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 (implemented in <command>hbc</command>) 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>Restrictions</title>
1274 There are several restrictions on the ways in which existentially-quantified
1275 constructors can be use.
1284 When pattern matching, each pattern match introduces a new,
1285 distinct, type for each existential type variable. These types cannot
1286 be unified with any other type, nor can they escape from the scope of
1287 the pattern match. For example, these fragments are incorrect:
1295 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1296 is the result of <function>f1</function>. One way to see why this is wrong is to
1297 ask what type <function>f1</function> has:
1301 f1 :: Foo -> a -- Weird!
1305 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1310 f1 :: forall a. Foo -> a -- Wrong!
1314 The original program is just plain wrong. Here's another sort of error
1318 f2 (Baz1 a b) (Baz1 p q) = a==q
1322 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1323 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1324 from the two <function>Baz1</function> constructors.
1332 You can't pattern-match on an existentially quantified
1333 constructor in a <literal>let</literal> or <literal>where</literal> group of
1334 bindings. So this is illegal:
1338 f3 x = a==b where { Baz1 a b = x }
1341 Instead, use a <literal>case</literal> expression:
1344 f3 x = case x of Baz1 a b -> a==b
1347 In general, you can only pattern-match
1348 on an existentially-quantified constructor in a <literal>case</literal> expression or
1349 in the patterns of a function definition.
1351 The reason for this restriction is really an implementation one.
1352 Type-checking binding groups is already a nightmare without
1353 existentials complicating the picture. Also an existential pattern
1354 binding at the top level of a module doesn't make sense, because it's
1355 not clear how to prevent the existentially-quantified type "escaping".
1356 So for now, there's a simple-to-state restriction. We'll see how
1364 You can't use existential quantification for <literal>newtype</literal>
1365 declarations. So this is illegal:
1369 newtype T = forall a. Ord a => MkT a
1373 Reason: a value of type <literal>T</literal> must be represented as a
1374 pair of a dictionary for <literal>Ord t</literal> and a value of type
1375 <literal>t</literal>. That contradicts the idea that
1376 <literal>newtype</literal> should have no concrete representation.
1377 You can get just the same efficiency and effect by using
1378 <literal>data</literal> instead of <literal>newtype</literal>. If
1379 there is no overloading involved, then there is more of a case for
1380 allowing an existentially-quantified <literal>newtype</literal>,
1381 because the <literal>data</literal> version does carry an
1382 implementation cost, but single-field existentially quantified
1383 constructors aren't much use. So the simple restriction (no
1384 existential stuff on <literal>newtype</literal>) stands, unless there
1385 are convincing reasons to change it.
1393 You can't use <literal>deriving</literal> to define instances of a
1394 data type with existentially quantified data constructors.
1396 Reason: in most cases it would not make sense. For example:#
1399 data T = forall a. MkT [a] deriving( Eq )
1402 To derive <literal>Eq</literal> in the standard way we would need to have equality
1403 between the single component of two <function>MkT</function> constructors:
1407 (MkT a) == (MkT b) = ???
1410 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1411 It's just about possible to imagine examples in which the derived instance
1412 would make sense, but it seems altogether simpler simply to prohibit such
1413 declarations. Define your own instances!
1428 <sect2 id="multi-param-type-classes">
1429 <title>Class declarations</title>
1432 This section, and the next one, documents GHC's type-class extensions.
1433 There's lots of background in the paper <ulink
1434 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1435 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1436 Jones, Erik Meijer).
1439 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1443 <title>Multi-parameter type classes</title>
1445 Multi-parameter type classes are permitted. For example:
1449 class Collection c a where
1450 union :: c a -> c a -> c a
1458 <title>The superclasses of a class declaration</title>
1461 There are no restrictions on the context in a class declaration
1462 (which introduces superclasses), except that the class hierarchy must
1463 be acyclic. So these class declarations are OK:
1467 class Functor (m k) => FiniteMap m k where
1470 class (Monad m, Monad (t m)) => Transform t m where
1471 lift :: m a -> (t m) a
1477 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1478 of "acyclic" involves only the superclass relationships. For example,
1484 op :: D b => a -> b -> b
1487 class C a => D a where { ... }
1491 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1492 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1493 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1500 <sect3 id="class-method-types">
1501 <title>Class method types</title>
1504 Haskell 98 prohibits class method types to mention constraints on the
1505 class type variable, thus:
1508 fromList :: [a] -> s a
1509 elem :: Eq a => a -> s a -> Bool
1511 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1512 contains the constraint <literal>Eq a</literal>, constrains only the
1513 class type variable (in this case <literal>a</literal>).
1514 GHC lifts this restriction.
1521 <sect3 id="functional-dependencies">
1522 <title>Functional dependencies
1525 <para> Functional dependencies are implemented as described by Mark Jones
1526 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1527 In Proceedings of the 9th European Symposium on Programming,
1528 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1532 Functional dependencies are introduced by a vertical bar in the syntax of a
1533 class declaration; e.g.
1535 class (Monad m) => MonadState s m | m -> s where ...
1537 class Foo a b c | a b -> c where ...
1539 There should be more documentation, but there isn't (yet). Yell if you need it.
1542 In a class declaration, all of the class type variables must be reachable (in the sense
1543 mentioned in <xref linkend="type-restrictions"/>)
1544 from the free variables of each method type.
1548 class Coll s a where
1550 insert :: s -> a -> s
1553 is not OK, because the type of <literal>empty</literal> doesn't mention
1554 <literal>a</literal>. Functional dependencies can make the type variable
1557 class Coll s a | s -> a where
1559 insert :: s -> a -> s
1562 Alternatively <literal>Coll</literal> might be rewritten
1565 class Coll s a where
1567 insert :: s a -> a -> s a
1571 which makes the connection between the type of a collection of
1572 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1573 Occasionally this really doesn't work, in which case you can split the
1581 class CollE s => Coll s a where
1582 insert :: s -> a -> s
1593 <sect2 id="instance-decls">
1594 <title>Instance declarations</title>
1596 <sect3 id="instance-heads">
1597 <title>Instance heads</title>
1600 The <emphasis>head</emphasis> of an instance declaration is the part to the
1601 right of the "<literal>=></literal>". In Haskell 98 the head of an instance
1603 must be of the form <literal>C (T a1 ... an)</literal>, where
1604 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1605 and the <literal>a1 ... an</literal> are distinct type variables.
1608 The <option>-fglasgow-exts</option> flag lifts this restriction and allows the
1609 instance head to be of form <literal>C t1 ... tn</literal> where <literal>t1
1610 ... tn</literal> are arbitrary types (provided, of course, everything is
1611 well-kinded). In particular, types <literal>ti</literal> can be type variables
1612 or structured types, and can contain repeated occurrences of a single type
1616 instance Eq (T a a) where ...
1617 -- Repeated type variable
1619 instance Eq (S [a]) where ...
1622 instance C Int [a] where ...
1623 -- Multiple parameters
1628 <sect3 id="instance-overlap">
1629 <title>Overlapping instances</title>
1631 In general, <emphasis>GHC requires that that it be unambiguous which instance
1633 should be used to resolve a type-class constraint</emphasis>. This behaviour
1634 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1635 <indexterm><primary>-fallow-overlapping-instances
1636 </primary></indexterm>
1637 and <option>-fallow-incoherent-instances</option>
1638 <indexterm><primary>-fallow-incoherent-instances
1639 </primary></indexterm>, as this section discusses.</para>
1641 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1642 it tries to match every instance declaration against the
1644 by instantiating the head of the instance declaration. For example, consider
1647 instance context1 => C Int a where ... -- (A)
1648 instance context2 => C a Bool where ... -- (B)
1649 instance context3 => C Int [a] where ... -- (C)
1650 instance context4 => C Int [Int] where ... -- (D)
1652 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
1653 but (C) and (D) do not. When matching, GHC takes
1654 no account of the context of the instance declaration
1655 (<literal>context1</literal> etc).
1656 GHC's default behaviour is that <emphasis>exactly one instance must match the
1657 constraint it is trying to resolve</emphasis>.
1658 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1659 including both declarations (A) and (B), say); an error is only reported if a
1660 particular constraint matches more than one.
1664 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1665 more than one instance to match, provided there is a most specific one. For
1666 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1667 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1668 most-specific match, the program is rejected.
1671 However, GHC is conservative about committing to an overlapping instance. For example:
1676 Suppose that from the RHS of <literal>f</literal> we get the constraint
1677 <literal>C Int [b]</literal>. But
1678 GHC does not commit to instance (C), because in a particular
1679 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1680 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1681 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1682 GHC will instead pick (C), without complaining about
1683 the problem of subsequent instantiations.
1686 The willingness to be overlapped or incoherent is a property of
1687 the <emphasis>instance declaration</emphasis> itself, controlled by the
1688 presence or otherwise of the <option>-fallow-overlapping-instances</option>
1689 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
1690 being defined. Neither flag is required in a module that imports and uses the
1691 instance declaration. Specifically, during the lookup process:
1694 An instance declaration is ignored during the lookup process if (a) a more specific
1695 match is found, and (b) the instance declaration was compiled with
1696 <option>-fallow-overlapping-instances</option>. The flag setting for the
1697 more-specific instance does not matter.
1700 Suppose an instance declaration does not matche the constraint being looked up, but
1701 does unify with it, so that it might match when the constraint is further
1702 instantiated. Usually GHC will regard this as a reason for not committing to
1703 some other constraint. But if the instance declaration was compiled with
1704 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
1705 check for that declaration.
1708 All this makes it possible for a library author to design a library that relies on
1709 overlapping instances without the library client having to know.
1711 <para>The <option>-fallow-incoherent-instances</option> flag implies the
1712 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
1717 <title>Type synonyms in the instance head</title>
1720 <emphasis>Unlike Haskell 98, instance heads may use type
1721 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1722 As always, using a type synonym is just shorthand for
1723 writing the RHS of the type synonym definition. For example:
1727 type Point = (Int,Int)
1728 instance C Point where ...
1729 instance C [Point] where ...
1733 is legal. However, if you added
1737 instance C (Int,Int) where ...
1741 as well, then the compiler will complain about the overlapping
1742 (actually, identical) instance declarations. As always, type synonyms
1743 must be fully applied. You cannot, for example, write:
1748 instance Monad P where ...
1752 This design decision is independent of all the others, and easily
1753 reversed, but it makes sense to me.
1758 <sect3 id="undecidable-instances">
1759 <title>Undecidable instances</title>
1761 <para>An instance declaration must normally obey the following rules:
1763 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1764 an instance declaration <emphasis>must not</emphasis> be a type variable.
1765 For example, these are OK:
1768 instance C Int a where ...
1770 instance D (Int, Int) where ...
1772 instance E [[a]] where ...
1776 instance F a where ...
1778 Note that instance heads may contain repeated type variables (<xref linkend="instance-heads"/>).
1779 For example, this is OK:
1781 instance Stateful (ST s) (MutVar s) where ...
1788 <para>All of the types in the <emphasis>context</emphasis> of
1789 an instance declaration <emphasis>must</emphasis> be type variables.
1792 instance C a b => Eq (a,b) where ...
1796 instance C Int b => Foo b where ...
1802 These restrictions ensure that
1803 context reduction terminates: each reduction step removes one type
1804 constructor. For example, the following would make the type checker
1805 loop if it wasn't excluded:
1807 instance C a => C a where ...
1809 There are two situations in which the rule is a bit of a pain. First,
1810 if one allows overlapping instance declarations then it's quite
1811 convenient to have a "default instance" declaration that applies if
1812 something more specific does not:
1821 Second, sometimes you might want to use the following to get the
1822 effect of a "class synonym":
1826 class (C1 a, C2 a, C3 a) => C a where { }
1828 instance (C1 a, C2 a, C3 a) => C a where { }
1832 This allows you to write shorter signatures:
1844 f :: (C1 a, C2 a, C3 a) => ...
1848 Voluminous correspondence on the Haskell mailing list has convinced me
1849 that it's worth experimenting with more liberal rules. If you use
1850 the experimental flag <option>-fallow-undecidable-instances</option>
1851 <indexterm><primary>-fallow-undecidable-instances
1852 option</primary></indexterm>, you can use arbitrary
1853 types in both an instance context and instance head. Termination is ensured by having a
1854 fixed-depth recursion stack. If you exceed the stack depth you get a
1855 sort of backtrace, and the opportunity to increase the stack depth
1856 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1859 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1860 allowing these idioms interesting idioms.
1867 <sect2 id="type-restrictions">
1868 <title>Type signatures</title>
1870 <sect3><title>The context of a type signature</title>
1872 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1873 the form <emphasis>(class type-variable)</emphasis> or
1874 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1875 these type signatures are perfectly OK
1878 g :: Ord (T a ()) => ...
1882 GHC imposes the following restrictions on the constraints in a type signature.
1886 forall tv1..tvn (c1, ...,cn) => type
1889 (Here, we write the "foralls" explicitly, although the Haskell source
1890 language omits them; in Haskell 98, all the free type variables of an
1891 explicit source-language type signature are universally quantified,
1892 except for the class type variables in a class declaration. However,
1893 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1902 <emphasis>Each universally quantified type variable
1903 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1905 A type variable <literal>a</literal> is "reachable" if it it appears
1906 in the same constraint as either a type variable free in in
1907 <literal>type</literal>, or another reachable type variable.
1908 A value with a type that does not obey
1909 this reachability restriction cannot be used without introducing
1910 ambiguity; that is why the type is rejected.
1911 Here, for example, is an illegal type:
1915 forall a. Eq a => Int
1919 When a value with this type was used, the constraint <literal>Eq tv</literal>
1920 would be introduced where <literal>tv</literal> is a fresh type variable, and
1921 (in the dictionary-translation implementation) the value would be
1922 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1923 can never know which instance of <literal>Eq</literal> to use because we never
1924 get any more information about <literal>tv</literal>.
1928 that the reachability condition is weaker than saying that <literal>a</literal> is
1929 functionally dependent on a type variable free in
1930 <literal>type</literal> (see <xref
1931 linkend="functional-dependencies"/>). The reason for this is there
1932 might be a "hidden" dependency, in a superclass perhaps. So
1933 "reachable" is a conservative approximation to "functionally dependent".
1934 For example, consider:
1936 class C a b | a -> b where ...
1937 class C a b => D a b where ...
1938 f :: forall a b. D a b => a -> a
1940 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1941 but that is not immediately apparent from <literal>f</literal>'s type.
1947 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1948 universally quantified type variables <literal>tvi</literal></emphasis>.
1950 For example, this type is OK because <literal>C a b</literal> mentions the
1951 universally quantified type variable <literal>b</literal>:
1955 forall a. C a b => burble
1959 The next type is illegal because the constraint <literal>Eq b</literal> does not
1960 mention <literal>a</literal>:
1964 forall a. Eq b => burble
1968 The reason for this restriction is milder than the other one. The
1969 excluded types are never useful or necessary (because the offending
1970 context doesn't need to be witnessed at this point; it can be floated
1971 out). Furthermore, floating them out increases sharing. Lastly,
1972 excluding them is a conservative choice; it leaves a patch of
1973 territory free in case we need it later.
1984 <title>For-all hoisting</title>
1986 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1987 end of an arrow, thus:
1989 type Discard a = forall b. a -> b -> a
1991 g :: Int -> Discard Int
1994 Simply expanding the type synonym would give
1996 g :: Int -> (forall b. Int -> b -> Int)
1998 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2000 g :: forall b. Int -> Int -> b -> Int
2002 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2003 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2004 performs the transformation:</emphasis>
2006 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2008 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2010 (In fact, GHC tries to retain as much synonym information as possible for use in
2011 error messages, but that is a usability issue.) This rule applies, of course, whether
2012 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2013 valid way to write <literal>g</literal>'s type signature:
2015 g :: Int -> Int -> forall b. b -> Int
2019 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2022 type Foo a = (?x::Int) => Bool -> a
2027 g :: (?x::Int) => Bool -> Bool -> Int
2035 <sect2 id="implicit-parameters">
2036 <title>Implicit parameters</title>
2038 <para> Implicit parameters are implemented as described in
2039 "Implicit parameters: dynamic scoping with static types",
2040 J Lewis, MB Shields, E Meijer, J Launchbury,
2041 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2045 <para>(Most of the following, stil rather incomplete, documentation is
2046 due to Jeff Lewis.)</para>
2048 <para>Implicit parameter support is enabled with the option
2049 <option>-fimplicit-params</option>.</para>
2052 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2053 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2054 context. In Haskell, all variables are statically bound. Dynamic
2055 binding of variables is a notion that goes back to Lisp, but was later
2056 discarded in more modern incarnations, such as Scheme. Dynamic binding
2057 can be very confusing in an untyped language, and unfortunately, typed
2058 languages, in particular Hindley-Milner typed languages like Haskell,
2059 only support static scoping of variables.
2062 However, by a simple extension to the type class system of Haskell, we
2063 can support dynamic binding. Basically, we express the use of a
2064 dynamically bound variable as a constraint on the type. These
2065 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2066 function uses a dynamically-bound variable <literal>?x</literal>
2067 of type <literal>t'</literal>". For
2068 example, the following expresses the type of a sort function,
2069 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2071 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2073 The dynamic binding constraints are just a new form of predicate in the type class system.
2076 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2077 where <literal>x</literal> is
2078 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2079 Use of this construct also introduces a new
2080 dynamic-binding constraint in the type of the expression.
2081 For example, the following definition
2082 shows how we can define an implicitly parameterized sort function in
2083 terms of an explicitly parameterized <literal>sortBy</literal> function:
2085 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2087 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2093 <title>Implicit-parameter type constraints</title>
2095 Dynamic binding constraints behave just like other type class
2096 constraints in that they are automatically propagated. Thus, when a
2097 function is used, its implicit parameters are inherited by the
2098 function that called it. For example, our <literal>sort</literal> function might be used
2099 to pick out the least value in a list:
2101 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2102 least xs = fst (sort xs)
2104 Without lifting a finger, the <literal>?cmp</literal> parameter is
2105 propagated to become a parameter of <literal>least</literal> as well. With explicit
2106 parameters, the default is that parameters must always be explicit
2107 propagated. With implicit parameters, the default is to always
2111 An implicit-parameter type constraint differs from other type class constraints in the
2112 following way: All uses of a particular implicit parameter must have
2113 the same type. This means that the type of <literal>(?x, ?x)</literal>
2114 is <literal>(?x::a) => (a,a)</literal>, and not
2115 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2119 <para> You can't have an implicit parameter in the context of a class or instance
2120 declaration. For example, both these declarations are illegal:
2122 class (?x::Int) => C a where ...
2123 instance (?x::a) => Foo [a] where ...
2125 Reason: exactly which implicit parameter you pick up depends on exactly where
2126 you invoke a function. But the ``invocation'' of instance declarations is done
2127 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2128 Easiest thing is to outlaw the offending types.</para>
2130 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2132 f :: (?x :: [a]) => Int -> Int
2135 g :: (Read a, Show a) => String -> String
2138 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2139 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2140 quite unambiguous, and fixes the type <literal>a</literal>.
2145 <title>Implicit-parameter bindings</title>
2148 An implicit parameter is <emphasis>bound</emphasis> using the standard
2149 <literal>let</literal> or <literal>where</literal> binding forms.
2150 For example, we define the <literal>min</literal> function by binding
2151 <literal>cmp</literal>.
2154 min = let ?cmp = (<=) in least
2158 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2159 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2160 (including in a list comprehension, or do-notation, or pattern guards),
2161 or a <literal>where</literal> clause.
2162 Note the following points:
2165 An implicit-parameter binding group must be a
2166 collection of simple bindings to implicit-style variables (no
2167 function-style bindings, and no type signatures); these bindings are
2168 neither polymorphic or recursive.
2171 You may not mix implicit-parameter bindings with ordinary bindings in a
2172 single <literal>let</literal>
2173 expression; use two nested <literal>let</literal>s instead.
2174 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2178 You may put multiple implicit-parameter bindings in a
2179 single binding group; but they are <emphasis>not</emphasis> treated
2180 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2181 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2182 parameter. The bindings are not nested, and may be re-ordered without changing
2183 the meaning of the program.
2184 For example, consider:
2186 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2188 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2189 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2191 f :: (?x::Int) => Int -> Int
2199 <sect3><title>Implicit parameters and polymorphic recursion</title>
2202 Consider these two definitions:
2205 len1 xs = let ?acc = 0 in len_acc1 xs
2208 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2213 len2 xs = let ?acc = 0 in len_acc2 xs
2215 len_acc2 :: (?acc :: Int) => [a] -> Int
2217 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2219 The only difference between the two groups is that in the second group
2220 <literal>len_acc</literal> is given a type signature.
2221 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2222 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2223 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2224 has a type signature, the recursive call is made to the
2225 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2226 as an implicit parameter. So we get the following results in GHCi:
2233 Adding a type signature dramatically changes the result! This is a rather
2234 counter-intuitive phenomenon, worth watching out for.
2238 <sect3><title>Implicit parameters and monomorphism</title>
2240 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2241 Haskell Report) to implicit parameters. For example, consider:
2249 Since the binding for <literal>y</literal> falls under the Monomorphism
2250 Restriction it is not generalised, so the type of <literal>y</literal> is
2251 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2252 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2253 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2254 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2255 <literal>y</literal> in the body of the <literal>let</literal> will see the
2256 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2257 <literal>14</literal>.
2262 <sect2 id="linear-implicit-parameters">
2263 <title>Linear implicit parameters</title>
2265 Linear implicit parameters are an idea developed by Koen Claessen,
2266 Mark Shields, and Simon PJ. They address the long-standing
2267 problem that monads seem over-kill for certain sorts of problem, notably:
2270 <listitem> <para> distributing a supply of unique names </para> </listitem>
2271 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2272 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2276 Linear implicit parameters are just like ordinary implicit parameters,
2277 except that they are "linear" -- that is, they cannot be copied, and
2278 must be explicitly "split" instead. Linear implicit parameters are
2279 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2280 (The '/' in the '%' suggests the split!)
2285 import GHC.Exts( Splittable )
2287 data NameSupply = ...
2289 splitNS :: NameSupply -> (NameSupply, NameSupply)
2290 newName :: NameSupply -> Name
2292 instance Splittable NameSupply where
2296 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2297 f env (Lam x e) = Lam x' (f env e)
2300 env' = extend env x x'
2301 ...more equations for f...
2303 Notice that the implicit parameter %ns is consumed
2305 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2306 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2310 So the translation done by the type checker makes
2311 the parameter explicit:
2313 f :: NameSupply -> Env -> Expr -> Expr
2314 f ns env (Lam x e) = Lam x' (f ns1 env e)
2316 (ns1,ns2) = splitNS ns
2318 env = extend env x x'
2320 Notice the call to 'split' introduced by the type checker.
2321 How did it know to use 'splitNS'? Because what it really did
2322 was to introduce a call to the overloaded function 'split',
2323 defined by the class <literal>Splittable</literal>:
2325 class Splittable a where
2328 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2329 split for name supplies. But we can simply write
2335 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2337 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2338 <literal>GHC.Exts</literal>.
2343 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2344 are entirely distinct implicit parameters: you
2345 can use them together and they won't intefere with each other. </para>
2348 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2350 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2351 in the context of a class or instance declaration. </para></listitem>
2355 <sect3><title>Warnings</title>
2358 The monomorphism restriction is even more important than usual.
2359 Consider the example above:
2361 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2362 f env (Lam x e) = Lam x' (f env e)
2365 env' = extend env x x'
2367 If we replaced the two occurrences of x' by (newName %ns), which is
2368 usually a harmless thing to do, we get:
2370 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2371 f env (Lam x e) = Lam (newName %ns) (f env e)
2373 env' = extend env x (newName %ns)
2375 But now the name supply is consumed in <emphasis>three</emphasis> places
2376 (the two calls to newName,and the recursive call to f), so
2377 the result is utterly different. Urk! We don't even have
2381 Well, this is an experimental change. With implicit
2382 parameters we have already lost beta reduction anyway, and
2383 (as John Launchbury puts it) we can't sensibly reason about
2384 Haskell programs without knowing their typing.
2389 <sect3><title>Recursive functions</title>
2390 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2393 foo :: %x::T => Int -> [Int]
2395 foo n = %x : foo (n-1)
2397 where T is some type in class Splittable.</para>
2399 Do you get a list of all the same T's or all different T's
2400 (assuming that split gives two distinct T's back)?
2402 If you supply the type signature, taking advantage of polymorphic
2403 recursion, you get what you'd probably expect. Here's the
2404 translated term, where the implicit param is made explicit:
2407 foo x n = let (x1,x2) = split x
2408 in x1 : foo x2 (n-1)
2410 But if you don't supply a type signature, GHC uses the Hindley
2411 Milner trick of using a single monomorphic instance of the function
2412 for the recursive calls. That is what makes Hindley Milner type inference
2413 work. So the translation becomes
2417 foom n = x : foom (n-1)
2421 Result: 'x' is not split, and you get a list of identical T's. So the
2422 semantics of the program depends on whether or not foo has a type signature.
2425 You may say that this is a good reason to dislike linear implicit parameters
2426 and you'd be right. That is why they are an experimental feature.
2432 <sect2 id="sec-kinding">
2433 <title>Explicitly-kinded quantification</title>
2436 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2437 to give the kind explicitly as (machine-checked) documentation,
2438 just as it is nice to give a type signature for a function. On some occasions,
2439 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2440 John Hughes had to define the data type:
2442 data Set cxt a = Set [a]
2443 | Unused (cxt a -> ())
2445 The only use for the <literal>Unused</literal> constructor was to force the correct
2446 kind for the type variable <literal>cxt</literal>.
2449 GHC now instead allows you to specify the kind of a type variable directly, wherever
2450 a type variable is explicitly bound. Namely:
2452 <listitem><para><literal>data</literal> declarations:
2454 data Set (cxt :: * -> *) a = Set [a]
2455 </screen></para></listitem>
2456 <listitem><para><literal>type</literal> declarations:
2458 type T (f :: * -> *) = f Int
2459 </screen></para></listitem>
2460 <listitem><para><literal>class</literal> declarations:
2462 class (Eq a) => C (f :: * -> *) a where ...
2463 </screen></para></listitem>
2464 <listitem><para><literal>forall</literal>'s in type signatures:
2466 f :: forall (cxt :: * -> *). Set cxt Int
2467 </screen></para></listitem>
2472 The parentheses are required. Some of the spaces are required too, to
2473 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2474 will get a parse error, because "<literal>::*->*</literal>" is a
2475 single lexeme in Haskell.
2479 As part of the same extension, you can put kind annotations in types
2482 f :: (Int :: *) -> Int
2483 g :: forall a. a -> (a :: *)
2487 atype ::= '(' ctype '::' kind ')
2489 The parentheses are required.
2494 <sect2 id="universal-quantification">
2495 <title>Arbitrary-rank polymorphism
2499 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2500 allows us to say exactly what this means. For example:
2508 g :: forall b. (b -> b)
2510 The two are treated identically.
2514 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2515 explicit universal quantification in
2517 For example, all the following types are legal:
2519 f1 :: forall a b. a -> b -> a
2520 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2522 f2 :: (forall a. a->a) -> Int -> Int
2523 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2525 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2527 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2528 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2529 The <literal>forall</literal> makes explicit the universal quantification that
2530 is implicitly added by Haskell.
2533 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2534 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2535 shows, the polymorphic type on the left of the function arrow can be overloaded.
2538 The function <literal>f3</literal> has a rank-3 type;
2539 it has rank-2 types on the left of a function arrow.
2542 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2543 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2544 that restriction has now been lifted.)
2545 In particular, a forall-type (also called a "type scheme"),
2546 including an operational type class context, is legal:
2548 <listitem> <para> On the left of a function arrow </para> </listitem>
2549 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2550 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2551 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2552 field type signatures.</para> </listitem>
2553 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2554 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2556 There is one place you cannot put a <literal>forall</literal>:
2557 you cannot instantiate a type variable with a forall-type. So you cannot
2558 make a forall-type the argument of a type constructor. So these types are illegal:
2560 x1 :: [forall a. a->a]
2561 x2 :: (forall a. a->a, Int)
2562 x3 :: Maybe (forall a. a->a)
2564 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2565 a type variable any more!
2574 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2575 the types of the constructor arguments. Here are several examples:
2581 data T a = T1 (forall b. b -> b -> b) a
2583 data MonadT m = MkMonad { return :: forall a. a -> m a,
2584 bind :: forall a b. m a -> (a -> m b) -> m b
2587 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2593 The constructors have rank-2 types:
2599 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2600 MkMonad :: forall m. (forall a. a -> m a)
2601 -> (forall a b. m a -> (a -> m b) -> m b)
2603 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2609 Notice that you don't need to use a <literal>forall</literal> if there's an
2610 explicit context. For example in the first argument of the
2611 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2612 prefixed to the argument type. The implicit <literal>forall</literal>
2613 quantifies all type variables that are not already in scope, and are
2614 mentioned in the type quantified over.
2618 As for type signatures, implicit quantification happens for non-overloaded
2619 types too. So if you write this:
2622 data T a = MkT (Either a b) (b -> b)
2625 it's just as if you had written this:
2628 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2631 That is, since the type variable <literal>b</literal> isn't in scope, it's
2632 implicitly universally quantified. (Arguably, it would be better
2633 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2634 where that is what is wanted. Feedback welcomed.)
2638 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2639 the constructor to suitable values, just as usual. For example,
2650 a3 = MkSwizzle reverse
2653 a4 = let r x = Just x
2660 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2661 mkTs f x y = [T1 f x, T1 f y]
2667 The type of the argument can, as usual, be more general than the type
2668 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2669 does not need the <literal>Ord</literal> constraint.)
2673 When you use pattern matching, the bound variables may now have
2674 polymorphic types. For example:
2680 f :: T a -> a -> (a, Char)
2681 f (T1 w k) x = (w k x, w 'c' 'd')
2683 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2684 g (MkSwizzle s) xs f = s (map f (s xs))
2686 h :: MonadT m -> [m a] -> m [a]
2687 h m [] = return m []
2688 h m (x:xs) = bind m x $ \y ->
2689 bind m (h m xs) $ \ys ->
2696 In the function <function>h</function> we use the record selectors <literal>return</literal>
2697 and <literal>bind</literal> to extract the polymorphic bind and return functions
2698 from the <literal>MonadT</literal> data structure, rather than using pattern
2704 <title>Type inference</title>
2707 In general, type inference for arbitrary-rank types is undecidable.
2708 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2709 to get a decidable algorithm by requiring some help from the programmer.
2710 We do not yet have a formal specification of "some help" but the rule is this:
2713 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2714 provides an explicit polymorphic type for x, or GHC's type inference will assume
2715 that x's type has no foralls in it</emphasis>.
2718 What does it mean to "provide" an explicit type for x? You can do that by
2719 giving a type signature for x directly, using a pattern type signature
2720 (<xref linkend="scoped-type-variables"/>), thus:
2722 \ f :: (forall a. a->a) -> (f True, f 'c')
2724 Alternatively, you can give a type signature to the enclosing
2725 context, which GHC can "push down" to find the type for the variable:
2727 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2729 Here the type signature on the expression can be pushed inwards
2730 to give a type signature for f. Similarly, and more commonly,
2731 one can give a type signature for the function itself:
2733 h :: (forall a. a->a) -> (Bool,Char)
2734 h f = (f True, f 'c')
2736 You don't need to give a type signature if the lambda bound variable
2737 is a constructor argument. Here is an example we saw earlier:
2739 f :: T a -> a -> (a, Char)
2740 f (T1 w k) x = (w k x, w 'c' 'd')
2742 Here we do not need to give a type signature to <literal>w</literal>, because
2743 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2750 <sect3 id="implicit-quant">
2751 <title>Implicit quantification</title>
2754 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2755 user-written types, if and only if there is no explicit <literal>forall</literal>,
2756 GHC finds all the type variables mentioned in the type that are not already
2757 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2761 f :: forall a. a -> a
2768 h :: forall b. a -> b -> b
2774 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2777 f :: (a -> a) -> Int
2779 f :: forall a. (a -> a) -> Int
2781 f :: (forall a. a -> a) -> Int
2784 g :: (Ord a => a -> a) -> Int
2785 -- MEANS the illegal type
2786 g :: forall a. (Ord a => a -> a) -> Int
2788 g :: (forall a. Ord a => a -> a) -> Int
2790 The latter produces an illegal type, which you might think is silly,
2791 but at least the rule is simple. If you want the latter type, you
2792 can write your for-alls explicitly. Indeed, doing so is strongly advised
2801 <sect2 id="scoped-type-variables">
2802 <title>Scoped type variables
2806 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2808 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2809 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2810 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2814 f (xs::[a]) = ys ++ ys
2819 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2820 This brings the type variable <literal>a</literal> into scope; it scopes over
2821 all the patterns and right hand sides for this equation for <function>f</function>.
2822 In particular, it is in scope at the type signature for <varname>y</varname>.
2826 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2827 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2828 implicitly universally quantified. (If there are no type variables in
2829 scope, all type variables mentioned in the signature are universally
2830 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2831 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2832 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2833 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2834 it becomes possible to do so.
2838 Scoped type variables are implemented in both GHC and Hugs. Where the
2839 implementations differ from the specification below, those differences
2844 So much for the basic idea. Here are the details.
2848 <title>What a scoped type variable means</title>
2850 A lexically-scoped type variable is simply
2851 the name for a type. The restriction it expresses is that all occurrences
2852 of the same name mean the same type. For example:
2854 f :: [Int] -> Int -> Int
2855 f (xs::[a]) (y::a) = (head xs + y) :: a
2857 The pattern type signatures on the left hand side of
2858 <literal>f</literal> express the fact that <literal>xs</literal>
2859 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2860 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2861 specifies that this expression must have the same type <literal>a</literal>.
2862 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2863 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2864 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2865 rules, which specified that a pattern-bound type variable should be universally quantified.)
2866 For example, all of these are legal:</para>
2869 t (x::a) (y::a) = x+y*2
2871 f (x::a) (y::b) = [x,y] -- a unifies with b
2873 g (x::a) = x + 1::Int -- a unifies with Int
2875 h x = let k (y::a) = [x,y] -- a is free in the
2876 in k x -- environment
2878 k (x::a) True = ... -- a unifies with Int
2879 k (x::Int) False = ...
2882 w (x::a) = x -- a unifies with [b]
2888 <title>Scope and implicit quantification</title>
2896 All the type variables mentioned in a pattern,
2897 that are not already in scope,
2898 are brought into scope by the pattern. We describe this set as
2899 the <emphasis>type variables bound by the pattern</emphasis>.
2902 f (x::a) = let g (y::(a,b)) = fst y
2906 The pattern <literal>(x::a)</literal> brings the type variable
2907 <literal>a</literal> into scope, as well as the term
2908 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2909 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2910 and brings into scope the type variable <literal>b</literal>.
2916 The type variable(s) bound by the pattern have the same scope
2917 as the term variable(s) bound by the pattern. For example:
2920 f (x::a) = <...rhs of f...>
2921 (p::b, q::b) = (1,2)
2922 in <...body of let...>
2924 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2925 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2926 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2927 just like <literal>p</literal> and <literal>q</literal> do.
2928 Indeed, the newly bound type variables also scope over any ordinary, separate
2929 type signatures in the <literal>let</literal> group.
2936 The type variables bound by the pattern may be
2937 mentioned in ordinary type signatures or pattern
2938 type signatures anywhere within their scope.
2945 In ordinary type signatures, any type variable mentioned in the
2946 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2954 Ordinary type signatures do not bring any new type variables
2955 into scope (except in the type signature itself!). So this is illegal:
2962 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2963 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2964 and that is an incorrect typing.
2971 The pattern type signature is a monotype:
2976 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2980 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2981 not to type schemes.
2985 There is no implicit universal quantification on pattern type signatures (in contrast to
2986 ordinary type signatures).
2996 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2997 scope over the methods defined in the <literal>where</literal> part. For example:
3011 (Not implemented in Hugs yet, Dec 98).
3021 <sect3 id="decl-type-sigs">
3022 <title>Declaration type signatures</title>
3023 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3024 quantification (using <literal>forall</literal>) brings into scope the
3025 explicitly-quantified
3026 type variables, in the definition of the named function(s). For example:
3028 f :: forall a. [a] -> [a]
3029 f (x:xs) = xs ++ [ x :: a ]
3031 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3032 the definition of "<literal>f</literal>".
3034 <para>This only happens if the quantification in <literal>f</literal>'s type
3035 signature is explicit. For example:
3038 g (x:xs) = xs ++ [ x :: a ]
3040 This program will be rejected, because "<literal>a</literal>" does not scope
3041 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3042 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3043 quantification rules.
3047 <sect3 id="pattern-type-sigs">
3048 <title>Where a pattern type signature can occur</title>
3051 A pattern type signature can occur in any pattern. For example:
3056 A pattern type signature can be on an arbitrary sub-pattern, not
3061 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3070 Pattern type signatures, including the result part, can be used
3071 in lambda abstractions:
3074 (\ (x::a, y) :: a -> x)
3081 Pattern type signatures, including the result part, can be used
3082 in <literal>case</literal> expressions:
3085 case e of { ((x::a, y) :: (a,b)) -> x }
3088 Note that the <literal>-></literal> symbol in a case alternative
3089 leads to difficulties when parsing a type signature in the pattern: in
3090 the absence of the extra parentheses in the example above, the parser
3091 would try to interpret the <literal>-></literal> as a function
3092 arrow and give a parse error later.
3100 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3101 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3102 token or a parenthesised type of some sort). To see why,
3103 consider how one would parse this:
3117 Pattern type signatures can bind existential type variables.
3122 data T = forall a. MkT [a]
3125 f (MkT [t::a]) = MkT t3
3138 Pattern type signatures
3139 can be used in pattern bindings:
3142 f x = let (y, z::a) = x in ...
3143 f1 x = let (y, z::Int) = x in ...
3144 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3145 f3 :: (b->b) = \x -> x
3148 In all such cases, the binding is not generalised over the pattern-bound
3149 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3150 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3151 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3152 In contrast, the binding
3157 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3158 in <literal>f4</literal>'s scope.
3164 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3165 type signatures. The two can be used independently or together.</para>
3169 <sect3 id="result-type-sigs">
3170 <title>Result type signatures</title>
3173 The result type of a function can be given a signature, thus:
3177 f (x::a) :: [a] = [x,x,x]
3181 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3182 result type. Sometimes this is the only way of naming the type variable
3187 f :: Int -> [a] -> [a]
3188 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3189 in \xs -> map g (reverse xs `zip` xs)
3194 The type variables bound in a result type signature scope over the right hand side
3195 of the definition. However, consider this corner-case:
3197 rev1 :: [a] -> [a] = \xs -> reverse xs
3199 foo ys = rev (ys::[a])
3201 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3202 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3203 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3204 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3205 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3208 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3209 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3213 rev1 :: [a] -> [a] = \xs -> reverse xs
3218 Result type signatures are not yet implemented in Hugs.
3225 <sect2 id="deriving-typeable">
3226 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3229 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3230 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3231 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3232 classes <literal>Eq</literal>, <literal>Ord</literal>,
3233 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3236 GHC extends this list with two more classes that may be automatically derived
3237 (provided the <option>-fglasgow-exts</option> flag is specified):
3238 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3239 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3240 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3242 <para>An instance of <literal>Typeable</literal> can only be derived if the
3243 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3244 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3246 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3247 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3249 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3250 are used, and only <literal>Typeable1</literal> up to
3251 <literal>Typeable7</literal> are provided in the library.)
3252 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3253 class, whose kind suits that of the data type constructor, and
3254 then writing the data type instance by hand.
3258 <sect2 id="newtype-deriving">
3259 <title>Generalised derived instances for newtypes</title>
3262 When you define an abstract type using <literal>newtype</literal>, you may want
3263 the new type to inherit some instances from its representation. In
3264 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3265 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3266 other classes you have to write an explicit instance declaration. For
3267 example, if you define
3270 newtype Dollars = Dollars Int
3273 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3274 explicitly define an instance of <literal>Num</literal>:
3277 instance Num Dollars where
3278 Dollars a + Dollars b = Dollars (a+b)
3281 All the instance does is apply and remove the <literal>newtype</literal>
3282 constructor. It is particularly galling that, since the constructor
3283 doesn't appear at run-time, this instance declaration defines a
3284 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3285 dictionary, only slower!
3289 <sect3> <title> Generalising the deriving clause </title>
3291 GHC now permits such instances to be derived instead, so one can write
3293 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3296 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3297 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3298 derives an instance declaration of the form
3301 instance Num Int => Num Dollars
3304 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3308 We can also derive instances of constructor classes in a similar
3309 way. For example, suppose we have implemented state and failure monad
3310 transformers, such that
3313 instance Monad m => Monad (State s m)
3314 instance Monad m => Monad (Failure m)
3316 In Haskell 98, we can define a parsing monad by
3318 type Parser tok m a = State [tok] (Failure m) a
3321 which is automatically a monad thanks to the instance declarations
3322 above. With the extension, we can make the parser type abstract,
3323 without needing to write an instance of class <literal>Monad</literal>, via
3326 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3329 In this case the derived instance declaration is of the form
3331 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3334 Notice that, since <literal>Monad</literal> is a constructor class, the
3335 instance is a <emphasis>partial application</emphasis> of the new type, not the
3336 entire left hand side. We can imagine that the type declaration is
3337 ``eta-converted'' to generate the context of the instance
3342 We can even derive instances of multi-parameter classes, provided the
3343 newtype is the last class parameter. In this case, a ``partial
3344 application'' of the class appears in the <literal>deriving</literal>
3345 clause. For example, given the class
3348 class StateMonad s m | m -> s where ...
3349 instance Monad m => StateMonad s (State s m) where ...
3351 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3353 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3354 deriving (Monad, StateMonad [tok])
3357 The derived instance is obtained by completing the application of the
3358 class to the new type:
3361 instance StateMonad [tok] (State [tok] (Failure m)) =>
3362 StateMonad [tok] (Parser tok m)
3367 As a result of this extension, all derived instances in newtype
3368 declarations are treated uniformly (and implemented just by reusing
3369 the dictionary for the representation type), <emphasis>except</emphasis>
3370 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3371 the newtype and its representation.
3375 <sect3> <title> A more precise specification </title>
3377 Derived instance declarations are constructed as follows. Consider the
3378 declaration (after expansion of any type synonyms)
3381 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3387 <literal>S</literal> is a type constructor,
3390 The <literal>t1...tk</literal> are types,
3393 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3394 the <literal>ti</literal>, and
3397 The <literal>ci</literal> are partial applications of
3398 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3399 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3402 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3403 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3404 should not "look through" the type or its constructor. You can still
3405 derive these classes for a newtype, but it happens in the usual way, not
3406 via this new mechanism.
3409 Then, for each <literal>ci</literal>, the derived instance
3412 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3414 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3415 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3419 As an example which does <emphasis>not</emphasis> work, consider
3421 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3423 Here we cannot derive the instance
3425 instance Monad (State s m) => Monad (NonMonad m)
3428 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3429 and so cannot be "eta-converted" away. It is a good thing that this
3430 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3431 not, in fact, a monad --- for the same reason. Try defining
3432 <literal>>>=</literal> with the correct type: you won't be able to.
3436 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3437 important, since we can only derive instances for the last one. If the
3438 <literal>StateMonad</literal> class above were instead defined as
3441 class StateMonad m s | m -> s where ...
3444 then we would not have been able to derive an instance for the
3445 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3446 classes usually have one "main" parameter for which deriving new
3447 instances is most interesting.
3449 <para>Lastly, all of this applies only for classes other than
3450 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3451 and <literal>Data</literal>, for which the built-in derivation applies (section
3452 4.3.3. of the Haskell Report).
3453 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3454 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3455 the standard method is used or the one described here.)
3461 <sect2 id="typing-binds">
3462 <title>Generalised typing of mutually recursive bindings</title>
3465 The Haskell Report specifies that a group of bindings (at top level, or in a
3466 <literal>let</literal> or <literal>where</literal>) should be sorted into
3467 strongly-connected components, and then type-checked in dependency order
3468 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3469 Report, Section 4.5.1</ulink>).
3470 As each group is type-checked, any binders of the group that
3472 an explicit type signature are put in the type environment with the specified
3474 and all others are monomorphic until the group is generalised
3475 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3478 <para>Following a suggestion of Mark Jones, in his paper
3479 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3481 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3483 <emphasis>the dependency analysis ignores references to variables that have an explicit
3484 type signature</emphasis>.
3485 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3486 typecheck. For example, consider:
3488 f :: Eq a => a -> Bool
3489 f x = (x == x) || g True || g "Yes"
3491 g y = (y <= y) || f True
3493 This is rejected by Haskell 98, but under Jones's scheme the definition for
3494 <literal>g</literal> is typechecked first, separately from that for
3495 <literal>f</literal>,
3496 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3497 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3498 type is generalised, to get
3500 g :: Ord a => a -> Bool
3502 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3503 <literal>g</literal> in the type environment.
3507 The same refined dependency analysis also allows the type signatures of
3508 mutually-recursive functions to have different contexts, something that is illegal in
3509 Haskell 98 (Section 4.5.2, last sentence). With
3510 <option>-fglasgow-exts</option>
3511 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3512 type signatures; in practice this means that only variables bound by the same
3513 pattern binding must have the same context. For example, this is fine:
3515 f :: Eq a => a -> Bool
3516 f x = (x == x) || g True
3518 g :: Ord a => a -> Bool
3519 g y = (y <= y) || f True
3525 <!-- ==================== End of type system extensions ================= -->
3527 <!-- ====================== Generalised algebraic data types ======================= -->
3530 <title>Generalised Algebraic Data Types</title>
3532 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3533 to give the type signatures of constructors explicitly. For example:
3536 Lit :: Int -> Term Int
3537 Succ :: Term Int -> Term Int
3538 IsZero :: Term Int -> Term Bool
3539 If :: Term Bool -> Term a -> Term a -> Term a
3540 Pair :: Term a -> Term b -> Term (a,b)
3542 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3543 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3544 for these <literal>Terms</literal>:
3548 eval (Succ t) = 1 + eval t
3549 eval (IsZero i) = eval i == 0
3550 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3551 eval (Pair e1 e2) = (eval e2, eval e2)
3553 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3555 <para> The extensions to GHC are these:
3558 Data type declarations have a 'where' form, as exemplified above. The type signature of
3559 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3560 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3561 have no scope. Indeed, one can write a kind signature instead:
3563 data Term :: * -> * where ...
3565 or even a mixture of the two:
3567 data Foo a :: (* -> *) -> * where ...
3569 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3572 data Foo a (b :: * -> *) where ...
3577 There are no restrictions on the type of the data constructor, except that the result
3578 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3579 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3583 You cannot use record syntax on a GADT-style data type declaration. (
3584 It's not clear what these it would mean. For example,
3585 the record selectors might ill-typed.)
3586 However, you can use strictness annotations, in the obvious places
3587 in the constructor type:
3590 Lit :: !Int -> Term Int
3591 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3592 Pair :: Term a -> Term b -> Term (a,b)
3597 You can use a <literal>deriving</literal> clause on a GADT-style data type
3598 declaration, but only if the data type could also have been declared in
3599 Haskell-98 syntax. For example, these two declarations are equivalent
3601 data Maybe1 a where {
3602 Nothing1 :: Maybe a ;
3603 Just1 :: a -> Maybe a
3604 } deriving( Eq, Ord )
3606 data Maybe2 a = Nothing2 | Just2 a
3609 This simply allows you to declare a vanilla Haskell-98 data type using the
3610 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3614 Pattern matching causes type refinement. For example, in the right hand side of the equation
3619 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3620 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3621 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3623 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3624 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3625 occur. However, the refinement is quite general. For example, if we had:
3627 eval :: Term a -> a -> a
3628 eval (Lit i) j = i+j
3630 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3631 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3632 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3638 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3640 data T a = forall b. MkT b (b->a)
3641 data T' a where { MKT :: b -> (b->a) -> T' a }
3646 <!-- ====================== End of Generalised algebraic data types ======================= -->
3648 <!-- ====================== TEMPLATE HASKELL ======================= -->
3650 <sect1 id="template-haskell">
3651 <title>Template Haskell</title>
3653 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3654 Template Haskell at <ulink url="http://www.haskell.org/th/">
3655 http://www.haskell.org/th/</ulink>, while
3657 the main technical innovations is discussed in "<ulink
3658 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3659 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3660 The details of the Template Haskell design are still in flux. Make sure you
3661 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3662 (search for the type ExpQ).
3663 [Temporary: many changes to the original design are described in
3664 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3665 Not all of these changes are in GHC 6.2.]
3668 <para> The first example from that paper is set out below as a worked example to help get you started.
3672 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3673 Tim Sheard is going to expand it.)
3677 <title>Syntax</title>
3679 <para> Template Haskell has the following new syntactic
3680 constructions. You need to use the flag
3681 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3682 </indexterm>to switch these syntactic extensions on
3683 (<option>-fth</option> is currently implied by
3684 <option>-fglasgow-exts</option>, but you are encouraged to
3685 specify it explicitly).</para>
3689 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3690 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3691 There must be no space between the "$" and the identifier or parenthesis. This use
3692 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3693 of "." as an infix operator. If you want the infix operator, put spaces around it.
3695 <para> A splice can occur in place of
3697 <listitem><para> an expression; the spliced expression must
3698 have type <literal>Q Exp</literal></para></listitem>
3699 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3700 <listitem><para> [Planned, but not implemented yet.] a
3701 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
3703 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3704 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3710 A expression quotation is written in Oxford brackets, thus:
3712 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3713 the quotation has type <literal>Expr</literal>.</para></listitem>
3714 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3715 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3716 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
3717 the quotation has type <literal>Type</literal>.</para></listitem>
3718 </itemizedlist></para></listitem>
3721 Reification is written thus:
3723 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3724 has type <literal>Dec</literal>. </para></listitem>
3725 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3726 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3727 <listitem><para> Still to come: fixities </para></listitem>
3729 </itemizedlist></para>
3736 <sect2> <title> Using Template Haskell </title>
3740 The data types and monadic constructor functions for Template Haskell are in the library
3741 <literal>Language.Haskell.THSyntax</literal>.
3745 You can only run a function at compile time if it is imported from another module. That is,
3746 you can't define a function in a module, and call it from within a splice in the same module.
3747 (It would make sense to do so, but it's hard to implement.)
3751 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3754 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3755 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3756 compiles and runs a program, and then looks at the result. So it's important that
3757 the program it compiles produces results whose representations are identical to
3758 those of the compiler itself.
3762 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3763 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3768 <sect2> <title> A Template Haskell Worked Example </title>
3769 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3770 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3777 -- Import our template "pr"
3778 import Printf ( pr )
3780 -- The splice operator $ takes the Haskell source code
3781 -- generated at compile time by "pr" and splices it into
3782 -- the argument of "putStrLn".
3783 main = putStrLn ( $(pr "Hello") )
3789 -- Skeletal printf from the paper.
3790 -- It needs to be in a separate module to the one where
3791 -- you intend to use it.
3793 -- Import some Template Haskell syntax
3794 import Language.Haskell.TH
3796 -- Describe a format string
3797 data Format = D | S | L String
3799 -- Parse a format string. This is left largely to you
3800 -- as we are here interested in building our first ever
3801 -- Template Haskell program and not in building printf.
3802 parse :: String -> [Format]
3805 -- Generate Haskell source code from a parsed representation
3806 -- of the format string. This code will be spliced into
3807 -- the module which calls "pr", at compile time.
3808 gen :: [Format] -> ExpQ
3809 gen [D] = [| \n -> show n |]
3810 gen [S] = [| \s -> s |]
3811 gen [L s] = stringE s
3813 -- Here we generate the Haskell code for the splice
3814 -- from an input format string.
3815 pr :: String -> ExpQ
3816 pr s = gen (parse s)
3819 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3822 $ ghc --make -fth main.hs -o main.exe
3825 <para>Run "main.exe" and here is your output:</para>
3836 <!-- ===================== Arrow notation =================== -->
3838 <sect1 id="arrow-notation">
3839 <title>Arrow notation
3842 <para>Arrows are a generalization of monads introduced by John Hughes.
3843 For more details, see
3848 “Generalising Monads to Arrows”,
3849 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3850 pp67–111, May 2000.
3856 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3857 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3863 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3864 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3870 and the arrows web page at
3871 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3872 With the <option>-farrows</option> flag, GHC supports the arrow
3873 notation described in the second of these papers.
3874 What follows is a brief introduction to the notation;
3875 it won't make much sense unless you've read Hughes's paper.
3876 This notation is translated to ordinary Haskell,
3877 using combinators from the
3878 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
3882 <para>The extension adds a new kind of expression for defining arrows:
3884 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3885 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3887 where <literal>proc</literal> is a new keyword.
3888 The variables of the pattern are bound in the body of the
3889 <literal>proc</literal>-expression,
3890 which is a new sort of thing called a <firstterm>command</firstterm>.
3891 The syntax of commands is as follows:
3893 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3894 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3895 | <replaceable>cmd</replaceable><superscript>0</superscript>
3897 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3898 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3899 infix operators as for expressions, and
3901 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3902 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3903 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3904 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3905 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3906 | <replaceable>fcmd</replaceable>
3908 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3909 | ( <replaceable>cmd</replaceable> )
3910 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3912 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3913 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3914 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3915 | <replaceable>cmd</replaceable>
3917 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3918 except that the bodies are commands instead of expressions.
3922 Commands produce values, but (like monadic computations)
3923 may yield more than one value,
3924 or none, and may do other things as well.
3925 For the most part, familiarity with monadic notation is a good guide to
3927 However the values of expressions, even monadic ones,
3928 are determined by the values of the variables they contain;
3929 this is not necessarily the case for commands.
3933 A simple example of the new notation is the expression
3935 proc x -> f -< x+1
3937 We call this a <firstterm>procedure</firstterm> or
3938 <firstterm>arrow abstraction</firstterm>.
3939 As with a lambda expression, the variable <literal>x</literal>
3940 is a new variable bound within the <literal>proc</literal>-expression.
3941 It refers to the input to the arrow.
3942 In the above example, <literal>-<</literal> is not an identifier but an
3943 new reserved symbol used for building commands from an expression of arrow
3944 type and an expression to be fed as input to that arrow.
3945 (The weird look will make more sense later.)
3946 It may be read as analogue of application for arrows.
3947 The above example is equivalent to the Haskell expression
3949 arr (\ x -> x+1) >>> f
3951 That would make no sense if the expression to the left of
3952 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3953 More generally, the expression to the left of <literal>-<</literal>
3954 may not involve any <firstterm>local variable</firstterm>,
3955 i.e. a variable bound in the current arrow abstraction.
3956 For such a situation there is a variant <literal>-<<</literal>, as in
3958 proc x -> f x -<< x+1
3960 which is equivalent to
3962 arr (\ x -> (f x, x+1)) >>> app
3964 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3966 Such an arrow is equivalent to a monad, so if you're using this form
3967 you may find a monadic formulation more convenient.
3971 <title>do-notation for commands</title>
3974 Another form of command is a form of <literal>do</literal>-notation.
3975 For example, you can write
3984 You can read this much like ordinary <literal>do</literal>-notation,
3985 but with commands in place of monadic expressions.
3986 The first line sends the value of <literal>x+1</literal> as an input to
3987 the arrow <literal>f</literal>, and matches its output against
3988 <literal>y</literal>.
3989 In the next line, the output is discarded.
3990 The arrow <function>returnA</function> is defined in the
3991 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
3992 module as <literal>arr id</literal>.
3993 The above example is treated as an abbreviation for
3995 arr (\ x -> (x, x)) >>>
3996 first (arr (\ x -> x+1) >>> f) >>>
3997 arr (\ (y, x) -> (y, (x, y))) >>>
3998 first (arr (\ y -> 2*y) >>> g) >>>
4000 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4001 first (arr (\ (x, z) -> x*z) >>> h) >>>
4002 arr (\ (t, z) -> t+z) >>>
4005 Note that variables not used later in the composition are projected out.
4006 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4008 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4009 module, this reduces to
4011 arr (\ x -> (x+1, x)) >>>
4013 arr (\ (y, x) -> (2*y, (x, y))) >>>
4015 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4017 arr (\ (t, z) -> t+z)
4019 which is what you might have written by hand.
4020 With arrow notation, GHC keeps track of all those tuples of variables for you.
4024 Note that although the above translation suggests that
4025 <literal>let</literal>-bound variables like <literal>z</literal> must be
4026 monomorphic, the actual translation produces Core,
4027 so polymorphic variables are allowed.
4031 It's also possible to have mutually recursive bindings,
4032 using the new <literal>rec</literal> keyword, as in the following example:
4034 counter :: ArrowCircuit a => a Bool Int
4035 counter = proc reset -> do
4036 rec output <- returnA -< if reset then 0 else next
4037 next <- delay 0 -< output+1
4038 returnA -< output
4040 The translation of such forms uses the <function>loop</function> combinator,
4041 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4047 <title>Conditional commands</title>
4050 In the previous example, we used a conditional expression to construct the
4052 Sometimes we want to conditionally execute different commands, as in
4059 which is translated to
4061 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4062 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4064 Since the translation uses <function>|||</function>,
4065 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4069 There are also <literal>case</literal> commands, like
4075 y <- h -< (x1, x2)
4079 The syntax is the same as for <literal>case</literal> expressions,
4080 except that the bodies of the alternatives are commands rather than expressions.
4081 The translation is similar to that of <literal>if</literal> commands.
4087 <title>Defining your own control structures</title>
4090 As we're seen, arrow notation provides constructs,
4091 modelled on those for expressions,
4092 for sequencing, value recursion and conditionals.
4093 But suitable combinators,
4094 which you can define in ordinary Haskell,
4095 may also be used to build new commands out of existing ones.
4096 The basic idea is that a command defines an arrow from environments to values.
4097 These environments assign values to the free local variables of the command.
4098 Thus combinators that produce arrows from arrows
4099 may also be used to build commands from commands.
4100 For example, the <literal>ArrowChoice</literal> class includes a combinator
4102 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4104 so we can use it to build commands:
4106 expr' = proc x -> do
4109 symbol Plus -< ()
4110 y <- term -< ()
4113 symbol Minus -< ()
4114 y <- term -< ()
4117 (The <literal>do</literal> on the first line is needed to prevent the first
4118 <literal><+> ...</literal> from being interpreted as part of the
4119 expression on the previous line.)
4120 This is equivalent to
4122 expr' = (proc x -> returnA -< x)
4123 <+> (proc x -> do
4124 symbol Plus -< ()
4125 y <- term -< ()
4127 <+> (proc x -> do
4128 symbol Minus -< ()
4129 y <- term -< ()
4132 It is essential that this operator be polymorphic in <literal>e</literal>
4133 (representing the environment input to the command
4134 and thence to its subcommands)
4135 and satisfy the corresponding naturality property
4137 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4139 at least for strict <literal>k</literal>.
4140 (This should be automatic if you're not using <function>seq</function>.)
4141 This ensures that environments seen by the subcommands are environments
4142 of the whole command,
4143 and also allows the translation to safely trim these environments.
4144 The operator must also not use any variable defined within the current
4149 We could define our own operator
4151 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4152 untilA body cond = proc x ->
4153 if cond x then returnA -< ()
4156 untilA body cond -< x
4158 and use it in the same way.
4159 Of course this infix syntax only makes sense for binary operators;
4160 there is also a more general syntax involving special brackets:
4164 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4171 <title>Primitive constructs</title>
4174 Some operators will need to pass additional inputs to their subcommands.
4175 For example, in an arrow type supporting exceptions,
4176 the operator that attaches an exception handler will wish to pass the
4177 exception that occurred to the handler.
4178 Such an operator might have a type
4180 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4182 where <literal>Ex</literal> is the type of exceptions handled.
4183 You could then use this with arrow notation by writing a command
4185 body `handleA` \ ex -> handler
4187 so that if an exception is raised in the command <literal>body</literal>,
4188 the variable <literal>ex</literal> is bound to the value of the exception
4189 and the command <literal>handler</literal>,
4190 which typically refers to <literal>ex</literal>, is entered.
4191 Though the syntax here looks like a functional lambda,
4192 we are talking about commands, and something different is going on.
4193 The input to the arrow represented by a command consists of values for
4194 the free local variables in the command, plus a stack of anonymous values.
4195 In all the prior examples, this stack was empty.
4196 In the second argument to <function>handleA</function>,
4197 this stack consists of one value, the value of the exception.
4198 The command form of lambda merely gives this value a name.
4203 the values on the stack are paired to the right of the environment.
4204 So operators like <function>handleA</function> that pass
4205 extra inputs to their subcommands can be designed for use with the notation
4206 by pairing the values with the environment in this way.
4207 More precisely, the type of each argument of the operator (and its result)
4208 should have the form
4210 a (...(e,t1), ... tn) t
4212 where <replaceable>e</replaceable> is a polymorphic variable
4213 (representing the environment)
4214 and <replaceable>ti</replaceable> are the types of the values on the stack,
4215 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4216 The polymorphic variable <replaceable>e</replaceable> must not occur in
4217 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4218 <replaceable>t</replaceable>.
4219 However the arrows involved need not be the same.
4220 Here are some more examples of suitable operators:
4222 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4223 runReader :: ... => a e c -> a' (e,State) c
4224 runState :: ... => a e c -> a' (e,State) (c,State)
4226 We can supply the extra input required by commands built with the last two
4227 by applying them to ordinary expressions, as in
4231 (|runReader (do { ... })|) s
4233 which adds <literal>s</literal> to the stack of inputs to the command
4234 built using <function>runReader</function>.
4238 The command versions of lambda abstraction and application are analogous to
4239 the expression versions.
4240 In particular, the beta and eta rules describe equivalences of commands.
4241 These three features (operators, lambda abstraction and application)
4242 are the core of the notation; everything else can be built using them,
4243 though the results would be somewhat clumsy.
4244 For example, we could simulate <literal>do</literal>-notation by defining
4246 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4247 u `bind` f = returnA &&& u >>> f
4249 bind_ :: Arrow a => a e b -> a e c -> a e c
4250 u `bind_` f = u `bind` (arr fst >>> f)
4252 We could simulate <literal>if</literal> by defining
4254 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4255 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4262 <title>Differences with the paper</title>
4267 <para>Instead of a single form of arrow application (arrow tail) with two
4268 translations, the implementation provides two forms
4269 <quote><literal>-<</literal></quote> (first-order)
4270 and <quote><literal>-<<</literal></quote> (higher-order).
4275 <para>User-defined operators are flagged with banana brackets instead of
4276 a new <literal>form</literal> keyword.
4285 <title>Portability</title>
4288 Although only GHC implements arrow notation directly,
4289 there is also a preprocessor
4291 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4292 that translates arrow notation into Haskell 98
4293 for use with other Haskell systems.
4294 You would still want to check arrow programs with GHC;
4295 tracing type errors in the preprocessor output is not easy.
4296 Modules intended for both GHC and the preprocessor must observe some
4297 additional restrictions:
4302 The module must import
4303 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4309 The preprocessor cannot cope with other Haskell extensions.
4310 These would have to go in separate modules.
4316 Because the preprocessor targets Haskell (rather than Core),
4317 <literal>let</literal>-bound variables are monomorphic.
4328 <!-- ==================== ASSERTIONS ================= -->
4330 <sect1 id="sec-assertions">
4332 <indexterm><primary>Assertions</primary></indexterm>
4336 If you want to make use of assertions in your standard Haskell code, you
4337 could define a function like the following:
4343 assert :: Bool -> a -> a
4344 assert False x = error "assertion failed!"
4351 which works, but gives you back a less than useful error message --
4352 an assertion failed, but which and where?
4356 One way out is to define an extended <function>assert</function> function which also
4357 takes a descriptive string to include in the error message and
4358 perhaps combine this with the use of a pre-processor which inserts
4359 the source location where <function>assert</function> was used.
4363 Ghc offers a helping hand here, doing all of this for you. For every
4364 use of <function>assert</function> in the user's source:
4370 kelvinToC :: Double -> Double
4371 kelvinToC k = assert (k >= 0.0) (k+273.15)
4377 Ghc will rewrite this to also include the source location where the
4384 assert pred val ==> assertError "Main.hs|15" pred val
4390 The rewrite is only performed by the compiler when it spots
4391 applications of <function>Control.Exception.assert</function>, so you
4392 can still define and use your own versions of
4393 <function>assert</function>, should you so wish. If not, import
4394 <literal>Control.Exception</literal> to make use
4395 <function>assert</function> in your code.
4399 GHC ignores assertions when optimisation is turned on with the
4400 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4401 <literal>assert pred e</literal> will be rewritten to
4402 <literal>e</literal>. You can also disable assertions using the
4403 <option>-fignore-asserts</option>
4404 option<indexterm><primary><option>-fignore-asserts</option></primary>
4405 </indexterm>.</para>
4408 Assertion failures can be caught, see the documentation for the
4409 <literal>Control.Exception</literal> library for the details.
4415 <!-- =============================== PRAGMAS =========================== -->
4417 <sect1 id="pragmas">
4418 <title>Pragmas</title>
4420 <indexterm><primary>pragma</primary></indexterm>
4422 <para>GHC supports several pragmas, or instructions to the
4423 compiler placed in the source code. Pragmas don't normally affect
4424 the meaning of the program, but they might affect the efficiency
4425 of the generated code.</para>
4427 <para>Pragmas all take the form
4429 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4431 where <replaceable>word</replaceable> indicates the type of
4432 pragma, and is followed optionally by information specific to that
4433 type of pragma. Case is ignored in
4434 <replaceable>word</replaceable>. The various values for
4435 <replaceable>word</replaceable> that GHC understands are described
4436 in the following sections; any pragma encountered with an
4437 unrecognised <replaceable>word</replaceable> is (silently)
4440 <sect2 id="deprecated-pragma">
4441 <title>DEPRECATED pragma</title>
4442 <indexterm><primary>DEPRECATED</primary>
4445 <para>The DEPRECATED pragma lets you specify that a particular
4446 function, class, or type, is deprecated. There are two
4451 <para>You can deprecate an entire module thus:</para>
4453 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4456 <para>When you compile any module that import
4457 <literal>Wibble</literal>, GHC will print the specified
4462 <para>You can deprecate a function, class, type, or data constructor, with the
4463 following top-level declaration:</para>
4465 {-# DEPRECATED f, C, T "Don't use these" #-}
4467 <para>When you compile any module that imports and uses any
4468 of the specified entities, GHC will print the specified
4470 <para> You can only depecate entities declared at top level in the module
4471 being compiled, and you can only use unqualified names in the list of
4472 entities being deprecated. A capitalised name, such as <literal>T</literal>
4473 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4474 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4475 both are in scope. If both are in scope, there is currently no way to deprecate
4476 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4479 Any use of the deprecated item, or of anything from a deprecated
4480 module, will be flagged with an appropriate message. However,
4481 deprecations are not reported for
4482 (a) uses of a deprecated function within its defining module, and
4483 (b) uses of a deprecated function in an export list.
4484 The latter reduces spurious complaints within a library
4485 in which one module gathers together and re-exports
4486 the exports of several others.
4488 <para>You can suppress the warnings with the flag
4489 <option>-fno-warn-deprecations</option>.</para>
4492 <sect2 id="include-pragma">
4493 <title>INCLUDE pragma</title>
4495 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4496 of C header files that should be <literal>#include</literal>'d into
4497 the C source code generated by the compiler for the current module (if
4498 compiling via C). For example:</para>
4501 {-# INCLUDE "foo.h" #-}
4502 {-# INCLUDE <stdio.h> #-}</programlisting>
4504 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4505 your source file with any <literal>OPTIONS_GHC</literal>
4508 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4509 to the <option>-#include</option> option (<xref
4510 linkend="options-C-compiler" />), because the
4511 <literal>INCLUDE</literal> pragma is understood by other
4512 compilers. Yet another alternative is to add the include file to each
4513 <literal>foreign import</literal> declaration in your code, but we
4514 don't recommend using this approach with GHC.</para>
4517 <sect2 id="inline-noinline-pragma">
4518 <title>INLINE and NOINLINE pragmas</title>
4520 <para>These pragmas control the inlining of function
4523 <sect3 id="inline-pragma">
4524 <title>INLINE pragma</title>
4525 <indexterm><primary>INLINE</primary></indexterm>
4527 <para>GHC (with <option>-O</option>, as always) tries to
4528 inline (or “unfold”) functions/values that are
4529 “small enough,” thus avoiding the call overhead
4530 and possibly exposing other more-wonderful optimisations.
4531 Normally, if GHC decides a function is “too
4532 expensive” to inline, it will not do so, nor will it
4533 export that unfolding for other modules to use.</para>
4535 <para>The sledgehammer you can bring to bear is the
4536 <literal>INLINE</literal><indexterm><primary>INLINE
4537 pragma</primary></indexterm> pragma, used thusly:</para>
4540 key_function :: Int -> String -> (Bool, Double)
4542 #ifdef __GLASGOW_HASKELL__
4543 {-# INLINE key_function #-}
4547 <para>(You don't need to do the C pre-processor carry-on
4548 unless you're going to stick the code through HBC—it
4549 doesn't like <literal>INLINE</literal> pragmas.)</para>
4551 <para>The major effect of an <literal>INLINE</literal> pragma
4552 is to declare a function's “cost” to be very low.
4553 The normal unfolding machinery will then be very keen to
4556 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4557 function can be put anywhere its type signature could be
4560 <para><literal>INLINE</literal> pragmas are a particularly
4562 <literal>then</literal>/<literal>return</literal> (or
4563 <literal>bind</literal>/<literal>unit</literal>) functions in
4564 a monad. For example, in GHC's own
4565 <literal>UniqueSupply</literal> monad code, we have:</para>
4568 #ifdef __GLASGOW_HASKELL__
4569 {-# INLINE thenUs #-}
4570 {-# INLINE returnUs #-}
4574 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4575 linkend="noinline-pragma"/>).</para>
4578 <sect3 id="noinline-pragma">
4579 <title>NOINLINE pragma</title>
4581 <indexterm><primary>NOINLINE</primary></indexterm>
4582 <indexterm><primary>NOTINLINE</primary></indexterm>
4584 <para>The <literal>NOINLINE</literal> pragma does exactly what
4585 you'd expect: it stops the named function from being inlined
4586 by the compiler. You shouldn't ever need to do this, unless
4587 you're very cautious about code size.</para>
4589 <para><literal>NOTINLINE</literal> is a synonym for
4590 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4591 specified by Haskell 98 as the standard way to disable
4592 inlining, so it should be used if you want your code to be
4596 <sect3 id="phase-control">
4597 <title>Phase control</title>
4599 <para> Sometimes you want to control exactly when in GHC's
4600 pipeline the INLINE pragma is switched on. Inlining happens
4601 only during runs of the <emphasis>simplifier</emphasis>. Each
4602 run of the simplifier has a different <emphasis>phase
4603 number</emphasis>; the phase number decreases towards zero.
4604 If you use <option>-dverbose-core2core</option> you'll see the
4605 sequence of phase numbers for successive runs of the
4606 simplifier. In an INLINE pragma you can optionally specify a
4607 phase number, thus:</para>
4611 <para>You can say "inline <literal>f</literal> in Phase 2
4612 and all subsequent phases":
4614 {-# INLINE [2] f #-}
4620 <para>You can say "inline <literal>g</literal> in all
4621 phases up to, but not including, Phase 3":
4623 {-# INLINE [~3] g #-}
4629 <para>If you omit the phase indicator, you mean "inline in
4634 <para>You can use a phase number on a NOINLINE pragma too:</para>
4638 <para>You can say "do not inline <literal>f</literal>
4639 until Phase 2; in Phase 2 and subsequently behave as if
4640 there was no pragma at all":
4642 {-# NOINLINE [2] f #-}
4648 <para>You can say "do not inline <literal>g</literal> in
4649 Phase 3 or any subsequent phase; before that, behave as if
4650 there was no pragma":
4652 {-# NOINLINE [~3] g #-}
4658 <para>If you omit the phase indicator, you mean "never
4659 inline this function".</para>
4663 <para>The same phase-numbering control is available for RULES
4664 (<xref linkend="rewrite-rules"/>).</para>
4668 <sect2 id="language-pragma">
4669 <title>LANGUAGE pragma</title>
4671 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
4672 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
4674 <para>This allows language extensions to be enabled in a portable way.
4675 It is the intention that all Haskell compilers support the
4676 <literal>LANGUAGE</literal> pragma with the same syntax, although not
4677 all extensions are supported by all compilers, of
4678 course. The <literal>LANGUAGE</literal> pragma should be used instead
4679 of <literal>OPTIONS_GHC</literal>, if possible.</para>
4681 <para>For example, to enable the FFI and preprocessing with CPP:</para>
4683 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
4685 <para>Any extension from the <literal>Extension</literal> type defined in
4687 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>
4691 <sect2 id="line-pragma">
4692 <title>LINE pragma</title>
4694 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4695 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4696 <para>This pragma is similar to C's <literal>#line</literal>
4697 pragma, and is mainly for use in automatically generated Haskell
4698 code. It lets you specify the line number and filename of the
4699 original code; for example</para>
4701 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
4703 <para>if you'd generated the current file from something called
4704 <filename>Foo.vhs</filename> and this line corresponds to line
4705 42 in the original. GHC will adjust its error messages to refer
4706 to the line/file named in the <literal>LINE</literal>
4710 <sect2 id="options-pragma">
4711 <title>OPTIONS_GHC pragma</title>
4712 <indexterm><primary>OPTIONS_GHC</primary>
4714 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4717 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4718 additional options that are given to the compiler when compiling
4719 this source file. See <xref linkend="source-file-options"/> for
4722 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4723 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4727 <title>RULES pragma</title>
4729 <para>The RULES pragma lets you specify rewrite rules. It is
4730 described in <xref linkend="rewrite-rules"/>.</para>
4733 <sect2 id="specialize-pragma">
4734 <title>SPECIALIZE pragma</title>
4736 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4737 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4738 <indexterm><primary>overloading, death to</primary></indexterm>
4740 <para>(UK spelling also accepted.) For key overloaded
4741 functions, you can create extra versions (NB: more code space)
4742 specialised to particular types. Thus, if you have an
4743 overloaded function:</para>
4746 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4749 <para>If it is heavily used on lists with
4750 <literal>Widget</literal> keys, you could specialise it as
4754 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4757 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4758 be put anywhere its type signature could be put.</para>
4760 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4761 (a) a specialised version of the function and (b) a rewrite rule
4762 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4763 un-specialised function into a call to the specialised one.</para>
4765 <para>The type in a SPECIALIZE pragma can be any type that is less
4766 polymorphic than the type of the original function. In concrete terms,
4767 if the original function is <literal>f</literal> then the pragma
4769 {-# SPECIALIZE f :: <type> #-}
4771 is valid if and only if the defintion
4773 f_spec :: <type>
4776 is valid. Here are some examples (where we only give the type signature
4777 for the original function, not its code):
4779 f :: Eq a => a -> b -> b
4780 {-# SPECIALISE g :: Int -> b -> b #-}
4782 g :: (Eq a, Ix b) => a -> b -> b
4783 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
4785 h :: Eq a => a -> a -> a
4786 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
4788 The last of these examples will generate a
4789 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
4790 well. If you use this kind of specialisation, let us know how well it works.
4793 <para>Note: In earlier versions of GHC, it was possible to provide your own
4794 specialised function for a given type:
4797 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4800 This feature has been removed, as it is now subsumed by the
4801 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4805 <sect2 id="specialize-instance-pragma">
4806 <title>SPECIALIZE instance pragma
4810 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4811 <indexterm><primary>overloading, death to</primary></indexterm>
4812 Same idea, except for instance declarations. For example:
4815 instance (Eq a) => Eq (Foo a) where {
4816 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4820 The pragma must occur inside the <literal>where</literal> part
4821 of the instance declaration.
4824 Compatible with HBC, by the way, except perhaps in the placement
4830 <sect2 id="unpack-pragma">
4831 <title>UNPACK pragma</title>
4833 <indexterm><primary>UNPACK</primary></indexterm>
4835 <para>The <literal>UNPACK</literal> indicates to the compiler
4836 that it should unpack the contents of a constructor field into
4837 the constructor itself, removing a level of indirection. For
4841 data T = T {-# UNPACK #-} !Float
4842 {-# UNPACK #-} !Float
4845 <para>will create a constructor <literal>T</literal> containing
4846 two unboxed floats. This may not always be an optimisation: if
4847 the <function>T</function> constructor is scrutinised and the
4848 floats passed to a non-strict function for example, they will
4849 have to be reboxed (this is done automatically by the
4852 <para>Unpacking constructor fields should only be used in
4853 conjunction with <option>-O</option>, in order to expose
4854 unfoldings to the compiler so the reboxing can be removed as
4855 often as possible. For example:</para>
4859 f (T f1 f2) = f1 + f2
4862 <para>The compiler will avoid reboxing <function>f1</function>
4863 and <function>f2</function> by inlining <function>+</function>
4864 on floats, but only when <option>-O</option> is on.</para>
4866 <para>Any single-constructor data is eligible for unpacking; for
4870 data T = T {-# UNPACK #-} !(Int,Int)
4873 <para>will store the two <literal>Int</literal>s directly in the
4874 <function>T</function> constructor, by flattening the pair.
4875 Multi-level unpacking is also supported:</para>
4878 data T = T {-# UNPACK #-} !S
4879 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4882 <para>will store two unboxed <literal>Int#</literal>s
4883 directly in the <function>T</function> constructor. The
4884 unpacker can see through newtypes, too.</para>
4886 <para>If a field cannot be unpacked, you will not get a warning,
4887 so it might be an idea to check the generated code with
4888 <option>-ddump-simpl</option>.</para>
4890 <para>See also the <option>-funbox-strict-fields</option> flag,
4891 which essentially has the effect of adding
4892 <literal>{-# UNPACK #-}</literal> to every strict
4893 constructor field.</para>
4898 <!-- ======================= REWRITE RULES ======================== -->
4900 <sect1 id="rewrite-rules">
4901 <title>Rewrite rules
4903 <indexterm><primary>RULES pragma</primary></indexterm>
4904 <indexterm><primary>pragma, RULES</primary></indexterm>
4905 <indexterm><primary>rewrite rules</primary></indexterm></title>
4908 The programmer can specify rewrite rules as part of the source program
4909 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4910 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4911 and (b) the <option>-frules-off</option> flag
4912 (<xref linkend="options-f"/>) is not specified.
4920 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4927 <title>Syntax</title>
4930 From a syntactic point of view:
4936 There may be zero or more rules in a <literal>RULES</literal> pragma.
4943 Each rule has a name, enclosed in double quotes. The name itself has
4944 no significance at all. It is only used when reporting how many times the rule fired.
4950 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4951 immediately after the name of the rule. Thus:
4954 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4957 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4958 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4967 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4968 is set, so you must lay out your rules starting in the same column as the
4969 enclosing definitions.
4976 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4977 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4978 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4979 by spaces, just like in a type <literal>forall</literal>.
4985 A pattern variable may optionally have a type signature.
4986 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4987 For example, here is the <literal>foldr/build</literal> rule:
4990 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4991 foldr k z (build g) = g k z
4994 Since <function>g</function> has a polymorphic type, it must have a type signature.
5001 The left hand side of a rule must consist of a top-level variable applied
5002 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5005 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5006 "wrong2" forall f. f True = True
5009 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5016 A rule does not need to be in the same module as (any of) the
5017 variables it mentions, though of course they need to be in scope.
5023 Rules are automatically exported from a module, just as instance declarations are.
5034 <title>Semantics</title>
5037 From a semantic point of view:
5043 Rules are only applied if you use the <option>-O</option> flag.
5049 Rules are regarded as left-to-right rewrite rules.
5050 When GHC finds an expression that is a substitution instance of the LHS
5051 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5052 By "a substitution instance" we mean that the LHS can be made equal to the
5053 expression by substituting for the pattern variables.
5060 The LHS and RHS of a rule are typechecked, and must have the
5068 GHC makes absolutely no attempt to verify that the LHS and RHS
5069 of a rule have the same meaning. That is undecidable in general, and
5070 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5077 GHC makes no attempt to make sure that the rules are confluent or
5078 terminating. For example:
5081 "loop" forall x,y. f x y = f y x
5084 This rule will cause the compiler to go into an infinite loop.
5091 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5097 GHC currently uses a very simple, syntactic, matching algorithm
5098 for matching a rule LHS with an expression. It seeks a substitution
5099 which makes the LHS and expression syntactically equal modulo alpha
5100 conversion. The pattern (rule), but not the expression, is eta-expanded if
5101 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5102 But not beta conversion (that's called higher-order matching).
5106 Matching is carried out on GHC's intermediate language, which includes
5107 type abstractions and applications. So a rule only matches if the
5108 types match too. See <xref linkend="rule-spec"/> below.
5114 GHC keeps trying to apply the rules as it optimises the program.
5115 For example, consider:
5124 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5125 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5126 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5127 not be substituted, and the rule would not fire.
5134 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5135 that appears on the LHS of a rule</emphasis>, because once you have substituted
5136 for something you can't match against it (given the simple minded
5137 matching). So if you write the rule
5140 "map/map" forall f,g. map f . map g = map (f.g)
5143 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5144 It will only match something written with explicit use of ".".
5145 Well, not quite. It <emphasis>will</emphasis> match the expression
5151 where <function>wibble</function> is defined:
5154 wibble f g = map f . map g
5157 because <function>wibble</function> will be inlined (it's small).
5159 Later on in compilation, GHC starts inlining even things on the
5160 LHS of rules, but still leaves the rules enabled. This inlining
5161 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5168 All rules are implicitly exported from the module, and are therefore
5169 in force in any module that imports the module that defined the rule, directly
5170 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5171 in force when compiling A.) The situation is very similar to that for instance
5183 <title>List fusion</title>
5186 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5187 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5188 intermediate list should be eliminated entirely.
5192 The following are good producers:
5204 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5210 Explicit lists (e.g. <literal>[True, False]</literal>)
5216 The cons constructor (e.g <literal>3:4:[]</literal>)
5222 <function>++</function>
5228 <function>map</function>
5234 <function>filter</function>
5240 <function>iterate</function>, <function>repeat</function>
5246 <function>zip</function>, <function>zipWith</function>
5255 The following are good consumers:
5267 <function>array</function> (on its second argument)
5273 <function>length</function>
5279 <function>++</function> (on its first argument)
5285 <function>foldr</function>
5291 <function>map</function>
5297 <function>filter</function>
5303 <function>concat</function>
5309 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5315 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5316 will fuse with one but not the other)
5322 <function>partition</function>
5328 <function>head</function>
5334 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5340 <function>sequence_</function>
5346 <function>msum</function>
5352 <function>sortBy</function>
5361 So, for example, the following should generate no intermediate lists:
5364 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5370 This list could readily be extended; if there are Prelude functions that you use
5371 a lot which are not included, please tell us.
5375 If you want to write your own good consumers or producers, look at the
5376 Prelude definitions of the above functions to see how to do so.
5381 <sect2 id="rule-spec">
5382 <title>Specialisation
5386 Rewrite rules can be used to get the same effect as a feature
5387 present in earlier versions of GHC.
5388 For example, suppose that:
5391 genericLookup :: Ord a => Table a b -> a -> b
5392 intLookup :: Table Int b -> Int -> b
5395 where <function>intLookup</function> is an implementation of
5396 <function>genericLookup</function> that works very fast for
5397 keys of type <literal>Int</literal>. You might wish
5398 to tell GHC to use <function>intLookup</function> instead of
5399 <function>genericLookup</function> whenever the latter was called with
5400 type <literal>Table Int b -> Int -> b</literal>.
5401 It used to be possible to write
5404 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5407 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5410 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5413 This slightly odd-looking rule instructs GHC to replace
5414 <function>genericLookup</function> by <function>intLookup</function>
5415 <emphasis>whenever the types match</emphasis>.
5416 What is more, this rule does not need to be in the same
5417 file as <function>genericLookup</function>, unlike the
5418 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5419 have an original definition available to specialise).
5422 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5423 <function>intLookup</function> really behaves as a specialised version
5424 of <function>genericLookup</function>!!!</para>
5426 <para>An example in which using <literal>RULES</literal> for
5427 specialisation will Win Big:
5430 toDouble :: Real a => a -> Double
5431 toDouble = fromRational . toRational
5433 {-# RULES "toDouble/Int" toDouble = i2d #-}
5434 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5437 The <function>i2d</function> function is virtually one machine
5438 instruction; the default conversion—via an intermediate
5439 <literal>Rational</literal>—is obscenely expensive by
5446 <title>Controlling what's going on</title>
5454 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5460 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5461 If you add <option>-dppr-debug</option> you get a more detailed listing.
5467 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5470 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5471 {-# INLINE build #-}
5475 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5476 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5477 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5478 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5485 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5486 see how to write rules that will do fusion and yet give an efficient
5487 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5497 <sect2 id="core-pragma">
5498 <title>CORE pragma</title>
5500 <indexterm><primary>CORE pragma</primary></indexterm>
5501 <indexterm><primary>pragma, CORE</primary></indexterm>
5502 <indexterm><primary>core, annotation</primary></indexterm>
5505 The external core format supports <quote>Note</quote> annotations;
5506 the <literal>CORE</literal> pragma gives a way to specify what these
5507 should be in your Haskell source code. Syntactically, core
5508 annotations are attached to expressions and take a Haskell string
5509 literal as an argument. The following function definition shows an
5513 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5516 Semantically, this is equivalent to:
5524 However, when external for is generated (via
5525 <option>-fext-core</option>), there will be Notes attached to the
5526 expressions <function>show</function> and <varname>x</varname>.
5527 The core function declaration for <function>f</function> is:
5531 f :: %forall a . GHCziShow.ZCTShow a ->
5532 a -> GHCziBase.ZMZN GHCziBase.Char =
5533 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5535 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5537 (tpl1::GHCziBase.Int ->
5539 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5541 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5542 (tpl3::GHCziBase.ZMZN a ->
5543 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5551 Here, we can see that the function <function>show</function> (which
5552 has been expanded out to a case expression over the Show dictionary)
5553 has a <literal>%note</literal> attached to it, as does the
5554 expression <varname>eta</varname> (which used to be called
5555 <varname>x</varname>).
5562 <sect1 id="generic-classes">
5563 <title>Generic classes</title>
5565 <para>(Note: support for generic classes is currently broken in
5569 The ideas behind this extension are described in detail in "Derivable type classes",
5570 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5571 An example will give the idea:
5579 fromBin :: [Int] -> (a, [Int])
5581 toBin {| Unit |} Unit = []
5582 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5583 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5584 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5586 fromBin {| Unit |} bs = (Unit, bs)
5587 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5588 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5589 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5590 (y,bs'') = fromBin bs'
5593 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5594 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5595 which are defined thus in the library module <literal>Generics</literal>:
5599 data a :+: b = Inl a | Inr b
5600 data a :*: b = a :*: b
5603 Now you can make a data type into an instance of Bin like this:
5605 instance (Bin a, Bin b) => Bin (a,b)
5606 instance Bin a => Bin [a]
5608 That is, just leave off the "where" clause. Of course, you can put in the
5609 where clause and over-ride whichever methods you please.
5613 <title> Using generics </title>
5614 <para>To use generics you need to</para>
5617 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5618 <option>-fgenerics</option> (to generate extra per-data-type code),
5619 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5623 <para>Import the module <literal>Generics</literal> from the
5624 <literal>lang</literal> package. This import brings into
5625 scope the data types <literal>Unit</literal>,
5626 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5627 don't need this import if you don't mention these types
5628 explicitly; for example, if you are simply giving instance
5629 declarations.)</para>
5634 <sect2> <title> Changes wrt the paper </title>
5636 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5637 can be written infix (indeed, you can now use
5638 any operator starting in a colon as an infix type constructor). Also note that
5639 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5640 Finally, note that the syntax of the type patterns in the class declaration
5641 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5642 alone would ambiguous when they appear on right hand sides (an extension we
5643 anticipate wanting).
5647 <sect2> <title>Terminology and restrictions</title>
5649 Terminology. A "generic default method" in a class declaration
5650 is one that is defined using type patterns as above.
5651 A "polymorphic default method" is a default method defined as in Haskell 98.
5652 A "generic class declaration" is a class declaration with at least one
5653 generic default method.
5661 Alas, we do not yet implement the stuff about constructor names and
5668 A generic class can have only one parameter; you can't have a generic
5669 multi-parameter class.
5675 A default method must be defined entirely using type patterns, or entirely
5676 without. So this is illegal:
5679 op :: a -> (a, Bool)
5680 op {| Unit |} Unit = (Unit, True)
5683 However it is perfectly OK for some methods of a generic class to have
5684 generic default methods and others to have polymorphic default methods.
5690 The type variable(s) in the type pattern for a generic method declaration
5691 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:
5695 op {| p :*: q |} (x :*: y) = op (x :: p)
5703 The type patterns in a generic default method must take one of the forms:
5709 where "a" and "b" are type variables. Furthermore, all the type patterns for
5710 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5711 must use the same type variables. So this is illegal:
5715 op {| a :+: b |} (Inl x) = True
5716 op {| p :+: q |} (Inr y) = False
5718 The type patterns must be identical, even in equations for different methods of the class.
5719 So this too is illegal:
5723 op1 {| a :*: b |} (x :*: y) = True
5726 op2 {| p :*: q |} (x :*: y) = False
5728 (The reason for this restriction is that we gather all the equations for a particular type consructor
5729 into a single generic instance declaration.)
5735 A generic method declaration must give a case for each of the three type constructors.
5741 The type for a generic method can be built only from:
5743 <listitem> <para> Function arrows </para> </listitem>
5744 <listitem> <para> Type variables </para> </listitem>
5745 <listitem> <para> Tuples </para> </listitem>
5746 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5748 Here are some example type signatures for generic methods:
5751 op2 :: Bool -> (a,Bool)
5752 op3 :: [Int] -> a -> a
5755 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5759 This restriction is an implementation restriction: we just havn't got around to
5760 implementing the necessary bidirectional maps over arbitrary type constructors.
5761 It would be relatively easy to add specific type constructors, such as Maybe and list,
5762 to the ones that are allowed.</para>
5767 In an instance declaration for a generic class, the idea is that the compiler
5768 will fill in the methods for you, based on the generic templates. However it can only
5773 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5778 No constructor of the instance type has unboxed fields.
5782 (Of course, these things can only arise if you are already using GHC extensions.)
5783 However, you can still give an instance declarations for types which break these rules,
5784 provided you give explicit code to override any generic default methods.
5792 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5793 what the compiler does with generic declarations.
5798 <sect2> <title> Another example </title>
5800 Just to finish with, here's another example I rather like:
5804 nCons {| Unit |} _ = 1
5805 nCons {| a :*: b |} _ = 1
5806 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5809 tag {| Unit |} _ = 1
5810 tag {| a :*: b |} _ = 1
5811 tag {| a :+: b |} (Inl x) = tag x
5812 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5821 ;;; Local Variables: ***
5823 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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