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.pp</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.
346 A numerically-intensive program using unboxed types can
347 go a <emphasis>lot</emphasis> faster than its “standard”
348 counterpart—we saw a threefold speedup on one example.
352 There are some restrictions on the use of primitive types:
354 <listitem><para>The main restriction
355 is that you can't pass a primitive value to a polymorphic
356 function or store one in a polymorphic data type. This rules out
357 things like <literal>[Int#]</literal> (i.e. lists of primitive
358 integers). The reason for this restriction is that polymorphic
359 arguments and constructor fields are assumed to be pointers: if an
360 unboxed integer is stored in one of these, the garbage collector would
361 attempt to follow it, leading to unpredictable space leaks. Or a
362 <function>seq</function> operation on the polymorphic component may
363 attempt to dereference the pointer, with disastrous results. Even
364 worse, the unboxed value might be larger than a pointer
365 (<literal>Double#</literal> for instance).
368 <listitem><para> You cannot bind a variable with an unboxed type
369 in a <emphasis>top-level</emphasis> binding.
371 <listitem><para> You cannot bind a variable with an unboxed type
372 in a <emphasis>recursive</emphasis> binding.
374 <listitem><para> You may bind unboxed variables in a (non-recursive,
375 non-top-level) pattern binding, but any such variable causes the entire
377 to become strict. For example:
379 data Foo = Foo Int Int#
381 f x = let (Foo a b, w) = ..rhs.. in ..body..
383 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
385 is strict, and the program behaves as if you had written
387 data Foo = Foo Int Int#
389 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
398 <sect2 id="unboxed-tuples">
399 <title>Unboxed Tuples
403 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
404 they're available by default with <option>-fglasgow-exts</option>. An
405 unboxed tuple looks like this:
417 where <literal>e_1..e_n</literal> are expressions of any
418 type (primitive or non-primitive). The type of an unboxed tuple looks
423 Unboxed tuples are used for functions that need to return multiple
424 values, but they avoid the heap allocation normally associated with
425 using fully-fledged tuples. When an unboxed tuple is returned, the
426 components are put directly into registers or on the stack; the
427 unboxed tuple itself does not have a composite representation. Many
428 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
430 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
431 tuples to avoid unnecessary allocation during sequences of operations.
435 There are some pretty stringent restrictions on the use of unboxed tuples:
440 Values of unboxed tuple types are subject to the same restrictions as
441 other unboxed types; i.e. they may not be stored in polymorphic data
442 structures or passed to polymorphic functions.
449 No variable can have an unboxed tuple type, nor may a constructor or function
450 argument have an unboxed tuple type. The following are all illegal:
454 data Foo = Foo (# Int, Int #)
456 f :: (# Int, Int #) -> (# Int, Int #)
459 g :: (# Int, Int #) -> Int
462 h x = let y = (# x,x #) in ...
469 The typical use of unboxed tuples is simply to return multiple values,
470 binding those multiple results with a <literal>case</literal> expression, thus:
472 f x y = (# x+1, y-1 #)
473 g x = case f x x of { (# a, b #) -> a + b }
475 You can have an unboxed tuple in a pattern binding, thus
477 f x = let (# p,q #) = h x in ..body..
479 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
480 the resulting binding is lazy like any other Haskell pattern binding. The
481 above example desugars like this:
483 f x = let t = case h x o f{ (# p,q #) -> (p,q)
488 Indeed, the bindings can even be recursive.
495 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
497 <sect1 id="syntax-extns">
498 <title>Syntactic extensions</title>
500 <!-- ====================== HIERARCHICAL MODULES ======================= -->
502 <sect2 id="hierarchical-modules">
503 <title>Hierarchical Modules</title>
505 <para>GHC supports a small extension to the syntax of module
506 names: a module name is allowed to contain a dot
507 <literal>‘.’</literal>. This is also known as the
508 “hierarchical module namespace” extension, because
509 it extends the normally flat Haskell module namespace into a
510 more flexible hierarchy of modules.</para>
512 <para>This extension has very little impact on the language
513 itself; modules names are <emphasis>always</emphasis> fully
514 qualified, so you can just think of the fully qualified module
515 name as <quote>the module name</quote>. In particular, this
516 means that the full module name must be given after the
517 <literal>module</literal> keyword at the beginning of the
518 module; for example, the module <literal>A.B.C</literal> must
521 <programlisting>module A.B.C</programlisting>
524 <para>It is a common strategy to use the <literal>as</literal>
525 keyword to save some typing when using qualified names with
526 hierarchical modules. For example:</para>
529 import qualified Control.Monad.ST.Strict as ST
532 <para>For details on how GHC searches for source and interface
533 files in the presence of hierarchical modules, see <xref
534 linkend="search-path"/>.</para>
536 <para>GHC comes with a large collection of libraries arranged
537 hierarchically; see the accompanying library documentation.
538 There is an ongoing project to create and maintain a stable set
539 of <quote>core</quote> libraries used by several Haskell
540 compilers, and the libraries that GHC comes with represent the
541 current status of that project. For more details, see <ulink
542 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
543 Libraries</ulink>.</para>
547 <!-- ====================== PATTERN GUARDS ======================= -->
549 <sect2 id="pattern-guards">
550 <title>Pattern guards</title>
553 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
554 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.)
558 Suppose we have an abstract data type of finite maps, with a
562 lookup :: FiniteMap -> Int -> Maybe Int
565 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
566 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
570 clunky env var1 var2 | ok1 && ok2 = val1 + val2
571 | otherwise = var1 + var2
582 The auxiliary functions are
586 maybeToBool :: Maybe a -> Bool
587 maybeToBool (Just x) = True
588 maybeToBool Nothing = False
590 expectJust :: Maybe a -> a
591 expectJust (Just x) = x
592 expectJust Nothing = error "Unexpected Nothing"
596 What is <function>clunky</function> doing? The guard <literal>ok1 &&
597 ok2</literal> checks that both lookups succeed, using
598 <function>maybeToBool</function> to convert the <function>Maybe</function>
599 types to booleans. The (lazily evaluated) <function>expectJust</function>
600 calls extract the values from the results of the lookups, and binds the
601 returned values to <varname>val1</varname> and <varname>val2</varname>
602 respectively. If either lookup fails, then clunky takes the
603 <literal>otherwise</literal> case and returns the sum of its arguments.
607 This is certainly legal Haskell, but it is a tremendously verbose and
608 un-obvious way to achieve the desired effect. Arguably, a more direct way
609 to write clunky would be to use case expressions:
613 clunky env var1 var1 = case lookup env var1 of
615 Just val1 -> case lookup env var2 of
617 Just val2 -> val1 + val2
623 This is a bit shorter, but hardly better. Of course, we can rewrite any set
624 of pattern-matching, guarded equations as case expressions; that is
625 precisely what the compiler does when compiling equations! The reason that
626 Haskell provides guarded equations is because they allow us to write down
627 the cases we want to consider, one at a time, independently of each other.
628 This structure is hidden in the case version. Two of the right-hand sides
629 are really the same (<function>fail</function>), and the whole expression
630 tends to become more and more indented.
634 Here is how I would write clunky:
639 | Just val1 <- lookup env var1
640 , Just val2 <- lookup env var2
642 ...other equations for clunky...
646 The semantics should be clear enough. The qualifiers are matched in order.
647 For a <literal><-</literal> qualifier, which I call a pattern guard, the
648 right hand side is evaluated and matched against the pattern on the left.
649 If the match fails then the whole guard fails and the next equation is
650 tried. If it succeeds, then the appropriate binding takes place, and the
651 next qualifier is matched, in the augmented environment. Unlike list
652 comprehensions, however, the type of the expression to the right of the
653 <literal><-</literal> is the same as the type of the pattern to its
654 left. The bindings introduced by pattern guards scope over all the
655 remaining guard qualifiers, and over the right hand side of the equation.
659 Just as with list comprehensions, boolean expressions can be freely mixed
660 with among the pattern guards. For example:
671 Haskell's current guards therefore emerge as a special case, in which the
672 qualifier list has just one element, a boolean expression.
676 <!-- ===================== Recursive do-notation =================== -->
678 <sect2 id="mdo-notation">
679 <title>The recursive do-notation
682 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
683 "A recursive do for Haskell",
684 Levent Erkok, John Launchbury",
685 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
688 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
689 that is, the variables bound in a do-expression are visible only in the textually following
690 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
691 group. It turns out that several applications can benefit from recursive bindings in
692 the do-notation, and this extension provides the necessary syntactic support.
695 Here is a simple (yet contrived) example:
698 import Control.Monad.Fix
700 justOnes = mdo xs <- Just (1:xs)
704 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
708 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
711 class Monad m => MonadFix m where
712 mfix :: (a -> m a) -> m a
715 The function <literal>mfix</literal>
716 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
717 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
718 For details, see the above mentioned reference.
721 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
722 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
723 for Haskell's internal state monad (strict and lazy, respectively).
726 There are three important points in using the recursive-do notation:
729 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
730 than <literal>do</literal>).
734 You should <literal>import Control.Monad.Fix</literal>.
735 (Note: Strictly speaking, this import is required only when you need to refer to the name
736 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
737 are encouraged to always import this module when using the mdo-notation.)
741 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
747 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
748 contains up to date information on recursive monadic bindings.
752 Historical note: The old implementation of the mdo-notation (and most
753 of the existing documents) used the name
754 <literal>MonadRec</literal> for the class and the corresponding library.
755 This name is not supported by GHC.
761 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
763 <sect2 id="parallel-list-comprehensions">
764 <title>Parallel List Comprehensions</title>
765 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
767 <indexterm><primary>parallel list comprehensions</primary>
770 <para>Parallel list comprehensions are a natural extension to list
771 comprehensions. List comprehensions can be thought of as a nice
772 syntax for writing maps and filters. Parallel comprehensions
773 extend this to include the zipWith family.</para>
775 <para>A parallel list comprehension has multiple independent
776 branches of qualifier lists, each separated by a `|' symbol. For
777 example, the following zips together two lists:</para>
780 [ (x, y) | x <- xs | y <- ys ]
783 <para>The behavior of parallel list comprehensions follows that of
784 zip, in that the resulting list will have the same length as the
785 shortest branch.</para>
787 <para>We can define parallel list comprehensions by translation to
788 regular comprehensions. Here's the basic idea:</para>
790 <para>Given a parallel comprehension of the form: </para>
793 [ e | p1 <- e11, p2 <- e12, ...
794 | q1 <- e21, q2 <- e22, ...
799 <para>This will be translated to: </para>
802 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
803 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
808 <para>where `zipN' is the appropriate zip for the given number of
813 <sect2 id="rebindable-syntax">
814 <title>Rebindable syntax</title>
817 <para>GHC allows most kinds of built-in syntax to be rebound by
818 the user, to facilitate replacing the <literal>Prelude</literal>
819 with a home-grown version, for example.</para>
821 <para>You may want to define your own numeric class
822 hierarchy. It completely defeats that purpose if the
823 literal "1" means "<literal>Prelude.fromInteger
824 1</literal>", which is what the Haskell Report specifies.
825 So the <option>-fno-implicit-prelude</option> flag causes
826 the following pieces of built-in syntax to refer to
827 <emphasis>whatever is in scope</emphasis>, not the Prelude
832 <para>An integer literal <literal>368</literal> means
833 "<literal>fromInteger (368::Integer)</literal>", rather than
834 "<literal>Prelude.fromInteger (368::Integer)</literal>".
837 <listitem><para>Fractional literals are handed in just the same way,
838 except that the translation is
839 <literal>fromRational (3.68::Rational)</literal>.
842 <listitem><para>The equality test in an overloaded numeric pattern
843 uses whatever <literal>(==)</literal> is in scope.
846 <listitem><para>The subtraction operation, and the
847 greater-than-or-equal test, in <literal>n+k</literal> patterns
848 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
852 <para>Negation (e.g. "<literal>- (f x)</literal>")
853 means "<literal>negate (f x)</literal>", both in numeric
854 patterns, and expressions.
858 <para>"Do" notation is translated using whatever
859 functions <literal>(>>=)</literal>,
860 <literal>(>>)</literal>, and <literal>fail</literal>,
861 are in scope (not the Prelude
862 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
863 comprehensions, are unaffected. </para></listitem>
867 notation (see <xref linkend="arrow-notation"/>)
868 uses whatever <literal>arr</literal>,
869 <literal>(>>>)</literal>, <literal>first</literal>,
870 <literal>app</literal>, <literal>(|||)</literal> and
871 <literal>loop</literal> functions are in scope. But unlike the
872 other constructs, the types of these functions must match the
873 Prelude types very closely. Details are in flux; if you want
877 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
878 even if that is a little unexpected. For emample, the
879 static semantics of the literal <literal>368</literal>
880 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
881 <literal>fromInteger</literal> to have any of the types:
883 fromInteger :: Integer -> Integer
884 fromInteger :: forall a. Foo a => Integer -> a
885 fromInteger :: Num a => a -> Integer
886 fromInteger :: Integer -> Bool -> Bool
890 <para>Be warned: this is an experimental facility, with
891 fewer checks than usual. Use <literal>-dcore-lint</literal>
892 to typecheck the desugared program. If Core Lint is happy
893 you should be all right.</para>
899 <!-- TYPE SYSTEM EXTENSIONS -->
900 <sect1 id="type-extensions">
901 <title>Type system extensions</title>
905 <title>Data types and type synonyms</title>
907 <sect3 id="nullary-types">
908 <title>Data types with no constructors</title>
910 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
911 a data type with no constructors. For example:</para>
915 data T a -- T :: * -> *
918 <para>Syntactically, the declaration lacks the "= constrs" part. The
919 type can be parameterised over types of any kind, but if the kind is
920 not <literal>*</literal> then an explicit kind annotation must be used
921 (see <xref linkend="sec-kinding"/>).</para>
923 <para>Such data types have only one value, namely bottom.
924 Nevertheless, they can be useful when defining "phantom types".</para>
927 <sect3 id="infix-tycons">
928 <title>Infix type constructors, classes, and type variables</title>
931 GHC allows type constructors, classes, and type variables to be operators, and
932 to be written infix, very much like expressions. More specifically:
935 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
936 The lexical syntax is the same as that for data constructors.
939 Data type and type-synonym declarations can be written infix, parenthesised
940 if you want further arguments. E.g.
942 data a :*: b = Foo a b
943 type a :+: b = Either a b
944 class a :=: b where ...
946 data (a :**: b) x = Baz a b x
947 type (a :++: b) y = Either (a,b) y
951 Types, and class constraints, can be written infix. For example
954 f :: (a :=: b) => a -> b
958 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
959 The lexical syntax is the same as that for variable operators, excluding "(.)",
960 "(!)", and "(*)". In a binding position, the operator must be
961 parenthesised. For example:
963 type T (+) = Int + Int
968 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
974 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
975 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
978 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
979 one cannot distinguish between the two in a fixity declaration; a fixity declaration
980 sets the fixity for a data constructor and the corresponding type constructor. For example:
984 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
985 and similarly for <literal>:*:</literal>.
986 <literal>Int `a` Bool</literal>.
989 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
996 <sect3 id="type-synonyms">
997 <title>Liberalised type synonyms</title>
1000 Type synonyms are like macros at the type level, and
1001 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1002 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1004 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1005 in a type synonym, thus:
1007 type Discard a = forall b. Show b => a -> b -> (a, String)
1012 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1019 You can write an unboxed tuple in a type synonym:
1021 type Pr = (# Int, Int #)
1029 You can apply a type synonym to a forall type:
1031 type Foo a = a -> a -> Bool
1033 f :: Foo (forall b. b->b)
1035 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1037 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1042 You can apply a type synonym to a partially applied type synonym:
1044 type Generic i o = forall x. i x -> o x
1047 foo :: Generic Id []
1049 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1051 foo :: forall x. x -> [x]
1059 GHC currently does kind checking before expanding synonyms (though even that
1063 After expanding type synonyms, GHC does validity checking on types, looking for
1064 the following mal-formedness which isn't detected simply by kind checking:
1067 Type constructor applied to a type involving for-alls.
1070 Unboxed tuple on left of an arrow.
1073 Partially-applied type synonym.
1077 this will be rejected:
1079 type Pr = (# Int, Int #)
1084 because GHC does not allow unboxed tuples on the left of a function arrow.
1089 <sect3 id="existential-quantification">
1090 <title>Existentially quantified data constructors
1094 The idea of using existential quantification in data type declarations
1095 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1096 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1097 London, 1991). It was later formalised by Laufer and Odersky
1098 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1099 TOPLAS, 16(5), pp1411-1430, 1994).
1100 It's been in Lennart
1101 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1102 proved very useful. Here's the idea. Consider the declaration:
1108 data Foo = forall a. MkFoo a (a -> Bool)
1115 The data type <literal>Foo</literal> has two constructors with types:
1121 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1128 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1129 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1130 For example, the following expression is fine:
1136 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1142 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1143 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1144 isUpper</function> packages a character with a compatible function. These
1145 two things are each of type <literal>Foo</literal> and can be put in a list.
1149 What can we do with a value of type <literal>Foo</literal>?. In particular,
1150 what happens when we pattern-match on <function>MkFoo</function>?
1156 f (MkFoo val fn) = ???
1162 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1163 are compatible, the only (useful) thing we can do with them is to
1164 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1171 f (MkFoo val fn) = fn val
1177 What this allows us to do is to package heterogenous values
1178 together with a bunch of functions that manipulate them, and then treat
1179 that collection of packages in a uniform manner. You can express
1180 quite a bit of object-oriented-like programming this way.
1183 <sect4 id="existential">
1184 <title>Why existential?
1188 What has this to do with <emphasis>existential</emphasis> quantification?
1189 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1195 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1201 But Haskell programmers can safely think of the ordinary
1202 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1203 adding a new existential quantification construct.
1209 <title>Type classes</title>
1212 An easy extension is to allow
1213 arbitrary contexts before the constructor. For example:
1219 data Baz = forall a. Eq a => Baz1 a a
1220 | forall b. Show b => Baz2 b (b -> b)
1226 The two constructors have the types you'd expect:
1232 Baz1 :: forall a. Eq a => a -> a -> Baz
1233 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1239 But when pattern matching on <function>Baz1</function> the matched values can be compared
1240 for equality, and when pattern matching on <function>Baz2</function> the first matched
1241 value can be converted to a string (as well as applying the function to it).
1242 So this program is legal:
1249 f (Baz1 p q) | p == q = "Yes"
1251 f (Baz2 v fn) = show (fn v)
1257 Operationally, in a dictionary-passing implementation, the
1258 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1259 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1260 extract it on pattern matching.
1264 Notice the way that the syntax fits smoothly with that used for
1265 universal quantification earlier.
1271 <title>Record Constructors</title>
1274 GHC allows existentials to be used with records syntax as well. For example:
1277 data Counter a = forall self. NewCounter
1279 , _inc :: self -> self
1280 , _display :: self -> IO ()
1284 Here <literal>tag</literal> is a public field, with a well-typed selector
1285 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1286 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1287 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1288 compile-time error. In other words, <emphasis>GHC defines a record selector function
1289 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1290 (This example used an underscore in the fields for which record selectors
1291 will not be defined, but that is only programming style; GHC ignores them.)
1295 To make use of these hidden fields, we need to create some helper functions:
1298 inc :: Counter a -> Counter a
1299 inc (NewCounter x i d t) = NewCounter
1300 { _this = i x, _inc = i, _display = d, tag = t }
1302 display :: Counter a -> IO ()
1303 display NewCounter{ _this = x, _display = d } = d x
1306 Now we can define counters with different underlying implementations:
1309 counterA :: Counter String
1310 counterA = NewCounter
1311 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1313 counterB :: Counter String
1314 counterB = NewCounter
1315 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1318 display (inc counterA) -- prints "1"
1319 display (inc (inc counterB)) -- prints "##"
1322 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1323 <literal>forall</literal> may be omitted. For example, we can express
1324 the same <literal>Counter a</literal> using GADT:
1327 data Counter a where
1328 NewCounter { _this :: self
1329 , _inc :: self -> self
1330 , _display :: self -> IO ()
1336 At the moment, record update syntax is only supported for Haskell 98 data types,
1337 so the following function does <emphasis>not</emphasis> work:
1340 -- This is invalid; use explicit NewCounter instead for now
1341 setTag :: Counter a -> a -> Counter a
1342 setTag obj t = obj{ tag = t }
1351 <title>Restrictions</title>
1354 There are several restrictions on the ways in which existentially-quantified
1355 constructors can be use.
1364 When pattern matching, each pattern match introduces a new,
1365 distinct, type for each existential type variable. These types cannot
1366 be unified with any other type, nor can they escape from the scope of
1367 the pattern match. For example, these fragments are incorrect:
1375 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1376 is the result of <function>f1</function>. One way to see why this is wrong is to
1377 ask what type <function>f1</function> has:
1381 f1 :: Foo -> a -- Weird!
1385 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1390 f1 :: forall a. Foo -> a -- Wrong!
1394 The original program is just plain wrong. Here's another sort of error
1398 f2 (Baz1 a b) (Baz1 p q) = a==q
1402 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1403 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1404 from the two <function>Baz1</function> constructors.
1412 You can't pattern-match on an existentially quantified
1413 constructor in a <literal>let</literal> or <literal>where</literal> group of
1414 bindings. So this is illegal:
1418 f3 x = a==b where { Baz1 a b = x }
1421 Instead, use a <literal>case</literal> expression:
1424 f3 x = case x of Baz1 a b -> a==b
1427 In general, you can only pattern-match
1428 on an existentially-quantified constructor in a <literal>case</literal> expression or
1429 in the patterns of a function definition.
1431 The reason for this restriction is really an implementation one.
1432 Type-checking binding groups is already a nightmare without
1433 existentials complicating the picture. Also an existential pattern
1434 binding at the top level of a module doesn't make sense, because it's
1435 not clear how to prevent the existentially-quantified type "escaping".
1436 So for now, there's a simple-to-state restriction. We'll see how
1444 You can't use existential quantification for <literal>newtype</literal>
1445 declarations. So this is illegal:
1449 newtype T = forall a. Ord a => MkT a
1453 Reason: a value of type <literal>T</literal> must be represented as a
1454 pair of a dictionary for <literal>Ord t</literal> and a value of type
1455 <literal>t</literal>. That contradicts the idea that
1456 <literal>newtype</literal> should have no concrete representation.
1457 You can get just the same efficiency and effect by using
1458 <literal>data</literal> instead of <literal>newtype</literal>. If
1459 there is no overloading involved, then there is more of a case for
1460 allowing an existentially-quantified <literal>newtype</literal>,
1461 because the <literal>data</literal> version does carry an
1462 implementation cost, but single-field existentially quantified
1463 constructors aren't much use. So the simple restriction (no
1464 existential stuff on <literal>newtype</literal>) stands, unless there
1465 are convincing reasons to change it.
1473 You can't use <literal>deriving</literal> to define instances of a
1474 data type with existentially quantified data constructors.
1476 Reason: in most cases it would not make sense. For example:#
1479 data T = forall a. MkT [a] deriving( Eq )
1482 To derive <literal>Eq</literal> in the standard way we would need to have equality
1483 between the single component of two <function>MkT</function> constructors:
1487 (MkT a) == (MkT b) = ???
1490 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1491 It's just about possible to imagine examples in which the derived instance
1492 would make sense, but it seems altogether simpler simply to prohibit such
1493 declarations. Define your own instances!
1508 <sect2 id="multi-param-type-classes">
1509 <title>Class declarations</title>
1512 This section, and the next one, documents GHC's type-class extensions.
1513 There's lots of background in the paper <ulink
1514 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1515 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1516 Jones, Erik Meijer).
1519 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1523 <title>Multi-parameter type classes</title>
1525 Multi-parameter type classes are permitted. For example:
1529 class Collection c a where
1530 union :: c a -> c a -> c a
1538 <title>The superclasses of a class declaration</title>
1541 There are no restrictions on the context in a class declaration
1542 (which introduces superclasses), except that the class hierarchy must
1543 be acyclic. So these class declarations are OK:
1547 class Functor (m k) => FiniteMap m k where
1550 class (Monad m, Monad (t m)) => Transform t m where
1551 lift :: m a -> (t m) a
1557 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1558 of "acyclic" involves only the superclass relationships. For example,
1564 op :: D b => a -> b -> b
1567 class C a => D a where { ... }
1571 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1572 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1573 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1580 <sect3 id="class-method-types">
1581 <title>Class method types</title>
1584 Haskell 98 prohibits class method types to mention constraints on the
1585 class type variable, thus:
1588 fromList :: [a] -> s a
1589 elem :: Eq a => a -> s a -> Bool
1591 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1592 contains the constraint <literal>Eq a</literal>, constrains only the
1593 class type variable (in this case <literal>a</literal>).
1594 GHC lifts this restriction.
1601 <sect3 id="functional-dependencies">
1602 <title>Functional dependencies
1605 <para> Functional dependencies are implemented as described by Mark Jones
1606 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1607 In Proceedings of the 9th European Symposium on Programming,
1608 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1612 Functional dependencies are introduced by a vertical bar in the syntax of a
1613 class declaration; e.g.
1615 class (Monad m) => MonadState s m | m -> s where ...
1617 class Foo a b c | a b -> c where ...
1619 There should be more documentation, but there isn't (yet). Yell if you need it.
1622 In a class declaration, all of the class type variables must be reachable (in the sense
1623 mentioned in <xref linkend="type-restrictions"/>)
1624 from the free variables of each method type.
1628 class Coll s a where
1630 insert :: s -> a -> s
1633 is not OK, because the type of <literal>empty</literal> doesn't mention
1634 <literal>a</literal>. Functional dependencies can make the type variable
1637 class Coll s a | s -> a where
1639 insert :: s -> a -> s
1642 Alternatively <literal>Coll</literal> might be rewritten
1645 class Coll s a where
1647 insert :: s a -> a -> s a
1651 which makes the connection between the type of a collection of
1652 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1653 Occasionally this really doesn't work, in which case you can split the
1661 class CollE s => Coll s a where
1662 insert :: s -> a -> s
1673 <sect2 id="instance-decls">
1674 <title>Instance declarations</title>
1676 <sect3 id="instance-heads">
1677 <title>Instance heads</title>
1680 The <emphasis>head</emphasis> of an instance declaration is the part to the
1681 right of the "<literal>=></literal>". In Haskell 98 the head of an instance
1683 must be of the form <literal>C (T a1 ... an)</literal>, where
1684 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1685 and the <literal>a1 ... an</literal> are distinct type variables.
1688 The <option>-fglasgow-exts</option> flag lifts this restriction and allows the
1689 instance head to be of form <literal>C t1 ... tn</literal> where <literal>t1
1690 ... tn</literal> are arbitrary types (provided, of course, everything is
1691 well-kinded). In particular, types <literal>ti</literal> can be type variables
1692 or structured types, and can contain repeated occurrences of a single type
1696 instance Eq (T a a) where ...
1697 -- Repeated type variable
1699 instance Eq (S [a]) where ...
1702 instance C Int [a] where ...
1703 -- Multiple parameters
1708 <sect3 id="instance-overlap">
1709 <title>Overlapping instances</title>
1711 In general, <emphasis>GHC requires that that it be unambiguous which instance
1713 should be used to resolve a type-class constraint</emphasis>. This behaviour
1714 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1715 <indexterm><primary>-fallow-overlapping-instances
1716 </primary></indexterm>
1717 and <option>-fallow-incoherent-instances</option>
1718 <indexterm><primary>-fallow-incoherent-instances
1719 </primary></indexterm>, as this section discusses.</para>
1721 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1722 it tries to match every instance declaration against the
1724 by instantiating the head of the instance declaration. For example, consider
1727 instance context1 => C Int a where ... -- (A)
1728 instance context2 => C a Bool where ... -- (B)
1729 instance context3 => C Int [a] where ... -- (C)
1730 instance context4 => C Int [Int] where ... -- (D)
1732 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
1733 but (C) and (D) do not. When matching, GHC takes
1734 no account of the context of the instance declaration
1735 (<literal>context1</literal> etc).
1736 GHC's default behaviour is that <emphasis>exactly one instance must match the
1737 constraint it is trying to resolve</emphasis>.
1738 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1739 including both declarations (A) and (B), say); an error is only reported if a
1740 particular constraint matches more than one.
1744 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1745 more than one instance to match, provided there is a most specific one. For
1746 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1747 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1748 most-specific match, the program is rejected.
1751 However, GHC is conservative about committing to an overlapping instance. For example:
1756 Suppose that from the RHS of <literal>f</literal> we get the constraint
1757 <literal>C Int [b]</literal>. But
1758 GHC does not commit to instance (C), because in a particular
1759 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1760 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1761 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1762 GHC will instead pick (C), without complaining about
1763 the problem of subsequent instantiations.
1766 The willingness to be overlapped or incoherent is a property of
1767 the <emphasis>instance declaration</emphasis> itself, controlled by the
1768 presence or otherwise of the <option>-fallow-overlapping-instances</option>
1769 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
1770 being defined. Neither flag is required in a module that imports and uses the
1771 instance declaration. Specifically, during the lookup process:
1774 An instance declaration is ignored during the lookup process if (a) a more specific
1775 match is found, and (b) the instance declaration was compiled with
1776 <option>-fallow-overlapping-instances</option>. The flag setting for the
1777 more-specific instance does not matter.
1780 Suppose an instance declaration does not matche the constraint being looked up, but
1781 does unify with it, so that it might match when the constraint is further
1782 instantiated. Usually GHC will regard this as a reason for not committing to
1783 some other constraint. But if the instance declaration was compiled with
1784 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
1785 check for that declaration.
1788 All this makes it possible for a library author to design a library that relies on
1789 overlapping instances without the library client having to know.
1791 <para>The <option>-fallow-incoherent-instances</option> flag implies the
1792 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
1797 <title>Type synonyms in the instance head</title>
1800 <emphasis>Unlike Haskell 98, instance heads may use type
1801 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1802 As always, using a type synonym is just shorthand for
1803 writing the RHS of the type synonym definition. For example:
1807 type Point = (Int,Int)
1808 instance C Point where ...
1809 instance C [Point] where ...
1813 is legal. However, if you added
1817 instance C (Int,Int) where ...
1821 as well, then the compiler will complain about the overlapping
1822 (actually, identical) instance declarations. As always, type synonyms
1823 must be fully applied. You cannot, for example, write:
1828 instance Monad P where ...
1832 This design decision is independent of all the others, and easily
1833 reversed, but it makes sense to me.
1838 <sect3 id="undecidable-instances">
1839 <title>Undecidable instances</title>
1841 <para>An instance declaration must normally obey the following rules:
1843 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1844 an instance declaration <emphasis>must not</emphasis> be a type variable.
1845 For example, these are OK:
1848 instance C Int a where ...
1850 instance D (Int, Int) where ...
1852 instance E [[a]] where ...
1856 instance F a where ...
1858 Note that instance heads may contain repeated type variables (<xref linkend="instance-heads"/>).
1859 For example, this is OK:
1861 instance Stateful (ST s) (MutVar s) where ...
1868 <para>All of the types in the <emphasis>context</emphasis> of
1869 an instance declaration <emphasis>must</emphasis> be type variables, and
1870 there must be no repeated type variables in any one constraint.
1873 instance C a b => Eq (a,b) where ...
1877 instance C Int b => Foo [b] where ...
1879 is not OK (because of the non-type-variable <literal>Int</literal> in the context), and nor is
1881 instance C b b => Foo [b] where ...
1883 (because of the repeated type variable).
1887 These restrictions ensure that
1888 context reduction terminates: each reduction step removes one type
1889 constructor. For example, the following would make the type checker
1890 loop if it wasn't excluded:
1892 instance C a => C a where ...
1894 There are two situations in which the rule is a bit of a pain. First,
1895 if one allows overlapping instance declarations then it's quite
1896 convenient to have a "default instance" declaration that applies if
1897 something more specific does not:
1906 Second, sometimes you might want to use the following to get the
1907 effect of a "class synonym":
1911 class (C1 a, C2 a, C3 a) => C a where { }
1913 instance (C1 a, C2 a, C3 a) => C a where { }
1917 This allows you to write shorter signatures:
1929 f :: (C1 a, C2 a, C3 a) => ...
1933 Voluminous correspondence on the Haskell mailing list has convinced me
1934 that it's worth experimenting with more liberal rules. If you use
1935 the experimental flag <option>-fallow-undecidable-instances</option>
1936 <indexterm><primary>-fallow-undecidable-instances
1937 option</primary></indexterm>, you can use arbitrary
1938 types in both an instance context and instance head. Termination is ensured by having a
1939 fixed-depth recursion stack. If you exceed the stack depth you get a
1940 sort of backtrace, and the opportunity to increase the stack depth
1941 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1944 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1945 allowing these idioms interesting idioms.
1952 <sect2 id="type-restrictions">
1953 <title>Type signatures</title>
1955 <sect3><title>The context of a type signature</title>
1957 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1958 the form <emphasis>(class type-variable)</emphasis> or
1959 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1960 these type signatures are perfectly OK
1963 g :: Ord (T a ()) => ...
1967 GHC imposes the following restrictions on the constraints in a type signature.
1971 forall tv1..tvn (c1, ...,cn) => type
1974 (Here, we write the "foralls" explicitly, although the Haskell source
1975 language omits them; in Haskell 98, all the free type variables of an
1976 explicit source-language type signature are universally quantified,
1977 except for the class type variables in a class declaration. However,
1978 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1987 <emphasis>Each universally quantified type variable
1988 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1990 A type variable <literal>a</literal> is "reachable" if it it appears
1991 in the same constraint as either a type variable free in in
1992 <literal>type</literal>, or another reachable type variable.
1993 A value with a type that does not obey
1994 this reachability restriction cannot be used without introducing
1995 ambiguity; that is why the type is rejected.
1996 Here, for example, is an illegal type:
2000 forall a. Eq a => Int
2004 When a value with this type was used, the constraint <literal>Eq tv</literal>
2005 would be introduced where <literal>tv</literal> is a fresh type variable, and
2006 (in the dictionary-translation implementation) the value would be
2007 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2008 can never know which instance of <literal>Eq</literal> to use because we never
2009 get any more information about <literal>tv</literal>.
2013 that the reachability condition is weaker than saying that <literal>a</literal> is
2014 functionally dependent on a type variable free in
2015 <literal>type</literal> (see <xref
2016 linkend="functional-dependencies"/>). The reason for this is there
2017 might be a "hidden" dependency, in a superclass perhaps. So
2018 "reachable" is a conservative approximation to "functionally dependent".
2019 For example, consider:
2021 class C a b | a -> b where ...
2022 class C a b => D a b where ...
2023 f :: forall a b. D a b => a -> a
2025 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2026 but that is not immediately apparent from <literal>f</literal>'s type.
2032 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2033 universally quantified type variables <literal>tvi</literal></emphasis>.
2035 For example, this type is OK because <literal>C a b</literal> mentions the
2036 universally quantified type variable <literal>b</literal>:
2040 forall a. C a b => burble
2044 The next type is illegal because the constraint <literal>Eq b</literal> does not
2045 mention <literal>a</literal>:
2049 forall a. Eq b => burble
2053 The reason for this restriction is milder than the other one. The
2054 excluded types are never useful or necessary (because the offending
2055 context doesn't need to be witnessed at this point; it can be floated
2056 out). Furthermore, floating them out increases sharing. Lastly,
2057 excluding them is a conservative choice; it leaves a patch of
2058 territory free in case we need it later.
2069 <title>For-all hoisting</title>
2071 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2072 end of an arrow, thus:
2074 type Discard a = forall b. a -> b -> a
2076 g :: Int -> Discard Int
2079 Simply expanding the type synonym would give
2081 g :: Int -> (forall b. Int -> b -> Int)
2083 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2085 g :: forall b. Int -> Int -> b -> Int
2087 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2088 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2089 performs the transformation:</emphasis>
2091 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2093 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2095 (In fact, GHC tries to retain as much synonym information as possible for use in
2096 error messages, but that is a usability issue.) This rule applies, of course, whether
2097 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2098 valid way to write <literal>g</literal>'s type signature:
2100 g :: Int -> Int -> forall b. b -> Int
2104 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2107 type Foo a = (?x::Int) => Bool -> a
2112 g :: (?x::Int) => Bool -> Bool -> Int
2120 <sect2 id="implicit-parameters">
2121 <title>Implicit parameters</title>
2123 <para> Implicit parameters are implemented as described in
2124 "Implicit parameters: dynamic scoping with static types",
2125 J Lewis, MB Shields, E Meijer, J Launchbury,
2126 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2130 <para>(Most of the following, stil rather incomplete, documentation is
2131 due to Jeff Lewis.)</para>
2133 <para>Implicit parameter support is enabled with the option
2134 <option>-fimplicit-params</option>.</para>
2137 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2138 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2139 context. In Haskell, all variables are statically bound. Dynamic
2140 binding of variables is a notion that goes back to Lisp, but was later
2141 discarded in more modern incarnations, such as Scheme. Dynamic binding
2142 can be very confusing in an untyped language, and unfortunately, typed
2143 languages, in particular Hindley-Milner typed languages like Haskell,
2144 only support static scoping of variables.
2147 However, by a simple extension to the type class system of Haskell, we
2148 can support dynamic binding. Basically, we express the use of a
2149 dynamically bound variable as a constraint on the type. These
2150 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2151 function uses a dynamically-bound variable <literal>?x</literal>
2152 of type <literal>t'</literal>". For
2153 example, the following expresses the type of a sort function,
2154 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2156 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2158 The dynamic binding constraints are just a new form of predicate in the type class system.
2161 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2162 where <literal>x</literal> is
2163 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2164 Use of this construct also introduces a new
2165 dynamic-binding constraint in the type of the expression.
2166 For example, the following definition
2167 shows how we can define an implicitly parameterized sort function in
2168 terms of an explicitly parameterized <literal>sortBy</literal> function:
2170 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2172 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2178 <title>Implicit-parameter type constraints</title>
2180 Dynamic binding constraints behave just like other type class
2181 constraints in that they are automatically propagated. Thus, when a
2182 function is used, its implicit parameters are inherited by the
2183 function that called it. For example, our <literal>sort</literal> function might be used
2184 to pick out the least value in a list:
2186 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2187 least xs = fst (sort xs)
2189 Without lifting a finger, the <literal>?cmp</literal> parameter is
2190 propagated to become a parameter of <literal>least</literal> as well. With explicit
2191 parameters, the default is that parameters must always be explicit
2192 propagated. With implicit parameters, the default is to always
2196 An implicit-parameter type constraint differs from other type class constraints in the
2197 following way: All uses of a particular implicit parameter must have
2198 the same type. This means that the type of <literal>(?x, ?x)</literal>
2199 is <literal>(?x::a) => (a,a)</literal>, and not
2200 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2204 <para> You can't have an implicit parameter in the context of a class or instance
2205 declaration. For example, both these declarations are illegal:
2207 class (?x::Int) => C a where ...
2208 instance (?x::a) => Foo [a] where ...
2210 Reason: exactly which implicit parameter you pick up depends on exactly where
2211 you invoke a function. But the ``invocation'' of instance declarations is done
2212 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2213 Easiest thing is to outlaw the offending types.</para>
2215 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2217 f :: (?x :: [a]) => Int -> Int
2220 g :: (Read a, Show a) => String -> String
2223 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2224 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2225 quite unambiguous, and fixes the type <literal>a</literal>.
2230 <title>Implicit-parameter bindings</title>
2233 An implicit parameter is <emphasis>bound</emphasis> using the standard
2234 <literal>let</literal> or <literal>where</literal> binding forms.
2235 For example, we define the <literal>min</literal> function by binding
2236 <literal>cmp</literal>.
2239 min = let ?cmp = (<=) in least
2243 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2244 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2245 (including in a list comprehension, or do-notation, or pattern guards),
2246 or a <literal>where</literal> clause.
2247 Note the following points:
2250 An implicit-parameter binding group must be a
2251 collection of simple bindings to implicit-style variables (no
2252 function-style bindings, and no type signatures); these bindings are
2253 neither polymorphic or recursive.
2256 You may not mix implicit-parameter bindings with ordinary bindings in a
2257 single <literal>let</literal>
2258 expression; use two nested <literal>let</literal>s instead.
2259 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2263 You may put multiple implicit-parameter bindings in a
2264 single binding group; but they are <emphasis>not</emphasis> treated
2265 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2266 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2267 parameter. The bindings are not nested, and may be re-ordered without changing
2268 the meaning of the program.
2269 For example, consider:
2271 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2273 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2274 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2276 f :: (?x::Int) => Int -> Int
2284 <sect3><title>Implicit parameters and polymorphic recursion</title>
2287 Consider these two definitions:
2290 len1 xs = let ?acc = 0 in len_acc1 xs
2293 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2298 len2 xs = let ?acc = 0 in len_acc2 xs
2300 len_acc2 :: (?acc :: Int) => [a] -> Int
2302 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2304 The only difference between the two groups is that in the second group
2305 <literal>len_acc</literal> is given a type signature.
2306 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2307 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2308 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2309 has a type signature, the recursive call is made to the
2310 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2311 as an implicit parameter. So we get the following results in GHCi:
2318 Adding a type signature dramatically changes the result! This is a rather
2319 counter-intuitive phenomenon, worth watching out for.
2323 <sect3><title>Implicit parameters and monomorphism</title>
2325 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2326 Haskell Report) to implicit parameters. For example, consider:
2334 Since the binding for <literal>y</literal> falls under the Monomorphism
2335 Restriction it is not generalised, so the type of <literal>y</literal> is
2336 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2337 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2338 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2339 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2340 <literal>y</literal> in the body of the <literal>let</literal> will see the
2341 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2342 <literal>14</literal>.
2347 <sect2 id="linear-implicit-parameters">
2348 <title>Linear implicit parameters</title>
2350 Linear implicit parameters are an idea developed by Koen Claessen,
2351 Mark Shields, and Simon PJ. They address the long-standing
2352 problem that monads seem over-kill for certain sorts of problem, notably:
2355 <listitem> <para> distributing a supply of unique names </para> </listitem>
2356 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2357 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2361 Linear implicit parameters are just like ordinary implicit parameters,
2362 except that they are "linear" -- that is, they cannot be copied, and
2363 must be explicitly "split" instead. Linear implicit parameters are
2364 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2365 (The '/' in the '%' suggests the split!)
2370 import GHC.Exts( Splittable )
2372 data NameSupply = ...
2374 splitNS :: NameSupply -> (NameSupply, NameSupply)
2375 newName :: NameSupply -> Name
2377 instance Splittable NameSupply where
2381 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2382 f env (Lam x e) = Lam x' (f env e)
2385 env' = extend env x x'
2386 ...more equations for f...
2388 Notice that the implicit parameter %ns is consumed
2390 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2391 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2395 So the translation done by the type checker makes
2396 the parameter explicit:
2398 f :: NameSupply -> Env -> Expr -> Expr
2399 f ns env (Lam x e) = Lam x' (f ns1 env e)
2401 (ns1,ns2) = splitNS ns
2403 env = extend env x x'
2405 Notice the call to 'split' introduced by the type checker.
2406 How did it know to use 'splitNS'? Because what it really did
2407 was to introduce a call to the overloaded function 'split',
2408 defined by the class <literal>Splittable</literal>:
2410 class Splittable a where
2413 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2414 split for name supplies. But we can simply write
2420 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2422 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2423 <literal>GHC.Exts</literal>.
2428 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2429 are entirely distinct implicit parameters: you
2430 can use them together and they won't intefere with each other. </para>
2433 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2435 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2436 in the context of a class or instance declaration. </para></listitem>
2440 <sect3><title>Warnings</title>
2443 The monomorphism restriction is even more important than usual.
2444 Consider the example above:
2446 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2447 f env (Lam x e) = Lam x' (f env e)
2450 env' = extend env x x'
2452 If we replaced the two occurrences of x' by (newName %ns), which is
2453 usually a harmless thing to do, we get:
2455 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2456 f env (Lam x e) = Lam (newName %ns) (f env e)
2458 env' = extend env x (newName %ns)
2460 But now the name supply is consumed in <emphasis>three</emphasis> places
2461 (the two calls to newName,and the recursive call to f), so
2462 the result is utterly different. Urk! We don't even have
2466 Well, this is an experimental change. With implicit
2467 parameters we have already lost beta reduction anyway, and
2468 (as John Launchbury puts it) we can't sensibly reason about
2469 Haskell programs without knowing their typing.
2474 <sect3><title>Recursive functions</title>
2475 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2478 foo :: %x::T => Int -> [Int]
2480 foo n = %x : foo (n-1)
2482 where T is some type in class Splittable.</para>
2484 Do you get a list of all the same T's or all different T's
2485 (assuming that split gives two distinct T's back)?
2487 If you supply the type signature, taking advantage of polymorphic
2488 recursion, you get what you'd probably expect. Here's the
2489 translated term, where the implicit param is made explicit:
2492 foo x n = let (x1,x2) = split x
2493 in x1 : foo x2 (n-1)
2495 But if you don't supply a type signature, GHC uses the Hindley
2496 Milner trick of using a single monomorphic instance of the function
2497 for the recursive calls. That is what makes Hindley Milner type inference
2498 work. So the translation becomes
2502 foom n = x : foom (n-1)
2506 Result: 'x' is not split, and you get a list of identical T's. So the
2507 semantics of the program depends on whether or not foo has a type signature.
2510 You may say that this is a good reason to dislike linear implicit parameters
2511 and you'd be right. That is why they are an experimental feature.
2517 <sect2 id="sec-kinding">
2518 <title>Explicitly-kinded quantification</title>
2521 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2522 to give the kind explicitly as (machine-checked) documentation,
2523 just as it is nice to give a type signature for a function. On some occasions,
2524 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2525 John Hughes had to define the data type:
2527 data Set cxt a = Set [a]
2528 | Unused (cxt a -> ())
2530 The only use for the <literal>Unused</literal> constructor was to force the correct
2531 kind for the type variable <literal>cxt</literal>.
2534 GHC now instead allows you to specify the kind of a type variable directly, wherever
2535 a type variable is explicitly bound. Namely:
2537 <listitem><para><literal>data</literal> declarations:
2539 data Set (cxt :: * -> *) a = Set [a]
2540 </screen></para></listitem>
2541 <listitem><para><literal>type</literal> declarations:
2543 type T (f :: * -> *) = f Int
2544 </screen></para></listitem>
2545 <listitem><para><literal>class</literal> declarations:
2547 class (Eq a) => C (f :: * -> *) a where ...
2548 </screen></para></listitem>
2549 <listitem><para><literal>forall</literal>'s in type signatures:
2551 f :: forall (cxt :: * -> *). Set cxt Int
2552 </screen></para></listitem>
2557 The parentheses are required. Some of the spaces are required too, to
2558 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2559 will get a parse error, because "<literal>::*->*</literal>" is a
2560 single lexeme in Haskell.
2564 As part of the same extension, you can put kind annotations in types
2567 f :: (Int :: *) -> Int
2568 g :: forall a. a -> (a :: *)
2572 atype ::= '(' ctype '::' kind ')
2574 The parentheses are required.
2579 <sect2 id="universal-quantification">
2580 <title>Arbitrary-rank polymorphism
2584 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2585 allows us to say exactly what this means. For example:
2593 g :: forall b. (b -> b)
2595 The two are treated identically.
2599 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2600 explicit universal quantification in
2602 For example, all the following types are legal:
2604 f1 :: forall a b. a -> b -> a
2605 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2607 f2 :: (forall a. a->a) -> Int -> Int
2608 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2610 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2612 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2613 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2614 The <literal>forall</literal> makes explicit the universal quantification that
2615 is implicitly added by Haskell.
2618 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2619 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2620 shows, the polymorphic type on the left of the function arrow can be overloaded.
2623 The function <literal>f3</literal> has a rank-3 type;
2624 it has rank-2 types on the left of a function arrow.
2627 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2628 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2629 that restriction has now been lifted.)
2630 In particular, a forall-type (also called a "type scheme"),
2631 including an operational type class context, is legal:
2633 <listitem> <para> On the left of a function arrow </para> </listitem>
2634 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2635 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2636 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2637 field type signatures.</para> </listitem>
2638 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2639 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2641 There is one place you cannot put a <literal>forall</literal>:
2642 you cannot instantiate a type variable with a forall-type. So you cannot
2643 make a forall-type the argument of a type constructor. So these types are illegal:
2645 x1 :: [forall a. a->a]
2646 x2 :: (forall a. a->a, Int)
2647 x3 :: Maybe (forall a. a->a)
2649 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2650 a type variable any more!
2659 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2660 the types of the constructor arguments. Here are several examples:
2666 data T a = T1 (forall b. b -> b -> b) a
2668 data MonadT m = MkMonad { return :: forall a. a -> m a,
2669 bind :: forall a b. m a -> (a -> m b) -> m b
2672 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2678 The constructors have rank-2 types:
2684 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2685 MkMonad :: forall m. (forall a. a -> m a)
2686 -> (forall a b. m a -> (a -> m b) -> m b)
2688 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2694 Notice that you don't need to use a <literal>forall</literal> if there's an
2695 explicit context. For example in the first argument of the
2696 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2697 prefixed to the argument type. The implicit <literal>forall</literal>
2698 quantifies all type variables that are not already in scope, and are
2699 mentioned in the type quantified over.
2703 As for type signatures, implicit quantification happens for non-overloaded
2704 types too. So if you write this:
2707 data T a = MkT (Either a b) (b -> b)
2710 it's just as if you had written this:
2713 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2716 That is, since the type variable <literal>b</literal> isn't in scope, it's
2717 implicitly universally quantified. (Arguably, it would be better
2718 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2719 where that is what is wanted. Feedback welcomed.)
2723 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2724 the constructor to suitable values, just as usual. For example,
2735 a3 = MkSwizzle reverse
2738 a4 = let r x = Just x
2745 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2746 mkTs f x y = [T1 f x, T1 f y]
2752 The type of the argument can, as usual, be more general than the type
2753 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2754 does not need the <literal>Ord</literal> constraint.)
2758 When you use pattern matching, the bound variables may now have
2759 polymorphic types. For example:
2765 f :: T a -> a -> (a, Char)
2766 f (T1 w k) x = (w k x, w 'c' 'd')
2768 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2769 g (MkSwizzle s) xs f = s (map f (s xs))
2771 h :: MonadT m -> [m a] -> m [a]
2772 h m [] = return m []
2773 h m (x:xs) = bind m x $ \y ->
2774 bind m (h m xs) $ \ys ->
2781 In the function <function>h</function> we use the record selectors <literal>return</literal>
2782 and <literal>bind</literal> to extract the polymorphic bind and return functions
2783 from the <literal>MonadT</literal> data structure, rather than using pattern
2789 <title>Type inference</title>
2792 In general, type inference for arbitrary-rank types is undecidable.
2793 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2794 to get a decidable algorithm by requiring some help from the programmer.
2795 We do not yet have a formal specification of "some help" but the rule is this:
2798 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2799 provides an explicit polymorphic type for x, or GHC's type inference will assume
2800 that x's type has no foralls in it</emphasis>.
2803 What does it mean to "provide" an explicit type for x? You can do that by
2804 giving a type signature for x directly, using a pattern type signature
2805 (<xref linkend="scoped-type-variables"/>), thus:
2807 \ f :: (forall a. a->a) -> (f True, f 'c')
2809 Alternatively, you can give a type signature to the enclosing
2810 context, which GHC can "push down" to find the type for the variable:
2812 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2814 Here the type signature on the expression can be pushed inwards
2815 to give a type signature for f. Similarly, and more commonly,
2816 one can give a type signature for the function itself:
2818 h :: (forall a. a->a) -> (Bool,Char)
2819 h f = (f True, f 'c')
2821 You don't need to give a type signature if the lambda bound variable
2822 is a constructor argument. Here is an example we saw earlier:
2824 f :: T a -> a -> (a, Char)
2825 f (T1 w k) x = (w k x, w 'c' 'd')
2827 Here we do not need to give a type signature to <literal>w</literal>, because
2828 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2835 <sect3 id="implicit-quant">
2836 <title>Implicit quantification</title>
2839 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2840 user-written types, if and only if there is no explicit <literal>forall</literal>,
2841 GHC finds all the type variables mentioned in the type that are not already
2842 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2846 f :: forall a. a -> a
2853 h :: forall b. a -> b -> b
2859 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2862 f :: (a -> a) -> Int
2864 f :: forall a. (a -> a) -> Int
2866 f :: (forall a. a -> a) -> Int
2869 g :: (Ord a => a -> a) -> Int
2870 -- MEANS the illegal type
2871 g :: forall a. (Ord a => a -> a) -> Int
2873 g :: (forall a. Ord a => a -> a) -> Int
2875 The latter produces an illegal type, which you might think is silly,
2876 but at least the rule is simple. If you want the latter type, you
2877 can write your for-alls explicitly. Indeed, doing so is strongly advised
2886 <sect2 id="scoped-type-variables">
2887 <title>Scoped type variables
2891 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2893 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2894 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2895 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2899 f (xs::[a]) = ys ++ ys
2904 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2905 This brings the type variable <literal>a</literal> into scope; it scopes over
2906 all the patterns and right hand sides for this equation for <function>f</function>.
2907 In particular, it is in scope at the type signature for <varname>y</varname>.
2911 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2912 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2913 implicitly universally quantified. (If there are no type variables in
2914 scope, all type variables mentioned in the signature are universally
2915 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2916 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2917 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2918 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2919 it becomes possible to do so.
2923 Scoped type variables are implemented in both GHC and Hugs. Where the
2924 implementations differ from the specification below, those differences
2929 So much for the basic idea. Here are the details.
2933 <title>What a scoped type variable means</title>
2935 A lexically-scoped type variable is simply
2936 the name for a type. The restriction it expresses is that all occurrences
2937 of the same name mean the same type. For example:
2939 f :: [Int] -> Int -> Int
2940 f (xs::[a]) (y::a) = (head xs + y) :: a
2942 The pattern type signatures on the left hand side of
2943 <literal>f</literal> express the fact that <literal>xs</literal>
2944 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2945 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2946 specifies that this expression must have the same type <literal>a</literal>.
2947 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2948 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2949 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2950 rules, which specified that a pattern-bound type variable should be universally quantified.)
2951 For example, all of these are legal:</para>
2954 t (x::a) (y::a) = x+y*2
2956 f (x::a) (y::b) = [x,y] -- a unifies with b
2958 g (x::a) = x + 1::Int -- a unifies with Int
2960 h x = let k (y::a) = [x,y] -- a is free in the
2961 in k x -- environment
2963 k (x::a) True = ... -- a unifies with Int
2964 k (x::Int) False = ...
2967 w (x::a) = x -- a unifies with [b]
2973 <title>Scope and implicit quantification</title>
2981 All the type variables mentioned in a pattern,
2982 that are not already in scope,
2983 are brought into scope by the pattern. We describe this set as
2984 the <emphasis>type variables bound by the pattern</emphasis>.
2987 f (x::a) = let g (y::(a,b)) = fst y
2991 The pattern <literal>(x::a)</literal> brings the type variable
2992 <literal>a</literal> into scope, as well as the term
2993 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2994 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2995 and brings into scope the type variable <literal>b</literal>.
3001 The type variable(s) bound by the pattern have the same scope
3002 as the term variable(s) bound by the pattern. For example:
3005 f (x::a) = <...rhs of f...>
3006 (p::b, q::b) = (1,2)
3007 in <...body of let...>
3009 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3010 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3011 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3012 just like <literal>p</literal> and <literal>q</literal> do.
3013 Indeed, the newly bound type variables also scope over any ordinary, separate
3014 type signatures in the <literal>let</literal> group.
3021 The type variables bound by the pattern may be
3022 mentioned in ordinary type signatures or pattern
3023 type signatures anywhere within their scope.
3030 In ordinary type signatures, any type variable mentioned in the
3031 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3039 Ordinary type signatures do not bring any new type variables
3040 into scope (except in the type signature itself!). So this is illegal:
3047 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3048 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3049 and that is an incorrect typing.
3056 The pattern type signature is a monotype:
3061 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3065 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3066 not to type schemes.
3070 There is no implicit universal quantification on pattern type signatures (in contrast to
3071 ordinary type signatures).
3081 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3082 scope over the methods defined in the <literal>where</literal> part. For example:
3096 (Not implemented in Hugs yet, Dec 98).
3106 <sect3 id="decl-type-sigs">
3107 <title>Declaration type signatures</title>
3108 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3109 quantification (using <literal>forall</literal>) brings into scope the
3110 explicitly-quantified
3111 type variables, in the definition of the named function(s). For example:
3113 f :: forall a. [a] -> [a]
3114 f (x:xs) = xs ++ [ x :: a ]
3116 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3117 the definition of "<literal>f</literal>".
3119 <para>This only happens if the quantification in <literal>f</literal>'s type
3120 signature is explicit. For example:
3123 g (x:xs) = xs ++ [ x :: a ]
3125 This program will be rejected, because "<literal>a</literal>" does not scope
3126 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3127 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3128 quantification rules.
3132 <sect3 id="pattern-type-sigs">
3133 <title>Where a pattern type signature can occur</title>
3136 A pattern type signature can occur in any pattern. For example:
3141 A pattern type signature can be on an arbitrary sub-pattern, not
3146 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3155 Pattern type signatures, including the result part, can be used
3156 in lambda abstractions:
3159 (\ (x::a, y) :: a -> x)
3166 Pattern type signatures, including the result part, can be used
3167 in <literal>case</literal> expressions:
3170 case e of { ((x::a, y) :: (a,b)) -> x }
3173 Note that the <literal>-></literal> symbol in a case alternative
3174 leads to difficulties when parsing a type signature in the pattern: in
3175 the absence of the extra parentheses in the example above, the parser
3176 would try to interpret the <literal>-></literal> as a function
3177 arrow and give a parse error later.
3185 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3186 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3187 token or a parenthesised type of some sort). To see why,
3188 consider how one would parse this:
3202 Pattern type signatures can bind existential type variables.
3207 data T = forall a. MkT [a]
3210 f (MkT [t::a]) = MkT t3
3223 Pattern type signatures
3224 can be used in pattern bindings:
3227 f x = let (y, z::a) = x in ...
3228 f1 x = let (y, z::Int) = x in ...
3229 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3230 f3 :: (b->b) = \x -> x
3233 In all such cases, the binding is not generalised over the pattern-bound
3234 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3235 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3236 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3237 In contrast, the binding
3242 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3243 in <literal>f4</literal>'s scope.
3249 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3250 type signatures. The two can be used independently or together.</para>
3254 <sect3 id="result-type-sigs">
3255 <title>Result type signatures</title>
3258 The result type of a function can be given a signature, thus:
3262 f (x::a) :: [a] = [x,x,x]
3266 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3267 result type. Sometimes this is the only way of naming the type variable
3272 f :: Int -> [a] -> [a]
3273 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3274 in \xs -> map g (reverse xs `zip` xs)
3279 The type variables bound in a result type signature scope over the right hand side
3280 of the definition. However, consider this corner-case:
3282 rev1 :: [a] -> [a] = \xs -> reverse xs
3284 foo ys = rev (ys::[a])
3286 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3287 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3288 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3289 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3290 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3293 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3294 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3298 rev1 :: [a] -> [a] = \xs -> reverse xs
3303 Result type signatures are not yet implemented in Hugs.
3310 <sect2 id="deriving-typeable">
3311 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3314 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3315 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3316 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3317 classes <literal>Eq</literal>, <literal>Ord</literal>,
3318 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3321 GHC extends this list with two more classes that may be automatically derived
3322 (provided the <option>-fglasgow-exts</option> flag is specified):
3323 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3324 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3325 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3327 <para>An instance of <literal>Typeable</literal> can only be derived if the
3328 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3329 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3331 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3332 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3334 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3335 are used, and only <literal>Typeable1</literal> up to
3336 <literal>Typeable7</literal> are provided in the library.)
3337 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3338 class, whose kind suits that of the data type constructor, and
3339 then writing the data type instance by hand.
3343 <sect2 id="newtype-deriving">
3344 <title>Generalised derived instances for newtypes</title>
3347 When you define an abstract type using <literal>newtype</literal>, you may want
3348 the new type to inherit some instances from its representation. In
3349 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3350 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3351 other classes you have to write an explicit instance declaration. For
3352 example, if you define
3355 newtype Dollars = Dollars Int
3358 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3359 explicitly define an instance of <literal>Num</literal>:
3362 instance Num Dollars where
3363 Dollars a + Dollars b = Dollars (a+b)
3366 All the instance does is apply and remove the <literal>newtype</literal>
3367 constructor. It is particularly galling that, since the constructor
3368 doesn't appear at run-time, this instance declaration defines a
3369 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3370 dictionary, only slower!
3374 <sect3> <title> Generalising the deriving clause </title>
3376 GHC now permits such instances to be derived instead, so one can write
3378 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3381 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3382 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3383 derives an instance declaration of the form
3386 instance Num Int => Num Dollars
3389 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3393 We can also derive instances of constructor classes in a similar
3394 way. For example, suppose we have implemented state and failure monad
3395 transformers, such that
3398 instance Monad m => Monad (State s m)
3399 instance Monad m => Monad (Failure m)
3401 In Haskell 98, we can define a parsing monad by
3403 type Parser tok m a = State [tok] (Failure m) a
3406 which is automatically a monad thanks to the instance declarations
3407 above. With the extension, we can make the parser type abstract,
3408 without needing to write an instance of class <literal>Monad</literal>, via
3411 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3414 In this case the derived instance declaration is of the form
3416 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3419 Notice that, since <literal>Monad</literal> is a constructor class, the
3420 instance is a <emphasis>partial application</emphasis> of the new type, not the
3421 entire left hand side. We can imagine that the type declaration is
3422 ``eta-converted'' to generate the context of the instance
3427 We can even derive instances of multi-parameter classes, provided the
3428 newtype is the last class parameter. In this case, a ``partial
3429 application'' of the class appears in the <literal>deriving</literal>
3430 clause. For example, given the class
3433 class StateMonad s m | m -> s where ...
3434 instance Monad m => StateMonad s (State s m) where ...
3436 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3438 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3439 deriving (Monad, StateMonad [tok])
3442 The derived instance is obtained by completing the application of the
3443 class to the new type:
3446 instance StateMonad [tok] (State [tok] (Failure m)) =>
3447 StateMonad [tok] (Parser tok m)
3452 As a result of this extension, all derived instances in newtype
3453 declarations are treated uniformly (and implemented just by reusing
3454 the dictionary for the representation type), <emphasis>except</emphasis>
3455 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3456 the newtype and its representation.
3460 <sect3> <title> A more precise specification </title>
3462 Derived instance declarations are constructed as follows. Consider the
3463 declaration (after expansion of any type synonyms)
3466 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3472 <literal>S</literal> is a type constructor,
3475 The <literal>t1...tk</literal> are types,
3478 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3479 the <literal>ti</literal>, and
3482 The <literal>ci</literal> are partial applications of
3483 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3484 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3487 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3488 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3489 should not "look through" the type or its constructor. You can still
3490 derive these classes for a newtype, but it happens in the usual way, not
3491 via this new mechanism.
3494 Then, for each <literal>ci</literal>, the derived instance
3497 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3499 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3500 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3504 As an example which does <emphasis>not</emphasis> work, consider
3506 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3508 Here we cannot derive the instance
3510 instance Monad (State s m) => Monad (NonMonad m)
3513 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3514 and so cannot be "eta-converted" away. It is a good thing that this
3515 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3516 not, in fact, a monad --- for the same reason. Try defining
3517 <literal>>>=</literal> with the correct type: you won't be able to.
3521 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3522 important, since we can only derive instances for the last one. If the
3523 <literal>StateMonad</literal> class above were instead defined as
3526 class StateMonad m s | m -> s where ...
3529 then we would not have been able to derive an instance for the
3530 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3531 classes usually have one "main" parameter for which deriving new
3532 instances is most interesting.
3534 <para>Lastly, all of this applies only for classes other than
3535 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3536 and <literal>Data</literal>, for which the built-in derivation applies (section
3537 4.3.3. of the Haskell Report).
3538 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3539 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3540 the standard method is used or the one described here.)
3546 <sect2 id="typing-binds">
3547 <title>Generalised typing of mutually recursive bindings</title>
3550 The Haskell Report specifies that a group of bindings (at top level, or in a
3551 <literal>let</literal> or <literal>where</literal>) should be sorted into
3552 strongly-connected components, and then type-checked in dependency order
3553 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3554 Report, Section 4.5.1</ulink>).
3555 As each group is type-checked, any binders of the group that
3557 an explicit type signature are put in the type environment with the specified
3559 and all others are monomorphic until the group is generalised
3560 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3563 <para>Following a suggestion of Mark Jones, in his paper
3564 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3566 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3568 <emphasis>the dependency analysis ignores references to variables that have an explicit
3569 type signature</emphasis>.
3570 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3571 typecheck. For example, consider:
3573 f :: Eq a => a -> Bool
3574 f x = (x == x) || g True || g "Yes"
3576 g y = (y <= y) || f True
3578 This is rejected by Haskell 98, but under Jones's scheme the definition for
3579 <literal>g</literal> is typechecked first, separately from that for
3580 <literal>f</literal>,
3581 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3582 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3583 type is generalised, to get
3585 g :: Ord a => a -> Bool
3587 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3588 <literal>g</literal> in the type environment.
3592 The same refined dependency analysis also allows the type signatures of
3593 mutually-recursive functions to have different contexts, something that is illegal in
3594 Haskell 98 (Section 4.5.2, last sentence). With
3595 <option>-fglasgow-exts</option>
3596 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3597 type signatures; in practice this means that only variables bound by the same
3598 pattern binding must have the same context. For example, this is fine:
3600 f :: Eq a => a -> Bool
3601 f x = (x == x) || g True
3603 g :: Ord a => a -> Bool
3604 g y = (y <= y) || f True
3610 <!-- ==================== End of type system extensions ================= -->
3612 <!-- ====================== Generalised algebraic data types ======================= -->
3615 <title>Generalised Algebraic Data Types</title>
3617 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3618 to give the type signatures of constructors explicitly. For example:
3621 Lit :: Int -> Term Int
3622 Succ :: Term Int -> Term Int
3623 IsZero :: Term Int -> Term Bool
3624 If :: Term Bool -> Term a -> Term a -> Term a
3625 Pair :: Term a -> Term b -> Term (a,b)
3627 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3628 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3629 for these <literal>Terms</literal>:
3633 eval (Succ t) = 1 + eval t
3634 eval (IsZero t) = eval t == 0
3635 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3636 eval (Pair e1 e2) = (eval e1, eval e2)
3638 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3640 <para> The extensions to GHC are these:
3643 Data type declarations have a 'where' form, as exemplified above. The type signature of
3644 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3645 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3646 have no scope. Indeed, one can write a kind signature instead:
3648 data Term :: * -> * where ...
3650 or even a mixture of the two:
3652 data Foo a :: (* -> *) -> * where ...
3654 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3657 data Foo a (b :: * -> *) where ...
3662 There are no restrictions on the type of the data constructor, except that the result
3663 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3664 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3668 You can use record syntax on a GADT-style data type declaration:
3672 Lit { val :: Int } :: Term Int
3673 Succ { num :: Term Int } :: Term Int
3674 Pred { num :: Term Int } :: Term Int
3675 IsZero { arg :: Term Int } :: Term Bool
3676 Pair { arg1 :: Term a
3679 If { cnd :: Term Bool
3684 For every constructor that has a field <literal>f</literal>, (a) the type of
3685 field <literal>f</literal> must be the same; and (b) the
3686 result type of the constructor must be the same; both modulo alpha conversion.
3687 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3689 single name. Although their field types are both <literal>Term Int</literal>,
3690 their selector functions actually have different types:
3693 num :: Term Int -> Term Int
3694 arg :: Term Bool -> Term Int
3697 At the moment, record updates are not yet possible with GADT, so support is
3698 limited to record construction, selection and pattern matching:
3701 someTerm :: Term Bool
3702 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3705 eval Lit { val = i } = i
3706 eval Succ { num = t } = eval t + 1
3707 eval Pred { num = t } = eval t - 1
3708 eval IsZero { arg = t } = eval t == 0
3709 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3710 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3716 You can use strictness annotations, in the obvious places
3717 in the constructor type:
3720 Lit :: !Int -> Term Int
3721 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3722 Pair :: Term a -> Term b -> Term (a,b)
3727 You can use a <literal>deriving</literal> clause on a GADT-style data type
3728 declaration, but only if the data type could also have been declared in
3729 Haskell-98 syntax. For example, these two declarations are equivalent
3731 data Maybe1 a where {
3732 Nothing1 :: Maybe a ;
3733 Just1 :: a -> Maybe a
3734 } deriving( Eq, Ord )
3736 data Maybe2 a = Nothing2 | Just2 a
3739 This simply allows you to declare a vanilla Haskell-98 data type using the
3740 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3744 Pattern matching causes type refinement. For example, in the right hand side of the equation
3749 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3750 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3751 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3753 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3754 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3755 occur. However, the refinement is quite general. For example, if we had:
3757 eval :: Term a -> a -> a
3758 eval (Lit i) j = i+j
3760 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3761 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3762 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3768 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3770 data T a = forall b. MkT b (b->a)
3771 data T' a where { MKT :: b -> (b->a) -> T' a }
3776 <!-- ====================== End of Generalised algebraic data types ======================= -->
3778 <!-- ====================== TEMPLATE HASKELL ======================= -->
3780 <sect1 id="template-haskell">
3781 <title>Template Haskell</title>
3783 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3784 Template Haskell at <ulink url="http://www.haskell.org/th/">
3785 http://www.haskell.org/th/</ulink>, while
3787 the main technical innovations is discussed in "<ulink
3788 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3789 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3790 The details of the Template Haskell design are still in flux. Make sure you
3791 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3792 (search for the type ExpQ).
3793 [Temporary: many changes to the original design are described in
3794 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3795 Not all of these changes are in GHC 6.2.]
3798 <para> The first example from that paper is set out below as a worked example to help get you started.
3802 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3803 Tim Sheard is going to expand it.)
3807 <title>Syntax</title>
3809 <para> Template Haskell has the following new syntactic
3810 constructions. You need to use the flag
3811 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3812 </indexterm>to switch these syntactic extensions on
3813 (<option>-fth</option> is currently implied by
3814 <option>-fglasgow-exts</option>, but you are encouraged to
3815 specify it explicitly).</para>
3819 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3820 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3821 There must be no space between the "$" and the identifier or parenthesis. This use
3822 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3823 of "." as an infix operator. If you want the infix operator, put spaces around it.
3825 <para> A splice can occur in place of
3827 <listitem><para> an expression; the spliced expression must
3828 have type <literal>Q Exp</literal></para></listitem>
3829 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3830 <listitem><para> [Planned, but not implemented yet.] a
3831 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
3833 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3834 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3840 A expression quotation is written in Oxford brackets, thus:
3842 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3843 the quotation has type <literal>Expr</literal>.</para></listitem>
3844 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3845 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3846 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
3847 the quotation has type <literal>Type</literal>.</para></listitem>
3848 </itemizedlist></para></listitem>
3851 Reification is written thus:
3853 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3854 has type <literal>Dec</literal>. </para></listitem>
3855 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3856 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3857 <listitem><para> Still to come: fixities </para></listitem>
3859 </itemizedlist></para>
3866 <sect2> <title> Using Template Haskell </title>
3870 The data types and monadic constructor functions for Template Haskell are in the library
3871 <literal>Language.Haskell.THSyntax</literal>.
3875 You can only run a function at compile time if it is imported from another module. That is,
3876 you can't define a function in a module, and call it from within a splice in the same module.
3877 (It would make sense to do so, but it's hard to implement.)
3881 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3884 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3885 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3886 compiles and runs a program, and then looks at the result. So it's important that
3887 the program it compiles produces results whose representations are identical to
3888 those of the compiler itself.
3892 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3893 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3898 <sect2> <title> A Template Haskell Worked Example </title>
3899 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3900 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3907 -- Import our template "pr"
3908 import Printf ( pr )
3910 -- The splice operator $ takes the Haskell source code
3911 -- generated at compile time by "pr" and splices it into
3912 -- the argument of "putStrLn".
3913 main = putStrLn ( $(pr "Hello") )
3919 -- Skeletal printf from the paper.
3920 -- It needs to be in a separate module to the one where
3921 -- you intend to use it.
3923 -- Import some Template Haskell syntax
3924 import Language.Haskell.TH
3926 -- Describe a format string
3927 data Format = D | S | L String
3929 -- Parse a format string. This is left largely to you
3930 -- as we are here interested in building our first ever
3931 -- Template Haskell program and not in building printf.
3932 parse :: String -> [Format]
3935 -- Generate Haskell source code from a parsed representation
3936 -- of the format string. This code will be spliced into
3937 -- the module which calls "pr", at compile time.
3938 gen :: [Format] -> ExpQ
3939 gen [D] = [| \n -> show n |]
3940 gen [S] = [| \s -> s |]
3941 gen [L s] = stringE s
3943 -- Here we generate the Haskell code for the splice
3944 -- from an input format string.
3945 pr :: String -> ExpQ
3946 pr s = gen (parse s)
3949 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3952 $ ghc --make -fth main.hs -o main.exe
3955 <para>Run "main.exe" and here is your output:</para>
3966 <!-- ===================== Arrow notation =================== -->
3968 <sect1 id="arrow-notation">
3969 <title>Arrow notation
3972 <para>Arrows are a generalization of monads introduced by John Hughes.
3973 For more details, see
3978 “Generalising Monads to Arrows”,
3979 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3980 pp67–111, May 2000.
3986 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3987 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3993 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3994 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4000 and the arrows web page at
4001 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4002 With the <option>-farrows</option> flag, GHC supports the arrow
4003 notation described in the second of these papers.
4004 What follows is a brief introduction to the notation;
4005 it won't make much sense unless you've read Hughes's paper.
4006 This notation is translated to ordinary Haskell,
4007 using combinators from the
4008 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4012 <para>The extension adds a new kind of expression for defining arrows:
4014 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4015 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4017 where <literal>proc</literal> is a new keyword.
4018 The variables of the pattern are bound in the body of the
4019 <literal>proc</literal>-expression,
4020 which is a new sort of thing called a <firstterm>command</firstterm>.
4021 The syntax of commands is as follows:
4023 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4024 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4025 | <replaceable>cmd</replaceable><superscript>0</superscript>
4027 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4028 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4029 infix operators as for expressions, and
4031 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4032 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4033 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4034 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4035 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4036 | <replaceable>fcmd</replaceable>
4038 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4039 | ( <replaceable>cmd</replaceable> )
4040 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4042 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4043 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4044 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4045 | <replaceable>cmd</replaceable>
4047 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4048 except that the bodies are commands instead of expressions.
4052 Commands produce values, but (like monadic computations)
4053 may yield more than one value,
4054 or none, and may do other things as well.
4055 For the most part, familiarity with monadic notation is a good guide to
4057 However the values of expressions, even monadic ones,
4058 are determined by the values of the variables they contain;
4059 this is not necessarily the case for commands.
4063 A simple example of the new notation is the expression
4065 proc x -> f -< x+1
4067 We call this a <firstterm>procedure</firstterm> or
4068 <firstterm>arrow abstraction</firstterm>.
4069 As with a lambda expression, the variable <literal>x</literal>
4070 is a new variable bound within the <literal>proc</literal>-expression.
4071 It refers to the input to the arrow.
4072 In the above example, <literal>-<</literal> is not an identifier but an
4073 new reserved symbol used for building commands from an expression of arrow
4074 type and an expression to be fed as input to that arrow.
4075 (The weird look will make more sense later.)
4076 It may be read as analogue of application for arrows.
4077 The above example is equivalent to the Haskell expression
4079 arr (\ x -> x+1) >>> f
4081 That would make no sense if the expression to the left of
4082 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4083 More generally, the expression to the left of <literal>-<</literal>
4084 may not involve any <firstterm>local variable</firstterm>,
4085 i.e. a variable bound in the current arrow abstraction.
4086 For such a situation there is a variant <literal>-<<</literal>, as in
4088 proc x -> f x -<< x+1
4090 which is equivalent to
4092 arr (\ x -> (f x, x+1)) >>> app
4094 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4096 Such an arrow is equivalent to a monad, so if you're using this form
4097 you may find a monadic formulation more convenient.
4101 <title>do-notation for commands</title>
4104 Another form of command is a form of <literal>do</literal>-notation.
4105 For example, you can write
4114 You can read this much like ordinary <literal>do</literal>-notation,
4115 but with commands in place of monadic expressions.
4116 The first line sends the value of <literal>x+1</literal> as an input to
4117 the arrow <literal>f</literal>, and matches its output against
4118 <literal>y</literal>.
4119 In the next line, the output is discarded.
4120 The arrow <function>returnA</function> is defined in the
4121 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4122 module as <literal>arr id</literal>.
4123 The above example is treated as an abbreviation for
4125 arr (\ x -> (x, x)) >>>
4126 first (arr (\ x -> x+1) >>> f) >>>
4127 arr (\ (y, x) -> (y, (x, y))) >>>
4128 first (arr (\ y -> 2*y) >>> g) >>>
4130 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4131 first (arr (\ (x, z) -> x*z) >>> h) >>>
4132 arr (\ (t, z) -> t+z) >>>
4135 Note that variables not used later in the composition are projected out.
4136 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4138 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4139 module, this reduces to
4141 arr (\ x -> (x+1, x)) >>>
4143 arr (\ (y, x) -> (2*y, (x, y))) >>>
4145 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4147 arr (\ (t, z) -> t+z)
4149 which is what you might have written by hand.
4150 With arrow notation, GHC keeps track of all those tuples of variables for you.
4154 Note that although the above translation suggests that
4155 <literal>let</literal>-bound variables like <literal>z</literal> must be
4156 monomorphic, the actual translation produces Core,
4157 so polymorphic variables are allowed.
4161 It's also possible to have mutually recursive bindings,
4162 using the new <literal>rec</literal> keyword, as in the following example:
4164 counter :: ArrowCircuit a => a Bool Int
4165 counter = proc reset -> do
4166 rec output <- returnA -< if reset then 0 else next
4167 next <- delay 0 -< output+1
4168 returnA -< output
4170 The translation of such forms uses the <function>loop</function> combinator,
4171 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4177 <title>Conditional commands</title>
4180 In the previous example, we used a conditional expression to construct the
4182 Sometimes we want to conditionally execute different commands, as in
4189 which is translated to
4191 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4192 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4194 Since the translation uses <function>|||</function>,
4195 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4199 There are also <literal>case</literal> commands, like
4205 y <- h -< (x1, x2)
4209 The syntax is the same as for <literal>case</literal> expressions,
4210 except that the bodies of the alternatives are commands rather than expressions.
4211 The translation is similar to that of <literal>if</literal> commands.
4217 <title>Defining your own control structures</title>
4220 As we're seen, arrow notation provides constructs,
4221 modelled on those for expressions,
4222 for sequencing, value recursion and conditionals.
4223 But suitable combinators,
4224 which you can define in ordinary Haskell,
4225 may also be used to build new commands out of existing ones.
4226 The basic idea is that a command defines an arrow from environments to values.
4227 These environments assign values to the free local variables of the command.
4228 Thus combinators that produce arrows from arrows
4229 may also be used to build commands from commands.
4230 For example, the <literal>ArrowChoice</literal> class includes a combinator
4232 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4234 so we can use it to build commands:
4236 expr' = proc x -> do
4239 symbol Plus -< ()
4240 y <- term -< ()
4243 symbol Minus -< ()
4244 y <- term -< ()
4247 (The <literal>do</literal> on the first line is needed to prevent the first
4248 <literal><+> ...</literal> from being interpreted as part of the
4249 expression on the previous line.)
4250 This is equivalent to
4252 expr' = (proc x -> returnA -< x)
4253 <+> (proc x -> do
4254 symbol Plus -< ()
4255 y <- term -< ()
4257 <+> (proc x -> do
4258 symbol Minus -< ()
4259 y <- term -< ()
4262 It is essential that this operator be polymorphic in <literal>e</literal>
4263 (representing the environment input to the command
4264 and thence to its subcommands)
4265 and satisfy the corresponding naturality property
4267 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4269 at least for strict <literal>k</literal>.
4270 (This should be automatic if you're not using <function>seq</function>.)
4271 This ensures that environments seen by the subcommands are environments
4272 of the whole command,
4273 and also allows the translation to safely trim these environments.
4274 The operator must also not use any variable defined within the current
4279 We could define our own operator
4281 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4282 untilA body cond = proc x ->
4283 if cond x then returnA -< ()
4286 untilA body cond -< x
4288 and use it in the same way.
4289 Of course this infix syntax only makes sense for binary operators;
4290 there is also a more general syntax involving special brackets:
4294 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4301 <title>Primitive constructs</title>
4304 Some operators will need to pass additional inputs to their subcommands.
4305 For example, in an arrow type supporting exceptions,
4306 the operator that attaches an exception handler will wish to pass the
4307 exception that occurred to the handler.
4308 Such an operator might have a type
4310 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4312 where <literal>Ex</literal> is the type of exceptions handled.
4313 You could then use this with arrow notation by writing a command
4315 body `handleA` \ ex -> handler
4317 so that if an exception is raised in the command <literal>body</literal>,
4318 the variable <literal>ex</literal> is bound to the value of the exception
4319 and the command <literal>handler</literal>,
4320 which typically refers to <literal>ex</literal>, is entered.
4321 Though the syntax here looks like a functional lambda,
4322 we are talking about commands, and something different is going on.
4323 The input to the arrow represented by a command consists of values for
4324 the free local variables in the command, plus a stack of anonymous values.
4325 In all the prior examples, this stack was empty.
4326 In the second argument to <function>handleA</function>,
4327 this stack consists of one value, the value of the exception.
4328 The command form of lambda merely gives this value a name.
4333 the values on the stack are paired to the right of the environment.
4334 So operators like <function>handleA</function> that pass
4335 extra inputs to their subcommands can be designed for use with the notation
4336 by pairing the values with the environment in this way.
4337 More precisely, the type of each argument of the operator (and its result)
4338 should have the form
4340 a (...(e,t1), ... tn) t
4342 where <replaceable>e</replaceable> is a polymorphic variable
4343 (representing the environment)
4344 and <replaceable>ti</replaceable> are the types of the values on the stack,
4345 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4346 The polymorphic variable <replaceable>e</replaceable> must not occur in
4347 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4348 <replaceable>t</replaceable>.
4349 However the arrows involved need not be the same.
4350 Here are some more examples of suitable operators:
4352 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4353 runReader :: ... => a e c -> a' (e,State) c
4354 runState :: ... => a e c -> a' (e,State) (c,State)
4356 We can supply the extra input required by commands built with the last two
4357 by applying them to ordinary expressions, as in
4361 (|runReader (do { ... })|) s
4363 which adds <literal>s</literal> to the stack of inputs to the command
4364 built using <function>runReader</function>.
4368 The command versions of lambda abstraction and application are analogous to
4369 the expression versions.
4370 In particular, the beta and eta rules describe equivalences of commands.
4371 These three features (operators, lambda abstraction and application)
4372 are the core of the notation; everything else can be built using them,
4373 though the results would be somewhat clumsy.
4374 For example, we could simulate <literal>do</literal>-notation by defining
4376 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4377 u `bind` f = returnA &&& u >>> f
4379 bind_ :: Arrow a => a e b -> a e c -> a e c
4380 u `bind_` f = u `bind` (arr fst >>> f)
4382 We could simulate <literal>if</literal> by defining
4384 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4385 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4392 <title>Differences with the paper</title>
4397 <para>Instead of a single form of arrow application (arrow tail) with two
4398 translations, the implementation provides two forms
4399 <quote><literal>-<</literal></quote> (first-order)
4400 and <quote><literal>-<<</literal></quote> (higher-order).
4405 <para>User-defined operators are flagged with banana brackets instead of
4406 a new <literal>form</literal> keyword.
4415 <title>Portability</title>
4418 Although only GHC implements arrow notation directly,
4419 there is also a preprocessor
4421 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4422 that translates arrow notation into Haskell 98
4423 for use with other Haskell systems.
4424 You would still want to check arrow programs with GHC;
4425 tracing type errors in the preprocessor output is not easy.
4426 Modules intended for both GHC and the preprocessor must observe some
4427 additional restrictions:
4432 The module must import
4433 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4439 The preprocessor cannot cope with other Haskell extensions.
4440 These would have to go in separate modules.
4446 Because the preprocessor targets Haskell (rather than Core),
4447 <literal>let</literal>-bound variables are monomorphic.
4458 <!-- ==================== ASSERTIONS ================= -->
4460 <sect1 id="sec-assertions">
4462 <indexterm><primary>Assertions</primary></indexterm>
4466 If you want to make use of assertions in your standard Haskell code, you
4467 could define a function like the following:
4473 assert :: Bool -> a -> a
4474 assert False x = error "assertion failed!"
4481 which works, but gives you back a less than useful error message --
4482 an assertion failed, but which and where?
4486 One way out is to define an extended <function>assert</function> function which also
4487 takes a descriptive string to include in the error message and
4488 perhaps combine this with the use of a pre-processor which inserts
4489 the source location where <function>assert</function> was used.
4493 Ghc offers a helping hand here, doing all of this for you. For every
4494 use of <function>assert</function> in the user's source:
4500 kelvinToC :: Double -> Double
4501 kelvinToC k = assert (k >= 0.0) (k+273.15)
4507 Ghc will rewrite this to also include the source location where the
4514 assert pred val ==> assertError "Main.hs|15" pred val
4520 The rewrite is only performed by the compiler when it spots
4521 applications of <function>Control.Exception.assert</function>, so you
4522 can still define and use your own versions of
4523 <function>assert</function>, should you so wish. If not, import
4524 <literal>Control.Exception</literal> to make use
4525 <function>assert</function> in your code.
4529 GHC ignores assertions when optimisation is turned on with the
4530 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4531 <literal>assert pred e</literal> will be rewritten to
4532 <literal>e</literal>. You can also disable assertions using the
4533 <option>-fignore-asserts</option>
4534 option<indexterm><primary><option>-fignore-asserts</option></primary>
4535 </indexterm>.</para>
4538 Assertion failures can be caught, see the documentation for the
4539 <literal>Control.Exception</literal> library for the details.
4545 <!-- =============================== PRAGMAS =========================== -->
4547 <sect1 id="pragmas">
4548 <title>Pragmas</title>
4550 <indexterm><primary>pragma</primary></indexterm>
4552 <para>GHC supports several pragmas, or instructions to the
4553 compiler placed in the source code. Pragmas don't normally affect
4554 the meaning of the program, but they might affect the efficiency
4555 of the generated code.</para>
4557 <para>Pragmas all take the form
4559 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4561 where <replaceable>word</replaceable> indicates the type of
4562 pragma, and is followed optionally by information specific to that
4563 type of pragma. Case is ignored in
4564 <replaceable>word</replaceable>. The various values for
4565 <replaceable>word</replaceable> that GHC understands are described
4566 in the following sections; any pragma encountered with an
4567 unrecognised <replaceable>word</replaceable> is (silently)
4570 <sect2 id="deprecated-pragma">
4571 <title>DEPRECATED pragma</title>
4572 <indexterm><primary>DEPRECATED</primary>
4575 <para>The DEPRECATED pragma lets you specify that a particular
4576 function, class, or type, is deprecated. There are two
4581 <para>You can deprecate an entire module thus:</para>
4583 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4586 <para>When you compile any module that import
4587 <literal>Wibble</literal>, GHC will print the specified
4592 <para>You can deprecate a function, class, type, or data constructor, with the
4593 following top-level declaration:</para>
4595 {-# DEPRECATED f, C, T "Don't use these" #-}
4597 <para>When you compile any module that imports and uses any
4598 of the specified entities, GHC will print the specified
4600 <para> You can only depecate entities declared at top level in the module
4601 being compiled, and you can only use unqualified names in the list of
4602 entities being deprecated. A capitalised name, such as <literal>T</literal>
4603 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4604 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4605 both are in scope. If both are in scope, there is currently no way to deprecate
4606 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4609 Any use of the deprecated item, or of anything from a deprecated
4610 module, will be flagged with an appropriate message. However,
4611 deprecations are not reported for
4612 (a) uses of a deprecated function within its defining module, and
4613 (b) uses of a deprecated function in an export list.
4614 The latter reduces spurious complaints within a library
4615 in which one module gathers together and re-exports
4616 the exports of several others.
4618 <para>You can suppress the warnings with the flag
4619 <option>-fno-warn-deprecations</option>.</para>
4622 <sect2 id="include-pragma">
4623 <title>INCLUDE pragma</title>
4625 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4626 of C header files that should be <literal>#include</literal>'d into
4627 the C source code generated by the compiler for the current module (if
4628 compiling via C). For example:</para>
4631 {-# INCLUDE "foo.h" #-}
4632 {-# INCLUDE <stdio.h> #-}</programlisting>
4634 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4635 your source file with any <literal>OPTIONS_GHC</literal>
4638 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4639 to the <option>-#include</option> option (<xref
4640 linkend="options-C-compiler" />), because the
4641 <literal>INCLUDE</literal> pragma is understood by other
4642 compilers. Yet another alternative is to add the include file to each
4643 <literal>foreign import</literal> declaration in your code, but we
4644 don't recommend using this approach with GHC.</para>
4647 <sect2 id="inline-noinline-pragma">
4648 <title>INLINE and NOINLINE pragmas</title>
4650 <para>These pragmas control the inlining of function
4653 <sect3 id="inline-pragma">
4654 <title>INLINE pragma</title>
4655 <indexterm><primary>INLINE</primary></indexterm>
4657 <para>GHC (with <option>-O</option>, as always) tries to
4658 inline (or “unfold”) functions/values that are
4659 “small enough,” thus avoiding the call overhead
4660 and possibly exposing other more-wonderful optimisations.
4661 Normally, if GHC decides a function is “too
4662 expensive” to inline, it will not do so, nor will it
4663 export that unfolding for other modules to use.</para>
4665 <para>The sledgehammer you can bring to bear is the
4666 <literal>INLINE</literal><indexterm><primary>INLINE
4667 pragma</primary></indexterm> pragma, used thusly:</para>
4670 key_function :: Int -> String -> (Bool, Double)
4672 #ifdef __GLASGOW_HASKELL__
4673 {-# INLINE key_function #-}
4677 <para>(You don't need to do the C pre-processor carry-on
4678 unless you're going to stick the code through HBC—it
4679 doesn't like <literal>INLINE</literal> pragmas.)</para>
4681 <para>The major effect of an <literal>INLINE</literal> pragma
4682 is to declare a function's “cost” to be very low.
4683 The normal unfolding machinery will then be very keen to
4686 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4687 function can be put anywhere its type signature could be
4690 <para><literal>INLINE</literal> pragmas are a particularly
4692 <literal>then</literal>/<literal>return</literal> (or
4693 <literal>bind</literal>/<literal>unit</literal>) functions in
4694 a monad. For example, in GHC's own
4695 <literal>UniqueSupply</literal> monad code, we have:</para>
4698 #ifdef __GLASGOW_HASKELL__
4699 {-# INLINE thenUs #-}
4700 {-# INLINE returnUs #-}
4704 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4705 linkend="noinline-pragma"/>).</para>
4708 <sect3 id="noinline-pragma">
4709 <title>NOINLINE pragma</title>
4711 <indexterm><primary>NOINLINE</primary></indexterm>
4712 <indexterm><primary>NOTINLINE</primary></indexterm>
4714 <para>The <literal>NOINLINE</literal> pragma does exactly what
4715 you'd expect: it stops the named function from being inlined
4716 by the compiler. You shouldn't ever need to do this, unless
4717 you're very cautious about code size.</para>
4719 <para><literal>NOTINLINE</literal> is a synonym for
4720 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4721 specified by Haskell 98 as the standard way to disable
4722 inlining, so it should be used if you want your code to be
4726 <sect3 id="phase-control">
4727 <title>Phase control</title>
4729 <para> Sometimes you want to control exactly when in GHC's
4730 pipeline the INLINE pragma is switched on. Inlining happens
4731 only during runs of the <emphasis>simplifier</emphasis>. Each
4732 run of the simplifier has a different <emphasis>phase
4733 number</emphasis>; the phase number decreases towards zero.
4734 If you use <option>-dverbose-core2core</option> you'll see the
4735 sequence of phase numbers for successive runs of the
4736 simplifier. In an INLINE pragma you can optionally specify a
4737 phase number, thus:</para>
4741 <para>You can say "inline <literal>f</literal> in Phase 2
4742 and all subsequent phases":
4744 {-# INLINE [2] f #-}
4750 <para>You can say "inline <literal>g</literal> in all
4751 phases up to, but not including, Phase 3":
4753 {-# INLINE [~3] g #-}
4759 <para>If you omit the phase indicator, you mean "inline in
4764 <para>You can use a phase number on a NOINLINE pragma too:</para>
4768 <para>You can say "do not inline <literal>f</literal>
4769 until Phase 2; in Phase 2 and subsequently behave as if
4770 there was no pragma at all":
4772 {-# NOINLINE [2] f #-}
4778 <para>You can say "do not inline <literal>g</literal> in
4779 Phase 3 or any subsequent phase; before that, behave as if
4780 there was no pragma":
4782 {-# NOINLINE [~3] g #-}
4788 <para>If you omit the phase indicator, you mean "never
4789 inline this function".</para>
4793 <para>The same phase-numbering control is available for RULES
4794 (<xref linkend="rewrite-rules"/>).</para>
4798 <sect2 id="language-pragma">
4799 <title>LANGUAGE pragma</title>
4801 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
4802 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
4804 <para>This allows language extensions to be enabled in a portable way.
4805 It is the intention that all Haskell compilers support the
4806 <literal>LANGUAGE</literal> pragma with the same syntax, although not
4807 all extensions are supported by all compilers, of
4808 course. The <literal>LANGUAGE</literal> pragma should be used instead
4809 of <literal>OPTIONS_GHC</literal>, if possible.</para>
4811 <para>For example, to enable the FFI and preprocessing with CPP:</para>
4813 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
4815 <para>Any extension from the <literal>Extension</literal> type defined in
4817 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink> may be used. GHC will report an error if any of the requested extensions are not supported.</para>
4821 <sect2 id="line-pragma">
4822 <title>LINE pragma</title>
4824 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4825 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4826 <para>This pragma is similar to C's <literal>#line</literal>
4827 pragma, and is mainly for use in automatically generated Haskell
4828 code. It lets you specify the line number and filename of the
4829 original code; for example</para>
4831 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
4833 <para>if you'd generated the current file from something called
4834 <filename>Foo.vhs</filename> and this line corresponds to line
4835 42 in the original. GHC will adjust its error messages to refer
4836 to the line/file named in the <literal>LINE</literal>
4840 <sect2 id="options-pragma">
4841 <title>OPTIONS_GHC pragma</title>
4842 <indexterm><primary>OPTIONS_GHC</primary>
4844 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4847 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4848 additional options that are given to the compiler when compiling
4849 this source file. See <xref linkend="source-file-options"/> for
4852 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4853 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4857 <title>RULES pragma</title>
4859 <para>The RULES pragma lets you specify rewrite rules. It is
4860 described in <xref linkend="rewrite-rules"/>.</para>
4863 <sect2 id="specialize-pragma">
4864 <title>SPECIALIZE pragma</title>
4866 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4867 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4868 <indexterm><primary>overloading, death to</primary></indexterm>
4870 <para>(UK spelling also accepted.) For key overloaded
4871 functions, you can create extra versions (NB: more code space)
4872 specialised to particular types. Thus, if you have an
4873 overloaded function:</para>
4876 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4879 <para>If it is heavily used on lists with
4880 <literal>Widget</literal> keys, you could specialise it as
4884 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4887 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4888 be put anywhere its type signature could be put.</para>
4890 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4891 (a) a specialised version of the function and (b) a rewrite rule
4892 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4893 un-specialised function into a call to the specialised one.</para>
4895 <para>The type in a SPECIALIZE pragma can be any type that is less
4896 polymorphic than the type of the original function. In concrete terms,
4897 if the original function is <literal>f</literal> then the pragma
4899 {-# SPECIALIZE f :: <type> #-}
4901 is valid if and only if the defintion
4903 f_spec :: <type>
4906 is valid. Here are some examples (where we only give the type signature
4907 for the original function, not its code):
4909 f :: Eq a => a -> b -> b
4910 {-# SPECIALISE f :: Int -> b -> b #-}
4912 g :: (Eq a, Ix b) => a -> b -> b
4913 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
4915 h :: Eq a => a -> a -> a
4916 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
4918 The last of these examples will generate a
4919 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
4920 well. If you use this kind of specialisation, let us know how well it works.
4923 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
4924 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
4925 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
4926 The <literal>INLINE</literal> pragma affects the specialised verison of the
4927 function (only), and applies even if the function is recursive. The motivating
4930 -- A GADT for arrays with type-indexed representation
4932 ArrInt :: !Int -> ByteArray# -> Arr Int
4933 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
4935 (!:) :: Arr e -> Int -> e
4936 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
4937 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
4938 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
4939 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
4941 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
4942 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
4943 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
4944 the specialised function will be inlined. It has two calls to
4945 <literal>(!:)</literal>,
4946 both at type <literal>Int</literal>. Both these calls fire the first
4947 specialisation, whose body is also inlined. The result is a type-based
4948 unrolling of the indexing function.</para>
4949 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
4950 on an ordinarily-recursive function.</para>
4952 <para>Note: In earlier versions of GHC, it was possible to provide your own
4953 specialised function for a given type:
4956 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4959 This feature has been removed, as it is now subsumed by the
4960 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4964 <sect2 id="specialize-instance-pragma">
4965 <title>SPECIALIZE instance pragma
4969 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4970 <indexterm><primary>overloading, death to</primary></indexterm>
4971 Same idea, except for instance declarations. For example:
4974 instance (Eq a) => Eq (Foo a) where {
4975 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4979 The pragma must occur inside the <literal>where</literal> part
4980 of the instance declaration.
4983 Compatible with HBC, by the way, except perhaps in the placement
4989 <sect2 id="unpack-pragma">
4990 <title>UNPACK pragma</title>
4992 <indexterm><primary>UNPACK</primary></indexterm>
4994 <para>The <literal>UNPACK</literal> indicates to the compiler
4995 that it should unpack the contents of a constructor field into
4996 the constructor itself, removing a level of indirection. For
5000 data T = T {-# UNPACK #-} !Float
5001 {-# UNPACK #-} !Float
5004 <para>will create a constructor <literal>T</literal> containing
5005 two unboxed floats. This may not always be an optimisation: if
5006 the <function>T</function> constructor is scrutinised and the
5007 floats passed to a non-strict function for example, they will
5008 have to be reboxed (this is done automatically by the
5011 <para>Unpacking constructor fields should only be used in
5012 conjunction with <option>-O</option>, in order to expose
5013 unfoldings to the compiler so the reboxing can be removed as
5014 often as possible. For example:</para>
5018 f (T f1 f2) = f1 + f2
5021 <para>The compiler will avoid reboxing <function>f1</function>
5022 and <function>f2</function> by inlining <function>+</function>
5023 on floats, but only when <option>-O</option> is on.</para>
5025 <para>Any single-constructor data is eligible for unpacking; for
5029 data T = T {-# UNPACK #-} !(Int,Int)
5032 <para>will store the two <literal>Int</literal>s directly in the
5033 <function>T</function> constructor, by flattening the pair.
5034 Multi-level unpacking is also supported:</para>
5037 data T = T {-# UNPACK #-} !S
5038 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5041 <para>will store two unboxed <literal>Int#</literal>s
5042 directly in the <function>T</function> constructor. The
5043 unpacker can see through newtypes, too.</para>
5045 <para>If a field cannot be unpacked, you will not get a warning,
5046 so it might be an idea to check the generated code with
5047 <option>-ddump-simpl</option>.</para>
5049 <para>See also the <option>-funbox-strict-fields</option> flag,
5050 which essentially has the effect of adding
5051 <literal>{-# UNPACK #-}</literal> to every strict
5052 constructor field.</para>
5057 <!-- ======================= REWRITE RULES ======================== -->
5059 <sect1 id="rewrite-rules">
5060 <title>Rewrite rules
5062 <indexterm><primary>RULES pragma</primary></indexterm>
5063 <indexterm><primary>pragma, RULES</primary></indexterm>
5064 <indexterm><primary>rewrite rules</primary></indexterm></title>
5067 The programmer can specify rewrite rules as part of the source program
5068 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5069 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5070 and (b) the <option>-frules-off</option> flag
5071 (<xref linkend="options-f"/>) is not specified.
5079 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5086 <title>Syntax</title>
5089 From a syntactic point of view:
5095 There may be zero or more rules in a <literal>RULES</literal> pragma.
5102 Each rule has a name, enclosed in double quotes. The name itself has
5103 no significance at all. It is only used when reporting how many times the rule fired.
5109 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5110 immediately after the name of the rule. Thus:
5113 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5116 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5117 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5126 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5127 is set, so you must lay out your rules starting in the same column as the
5128 enclosing definitions.
5135 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5136 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5137 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5138 by spaces, just like in a type <literal>forall</literal>.
5144 A pattern variable may optionally have a type signature.
5145 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5146 For example, here is the <literal>foldr/build</literal> rule:
5149 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5150 foldr k z (build g) = g k z
5153 Since <function>g</function> has a polymorphic type, it must have a type signature.
5160 The left hand side of a rule must consist of a top-level variable applied
5161 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5164 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5165 "wrong2" forall f. f True = True
5168 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5175 A rule does not need to be in the same module as (any of) the
5176 variables it mentions, though of course they need to be in scope.
5182 Rules are automatically exported from a module, just as instance declarations are.
5193 <title>Semantics</title>
5196 From a semantic point of view:
5202 Rules are only applied if you use the <option>-O</option> flag.
5208 Rules are regarded as left-to-right rewrite rules.
5209 When GHC finds an expression that is a substitution instance of the LHS
5210 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5211 By "a substitution instance" we mean that the LHS can be made equal to the
5212 expression by substituting for the pattern variables.
5219 The LHS and RHS of a rule are typechecked, and must have the
5227 GHC makes absolutely no attempt to verify that the LHS and RHS
5228 of a rule have the same meaning. That is undecidable in general, and
5229 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5236 GHC makes no attempt to make sure that the rules are confluent or
5237 terminating. For example:
5240 "loop" forall x,y. f x y = f y x
5243 This rule will cause the compiler to go into an infinite loop.
5250 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5256 GHC currently uses a very simple, syntactic, matching algorithm
5257 for matching a rule LHS with an expression. It seeks a substitution
5258 which makes the LHS and expression syntactically equal modulo alpha
5259 conversion. The pattern (rule), but not the expression, is eta-expanded if
5260 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5261 But not beta conversion (that's called higher-order matching).
5265 Matching is carried out on GHC's intermediate language, which includes
5266 type abstractions and applications. So a rule only matches if the
5267 types match too. See <xref linkend="rule-spec"/> below.
5273 GHC keeps trying to apply the rules as it optimises the program.
5274 For example, consider:
5283 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5284 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5285 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5286 not be substituted, and the rule would not fire.
5293 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5294 that appears on the LHS of a rule</emphasis>, because once you have substituted
5295 for something you can't match against it (given the simple minded
5296 matching). So if you write the rule
5299 "map/map" forall f,g. map f . map g = map (f.g)
5302 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5303 It will only match something written with explicit use of ".".
5304 Well, not quite. It <emphasis>will</emphasis> match the expression
5310 where <function>wibble</function> is defined:
5313 wibble f g = map f . map g
5316 because <function>wibble</function> will be inlined (it's small).
5318 Later on in compilation, GHC starts inlining even things on the
5319 LHS of rules, but still leaves the rules enabled. This inlining
5320 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5327 All rules are implicitly exported from the module, and are therefore
5328 in force in any module that imports the module that defined the rule, directly
5329 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5330 in force when compiling A.) The situation is very similar to that for instance
5342 <title>List fusion</title>
5345 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5346 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5347 intermediate list should be eliminated entirely.
5351 The following are good producers:
5363 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5369 Explicit lists (e.g. <literal>[True, False]</literal>)
5375 The cons constructor (e.g <literal>3:4:[]</literal>)
5381 <function>++</function>
5387 <function>map</function>
5393 <function>filter</function>
5399 <function>iterate</function>, <function>repeat</function>
5405 <function>zip</function>, <function>zipWith</function>
5414 The following are good consumers:
5426 <function>array</function> (on its second argument)
5432 <function>length</function>
5438 <function>++</function> (on its first argument)
5444 <function>foldr</function>
5450 <function>map</function>
5456 <function>filter</function>
5462 <function>concat</function>
5468 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5474 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5475 will fuse with one but not the other)
5481 <function>partition</function>
5487 <function>head</function>
5493 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5499 <function>sequence_</function>
5505 <function>msum</function>
5511 <function>sortBy</function>
5520 So, for example, the following should generate no intermediate lists:
5523 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5529 This list could readily be extended; if there are Prelude functions that you use
5530 a lot which are not included, please tell us.
5534 If you want to write your own good consumers or producers, look at the
5535 Prelude definitions of the above functions to see how to do so.
5540 <sect2 id="rule-spec">
5541 <title>Specialisation
5545 Rewrite rules can be used to get the same effect as a feature
5546 present in earlier versions of GHC.
5547 For example, suppose that:
5550 genericLookup :: Ord a => Table a b -> a -> b
5551 intLookup :: Table Int b -> Int -> b
5554 where <function>intLookup</function> is an implementation of
5555 <function>genericLookup</function> that works very fast for
5556 keys of type <literal>Int</literal>. You might wish
5557 to tell GHC to use <function>intLookup</function> instead of
5558 <function>genericLookup</function> whenever the latter was called with
5559 type <literal>Table Int b -> Int -> b</literal>.
5560 It used to be possible to write
5563 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5566 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5569 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5572 This slightly odd-looking rule instructs GHC to replace
5573 <function>genericLookup</function> by <function>intLookup</function>
5574 <emphasis>whenever the types match</emphasis>.
5575 What is more, this rule does not need to be in the same
5576 file as <function>genericLookup</function>, unlike the
5577 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5578 have an original definition available to specialise).
5581 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5582 <function>intLookup</function> really behaves as a specialised version
5583 of <function>genericLookup</function>!!!</para>
5585 <para>An example in which using <literal>RULES</literal> for
5586 specialisation will Win Big:
5589 toDouble :: Real a => a -> Double
5590 toDouble = fromRational . toRational
5592 {-# RULES "toDouble/Int" toDouble = i2d #-}
5593 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5596 The <function>i2d</function> function is virtually one machine
5597 instruction; the default conversion—via an intermediate
5598 <literal>Rational</literal>—is obscenely expensive by
5605 <title>Controlling what's going on</title>
5613 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5619 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5620 If you add <option>-dppr-debug</option> you get a more detailed listing.
5626 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5629 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5630 {-# INLINE build #-}
5634 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5635 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5636 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5637 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5644 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5645 see how to write rules that will do fusion and yet give an efficient
5646 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5656 <sect2 id="core-pragma">
5657 <title>CORE pragma</title>
5659 <indexterm><primary>CORE pragma</primary></indexterm>
5660 <indexterm><primary>pragma, CORE</primary></indexterm>
5661 <indexterm><primary>core, annotation</primary></indexterm>
5664 The external core format supports <quote>Note</quote> annotations;
5665 the <literal>CORE</literal> pragma gives a way to specify what these
5666 should be in your Haskell source code. Syntactically, core
5667 annotations are attached to expressions and take a Haskell string
5668 literal as an argument. The following function definition shows an
5672 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5675 Semantically, this is equivalent to:
5683 However, when external for is generated (via
5684 <option>-fext-core</option>), there will be Notes attached to the
5685 expressions <function>show</function> and <varname>x</varname>.
5686 The core function declaration for <function>f</function> is:
5690 f :: %forall a . GHCziShow.ZCTShow a ->
5691 a -> GHCziBase.ZMZN GHCziBase.Char =
5692 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5694 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5696 (tpl1::GHCziBase.Int ->
5698 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5700 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5701 (tpl3::GHCziBase.ZMZN a ->
5702 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5710 Here, we can see that the function <function>show</function> (which
5711 has been expanded out to a case expression over the Show dictionary)
5712 has a <literal>%note</literal> attached to it, as does the
5713 expression <varname>eta</varname> (which used to be called
5714 <varname>x</varname>).
5721 <sect1 id="generic-classes">
5722 <title>Generic classes</title>
5724 <para>(Note: support for generic classes is currently broken in
5728 The ideas behind this extension are described in detail in "Derivable type classes",
5729 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5730 An example will give the idea:
5738 fromBin :: [Int] -> (a, [Int])
5740 toBin {| Unit |} Unit = []
5741 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5742 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5743 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5745 fromBin {| Unit |} bs = (Unit, bs)
5746 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5747 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5748 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5749 (y,bs'') = fromBin bs'
5752 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5753 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5754 which are defined thus in the library module <literal>Generics</literal>:
5758 data a :+: b = Inl a | Inr b
5759 data a :*: b = a :*: b
5762 Now you can make a data type into an instance of Bin like this:
5764 instance (Bin a, Bin b) => Bin (a,b)
5765 instance Bin a => Bin [a]
5767 That is, just leave off the "where" clause. Of course, you can put in the
5768 where clause and over-ride whichever methods you please.
5772 <title> Using generics </title>
5773 <para>To use generics you need to</para>
5776 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5777 <option>-fgenerics</option> (to generate extra per-data-type code),
5778 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5782 <para>Import the module <literal>Generics</literal> from the
5783 <literal>lang</literal> package. This import brings into
5784 scope the data types <literal>Unit</literal>,
5785 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5786 don't need this import if you don't mention these types
5787 explicitly; for example, if you are simply giving instance
5788 declarations.)</para>
5793 <sect2> <title> Changes wrt the paper </title>
5795 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5796 can be written infix (indeed, you can now use
5797 any operator starting in a colon as an infix type constructor). Also note that
5798 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5799 Finally, note that the syntax of the type patterns in the class declaration
5800 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5801 alone would ambiguous when they appear on right hand sides (an extension we
5802 anticipate wanting).
5806 <sect2> <title>Terminology and restrictions</title>
5808 Terminology. A "generic default method" in a class declaration
5809 is one that is defined using type patterns as above.
5810 A "polymorphic default method" is a default method defined as in Haskell 98.
5811 A "generic class declaration" is a class declaration with at least one
5812 generic default method.
5820 Alas, we do not yet implement the stuff about constructor names and
5827 A generic class can have only one parameter; you can't have a generic
5828 multi-parameter class.
5834 A default method must be defined entirely using type patterns, or entirely
5835 without. So this is illegal:
5838 op :: a -> (a, Bool)
5839 op {| Unit |} Unit = (Unit, True)
5842 However it is perfectly OK for some methods of a generic class to have
5843 generic default methods and others to have polymorphic default methods.
5849 The type variable(s) in the type pattern for a generic method declaration
5850 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:
5854 op {| p :*: q |} (x :*: y) = op (x :: p)
5862 The type patterns in a generic default method must take one of the forms:
5868 where "a" and "b" are type variables. Furthermore, all the type patterns for
5869 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5870 must use the same type variables. So this is illegal:
5874 op {| a :+: b |} (Inl x) = True
5875 op {| p :+: q |} (Inr y) = False
5877 The type patterns must be identical, even in equations for different methods of the class.
5878 So this too is illegal:
5882 op1 {| a :*: b |} (x :*: y) = True
5885 op2 {| p :*: q |} (x :*: y) = False
5887 (The reason for this restriction is that we gather all the equations for a particular type consructor
5888 into a single generic instance declaration.)
5894 A generic method declaration must give a case for each of the three type constructors.
5900 The type for a generic method can be built only from:
5902 <listitem> <para> Function arrows </para> </listitem>
5903 <listitem> <para> Type variables </para> </listitem>
5904 <listitem> <para> Tuples </para> </listitem>
5905 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5907 Here are some example type signatures for generic methods:
5910 op2 :: Bool -> (a,Bool)
5911 op3 :: [Int] -> a -> a
5914 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5918 This restriction is an implementation restriction: we just havn't got around to
5919 implementing the necessary bidirectional maps over arbitrary type constructors.
5920 It would be relatively easy to add specific type constructors, such as Maybe and list,
5921 to the ones that are allowed.</para>
5926 In an instance declaration for a generic class, the idea is that the compiler
5927 will fill in the methods for you, based on the generic templates. However it can only
5932 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5937 No constructor of the instance type has unboxed fields.
5941 (Of course, these things can only arise if you are already using GHC extensions.)
5942 However, you can still give an instance declarations for types which break these rules,
5943 provided you give explicit code to override any generic default methods.
5951 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5952 what the compiler does with generic declarations.
5957 <sect2> <title> Another example </title>
5959 Just to finish with, here's another example I rather like:
5963 nCons {| Unit |} _ = 1
5964 nCons {| a :*: b |} _ = 1
5965 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5968 tag {| Unit |} _ = 1
5969 tag {| a :*: b |} _ = 1
5970 tag {| a :+: b |} (Inl x) = tag x
5971 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5980 ;;; Local Variables: ***
5982 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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