse xs
3022 foo ys = rev (ys::[a])
3024 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3025 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3026 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3027 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3028 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3031 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3032 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3036 rev1 :: [a] -> [a] = \xs -> reverse xs
3041 Result type signatures are not yet implemented in Hugs.
3048 <sect2 id="deriving-typeable">
3049 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3052 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3053 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3054 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3055 classes <literal>Eq</literal>, <literal>Ord</literal>,
3056 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3059 GHC extends this list with two more classes that may be automatically derived
3060 (provided the <option>-fglasgow-exts</option> flag is specified):
3061 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3062 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3063 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3067 <sect2 id="newtype-deriving">
3068 <title>Generalised derived instances for newtypes</title>
3071 When you define an abstract type using <literal>newtype</literal>, you may want
3072 the new type to inherit some instances from its representation. In
3073 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3074 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3075 other classes you have to write an explicit instance declaration. For
3076 example, if you define
3079 newtype Dollars = Dollars Int
3082 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3083 explicitly define an instance of <literal>Num</literal>:
3086 instance Num Dollars where
3087 Dollars a + Dollars b = Dollars (a+b)
3090 All the instance does is apply and remove the <literal>newtype</literal>
3091 constructor. It is particularly galling that, since the constructor
3092 doesn't appear at run-time, this instance declaration defines a
3093 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3094 dictionary, only slower!
3098 <sect3> <title> Generalising the deriving clause </title>
3100 GHC now permits such instances to be derived instead, so one can write
3102 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3105 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3106 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3107 derives an instance declaration of the form
3110 instance Num Int => Num Dollars
3113 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3117 We can also derive instances of constructor classes in a similar
3118 way. For example, suppose we have implemented state and failure monad
3119 transformers, such that
3122 instance Monad m => Monad (State s m)
3123 instance Monad m => Monad (Failure m)
3125 In Haskell 98, we can define a parsing monad by
3127 type Parser tok m a = State [tok] (Failure m) a
3130 which is automatically a monad thanks to the instance declarations
3131 above. With the extension, we can make the parser type abstract,
3132 without needing to write an instance of class <literal>Monad</literal>, via
3135 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3138 In this case the derived instance declaration is of the form
3140 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3143 Notice that, since <literal>Monad</literal> is a constructor class, the
3144 instance is a <emphasis>partial application</emphasis> of the new type, not the
3145 entire left hand side. We can imagine that the type declaration is
3146 ``eta-converted'' to generate the context of the instance
3151 We can even derive instances of multi-parameter classes, provided the
3152 newtype is the last class parameter. In this case, a ``partial
3153 application'' of the class appears in the <literal>deriving</literal>
3154 clause. For example, given the class
3157 class StateMonad s m | m -> s where ...
3158 instance Monad m => StateMonad s (State s m) where ...
3160 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3162 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3163 deriving (Monad, StateMonad [tok])
3166 The derived instance is obtained by completing the application of the
3167 class to the new type:
3170 instance StateMonad [tok] (State [tok] (Failure m)) =>
3171 StateMonad [tok] (Parser tok m)
3176 As a result of this extension, all derived instances in newtype
3177 declarations are treated uniformly (and implemented just by reusing
3178 the dictionary for the representation type), <emphasis>except</emphasis>
3179 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3180 the newtype and its representation.
3184 <sect3> <title> A more precise specification </title>
3186 Derived instance declarations are constructed as follows. Consider the
3187 declaration (after expansion of any type synonyms)
3190 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3196 <literal>S</literal> is a type constructor,
3199 The <literal>t1...tk</literal> are types,
3202 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3203 the <literal>ti</literal>, and
3206 The <literal>ci</literal> are partial applications of
3207 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3208 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3211 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3212 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3213 should not "look through" the type or its constructor. You can still
3214 derive these classes for a newtype, but it happens in the usual way, not
3215 via this new mechanism.
3218 Then, for each <literal>ci</literal>, the derived instance
3221 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3223 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3224 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3228 As an example which does <emphasis>not</emphasis> work, consider
3230 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3232 Here we cannot derive the instance
3234 instance Monad (State s m) => Monad (NonMonad m)
3237 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3238 and so cannot be "eta-converted" away. It is a good thing that this
3239 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3240 not, in fact, a monad --- for the same reason. Try defining
3241 <literal>>>=</literal> with the correct type: you won't be able to.
3245 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3246 important, since we can only derive instances for the last one. If the
3247 <literal>StateMonad</literal> class above were instead defined as
3250 class StateMonad m s | m -> s where ...
3253 then we would not have been able to derive an instance for the
3254 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3255 classes usually have one "main" parameter for which deriving new
3256 instances is most interesting.
3264 <!-- ==================== End of type system extensions ================= -->
3266 <!-- ====================== Generalised algebraic data types ======================= -->
3269 <title>Generalised Algebraic Data Types</title>
3271 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3272 to give the type signatures of constructors explicitly. For example:
3275 Lit :: Int -> Term Int
3276 Succ :: Term Int -> Term Int
3277 IsZero :: Term Int -> Term Bool
3278 If :: Term Bool -> Term a -> Term a -> Term a
3279 Pair :: Term a -> Term b -> Term (a,b)
3281 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3282 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3283 for these <literal>Terms</literal>:
3287 eval (Succ t) = 1 + eval t
3288 eval (IsZero i) = eval i == 0
3289 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3290 eval (Pair e1 e2) = (eval e2, eval e2)
3292 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3294 <para> The extensions to GHC are these:
3297 Data type declarations have a 'where' form, as exemplified above. The type signature of
3298 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3299 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3300 have no scope. Indeed, one can write a kind signature instead:
3302 data Term :: * -> * where ...
3304 or even a mixture of the two:
3306 data Foo a :: (* -> *) -> * where ...
3308 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3311 data Foo a (b :: * -> *) where ...
3316 There are no restrictions on the type of the data constructor, except that the result
3317 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3318 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3322 You cannot use a <literal>deriving</literal> clause on a GADT-style data type declaration,
3323 nor can you use record syntax. (It's not clear what these constructs would mean. For example,
3324 the record selectors might ill-typed.) However, you can use strictness annotations, in the obvious places
3325 in the constructor type:
3328 Lit :: !Int -> Term Int
3329 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3330 Pair :: Term a -> Term b -> Term (a,b)
3335 Pattern matching causes type refinement. For example, in the right hand side of the equation
3340 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3341 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3342 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3344 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3345 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3346 occur. However, the refinement is quite general. For example, if we had:
3348 eval :: Term a -> a -> a
3349 eval (Lit i) j = i+j
3351 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3352 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3353 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3359 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3361 data T a = forall b. MkT b (b->a)
3362 data T' a where { MKT :: b -> (b->a) -> T a }
3367 <!-- ====================== End of Generalised algebraic data types ======================= -->
3369 <!-- ====================== TEMPLATE HASKELL ======================= -->
3371 <sect1 id="template-haskell">
3372 <title>Template Haskell</title>
3374 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3375 Template Haskell at <ulink url="http://www.haskell.org/th/">
3376 http://www.haskell.org/th/</ulink>, while
3378 the main technical innovations is discussed in "<ulink
3379 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3380 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3381 The details of the Template Haskell design are still in flux. Make sure you
3382 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3383 (search for the type ExpQ).
3384 [Temporary: many changes to the original design are described in
3385 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3386 Not all of these changes are in GHC 6.2.]
3389 <para> The first example from that paper is set out below as a worked example to help get you started.
3393 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3394 Tim Sheard is going to expand it.)
3398 <title>Syntax</title>
3400 <para> Template Haskell has the following new syntactic
3401 constructions. You need to use the flag
3402 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3403 </indexterm>to switch these syntactic extensions on
3404 (<option>-fth</option> is currently implied by
3405 <option>-fglasgow-exts</option>, but you are encouraged to
3406 specify it explicitly).</para>
3410 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3411 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3412 There must be no space between the "$" and the identifier or parenthesis. This use
3413 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3414 of "." as an infix operator. If you want the infix operator, put spaces around it.
3416 <para> A splice can occur in place of
3418 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3419 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3420 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3422 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3423 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3429 A expression quotation is written in Oxford brackets, thus:
3431 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3432 the quotation has type <literal>Expr</literal>.</para></listitem>
3433 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3434 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3435 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3436 the quotation has type <literal>Type</literal>.</para></listitem>
3437 </itemizedlist></para></listitem>
3440 Reification is written thus:
3442 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3443 has type <literal>Dec</literal>. </para></listitem>
3444 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3445 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3446 <listitem><para> Still to come: fixities </para></listitem>
3448 </itemizedlist></para>
3455 <sect2> <title> Using Template Haskell </title>
3459 The data types and monadic constructor functions for Template Haskell are in the library
3460 <literal>Language.Haskell.THSyntax</literal>.
3464 You can only run a function at compile time if it is imported from another module. That is,
3465 you can't define a function in a module, and call it from within a splice in the same module.
3466 (It would make sense to do so, but it's hard to implement.)
3470 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3473 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3474 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3475 compiles and runs a program, and then looks at the result. So it's important that
3476 the program it compiles produces results whose representations are identical to
3477 those of the compiler itself.
3481 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3482 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3487 <sect2> <title> A Template Haskell Worked Example </title>
3488 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3489 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3496 -- Import our template "pr"
3497 import Printf ( pr )
3499 -- The splice operator $ takes the Haskell source code
3500 -- generated at compile time by "pr" and splices it into
3501 -- the argument of "putStrLn".
3502 main = putStrLn ( $(pr "Hello") )
3508 -- Skeletal printf from the paper.
3509 -- It needs to be in a separate module to the one where
3510 -- you intend to use it.
3512 -- Import some Template Haskell syntax
3513 import Language.Haskell.TH
3515 -- Describe a format string
3516 data Format = D | S | L String
3518 -- Parse a format string. This is left largely to you
3519 -- as we are here interested in building our first ever
3520 -- Template Haskell program and not in building printf.
3521 parse :: String -> [Format]
3524 -- Generate Haskell source code from a parsed representation
3525 -- of the format string. This code will be spliced into
3526 -- the module which calls "pr", at compile time.
3527 gen :: [Format] -> ExpQ
3528 gen [D] = [| \n -> show n |]
3529 gen [S] = [| \s -> s |]
3530 gen [L s] = stringE s
3532 -- Here we generate the Haskell code for the splice
3533 -- from an input format string.
3534 pr :: String -> ExpQ
3535 pr s = gen (parse s)
3538 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3541 $ ghc --make -fth main.hs -o main.exe
3544 <para>Run "main.exe" and here is your output:</para>
3555 <!-- ===================== Arrow notation =================== -->
3557 <sect1 id="arrow-notation">
3558 <title>Arrow notation
3561 <para>Arrows are a generalization of monads introduced by John Hughes.
3562 For more details, see
3567 “Generalising Monads to Arrows”,
3568 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3569 pp67–111, May 2000.
3575 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3576 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3582 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3583 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3589 and the arrows web page at
3590 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3591 With the <option>-farrows</option> flag, GHC supports the arrow
3592 notation described in the second of these papers.
3593 What follows is a brief introduction to the notation;
3594 it won't make much sense unless you've read Hughes's paper.
3595 This notation is translated to ordinary Haskell,
3596 using combinators from the
3597 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3601 <para>The extension adds a new kind of expression for defining arrows:
3603 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3604 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3606 where <literal>proc</literal> is a new keyword.
3607 The variables of the pattern are bound in the body of the
3608 <literal>proc</literal>-expression,
3609 which is a new sort of thing called a <firstterm>command</firstterm>.
3610 The syntax of commands is as follows:
3612 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3613 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3614 | <replaceable>cmd</replaceable><superscript>0</superscript>
3616 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3617 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3618 infix operators as for expressions, and
3620 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3621 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3622 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3623 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3624 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3625 | <replaceable>fcmd</replaceable>
3627 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3628 | ( <replaceable>cmd</replaceable> )
3629 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3631 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3632 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3633 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3634 | <replaceable>cmd</replaceable>
3636 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3637 except that the bodies are commands instead of expressions.
3641 Commands produce values, but (like monadic computations)
3642 may yield more than one value,
3643 or none, and may do other things as well.
3644 For the most part, familiarity with monadic notation is a good guide to
3646 However the values of expressions, even monadic ones,
3647 are determined by the values of the variables they contain;
3648 this is not necessarily the case for commands.
3652 A simple example of the new notation is the expression
3654 proc x -> f -< x+1
3656 We call this a <firstterm>procedure</firstterm> or
3657 <firstterm>arrow abstraction</firstterm>.
3658 As with a lambda expression, the variable <literal>x</literal>
3659 is a new variable bound within the <literal>proc</literal>-expression.
3660 It refers to the input to the arrow.
3661 In the above example, <literal>-<</literal> is not an identifier but an
3662 new reserved symbol used for building commands from an expression of arrow
3663 type and an expression to be fed as input to that arrow.
3664 (The weird look will make more sense later.)
3665 It may be read as analogue of application for arrows.
3666 The above example is equivalent to the Haskell expression
3668 arr (\ x -> x+1) >>> f
3670 That would make no sense if the expression to the left of
3671 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3672 More generally, the expression to the left of <literal>-<</literal>
3673 may not involve any <firstterm>local variable</firstterm>,
3674 i.e. a variable bound in the current arrow abstraction.
3675 For such a situation there is a variant <literal>-<<</literal>, as in
3677 proc x -> f x -<< x+1
3679 which is equivalent to
3681 arr (\ x -> (f, x+1)) >>> app
3683 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3685 Such an arrow is equivalent to a monad, so if you're using this form
3686 you may find a monadic formulation more convenient.
3690 <title>do-notation for commands</title>
3693 Another form of command is a form of <literal>do</literal>-notation.
3694 For example, you can write
3703 You can read this much like ordinary <literal>do</literal>-notation,
3704 but with commands in place of monadic expressions.
3705 The first line sends the value of <literal>x+1</literal> as an input to
3706 the arrow <literal>f</literal>, and matches its output against
3707 <literal>y</literal>.
3708 In the next line, the output is discarded.
3709 The arrow <function>returnA</function> is defined in the
3710 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3711 module as <literal>arr id</literal>.
3712 The above example is treated as an abbreviation for
3714 arr (\ x -> (x, x)) >>>
3715 first (arr (\ x -> x+1) >>> f) >>>
3716 arr (\ (y, x) -> (y, (x, y))) >>>
3717 first (arr (\ y -> 2*y) >>> g) >>>
3719 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3720 first (arr (\ (x, z) -> x*z) >>> h) >>>
3721 arr (\ (t, z) -> t+z) >>>
3724 Note that variables not used later in the composition are projected out.
3725 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3727 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3728 module, this reduces to
3730 arr (\ x -> (x+1, x)) >>>
3732 arr (\ (y, x) -> (2*y, (x, y))) >>>
3734 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3736 arr (\ (t, z) -> t+z)
3738 which is what you might have written by hand.
3739 With arrow notation, GHC keeps track of all those tuples of variables for you.
3743 Note that although the above translation suggests that
3744 <literal>let</literal>-bound variables like <literal>z</literal> must be
3745 monomorphic, the actual translation produces Core,
3746 so polymorphic variables are allowed.
3750 It's also possible to have mutually recursive bindings,
3751 using the new <literal>rec</literal> keyword, as in the following example:
3753 counter :: ArrowCircuit a => a Bool Int
3754 counter = proc reset -> do
3755 rec output <- returnA -< if reset then 0 else next
3756 next <- delay 0 -< output+1
3757 returnA -< output
3759 The translation of such forms uses the <function>loop</function> combinator,
3760 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3766 <title>Conditional commands</title>
3769 In the previous example, we used a conditional expression to construct the
3771 Sometimes we want to conditionally execute different commands, as in
3778 which is translated to
3780 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3781 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3783 Since the translation uses <function>|||</function>,
3784 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3788 There are also <literal>case</literal> commands, like
3794 y <- h -< (x1, x2)
3798 The syntax is the same as for <literal>case</literal> expressions,
3799 except that the bodies of the alternatives are commands rather than expressions.
3800 The translation is similar to that of <literal>if</literal> commands.
3806 <title>Defining your own control structures</title>
3809 As we're seen, arrow notation provides constructs,
3810 modelled on those for expressions,
3811 for sequencing, value recursion and conditionals.
3812 But suitable combinators,
3813 which you can define in ordinary Haskell,
3814 may also be used to build new commands out of existing ones.
3815 The basic idea is that a command defines an arrow from environments to values.
3816 These environments assign values to the free local variables of the command.
3817 Thus combinators that produce arrows from arrows
3818 may also be used to build commands from commands.
3819 For example, the <literal>ArrowChoice</literal> class includes a combinator
3821 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3823 so we can use it to build commands:
3825 expr' = proc x -> do
3828 symbol Plus -< ()
3829 y <- term -< ()
3832 symbol Minus -< ()
3833 y <- term -< ()
3836 (The <literal>do</literal> on the first line is needed to prevent the first
3837 <literal><+> ...</literal> from being interpreted as part of the
3838 expression on the previous line.)
3839 This is equivalent to
3841 expr' = (proc x -> returnA -< x)
3842 <+> (proc x -> do
3843 symbol Plus -< ()
3844 y <- term -< ()
3846 <+> (proc x -> do
3847 symbol Minus -< ()
3848 y <- term -< ()
3851 It is essential that this operator be polymorphic in <literal>e</literal>
3852 (representing the environment input to the command
3853 and thence to its subcommands)
3854 and satisfy the corresponding naturality property
3856 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3858 at least for strict <literal>k</literal>.
3859 (This should be automatic if you're not using <function>seq</function>.)
3860 This ensures that environments seen by the subcommands are environments
3861 of the whole command,
3862 and also allows the translation to safely trim these environments.
3863 The operator must also not use any variable defined within the current
3868 We could define our own operator
3870 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3871 untilA body cond = proc x ->
3872 if cond x then returnA -< ()
3875 untilA body cond -< x
3877 and use it in the same way.
3878 Of course this infix syntax only makes sense for binary operators;
3879 there is also a more general syntax involving special brackets:
3883 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3890 <title>Primitive constructs</title>
3893 Some operators will need to pass additional inputs to their subcommands.
3894 For example, in an arrow type supporting exceptions,
3895 the operator that attaches an exception handler will wish to pass the
3896 exception that occurred to the handler.
3897 Such an operator might have a type
3899 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3901 where <literal>Ex</literal> is the type of exceptions handled.
3902 You could then use this with arrow notation by writing a command
3904 body `handleA` \ ex -> handler
3906 so that if an exception is raised in the command <literal>body</literal>,
3907 the variable <literal>ex</literal> is bound to the value of the exception
3908 and the command <literal>handler</literal>,
3909 which typically refers to <literal>ex</literal>, is entered.
3910 Though the syntax here looks like a functional lambda,
3911 we are talking about commands, and something different is going on.
3912 The input to the arrow represented by a command consists of values for
3913 the free local variables in the command, plus a stack of anonymous values.
3914 In all the prior examples, this stack was empty.
3915 In the second argument to <function>handleA</function>,
3916 this stack consists of one value, the value of the exception.
3917 The command form of lambda merely gives this value a name.
3922 the values on the stack are paired to the right of the environment.
3923 So operators like <function>handleA</function> that pass
3924 extra inputs to their subcommands can be designed for use with the notation
3925 by pairing the values with the environment in this way.
3926 More precisely, the type of each argument of the operator (and its result)
3927 should have the form
3929 a (...(e,t1), ... tn) t
3931 where <replaceable>e</replaceable> is a polymorphic variable
3932 (representing the environment)
3933 and <replaceable>ti</replaceable> are the types of the values on the stack,
3934 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3935 The polymorphic variable <replaceable>e</replaceable> must not occur in
3936 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3937 <replaceable>t</replaceable>.
3938 However the arrows involved need not be the same.
3939 Here are some more examples of suitable operators:
3941 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3942 runReader :: ... => a e c -> a' (e,State) c
3943 runState :: ... => a e c -> a' (e,State) (c,State)
3945 We can supply the extra input required by commands built with the last two
3946 by applying them to ordinary expressions, as in
3950 (|runReader (do { ... })|) s
3952 which adds <literal>s</literal> to the stack of inputs to the command
3953 built using <function>runReader</function>.
3957 The command versions of lambda abstraction and application are analogous to
3958 the expression versions.
3959 In particular, the beta and eta rules describe equivalences of commands.
3960 These three features (operators, lambda abstraction and application)
3961 are the core of the notation; everything else can be built using them,
3962 though the results would be somewhat clumsy.
3963 For example, we could simulate <literal>do</literal>-notation by defining
3965 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3966 u `bind` f = returnA &&& u >>> f
3968 bind_ :: Arrow a => a e b -> a e c -> a e c
3969 u `bind_` f = u `bind` (arr fst >>> f)
3971 We could simulate <literal>if</literal> by defining
3973 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3974 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3981 <title>Differences with the paper</title>
3986 <para>Instead of a single form of arrow application (arrow tail) with two
3987 translations, the implementation provides two forms
3988 <quote><literal>-<</literal></quote> (first-order)
3989 and <quote><literal>-<<</literal></quote> (higher-order).
3994 <para>User-defined operators are flagged with banana brackets instead of
3995 a new <literal>form</literal> keyword.
4004 <title>Portability</title>
4007 Although only GHC implements arrow notation directly,
4008 there is also a preprocessor
4010 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4011 that translates arrow notation into Haskell 98
4012 for use with other Haskell systems.
4013 You would still want to check arrow programs with GHC;
4014 tracing type errors in the preprocessor output is not easy.
4015 Modules intended for both GHC and the preprocessor must observe some
4016 additional restrictions:
4021 The module must import
4022 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4028 The preprocessor cannot cope with other Haskell extensions.
4029 These would have to go in separate modules.
4035 Because the preprocessor targets Haskell (rather than Core),
4036 <literal>let</literal>-bound variables are monomorphic.
4047 <!-- ==================== ASSERTIONS ================= -->
4049 <sect1 id="sec-assertions">
4051 <indexterm><primary>Assertions</primary></indexterm>
4055 If you want to make use of assertions in your standard Haskell code, you
4056 could define a function like the following:
4062 assert :: Bool -> a -> a
4063 assert False x = error "assertion failed!"
4070 which works, but gives you back a less than useful error message --
4071 an assertion failed, but which and where?
4075 One way out is to define an extended <function>assert</function> function which also
4076 takes a descriptive string to include in the error message and
4077 perhaps combine this with the use of a pre-processor which inserts
4078 the source location where <function>assert</function> was used.
4082 Ghc offers a helping hand here, doing all of this for you. For every
4083 use of <function>assert</function> in the user's source:
4089 kelvinToC :: Double -> Double
4090 kelvinToC k = assert (k >= 0.0) (k+273.15)
4096 Ghc will rewrite this to also include the source location where the
4103 assert pred val ==> assertError "Main.hs|15" pred val
4109 The rewrite is only performed by the compiler when it spots
4110 applications of <function>Control.Exception.assert</function>, so you
4111 can still define and use your own versions of
4112 <function>assert</function>, should you so wish. If not, import
4113 <literal>Control.Exception</literal> to make use
4114 <function>assert</function> in your code.
4118 To have the compiler ignore uses of assert, use the compiler option
4119 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4120 option</primary></indexterm> That is, expressions of the form
4121 <literal>assert pred e</literal> will be rewritten to
4122 <literal>e</literal>.
4126 Assertion failures can be caught, see the documentation for the
4127 <literal>Control.Exception</literal> library for the details.
4133 <!-- =============================== PRAGMAS =========================== -->
4135 <sect1 id="pragmas">
4136 <title>Pragmas</title>
4138 <indexterm><primary>pragma</primary></indexterm>
4140 <para>GHC supports several pragmas, or instructions to the
4141 compiler placed in the source code. Pragmas don't normally affect
4142 the meaning of the program, but they might affect the efficiency
4143 of the generated code.</para>
4145 <para>Pragmas all take the form
4147 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4149 where <replaceable>word</replaceable> indicates the type of
4150 pragma, and is followed optionally by information specific to that
4151 type of pragma. Case is ignored in
4152 <replaceable>word</replaceable>. The various values for
4153 <replaceable>word</replaceable> that GHC understands are described
4154 in the following sections; any pragma encountered with an
4155 unrecognised <replaceable>word</replaceable> is (silently)
4158 <sect2 id="deprecated-pragma">
4159 <title>DEPRECATED pragma</title>
4160 <indexterm><primary>DEPRECATED</primary>
4163 <para>The DEPRECATED pragma lets you specify that a particular
4164 function, class, or type, is deprecated. There are two
4169 <para>You can deprecate an entire module thus:</para>
4171 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4174 <para>When you compile any module that import
4175 <literal>Wibble</literal>, GHC will print the specified
4180 <para>You can deprecate a function, class, or type, with the
4181 following top-level declaration:</para>
4183 {-# DEPRECATED f, C, T "Don't use these" #-}
4185 <para>When you compile any module that imports and uses any
4186 of the specified entities, GHC will print the specified
4190 Any use of the deprecated item, or of anything from a deprecated
4191 module, will be flagged with an appropriate message. However,
4192 deprecations are not reported for
4193 (a) uses of a deprecated function within its defining module, and
4194 (b) uses of a deprecated function in an export list.
4195 The latter reduces spurious complaints within a library
4196 in which one module gathers together and re-exports
4197 the exports of several others.
4199 <para>You can suppress the warnings with the flag
4200 <option>-fno-warn-deprecations</option>.</para>
4203 <sect2 id="include-pragma">
4204 <title>INCLUDE pragma</title>
4206 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4207 of C header files that should be <literal>#include</literal>'d into
4208 the C source code generated by the compiler for the current module (if
4209 compiling via C). For example:</para>
4212 {-# INCLUDE "foo.h" #-}
4213 {-# INCLUDE <stdio.h> #-}</programlisting>
4215 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4216 your source file with any <literal>OPTIONS_GHC</literal>
4219 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4220 to the <option>-#include</option> option (<xref
4221 linkend="options-C-compiler" />), because the
4222 <literal>INCLUDE</literal> pragma is understood by other
4223 compilers. Yet another alternative is to add the include file to each
4224 <literal>foreign import</literal> declaration in your code, but we
4225 don't recommend using this approach with GHC.</para>
4228 <sect2 id="inline-noinline-pragma">
4229 <title>INLINE and NOINLINE pragmas</title>
4231 <para>These pragmas control the inlining of function
4234 <sect3 id="inline-pragma">
4235 <title>INLINE pragma</title>
4236 <indexterm><primary>INLINE</primary></indexterm>
4238 <para>GHC (with <option>-O</option>, as always) tries to
4239 inline (or “unfold”) functions/values that are
4240 “small enough,” thus avoiding the call overhead
4241 and possibly exposing other more-wonderful optimisations.
4242 Normally, if GHC decides a function is “too
4243 expensive” to inline, it will not do so, nor will it
4244 export that unfolding for other modules to use.</para>
4246 <para>The sledgehammer you can bring to bear is the
4247 <literal>INLINE</literal><indexterm><primary>INLINE
4248 pragma</primary></indexterm> pragma, used thusly:</para>
4251 key_function :: Int -> String -> (Bool, Double)
4253 #ifdef __GLASGOW_HASKELL__
4254 {-# INLINE key_function #-}
4258 <para>(You don't need to do the C pre-processor carry-on
4259 unless you're going to stick the code through HBC—it
4260 doesn't like <literal>INLINE</literal> pragmas.)</para>
4262 <para>The major effect of an <literal>INLINE</literal> pragma
4263 is to declare a function's “cost” to be very low.
4264 The normal unfolding machinery will then be very keen to
4267 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4268 function can be put anywhere its type signature could be
4271 <para><literal>INLINE</literal> pragmas are a particularly
4273 <literal>then</literal>/<literal>return</literal> (or
4274 <literal>bind</literal>/<literal>unit</literal>) functions in
4275 a monad. For example, in GHC's own
4276 <literal>UniqueSupply</literal> monad code, we have:</para>
4279 #ifdef __GLASGOW_HASKELL__
4280 {-# INLINE thenUs #-}
4281 {-# INLINE returnUs #-}
4285 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4286 linkend="noinline-pragma"/>).</para>
4289 <sect3 id="noinline-pragma">
4290 <title>NOINLINE pragma</title>
4292 <indexterm><primary>NOINLINE</primary></indexterm>
4293 <indexterm><primary>NOTINLINE</primary></indexterm>
4295 <para>The <literal>NOINLINE</literal> pragma does exactly what
4296 you'd expect: it stops the named function from being inlined
4297 by the compiler. You shouldn't ever need to do this, unless
4298 you're very cautious about code size.</para>
4300 <para><literal>NOTINLINE</literal> is a synonym for
4301 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4302 specified by Haskell 98 as the standard way to disable
4303 inlining, so it should be used if you want your code to be
4307 <sect3 id="phase-control">
4308 <title>Phase control</title>
4310 <para> Sometimes you want to control exactly when in GHC's
4311 pipeline the INLINE pragma is switched on. Inlining happens
4312 only during runs of the <emphasis>simplifier</emphasis>. Each
4313 run of the simplifier has a different <emphasis>phase
4314 number</emphasis>; the phase number decreases towards zero.
4315 If you use <option>-dverbose-core2core</option> you'll see the
4316 sequence of phase numbers for successive runs of the
4317 simplifier. In an INLINE pragma you can optionally specify a
4318 phase number, thus:</para>
4322 <para>You can say "inline <literal>f</literal> in Phase 2
4323 and all subsequent phases":
4325 {-# INLINE [2] f #-}
4331 <para>You can say "inline <literal>g</literal> in all
4332 phases up to, but not including, Phase 3":
4334 {-# INLINE [~3] g #-}
4340 <para>If you omit the phase indicator, you mean "inline in
4345 <para>You can use a phase number on a NOINLINE pragma too:</para>
4349 <para>You can say "do not inline <literal>f</literal>
4350 until Phase 2; in Phase 2 and subsequently behave as if
4351 there was no pragma at all":
4353 {-# NOINLINE [2] f #-}
4359 <para>You can say "do not inline <literal>g</literal> in
4360 Phase 3 or any subsequent phase; before that, behave as if
4361 there was no pragma":
4363 {-# NOINLINE [~3] g #-}
4369 <para>If you omit the phase indicator, you mean "never
4370 inline this function".</para>
4374 <para>The same phase-numbering control is available for RULES
4375 (<xref linkend="rewrite-rules"/>).</para>
4379 <sect2 id="line-pragma">
4380 <title>LINE pragma</title>
4382 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4383 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4384 <para>This pragma is similar to C's <literal>#line</literal>
4385 pragma, and is mainly for use in automatically generated Haskell
4386 code. It lets you specify the line number and filename of the
4387 original code; for example</para>
4390 {-# LINE 42 "Foo.vhs" #-}
4393 <para>if you'd generated the current file from something called
4394 <filename>Foo.vhs</filename> and this line corresponds to line
4395 42 in the original. GHC will adjust its error messages to refer
4396 to the line/file named in the <literal>LINE</literal>
4400 <sect2 id="options-pragma">
4401 <title>OPTIONS_GHC pragma</title>
4402 <indexterm><primary>OPTIONS_GHC</primary>
4404 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4407 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4408 additional options that are given to the compiler when compiling
4409 this source file. See <xref linkend="source-file-options"/> for
4412 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4413 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4417 <title>RULES pragma</title>
4419 <para>The RULES pragma lets you specify rewrite rules. It is
4420 described in <xref linkend="rewrite-rules"/>.</para>
4423 <sect2 id="specialize-pragma">
4424 <title>SPECIALIZE pragma</title>
4426 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4427 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4428 <indexterm><primary>overloading, death to</primary></indexterm>
4430 <para>(UK spelling also accepted.) For key overloaded
4431 functions, you can create extra versions (NB: more code space)
4432 specialised to particular types. Thus, if you have an
4433 overloaded function:</para>
4436 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4439 <para>If it is heavily used on lists with
4440 <literal>Widget</literal> keys, you could specialise it as
4444 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4447 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4448 be put anywhere its type signature could be put.</para>
4450 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4451 (a) a specialised version of the function and (b) a rewrite rule
4452 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4453 un-specialised function into a call to the specialised one.</para>
4455 <para>In earlier versions of GHC, it was possible to provide your own
4456 specialised function for a given type:
4459 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4462 This feature has been removed, as it is now subsumed by the
4463 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4467 <sect2 id="specialize-instance-pragma">
4468 <title>SPECIALIZE instance pragma
4472 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4473 <indexterm><primary>overloading, death to</primary></indexterm>
4474 Same idea, except for instance declarations. For example:
4477 instance (Eq a) => Eq (Foo a) where {
4478 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4482 The pragma must occur inside the <literal>where</literal> part
4483 of the instance declaration.
4486 Compatible with HBC, by the way, except perhaps in the placement
4492 <sect2 id="unpack-pragma">
4493 <title>UNPACK pragma</title>
4495 <indexterm><primary>UNPACK</primary></indexterm>
4497 <para>The <literal>UNPACK</literal> indicates to the compiler
4498 that it should unpack the contents of a constructor field into
4499 the constructor itself, removing a level of indirection. For
4503 data T = T {-# UNPACK #-} !Float
4504 {-# UNPACK #-} !Float
4507 <para>will create a constructor <literal>T</literal> containing
4508 two unboxed floats. This may not always be an optimisation: if
4509 the <function>T</function> constructor is scrutinised and the
4510 floats passed to a non-strict function for example, they will
4511 have to be reboxed (this is done automatically by the
4514 <para>Unpacking constructor fields should only be used in
4515 conjunction with <option>-O</option>, in order to expose
4516 unfoldings to the compiler so the reboxing can be removed as
4517 often as possible. For example:</para>
4521 f (T f1 f2) = f1 + f2
4524 <para>The compiler will avoid reboxing <function>f1</function>
4525 and <function>f2</function> by inlining <function>+</function>
4526 on floats, but only when <option>-O</option> is on.</para>
4528 <para>Any single-constructor data is eligible for unpacking; for
4532 data T = T {-# UNPACK #-} !(Int,Int)
4535 <para>will store the two <literal>Int</literal>s directly in the
4536 <function>T</function> constructor, by flattening the pair.
4537 Multi-level unpacking is also supported:</para>
4540 data T = T {-# UNPACK #-} !S
4541 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4544 <para>will store two unboxed <literal>Int#</literal>s
4545 directly in the <function>T</function> constructor. The
4546 unpacker can see through newtypes, too.</para>
4548 <para>If a field cannot be unpacked, you will not get a warning,
4549 so it might be an idea to check the generated code with
4550 <option>-ddump-simpl</option>.</para>
4552 <para>See also the <option>-funbox-strict-fields</option> flag,
4553 which essentially has the effect of adding
4554 <literal>{-# UNPACK #-}</literal> to every strict
4555 constructor field.</para>
4560 <!-- ======================= REWRITE RULES ======================== -->
4562 <sect1 id="rewrite-rules">
4563 <title>Rewrite rules
4565 <indexterm><primary>RULES pragma</primary></indexterm>
4566 <indexterm><primary>pragma, RULES</primary></indexterm>
4567 <indexterm><primary>rewrite rules</primary></indexterm></title>
4570 The programmer can specify rewrite rules as part of the source program
4571 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4572 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4573 and (b) the <option>-frules-off</option> flag
4574 (<xref linkend="options-f"/>) is not specified.
4582 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4589 <title>Syntax</title>
4592 From a syntactic point of view:
4598 There may be zero or more rules in a <literal>RULES</literal> pragma.
4605 Each rule has a name, enclosed in double quotes. The name itself has
4606 no significance at all. It is only used when reporting how many times the rule fired.
4612 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4613 immediately after the name of the rule. Thus:
4616 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4619 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4620 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4629 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4630 is set, so you must lay out your rules starting in the same column as the
4631 enclosing definitions.
4638 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4639 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4640 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4641 by spaces, just like in a type <literal>forall</literal>.
4647 A pattern variable may optionally have a type signature.
4648 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4649 For example, here is the <literal>foldr/build</literal> rule:
4652 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4653 foldr k z (build g) = g k z
4656 Since <function>g</function> has a polymorphic type, it must have a type signature.
4663 The left hand side of a rule must consist of a top-level variable applied
4664 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4667 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4668 "wrong2" forall f. f True = True
4671 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4678 A rule does not need to be in the same module as (any of) the
4679 variables it mentions, though of course they need to be in scope.
4685 Rules are automatically exported from a module, just as instance declarations are.
4696 <title>Semantics</title>
4699 From a semantic point of view:
4705 Rules are only applied if you use the <option>-O</option> flag.
4711 Rules are regarded as left-to-right rewrite rules.
4712 When GHC finds an expression that is a substitution instance of the LHS
4713 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4714 By "a substitution instance" we mean that the LHS can be made equal to the
4715 expression by substituting for the pattern variables.
4722 The LHS and RHS of a rule are typechecked, and must have the
4730 GHC makes absolutely no attempt to verify that the LHS and RHS
4731 of a rule have the same meaning. That is undecidable in general, and
4732 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4739 GHC makes no attempt to make sure that the rules are confluent or
4740 terminating. For example:
4743 "loop" forall x,y. f x y = f y x
4746 This rule will cause the compiler to go into an infinite loop.
4753 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4759 GHC currently uses a very simple, syntactic, matching algorithm
4760 for matching a rule LHS with an expression. It seeks a substitution
4761 which makes the LHS and expression syntactically equal modulo alpha
4762 conversion. The pattern (rule), but not the expression, is eta-expanded if
4763 necessary. (Eta-expanding the expression can lead to laziness bugs.)
4764 But not beta conversion (that's called higher-order matching).
4768 Matching is carried out on GHC's intermediate language, which includes
4769 type abstractions and applications. So a rule only matches if the
4770 types match too. See <xref linkend="rule-spec"/> below.
4776 GHC keeps trying to apply the rules as it optimises the program.
4777 For example, consider:
4786 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4787 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4788 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4789 not be substituted, and the rule would not fire.
4796 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4797 that appears on the LHS of a rule</emphasis>, because once you have substituted
4798 for something you can't match against it (given the simple minded
4799 matching). So if you write the rule
4802 "map/map" forall f,g. map f . map g = map (f.g)
4805 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4806 It will only match something written with explicit use of ".".
4807 Well, not quite. It <emphasis>will</emphasis> match the expression
4813 where <function>wibble</function> is defined:
4816 wibble f g = map f . map g
4819 because <function>wibble</function> will be inlined (it's small).
4821 Later on in compilation, GHC starts inlining even things on the
4822 LHS of rules, but still leaves the rules enabled. This inlining
4823 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4830 All rules are implicitly exported from the module, and are therefore
4831 in force in any module that imports the module that defined the rule, directly
4832 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4833 in force when compiling A.) The situation is very similar to that for instance
4845 <title>List fusion</title>
4848 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4849 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4850 intermediate list should be eliminated entirely.
4854 The following are good producers:
4866 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4872 Explicit lists (e.g. <literal>[True, False]</literal>)
4878 The cons constructor (e.g <literal>3:4:[]</literal>)
4884 <function>++</function>
4890 <function>map</function>
4896 <function>filter</function>
4902 <function>iterate</function>, <function>repeat</function>
4908 <function>zip</function>, <function>zipWith</function>
4917 The following are good consumers:
4929 <function>array</function> (on its second argument)
4935 <function>length</function>
4941 <function>++</function> (on its first argument)
4947 <function>foldr</function>
4953 <function>map</function>
4959 <function>filter</function>
4965 <function>concat</function>
4971 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4977 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4978 will fuse with one but not the other)
4984 <function>partition</function>
4990 <function>head</function>
4996 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5002 <function>sequence_</function>
5008 <function>msum</function>
5014 <function>sortBy</function>
5023 So, for example, the following should generate no intermediate lists:
5026 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5032 This list could readily be extended; if there are Prelude functions that you use
5033 a lot which are not included, please tell us.
5037 If you want to write your own good consumers or producers, look at the
5038 Prelude definitions of the above functions to see how to do so.
5043 <sect2 id="rule-spec">
5044 <title>Specialisation
5048 Rewrite rules can be used to get the same effect as a feature
5049 present in earlier versions of GHC.
5050 For example, suppose that:
5053 genericLookup :: Ord a => Table a b -> a -> b
5054 intLookup :: Table Int b -> Int -> b
5057 where <function>intLookup</function> is an implementation of
5058 <function>genericLookup</function> that works very fast for
5059 keys of type <literal>Int</literal>. You might wish
5060 to tell GHC to use <function>intLookup</function> instead of
5061 <function>genericLookup</function> whenever the latter was called with
5062 type <literal>Table Int b -> Int -> b</literal>.
5063 It used to be possible to write
5066 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5069 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5072 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5075 This slightly odd-looking rule instructs GHC to replace
5076 <function>genericLookup</function> by <function>intLookup</function>
5077 <emphasis>whenever the types match</emphasis>.
5078 What is more, this rule does not need to be in the same
5079 file as <function>genericLookup</function>, unlike the
5080 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5081 have an original definition available to specialise).
5084 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5085 <function>intLookup</function> really behaves as a specialised version
5086 of <function>genericLookup</function>!!!</para>
5088 <para>An example in which using <literal>RULES</literal> for
5089 specialisation will Win Big:
5092 toDouble :: Real a => a -> Double
5093 toDouble = fromRational . toRational
5095 {-# RULES "toDouble/Int" toDouble = i2d #-}
5096 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5099 The <function>i2d</function> function is virtually one machine
5100 instruction; the default conversion—via an intermediate
5101 <literal>Rational</literal>—is obscenely expensive by
5108 <title>Controlling what's going on</title>
5116 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5122 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5123 If you add <option>-dppr-debug</option> you get a more detailed listing.
5129 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5132 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5133 {-# INLINE build #-}
5137 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5138 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5139 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5140 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5147 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5148 see how to write rules that will do fusion and yet give an efficient
5149 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5159 <sect2 id="core-pragma">
5160 <title>CORE pragma</title>
5162 <indexterm><primary>CORE pragma</primary></indexterm>
5163 <indexterm><primary>pragma, CORE</primary></indexterm>
5164 <indexterm><primary>core, annotation</primary></indexterm>
5167 The external core format supports <quote>Note</quote> annotations;
5168 the <literal>CORE</literal> pragma gives a way to specify what these
5169 should be in your Haskell source code. Syntactically, core
5170 annotations are attached to expressions and take a Haskell string
5171 literal as an argument. The following function definition shows an
5175 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5178 Semantically, this is equivalent to:
5186 However, when external for is generated (via
5187 <option>-fext-core</option>), there will be Notes attached to the
5188 expressions <function>show</function> and <varname>x</varname>.
5189 The core function declaration for <function>f</function> is:
5193 f :: %forall a . GHCziShow.ZCTShow a ->
5194 a -> GHCziBase.ZMZN GHCziBase.Char =
5195 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5197 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5199 (tpl1::GHCziBase.Int ->
5201 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5203 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5204 (tpl3::GHCziBase.ZMZN a ->
5205 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5213 Here, we can see that the function <function>show</function> (which
5214 has been expanded out to a case expression over the Show dictionary)
5215 has a <literal>%note</literal> attached to it, as does the
5216 expression <varname>eta</varname> (which used to be called
5217 <varname>x</varname>).
5224 <sect1 id="generic-classes">
5225 <title>Generic classes</title>
5227 <para>(Note: support for generic classes is currently broken in
5231 The ideas behind this extension are described in detail in "Derivable type classes",
5232 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5233 An example will give the idea:
5241 fromBin :: [Int] -> (a, [Int])
5243 toBin {| Unit |} Unit = []
5244 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5245 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5246 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5248 fromBin {| Unit |} bs = (Unit, bs)
5249 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5250 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5251 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5252 (y,bs'') = fromBin bs'
5255 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5256 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5257 which are defined thus in the library module <literal>Generics</literal>:
5261 data a :+: b = Inl a | Inr b
5262 data a :*: b = a :*: b
5265 Now you can make a data type into an instance of Bin like this:
5267 instance (Bin a, Bin b) => Bin (a,b)
5268 instance Bin a => Bin [a]
5270 That is, just leave off the "where" clause. Of course, you can put in the
5271 where clause and over-ride whichever methods you please.
5275 <title> Using generics </title>
5276 <para>To use generics you need to</para>
5279 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5280 <option>-fgenerics</option> (to generate extra per-data-type code),
5281 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5285 <para>Import the module <literal>Generics</literal> from the
5286 <literal>lang</literal> package. This import brings into
5287 scope the data types <literal>Unit</literal>,
5288 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5289 don't need this import if you don't mention these types
5290 explicitly; for example, if you are simply giving instance
5291 declarations.)</para>
5296 <sect2> <title> Changes wrt the paper </title>
5298 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5299 can be written infix (indeed, you can now use
5300 any operator starting in a colon as an infix type constructor). Also note that
5301 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5302 Finally, note that the syntax of the type patterns in the class declaration
5303 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5304 alone would ambiguous when they appear on right hand sides (an extension we
5305 anticipate wanting).
5309 <sect2> <title>Terminology and restrictions</title>
5311 Terminology. A "generic default method" in a class declaration
5312 is one that is defined using type patterns as above.
5313 A "polymorphic default method" is a default method defined as in Haskell 98.
5314 A "generic class declaration" is a class declaration with at least one
5315 generic default method.
5323 Alas, we do not yet implement the stuff about constructor names and
5330 A generic class can have only one parameter; you can't have a generic
5331 multi-parameter class.
5337 A default method must be defined entirely using type patterns, or entirely
5338 without. So this is illegal:
5341 op :: a -> (a, Bool)
5342 op {| Unit |} Unit = (Unit, True)
5345 However it is perfectly OK for some methods of a generic class to have
5346 generic default methods and others to have polymorphic default methods.
5352 The type variable(s) in the type pattern for a generic method declaration
5353 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:
5357 op {| p :*: q |} (x :*: y) = op (x :: p)
5365 The type patterns in a generic default method must take one of the forms:
5371 where "a" and "b" are type variables. Furthermore, all the type patterns for
5372 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5373 must use the same type variables. So this is illegal:
5377 op {| a :+: b |} (Inl x) = True
5378 op {| p :+: q |} (Inr y) = False
5380 The type patterns must be identical, even in equations for different methods of the class.
5381 So this too is illegal:
5385 op1 {| a :*: b |} (x :*: y) = True
5388 op2 {| p :*: q |} (x :*: y) = False
5390 (The reason for this restriction is that we gather all the equations for a particular type consructor
5391 into a single generic instance declaration.)
5397 A generic method declaration must give a case for each of the three type constructors.
5403 The type for a generic method can be built only from:
5405 <listitem> <para> Function arrows </para> </listitem>
5406 <listitem> <para> Type variables </para> </listitem>
5407 <listitem> <para> Tuples </para> </listitem>
5408 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5410 Here are some example type signatures for generic methods:
5413 op2 :: Bool -> (a,Bool)
5414 op3 :: [Int] -> a -> a
5417 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5421 This restriction is an implementation restriction: we just havn't got around to
5422 implementing the necessary bidirectional maps over arbitrary type constructors.
5423 It would be relatively easy to add specific type constructors, such as Maybe and list,
5424 to the ones that are allowed.</para>
5429 In an instance declaration for a generic class, the idea is that the compiler
5430 will fill in the methods for you, based on the generic templates. However it can only
5435 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5440 No constructor of the instance type has unboxed fields.
5444 (Of course, these things can only arise if you are already using GHC extensions.)
5445 However, you can still give an instance declarations for types which break these rules,
5446 provided you give explicit code to override any generic default methods.
5454 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5455 what the compiler does with generic declarations.
5460 <sect2> <title> Another example </title>
5462 Just to finish with, here's another example I rather like:
5466 nCons {| Unit |} _ = 1
5467 nCons {| a :*: b |} _ = 1
5468 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5471 tag {| Unit |} _ = 1
5472 tag {| a :*: b |} _ = 1
5473 tag {| a :+: b |} (Inl x) = tag x
5474 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5483 ;;; Local Variables: ***
5485 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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