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 documents GHC's implementation of multi-parameter type
1433 classes. 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 There are the following constraints on class declarations:
1444 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1448 class Collection c a where
1449 union :: c a -> c a -> c a
1460 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1461 of "acyclic" involves only the superclass relationships. For example,
1467 op :: D b => a -> b -> b
1470 class C a => D a where { ... }
1474 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1475 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1476 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1483 <emphasis>There are no restrictions on the context in a class declaration
1484 (which introduces superclasses), except that the class hierarchy must
1485 be acyclic</emphasis>. So these class declarations are OK:
1489 class Functor (m k) => FiniteMap m k where
1492 class (Monad m, Monad (t m)) => Transform t m where
1493 lift :: m a -> (t m) a
1503 <emphasis>All of the class type variables must be reachable (in the sense
1504 mentioned in <xref linkend="type-restrictions"/>)
1505 from the free variables of each method type
1506 </emphasis>. For example:
1510 class Coll s a where
1512 insert :: s -> a -> s
1516 is not OK, because the type of <literal>empty</literal> doesn't mention
1517 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1518 types, and has the same motivation.
1520 Sometimes, offending class declarations exhibit misunderstandings. For
1521 example, <literal>Coll</literal> might be rewritten
1525 class Coll s a where
1527 insert :: s a -> a -> s a
1531 which makes the connection between the type of a collection of
1532 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1533 Occasionally this really doesn't work, in which case you can split the
1541 class CollE s => Coll s a where
1542 insert :: s -> a -> s
1552 <sect3 id="class-method-types">
1553 <title>Class method types</title>
1555 Haskell 98 prohibits class method types to mention constraints on the
1556 class type variable, thus:
1559 fromList :: [a] -> s a
1560 elem :: Eq a => a -> s a -> Bool
1562 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1563 contains the constraint <literal>Eq a</literal>, constrains only the
1564 class type variable (in this case <literal>a</literal>).
1567 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1574 <sect2 id="type-restrictions">
1575 <title>Type signatures</title>
1577 <sect3><title>The context of a type signature</title>
1579 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1580 the form <emphasis>(class type-variable)</emphasis> or
1581 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1582 these type signatures are perfectly OK
1585 g :: Ord (T a ()) => ...
1589 GHC imposes the following restrictions on the constraints in a type signature.
1593 forall tv1..tvn (c1, ...,cn) => type
1596 (Here, we write the "foralls" explicitly, although the Haskell source
1597 language omits them; in Haskell 98, all the free type variables of an
1598 explicit source-language type signature are universally quantified,
1599 except for the class type variables in a class declaration. However,
1600 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1609 <emphasis>Each universally quantified type variable
1610 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1612 A type variable <literal>a</literal> is "reachable" if it it appears
1613 in the same constraint as either a type variable free in in
1614 <literal>type</literal>, or another reachable type variable.
1615 A value with a type that does not obey
1616 this reachability restriction cannot be used without introducing
1617 ambiguity; that is why the type is rejected.
1618 Here, for example, is an illegal type:
1622 forall a. Eq a => Int
1626 When a value with this type was used, the constraint <literal>Eq tv</literal>
1627 would be introduced where <literal>tv</literal> is a fresh type variable, and
1628 (in the dictionary-translation implementation) the value would be
1629 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1630 can never know which instance of <literal>Eq</literal> to use because we never
1631 get any more information about <literal>tv</literal>.
1635 that the reachability condition is weaker than saying that <literal>a</literal> is
1636 functionally dependent on a type variable free in
1637 <literal>type</literal> (see <xref
1638 linkend="functional-dependencies"/>). The reason for this is there
1639 might be a "hidden" dependency, in a superclass perhaps. So
1640 "reachable" is a conservative approximation to "functionally dependent".
1641 For example, consider:
1643 class C a b | a -> b where ...
1644 class C a b => D a b where ...
1645 f :: forall a b. D a b => a -> a
1647 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1648 but that is not immediately apparent from <literal>f</literal>'s type.
1654 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1655 universally quantified type variables <literal>tvi</literal></emphasis>.
1657 For example, this type is OK because <literal>C a b</literal> mentions the
1658 universally quantified type variable <literal>b</literal>:
1662 forall a. C a b => burble
1666 The next type is illegal because the constraint <literal>Eq b</literal> does not
1667 mention <literal>a</literal>:
1671 forall a. Eq b => burble
1675 The reason for this restriction is milder than the other one. The
1676 excluded types are never useful or necessary (because the offending
1677 context doesn't need to be witnessed at this point; it can be floated
1678 out). Furthermore, floating them out increases sharing. Lastly,
1679 excluding them is a conservative choice; it leaves a patch of
1680 territory free in case we need it later.
1691 <title>For-all hoisting</title>
1693 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1694 end of an arrow, thus:
1696 type Discard a = forall b. a -> b -> a
1698 g :: Int -> Discard Int
1701 Simply expanding the type synonym would give
1703 g :: Int -> (forall b. Int -> b -> Int)
1705 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1707 g :: forall b. Int -> Int -> b -> Int
1709 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1710 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1711 performs the transformation:</emphasis>
1713 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1715 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1717 (In fact, GHC tries to retain as much synonym information as possible for use in
1718 error messages, but that is a usability issue.) This rule applies, of course, whether
1719 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1720 valid way to write <literal>g</literal>'s type signature:
1722 g :: Int -> Int -> forall b. b -> Int
1726 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1729 type Foo a = (?x::Int) => Bool -> a
1734 g :: (?x::Int) => Bool -> Bool -> Int
1742 <sect2 id="instance-decls">
1743 <title>Instance declarations</title>
1745 <sect3 id="instance-overlap">
1746 <title>Overlapping instances</title>
1748 In general, <emphasis>GHC requires that that it be unambiguous which instance
1750 should be used to resolve a type-class constraint</emphasis>. This behaviour
1751 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1752 <indexterm><primary>-fallow-overlapping-instances
1753 </primary></indexterm>
1754 and <option>-fallow-incoherent-instances</option>
1755 <indexterm><primary>-fallow-incoherent-instances
1756 </primary></indexterm>, as this section discusses.</para>
1758 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1759 it tries to match every instance declaration against the
1761 by instantiating the head of the instance declaration. For example, consider
1764 instance context1 => C Int a where ... -- (A)
1765 instance context2 => C a Bool where ... -- (B)
1766 instance context3 => C Int [a] where ... -- (C)
1767 instance context4 => C Int [Int] where ... -- (D)
1769 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
1770 but (C) and (D) do not. When matching, GHC takes
1771 no account of the context of the instance declaration
1772 (<literal>context1</literal> etc).
1773 GHC's default behaviour is that <emphasis>exactly one instance must match the
1774 constraint it is trying to resolve</emphasis>.
1775 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1776 including both declarations (A) and (B), say); an error is only reported if a
1777 particular constraint matches more than one.
1781 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1782 more than one instance to match, provided there is a most specific one. For
1783 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1784 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1785 most-specific match, the program is rejected.
1788 However, GHC is conservative about committing to an overlapping instance. For example:
1793 Suppose that from the RHS of <literal>f</literal> we get the constraint
1794 <literal>C Int [b]</literal>. But
1795 GHC does not commit to instance (C), because in a particular
1796 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1797 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1798 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1799 GHC will instead pick (C), without complaining about
1800 the problem of subsequent instantiations.
1803 The willingness to be overlapped or incoherent is a property of
1804 the <emphasis>instance declaration</emphasis> itself, controlled by the
1805 presence or otherwise of the <option>-fallow-overlapping-instances</option>
1806 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
1807 being defined. Neither flag is required in a module that imports and uses the
1808 instance declaration. Specifically, during the lookup process:
1811 An instance declaration is ignored during the lookup process if (a) a more specific
1812 match is found, and (b) the instance declaration was compiled with
1813 <option>-fallow-overlapping-instances</option>. The flag setting for the
1814 more-specific instance does not matter.
1817 Suppose an instance declaration does not matche the constraint being looked up, but
1818 does unify with it, so that it might match when the constraint is further
1819 instantiated. Usually GHC will regard this as a reason for not committing to
1820 some other constraint. But if the instance declaration was compiled with
1821 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
1822 check for that declaration.
1825 All this makes it possible for a library author to design a library that relies on
1826 overlapping instances without the library client having to know.
1828 <para>The <option>-fallow-incoherent-instances</option> flag implies the
1829 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
1834 <title>Type synonyms in the instance head</title>
1837 <emphasis>Unlike Haskell 98, instance heads may use type
1838 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1839 As always, using a type synonym is just shorthand for
1840 writing the RHS of the type synonym definition. For example:
1844 type Point = (Int,Int)
1845 instance C Point where ...
1846 instance C [Point] where ...
1850 is legal. However, if you added
1854 instance C (Int,Int) where ...
1858 as well, then the compiler will complain about the overlapping
1859 (actually, identical) instance declarations. As always, type synonyms
1860 must be fully applied. You cannot, for example, write:
1865 instance Monad P where ...
1869 This design decision is independent of all the others, and easily
1870 reversed, but it makes sense to me.
1875 <sect3 id="undecidable-instances">
1876 <title>Undecidable instances</title>
1878 <para>An instance declaration must normally obey the following rules:
1880 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1881 an instance declaration <emphasis>must not</emphasis> be a type variable.
1882 For example, these are OK:
1885 instance C Int a where ...
1887 instance D (Int, Int) where ...
1889 instance E [[a]] where ...
1893 instance F a where ...
1895 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1896 For example, this is OK:
1898 instance Stateful (ST s) (MutVar s) where ...
1905 <para>All of the types in the <emphasis>context</emphasis> of
1906 an instance declaration <emphasis>must</emphasis> be type variables.
1909 instance C a b => Eq (a,b) where ...
1913 instance C Int b => Foo b where ...
1919 These restrictions ensure that
1920 context reduction terminates: each reduction step removes one type
1921 constructor. For example, the following would make the type checker
1922 loop if it wasn't excluded:
1924 instance C a => C a where ...
1926 There are two situations in which the rule is a bit of a pain. First,
1927 if one allows overlapping instance declarations then it's quite
1928 convenient to have a "default instance" declaration that applies if
1929 something more specific does not:
1938 Second, sometimes you might want to use the following to get the
1939 effect of a "class synonym":
1943 class (C1 a, C2 a, C3 a) => C a where { }
1945 instance (C1 a, C2 a, C3 a) => C a where { }
1949 This allows you to write shorter signatures:
1961 f :: (C1 a, C2 a, C3 a) => ...
1965 Voluminous correspondence on the Haskell mailing list has convinced me
1966 that it's worth experimenting with more liberal rules. If you use
1967 the experimental flag <option>-fallow-undecidable-instances</option>
1968 <indexterm><primary>-fallow-undecidable-instances
1969 option</primary></indexterm>, you can use arbitrary
1970 types in both an instance context and instance head. Termination is ensured by having a
1971 fixed-depth recursion stack. If you exceed the stack depth you get a
1972 sort of backtrace, and the opportunity to increase the stack depth
1973 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1976 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1977 allowing these idioms interesting idioms.
1984 <sect2 id="implicit-parameters">
1985 <title>Implicit parameters</title>
1987 <para> Implicit parameters are implemented as described in
1988 "Implicit parameters: dynamic scoping with static types",
1989 J Lewis, MB Shields, E Meijer, J Launchbury,
1990 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1994 <para>(Most of the following, stil rather incomplete, documentation is
1995 due to Jeff Lewis.)</para>
1997 <para>Implicit parameter support is enabled with the option
1998 <option>-fimplicit-params</option>.</para>
2001 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2002 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2003 context. In Haskell, all variables are statically bound. Dynamic
2004 binding of variables is a notion that goes back to Lisp, but was later
2005 discarded in more modern incarnations, such as Scheme. Dynamic binding
2006 can be very confusing in an untyped language, and unfortunately, typed
2007 languages, in particular Hindley-Milner typed languages like Haskell,
2008 only support static scoping of variables.
2011 However, by a simple extension to the type class system of Haskell, we
2012 can support dynamic binding. Basically, we express the use of a
2013 dynamically bound variable as a constraint on the type. These
2014 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2015 function uses a dynamically-bound variable <literal>?x</literal>
2016 of type <literal>t'</literal>". For
2017 example, the following expresses the type of a sort function,
2018 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2020 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2022 The dynamic binding constraints are just a new form of predicate in the type class system.
2025 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2026 where <literal>x</literal> is
2027 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2028 Use of this construct also introduces a new
2029 dynamic-binding constraint in the type of the expression.
2030 For example, the following definition
2031 shows how we can define an implicitly parameterized sort function in
2032 terms of an explicitly parameterized <literal>sortBy</literal> function:
2034 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2036 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2042 <title>Implicit-parameter type constraints</title>
2044 Dynamic binding constraints behave just like other type class
2045 constraints in that they are automatically propagated. Thus, when a
2046 function is used, its implicit parameters are inherited by the
2047 function that called it. For example, our <literal>sort</literal> function might be used
2048 to pick out the least value in a list:
2050 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2051 least xs = fst (sort xs)
2053 Without lifting a finger, the <literal>?cmp</literal> parameter is
2054 propagated to become a parameter of <literal>least</literal> as well. With explicit
2055 parameters, the default is that parameters must always be explicit
2056 propagated. With implicit parameters, the default is to always
2060 An implicit-parameter type constraint differs from other type class constraints in the
2061 following way: All uses of a particular implicit parameter must have
2062 the same type. This means that the type of <literal>(?x, ?x)</literal>
2063 is <literal>(?x::a) => (a,a)</literal>, and not
2064 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2068 <para> You can't have an implicit parameter in the context of a class or instance
2069 declaration. For example, both these declarations are illegal:
2071 class (?x::Int) => C a where ...
2072 instance (?x::a) => Foo [a] where ...
2074 Reason: exactly which implicit parameter you pick up depends on exactly where
2075 you invoke a function. But the ``invocation'' of instance declarations is done
2076 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2077 Easiest thing is to outlaw the offending types.</para>
2079 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2081 f :: (?x :: [a]) => Int -> Int
2084 g :: (Read a, Show a) => String -> String
2087 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2088 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2089 quite unambiguous, and fixes the type <literal>a</literal>.
2094 <title>Implicit-parameter bindings</title>
2097 An implicit parameter is <emphasis>bound</emphasis> using the standard
2098 <literal>let</literal> or <literal>where</literal> binding forms.
2099 For example, we define the <literal>min</literal> function by binding
2100 <literal>cmp</literal>.
2103 min = let ?cmp = (<=) in least
2107 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2108 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2109 (including in a list comprehension, or do-notation, or pattern guards),
2110 or a <literal>where</literal> clause.
2111 Note the following points:
2114 An implicit-parameter binding group must be a
2115 collection of simple bindings to implicit-style variables (no
2116 function-style bindings, and no type signatures); these bindings are
2117 neither polymorphic or recursive.
2120 You may not mix implicit-parameter bindings with ordinary bindings in a
2121 single <literal>let</literal>
2122 expression; use two nested <literal>let</literal>s instead.
2123 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2127 You may put multiple implicit-parameter bindings in a
2128 single binding group; but they are <emphasis>not</emphasis> treated
2129 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2130 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2131 parameter. The bindings are not nested, and may be re-ordered without changing
2132 the meaning of the program.
2133 For example, consider:
2135 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2137 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2138 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2140 f :: (?x::Int) => Int -> Int
2148 <sect3><title>Implicit parameters and polymorphic recursion</title>
2151 Consider these two definitions:
2154 len1 xs = let ?acc = 0 in len_acc1 xs
2157 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2162 len2 xs = let ?acc = 0 in len_acc2 xs
2164 len_acc2 :: (?acc :: Int) => [a] -> Int
2166 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2168 The only difference between the two groups is that in the second group
2169 <literal>len_acc</literal> is given a type signature.
2170 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2171 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2172 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2173 has a type signature, the recursive call is made to the
2174 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2175 as an implicit parameter. So we get the following results in GHCi:
2182 Adding a type signature dramatically changes the result! This is a rather
2183 counter-intuitive phenomenon, worth watching out for.
2187 <sect3><title>Implicit parameters and monomorphism</title>
2189 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2190 Haskell Report) to implicit parameters. For example, consider:
2198 Since the binding for <literal>y</literal> falls under the Monomorphism
2199 Restriction it is not generalised, so the type of <literal>y</literal> is
2200 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2201 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2202 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2203 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2204 <literal>y</literal> in the body of the <literal>let</literal> will see the
2205 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2206 <literal>14</literal>.
2211 <sect2 id="linear-implicit-parameters">
2212 <title>Linear implicit parameters</title>
2214 Linear implicit parameters are an idea developed by Koen Claessen,
2215 Mark Shields, and Simon PJ. They address the long-standing
2216 problem that monads seem over-kill for certain sorts of problem, notably:
2219 <listitem> <para> distributing a supply of unique names </para> </listitem>
2220 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2221 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2225 Linear implicit parameters are just like ordinary implicit parameters,
2226 except that they are "linear" -- that is, they cannot be copied, and
2227 must be explicitly "split" instead. Linear implicit parameters are
2228 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2229 (The '/' in the '%' suggests the split!)
2234 import GHC.Exts( Splittable )
2236 data NameSupply = ...
2238 splitNS :: NameSupply -> (NameSupply, NameSupply)
2239 newName :: NameSupply -> Name
2241 instance Splittable NameSupply where
2245 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2246 f env (Lam x e) = Lam x' (f env e)
2249 env' = extend env x x'
2250 ...more equations for f...
2252 Notice that the implicit parameter %ns is consumed
2254 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2255 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2259 So the translation done by the type checker makes
2260 the parameter explicit:
2262 f :: NameSupply -> Env -> Expr -> Expr
2263 f ns env (Lam x e) = Lam x' (f ns1 env e)
2265 (ns1,ns2) = splitNS ns
2267 env = extend env x x'
2269 Notice the call to 'split' introduced by the type checker.
2270 How did it know to use 'splitNS'? Because what it really did
2271 was to introduce a call to the overloaded function 'split',
2272 defined by the class <literal>Splittable</literal>:
2274 class Splittable a where
2277 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2278 split for name supplies. But we can simply write
2284 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2286 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2287 <literal>GHC.Exts</literal>.
2292 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2293 are entirely distinct implicit parameters: you
2294 can use them together and they won't intefere with each other. </para>
2297 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2299 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2300 in the context of a class or instance declaration. </para></listitem>
2304 <sect3><title>Warnings</title>
2307 The monomorphism restriction is even more important than usual.
2308 Consider the example above:
2310 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2311 f env (Lam x e) = Lam x' (f env e)
2314 env' = extend env x x'
2316 If we replaced the two occurrences of x' by (newName %ns), which is
2317 usually a harmless thing to do, we get:
2319 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2320 f env (Lam x e) = Lam (newName %ns) (f env e)
2322 env' = extend env x (newName %ns)
2324 But now the name supply is consumed in <emphasis>three</emphasis> places
2325 (the two calls to newName,and the recursive call to f), so
2326 the result is utterly different. Urk! We don't even have
2330 Well, this is an experimental change. With implicit
2331 parameters we have already lost beta reduction anyway, and
2332 (as John Launchbury puts it) we can't sensibly reason about
2333 Haskell programs without knowing their typing.
2338 <sect3><title>Recursive functions</title>
2339 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2342 foo :: %x::T => Int -> [Int]
2344 foo n = %x : foo (n-1)
2346 where T is some type in class Splittable.</para>
2348 Do you get a list of all the same T's or all different T's
2349 (assuming that split gives two distinct T's back)?
2351 If you supply the type signature, taking advantage of polymorphic
2352 recursion, you get what you'd probably expect. Here's the
2353 translated term, where the implicit param is made explicit:
2356 foo x n = let (x1,x2) = split x
2357 in x1 : foo x2 (n-1)
2359 But if you don't supply a type signature, GHC uses the Hindley
2360 Milner trick of using a single monomorphic instance of the function
2361 for the recursive calls. That is what makes Hindley Milner type inference
2362 work. So the translation becomes
2366 foom n = x : foom (n-1)
2370 Result: 'x' is not split, and you get a list of identical T's. So the
2371 semantics of the program depends on whether or not foo has a type signature.
2374 You may say that this is a good reason to dislike linear implicit parameters
2375 and you'd be right. That is why they are an experimental feature.
2381 <sect2 id="functional-dependencies">
2382 <title>Functional dependencies
2385 <para> Functional dependencies are implemented as described by Mark Jones
2386 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2387 In Proceedings of the 9th European Symposium on Programming,
2388 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2392 Functional dependencies are introduced by a vertical bar in the syntax of a
2393 class declaration; e.g.
2395 class (Monad m) => MonadState s m | m -> s where ...
2397 class Foo a b c | a b -> c where ...
2399 There should be more documentation, but there isn't (yet). Yell if you need it.
2405 <sect2 id="sec-kinding">
2406 <title>Explicitly-kinded quantification</title>
2409 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2410 to give the kind explicitly as (machine-checked) documentation,
2411 just as it is nice to give a type signature for a function. On some occasions,
2412 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2413 John Hughes had to define the data type:
2415 data Set cxt a = Set [a]
2416 | Unused (cxt a -> ())
2418 The only use for the <literal>Unused</literal> constructor was to force the correct
2419 kind for the type variable <literal>cxt</literal>.
2422 GHC now instead allows you to specify the kind of a type variable directly, wherever
2423 a type variable is explicitly bound. Namely:
2425 <listitem><para><literal>data</literal> declarations:
2427 data Set (cxt :: * -> *) a = Set [a]
2428 </screen></para></listitem>
2429 <listitem><para><literal>type</literal> declarations:
2431 type T (f :: * -> *) = f Int
2432 </screen></para></listitem>
2433 <listitem><para><literal>class</literal> declarations:
2435 class (Eq a) => C (f :: * -> *) a where ...
2436 </screen></para></listitem>
2437 <listitem><para><literal>forall</literal>'s in type signatures:
2439 f :: forall (cxt :: * -> *). Set cxt Int
2440 </screen></para></listitem>
2445 The parentheses are required. Some of the spaces are required too, to
2446 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2447 will get a parse error, because "<literal>::*->*</literal>" is a
2448 single lexeme in Haskell.
2452 As part of the same extension, you can put kind annotations in types
2455 f :: (Int :: *) -> Int
2456 g :: forall a. a -> (a :: *)
2460 atype ::= '(' ctype '::' kind ')
2462 The parentheses are required.
2467 <sect2 id="universal-quantification">
2468 <title>Arbitrary-rank polymorphism
2472 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2473 allows us to say exactly what this means. For example:
2481 g :: forall b. (b -> b)
2483 The two are treated identically.
2487 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2488 explicit universal quantification in
2490 For example, all the following types are legal:
2492 f1 :: forall a b. a -> b -> a
2493 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2495 f2 :: (forall a. a->a) -> Int -> Int
2496 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2498 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2500 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2501 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2502 The <literal>forall</literal> makes explicit the universal quantification that
2503 is implicitly added by Haskell.
2506 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2507 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2508 shows, the polymorphic type on the left of the function arrow can be overloaded.
2511 The function <literal>f3</literal> has a rank-3 type;
2512 it has rank-2 types on the left of a function arrow.
2515 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2516 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2517 that restriction has now been lifted.)
2518 In particular, a forall-type (also called a "type scheme"),
2519 including an operational type class context, is legal:
2521 <listitem> <para> On the left of a function arrow </para> </listitem>
2522 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2523 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2524 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2525 field type signatures.</para> </listitem>
2526 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2527 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2529 There is one place you cannot put a <literal>forall</literal>:
2530 you cannot instantiate a type variable with a forall-type. So you cannot
2531 make a forall-type the argument of a type constructor. So these types are illegal:
2533 x1 :: [forall a. a->a]
2534 x2 :: (forall a. a->a, Int)
2535 x3 :: Maybe (forall a. a->a)
2537 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2538 a type variable any more!
2547 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2548 the types of the constructor arguments. Here are several examples:
2554 data T a = T1 (forall b. b -> b -> b) a
2556 data MonadT m = MkMonad { return :: forall a. a -> m a,
2557 bind :: forall a b. m a -> (a -> m b) -> m b
2560 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2566 The constructors have rank-2 types:
2572 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2573 MkMonad :: forall m. (forall a. a -> m a)
2574 -> (forall a b. m a -> (a -> m b) -> m b)
2576 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2582 Notice that you don't need to use a <literal>forall</literal> if there's an
2583 explicit context. For example in the first argument of the
2584 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2585 prefixed to the argument type. The implicit <literal>forall</literal>
2586 quantifies all type variables that are not already in scope, and are
2587 mentioned in the type quantified over.
2591 As for type signatures, implicit quantification happens for non-overloaded
2592 types too. So if you write this:
2595 data T a = MkT (Either a b) (b -> b)
2598 it's just as if you had written this:
2601 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2604 That is, since the type variable <literal>b</literal> isn't in scope, it's
2605 implicitly universally quantified. (Arguably, it would be better
2606 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2607 where that is what is wanted. Feedback welcomed.)
2611 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2612 the constructor to suitable values, just as usual. For example,
2623 a3 = MkSwizzle reverse
2626 a4 = let r x = Just x
2633 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2634 mkTs f x y = [T1 f x, T1 f y]
2640 The type of the argument can, as usual, be more general than the type
2641 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2642 does not need the <literal>Ord</literal> constraint.)
2646 When you use pattern matching, the bound variables may now have
2647 polymorphic types. For example:
2653 f :: T a -> a -> (a, Char)
2654 f (T1 w k) x = (w k x, w 'c' 'd')
2656 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2657 g (MkSwizzle s) xs f = s (map f (s xs))
2659 h :: MonadT m -> [m a] -> m [a]
2660 h m [] = return m []
2661 h m (x:xs) = bind m x $ \y ->
2662 bind m (h m xs) $ \ys ->
2669 In the function <function>h</function> we use the record selectors <literal>return</literal>
2670 and <literal>bind</literal> to extract the polymorphic bind and return functions
2671 from the <literal>MonadT</literal> data structure, rather than using pattern
2677 <title>Type inference</title>
2680 In general, type inference for arbitrary-rank types is undecidable.
2681 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2682 to get a decidable algorithm by requiring some help from the programmer.
2683 We do not yet have a formal specification of "some help" but the rule is this:
2686 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2687 provides an explicit polymorphic type for x, or GHC's type inference will assume
2688 that x's type has no foralls in it</emphasis>.
2691 What does it mean to "provide" an explicit type for x? You can do that by
2692 giving a type signature for x directly, using a pattern type signature
2693 (<xref linkend="scoped-type-variables"/>), thus:
2695 \ f :: (forall a. a->a) -> (f True, f 'c')
2697 Alternatively, you can give a type signature to the enclosing
2698 context, which GHC can "push down" to find the type for the variable:
2700 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2702 Here the type signature on the expression can be pushed inwards
2703 to give a type signature for f. Similarly, and more commonly,
2704 one can give a type signature for the function itself:
2706 h :: (forall a. a->a) -> (Bool,Char)
2707 h f = (f True, f 'c')
2709 You don't need to give a type signature if the lambda bound variable
2710 is a constructor argument. Here is an example we saw earlier:
2712 f :: T a -> a -> (a, Char)
2713 f (T1 w k) x = (w k x, w 'c' 'd')
2715 Here we do not need to give a type signature to <literal>w</literal>, because
2716 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2723 <sect3 id="implicit-quant">
2724 <title>Implicit quantification</title>
2727 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2728 user-written types, if and only if there is no explicit <literal>forall</literal>,
2729 GHC finds all the type variables mentioned in the type that are not already
2730 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2734 f :: forall a. a -> a
2741 h :: forall b. a -> b -> b
2747 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2750 f :: (a -> a) -> Int
2752 f :: forall a. (a -> a) -> Int
2754 f :: (forall a. a -> a) -> Int
2757 g :: (Ord a => a -> a) -> Int
2758 -- MEANS the illegal type
2759 g :: forall a. (Ord a => a -> a) -> Int
2761 g :: (forall a. Ord a => a -> a) -> Int
2763 The latter produces an illegal type, which you might think is silly,
2764 but at least the rule is simple. If you want the latter type, you
2765 can write your for-alls explicitly. Indeed, doing so is strongly advised
2774 <sect2 id="scoped-type-variables">
2775 <title>Scoped type variables
2779 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2781 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2782 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2783 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2787 f (xs::[a]) = ys ++ ys
2792 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2793 This brings the type variable <literal>a</literal> into scope; it scopes over
2794 all the patterns and right hand sides for this equation for <function>f</function>.
2795 In particular, it is in scope at the type signature for <varname>y</varname>.
2799 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2800 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2801 implicitly universally quantified. (If there are no type variables in
2802 scope, all type variables mentioned in the signature are universally
2803 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2804 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2805 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2806 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2807 it becomes possible to do so.
2811 Scoped type variables are implemented in both GHC and Hugs. Where the
2812 implementations differ from the specification below, those differences
2817 So much for the basic idea. Here are the details.
2821 <title>What a scoped type variable means</title>
2823 A lexically-scoped type variable is simply
2824 the name for a type. The restriction it expresses is that all occurrences
2825 of the same name mean the same type. For example:
2827 f :: [Int] -> Int -> Int
2828 f (xs::[a]) (y::a) = (head xs + y) :: a
2830 The pattern type signatures on the left hand side of
2831 <literal>f</literal> express the fact that <literal>xs</literal>
2832 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2833 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2834 specifies that this expression must have the same type <literal>a</literal>.
2835 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2836 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2837 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2838 rules, which specified that a pattern-bound type variable should be universally quantified.)
2839 For example, all of these are legal:</para>
2842 t (x::a) (y::a) = x+y*2
2844 f (x::a) (y::b) = [x,y] -- a unifies with b
2846 g (x::a) = x + 1::Int -- a unifies with Int
2848 h x = let k (y::a) = [x,y] -- a is free in the
2849 in k x -- environment
2851 k (x::a) True = ... -- a unifies with Int
2852 k (x::Int) False = ...
2855 w (x::a) = x -- a unifies with [b]
2861 <title>Scope and implicit quantification</title>
2869 All the type variables mentioned in a pattern,
2870 that are not already in scope,
2871 are brought into scope by the pattern. We describe this set as
2872 the <emphasis>type variables bound by the pattern</emphasis>.
2875 f (x::a) = let g (y::(a,b)) = fst y
2879 The pattern <literal>(x::a)</literal> brings the type variable
2880 <literal>a</literal> into scope, as well as the term
2881 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2882 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2883 and brings into scope the type variable <literal>b</literal>.
2889 The type variable(s) bound by the pattern have the same scope
2890 as the term variable(s) bound by the pattern. For example:
2893 f (x::a) = <...rhs of f...>
2894 (p::b, q::b) = (1,2)
2895 in <...body of let...>
2897 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2898 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2899 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2900 just like <literal>p</literal> and <literal>q</literal> do.
2901 Indeed, the newly bound type variables also scope over any ordinary, separate
2902 type signatures in the <literal>let</literal> group.
2909 The type variables bound by the pattern may be
2910 mentioned in ordinary type signatures or pattern
2911 type signatures anywhere within their scope.
2918 In ordinary type signatures, any type variable mentioned in the
2919 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2927 Ordinary type signatures do not bring any new type variables
2928 into scope (except in the type signature itself!). So this is illegal:
2935 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2936 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2937 and that is an incorrect typing.
2944 The pattern type signature is a monotype:
2949 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2953 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2954 not to type schemes.
2958 There is no implicit universal quantification on pattern type signatures (in contrast to
2959 ordinary type signatures).
2969 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2970 scope over the methods defined in the <literal>where</literal> part. For example:
2984 (Not implemented in Hugs yet, Dec 98).
2994 <sect3 id="decl-type-sigs">
2995 <title>Declaration type signatures</title>
2996 <para>A declaration type signature that has <emphasis>explicit</emphasis>
2997 quantification (using <literal>forall</literal>) brings into scope the
2998 explicitly-quantified
2999 type variables, in the definition of the named function(s). For example:
3001 f :: forall a. [a] -> [a]
3002 f (x:xs) = xs ++ [ x :: a ]
3004 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3005 the definition of "<literal>f</literal>".
3007 <para>This only happens if the quantification in <literal>f</literal>'s type
3008 signature is explicit. For example:
3011 g (x:xs) = xs ++ [ x :: a ]
3013 This program will be rejected, because "<literal>a</literal>" does not scope
3014 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3015 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3016 quantification rules.
3020 <sect3 id="pattern-type-sigs">
3021 <title>Where a pattern type signature can occur</title>
3024 A pattern type signature can occur in any pattern. For example:
3029 A pattern type signature can be on an arbitrary sub-pattern, not
3034 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3043 Pattern type signatures, including the result part, can be used
3044 in lambda abstractions:
3047 (\ (x::a, y) :: a -> x)
3054 Pattern type signatures, including the result part, can be used
3055 in <literal>case</literal> expressions:
3058 case e of { ((x::a, y) :: (a,b)) -> x }
3061 Note that the <literal>-></literal> symbol in a case alternative
3062 leads to difficulties when parsing a type signature in the pattern: in
3063 the absence of the extra parentheses in the example above, the parser
3064 would try to interpret the <literal>-></literal> as a function
3065 arrow and give a parse error later.
3073 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3074 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3075 token or a parenthesised type of some sort). To see why,
3076 consider how one would parse this:
3090 Pattern type signatures can bind existential type variables.
3095 data T = forall a. MkT [a]
3098 f (MkT [t::a]) = MkT t3
3111 Pattern type signatures
3112 can be used in pattern bindings:
3115 f x = let (y, z::a) = x in ...
3116 f1 x = let (y, z::Int) = x in ...
3117 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3118 f3 :: (b->b) = \x -> x
3121 In all such cases, the binding is not generalised over the pattern-bound
3122 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3123 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3124 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3125 In contrast, the binding
3130 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3131 in <literal>f4</literal>'s scope.
3137 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3138 type signatures. The two can be used independently or together.</para>
3142 <sect3 id="result-type-sigs">
3143 <title>Result type signatures</title>
3146 The result type of a function can be given a signature, thus:
3150 f (x::a) :: [a] = [x,x,x]
3154 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3155 result type. Sometimes this is the only way of naming the type variable
3160 f :: Int -> [a] -> [a]
3161 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3162 in \xs -> map g (reverse xs `zip` xs)
3167 The type variables bound in a result type signature scope over the right hand side
3168 of the definition. However, consider this corner-case:
3170 rev1 :: [a] -> [a] = \xs -> reverse xs
3172 foo ys = rev (ys::[a])
3174 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3175 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3176 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3177 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3178 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3181 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3182 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3186 rev1 :: [a] -> [a] = \xs -> reverse xs
3191 Result type signatures are not yet implemented in Hugs.
3198 <sect2 id="deriving-typeable">
3199 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3202 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3203 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3204 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3205 classes <literal>Eq</literal>, <literal>Ord</literal>,
3206 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3209 GHC extends this list with two more classes that may be automatically derived
3210 (provided the <option>-fglasgow-exts</option> flag is specified):
3211 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3212 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3213 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3215 <para>An instance of <literal>Typeable</literal> can only be derived if the
3216 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3217 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3219 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3220 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3222 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3223 are used, and only <literal>Typeable1</literal> up to
3224 <literal>Typeable7</literal> are provided in the library.)
3225 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3226 class, whose kind suits that of the data type constructor, and
3227 then writing the data type instance by hand.
3231 <sect2 id="newtype-deriving">
3232 <title>Generalised derived instances for newtypes</title>
3235 When you define an abstract type using <literal>newtype</literal>, you may want
3236 the new type to inherit some instances from its representation. In
3237 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3238 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3239 other classes you have to write an explicit instance declaration. For
3240 example, if you define
3243 newtype Dollars = Dollars Int
3246 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3247 explicitly define an instance of <literal>Num</literal>:
3250 instance Num Dollars where
3251 Dollars a + Dollars b = Dollars (a+b)
3254 All the instance does is apply and remove the <literal>newtype</literal>
3255 constructor. It is particularly galling that, since the constructor
3256 doesn't appear at run-time, this instance declaration defines a
3257 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3258 dictionary, only slower!
3262 <sect3> <title> Generalising the deriving clause </title>
3264 GHC now permits such instances to be derived instead, so one can write
3266 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3269 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3270 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3271 derives an instance declaration of the form
3274 instance Num Int => Num Dollars
3277 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3281 We can also derive instances of constructor classes in a similar
3282 way. For example, suppose we have implemented state and failure monad
3283 transformers, such that
3286 instance Monad m => Monad (State s m)
3287 instance Monad m => Monad (Failure m)
3289 In Haskell 98, we can define a parsing monad by
3291 type Parser tok m a = State [tok] (Failure m) a
3294 which is automatically a monad thanks to the instance declarations
3295 above. With the extension, we can make the parser type abstract,
3296 without needing to write an instance of class <literal>Monad</literal>, via
3299 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3302 In this case the derived instance declaration is of the form
3304 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3307 Notice that, since <literal>Monad</literal> is a constructor class, the
3308 instance is a <emphasis>partial application</emphasis> of the new type, not the
3309 entire left hand side. We can imagine that the type declaration is
3310 ``eta-converted'' to generate the context of the instance
3315 We can even derive instances of multi-parameter classes, provided the
3316 newtype is the last class parameter. In this case, a ``partial
3317 application'' of the class appears in the <literal>deriving</literal>
3318 clause. For example, given the class
3321 class StateMonad s m | m -> s where ...
3322 instance Monad m => StateMonad s (State s m) where ...
3324 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3326 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3327 deriving (Monad, StateMonad [tok])
3330 The derived instance is obtained by completing the application of the
3331 class to the new type:
3334 instance StateMonad [tok] (State [tok] (Failure m)) =>
3335 StateMonad [tok] (Parser tok m)
3340 As a result of this extension, all derived instances in newtype
3341 declarations are treated uniformly (and implemented just by reusing
3342 the dictionary for the representation type), <emphasis>except</emphasis>
3343 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3344 the newtype and its representation.
3348 <sect3> <title> A more precise specification </title>
3350 Derived instance declarations are constructed as follows. Consider the
3351 declaration (after expansion of any type synonyms)
3354 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3360 <literal>S</literal> is a type constructor,
3363 The <literal>t1...tk</literal> are types,
3366 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3367 the <literal>ti</literal>, and
3370 The <literal>ci</literal> are partial applications of
3371 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3372 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3375 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3376 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3377 should not "look through" the type or its constructor. You can still
3378 derive these classes for a newtype, but it happens in the usual way, not
3379 via this new mechanism.
3382 Then, for each <literal>ci</literal>, the derived instance
3385 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3387 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3388 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3392 As an example which does <emphasis>not</emphasis> work, consider
3394 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3396 Here we cannot derive the instance
3398 instance Monad (State s m) => Monad (NonMonad m)
3401 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3402 and so cannot be "eta-converted" away. It is a good thing that this
3403 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3404 not, in fact, a monad --- for the same reason. Try defining
3405 <literal>>>=</literal> with the correct type: you won't be able to.
3409 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3410 important, since we can only derive instances for the last one. If the
3411 <literal>StateMonad</literal> class above were instead defined as
3414 class StateMonad m s | m -> s where ...
3417 then we would not have been able to derive an instance for the
3418 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3419 classes usually have one "main" parameter for which deriving new
3420 instances is most interesting.
3422 <para>Lastly, all of this applies only for classes other than
3423 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3424 and <literal>Data</literal>, for which the built-in derivation applies (section
3425 4.3.3. of the Haskell Report).
3426 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3427 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3428 the standard method is used or the one described here.)
3434 <sect2 id="typing-binds">
3435 <title>Generalised typing of mutually recursive bindings</title>
3438 The Haskell Report specifies that a group of bindings (at top level, or in a
3439 <literal>let</literal> or <literal>where</literal>) should be sorted into
3440 strongly-connected components, and then type-checked in dependency order
3441 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3442 Report, Section 4.5.1</ulink>).
3443 As each group is type-checked, any binders of the group that
3445 an explicit type signature are put in the type environment with the specified
3447 and all others are monomorphic until the group is generalised
3448 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3451 <para>Following a suggestion of Mark Jones, in his paper
3452 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3454 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3456 <emphasis>the dependency analysis ignores references to variables that have an explicit
3457 type signature</emphasis>.
3458 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3459 typecheck. For example, consider:
3461 f :: Eq a => a -> Bool
3462 f x = (x == x) || g True || g "Yes"
3464 g y = (y <= y) || f True
3466 This is rejected by Haskell 98, but under Jones's scheme the definition for
3467 <literal>g</literal> is typechecked first, separately from that for
3468 <literal>f</literal>,
3469 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3470 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3471 type is generalised, to get
3473 g :: Ord a => a -> Bool
3475 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3476 <literal>g</literal> in the type environment.
3480 The same refined dependency analysis also allows the type signatures of
3481 mutually-recursive functions to have different contexts, something that is illegal in
3482 Haskell 98 (Section 4.5.2, last sentence). With
3483 <option>-fglasgow-exts</option>
3484 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3485 type signatures; in practice this means that only variables bound by the same
3486 pattern binding must have the same context. For example, this is fine:
3488 f :: Eq a => a -> Bool
3489 f x = (x == x) || g True
3491 g :: Ord a => a -> Bool
3492 g y = (y <= y) || f True
3498 <!-- ==================== End of type system extensions ================= -->
3500 <!-- ====================== Generalised algebraic data types ======================= -->
3503 <title>Generalised Algebraic Data Types</title>
3505 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3506 to give the type signatures of constructors explicitly. For example:
3509 Lit :: Int -> Term Int
3510 Succ :: Term Int -> Term Int
3511 IsZero :: Term Int -> Term Bool
3512 If :: Term Bool -> Term a -> Term a -> Term a
3513 Pair :: Term a -> Term b -> Term (a,b)
3515 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3516 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3517 for these <literal>Terms</literal>:
3521 eval (Succ t) = 1 + eval t
3522 eval (IsZero i) = eval i == 0
3523 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3524 eval (Pair e1 e2) = (eval e2, eval e2)
3526 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3528 <para> The extensions to GHC are these:
3531 Data type declarations have a 'where' form, as exemplified above. The type signature of
3532 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3533 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3534 have no scope. Indeed, one can write a kind signature instead:
3536 data Term :: * -> * where ...
3538 or even a mixture of the two:
3540 data Foo a :: (* -> *) -> * where ...
3542 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3545 data Foo a (b :: * -> *) where ...
3550 There are no restrictions on the type of the data constructor, except that the result
3551 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3552 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3556 You cannot use record syntax on a GADT-style data type declaration. (
3557 It's not clear what these it would mean. For example,
3558 the record selectors might ill-typed.)
3559 However, you can use strictness annotations, in the obvious places
3560 in the constructor type:
3563 Lit :: !Int -> Term Int
3564 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3565 Pair :: Term a -> Term b -> Term (a,b)
3570 You can use a <literal>deriving</literal> clause on a GADT-style data type
3571 declaration, but only if the data type could also have been declared in
3572 Haskell-98 syntax. For example, these two declarations are equivalent
3574 data Maybe1 a where {
3575 Nothing1 :: Maybe a ;
3576 Just1 :: a -> Maybe a
3577 } deriving( Eq, Ord )
3579 data Maybe2 a = Nothing2 | Just2 a
3582 This simply allows you to declare a vanilla Haskell-98 data type using the
3583 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3587 Pattern matching causes type refinement. For example, in the right hand side of the equation
3592 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3593 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3594 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3596 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3597 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3598 occur. However, the refinement is quite general. For example, if we had:
3600 eval :: Term a -> a -> a
3601 eval (Lit i) j = i+j
3603 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3604 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3605 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3611 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3613 data T a = forall b. MkT b (b->a)
3614 data T' a where { MKT :: b -> (b->a) -> T' a }
3619 <!-- ====================== End of Generalised algebraic data types ======================= -->
3621 <!-- ====================== TEMPLATE HASKELL ======================= -->
3623 <sect1 id="template-haskell">
3624 <title>Template Haskell</title>
3626 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3627 Template Haskell at <ulink url="http://www.haskell.org/th/">
3628 http://www.haskell.org/th/</ulink>, while
3630 the main technical innovations is discussed in "<ulink
3631 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3632 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3633 The details of the Template Haskell design are still in flux. Make sure you
3634 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3635 (search for the type ExpQ).
3636 [Temporary: many changes to the original design are described in
3637 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3638 Not all of these changes are in GHC 6.2.]
3641 <para> The first example from that paper is set out below as a worked example to help get you started.
3645 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3646 Tim Sheard is going to expand it.)
3650 <title>Syntax</title>
3652 <para> Template Haskell has the following new syntactic
3653 constructions. You need to use the flag
3654 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3655 </indexterm>to switch these syntactic extensions on
3656 (<option>-fth</option> is currently implied by
3657 <option>-fglasgow-exts</option>, but you are encouraged to
3658 specify it explicitly).</para>
3662 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3663 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3664 There must be no space between the "$" and the identifier or parenthesis. This use
3665 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3666 of "." as an infix operator. If you want the infix operator, put spaces around it.
3668 <para> A splice can occur in place of
3670 <listitem><para> an expression; the spliced expression must
3671 have type <literal>Q Exp</literal></para></listitem>
3672 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3673 <listitem><para> [Planned, but not implemented yet.] a
3674 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
3676 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3677 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3683 A expression quotation is written in Oxford brackets, thus:
3685 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3686 the quotation has type <literal>Expr</literal>.</para></listitem>
3687 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3688 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3689 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
3690 the quotation has type <literal>Type</literal>.</para></listitem>
3691 </itemizedlist></para></listitem>
3694 Reification is written thus:
3696 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3697 has type <literal>Dec</literal>. </para></listitem>
3698 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3699 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3700 <listitem><para> Still to come: fixities </para></listitem>
3702 </itemizedlist></para>
3709 <sect2> <title> Using Template Haskell </title>
3713 The data types and monadic constructor functions for Template Haskell are in the library
3714 <literal>Language.Haskell.THSyntax</literal>.
3718 You can only run a function at compile time if it is imported from another module. That is,
3719 you can't define a function in a module, and call it from within a splice in the same module.
3720 (It would make sense to do so, but it's hard to implement.)
3724 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3727 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3728 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3729 compiles and runs a program, and then looks at the result. So it's important that
3730 the program it compiles produces results whose representations are identical to
3731 those of the compiler itself.
3735 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3736 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3741 <sect2> <title> A Template Haskell Worked Example </title>
3742 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3743 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3750 -- Import our template "pr"
3751 import Printf ( pr )
3753 -- The splice operator $ takes the Haskell source code
3754 -- generated at compile time by "pr" and splices it into
3755 -- the argument of "putStrLn".
3756 main = putStrLn ( $(pr "Hello") )
3762 -- Skeletal printf from the paper.
3763 -- It needs to be in a separate module to the one where
3764 -- you intend to use it.
3766 -- Import some Template Haskell syntax
3767 import Language.Haskell.TH
3769 -- Describe a format string
3770 data Format = D | S | L String
3772 -- Parse a format string. This is left largely to you
3773 -- as we are here interested in building our first ever
3774 -- Template Haskell program and not in building printf.
3775 parse :: String -> [Format]
3778 -- Generate Haskell source code from a parsed representation
3779 -- of the format string. This code will be spliced into
3780 -- the module which calls "pr", at compile time.
3781 gen :: [Format] -> ExpQ
3782 gen [D] = [| \n -> show n |]
3783 gen [S] = [| \s -> s |]
3784 gen [L s] = stringE s
3786 -- Here we generate the Haskell code for the splice
3787 -- from an input format string.
3788 pr :: String -> ExpQ
3789 pr s = gen (parse s)
3792 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3795 $ ghc --make -fth main.hs -o main.exe
3798 <para>Run "main.exe" and here is your output:</para>
3809 <!-- ===================== Arrow notation =================== -->
3811 <sect1 id="arrow-notation">
3812 <title>Arrow notation
3815 <para>Arrows are a generalization of monads introduced by John Hughes.
3816 For more details, see
3821 “Generalising Monads to Arrows”,
3822 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3823 pp67–111, May 2000.
3829 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3830 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3836 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3837 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3843 and the arrows web page at
3844 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3845 With the <option>-farrows</option> flag, GHC supports the arrow
3846 notation described in the second of these papers.
3847 What follows is a brief introduction to the notation;
3848 it won't make much sense unless you've read Hughes's paper.
3849 This notation is translated to ordinary Haskell,
3850 using combinators from the
3851 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3855 <para>The extension adds a new kind of expression for defining arrows:
3857 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3858 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3860 where <literal>proc</literal> is a new keyword.
3861 The variables of the pattern are bound in the body of the
3862 <literal>proc</literal>-expression,
3863 which is a new sort of thing called a <firstterm>command</firstterm>.
3864 The syntax of commands is as follows:
3866 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3867 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3868 | <replaceable>cmd</replaceable><superscript>0</superscript>
3870 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3871 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3872 infix operators as for expressions, and
3874 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3875 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3876 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3877 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3878 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3879 | <replaceable>fcmd</replaceable>
3881 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3882 | ( <replaceable>cmd</replaceable> )
3883 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3885 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3886 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3887 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3888 | <replaceable>cmd</replaceable>
3890 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3891 except that the bodies are commands instead of expressions.
3895 Commands produce values, but (like monadic computations)
3896 may yield more than one value,
3897 or none, and may do other things as well.
3898 For the most part, familiarity with monadic notation is a good guide to
3900 However the values of expressions, even monadic ones,
3901 are determined by the values of the variables they contain;
3902 this is not necessarily the case for commands.
3906 A simple example of the new notation is the expression
3908 proc x -> f -< x+1
3910 We call this a <firstterm>procedure</firstterm> or
3911 <firstterm>arrow abstraction</firstterm>.
3912 As with a lambda expression, the variable <literal>x</literal>
3913 is a new variable bound within the <literal>proc</literal>-expression.
3914 It refers to the input to the arrow.
3915 In the above example, <literal>-<</literal> is not an identifier but an
3916 new reserved symbol used for building commands from an expression of arrow
3917 type and an expression to be fed as input to that arrow.
3918 (The weird look will make more sense later.)
3919 It may be read as analogue of application for arrows.
3920 The above example is equivalent to the Haskell expression
3922 arr (\ x -> x+1) >>> f
3924 That would make no sense if the expression to the left of
3925 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3926 More generally, the expression to the left of <literal>-<</literal>
3927 may not involve any <firstterm>local variable</firstterm>,
3928 i.e. a variable bound in the current arrow abstraction.
3929 For such a situation there is a variant <literal>-<<</literal>, as in
3931 proc x -> f x -<< x+1
3933 which is equivalent to
3935 arr (\ x -> (f x, x+1)) >>> app
3937 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3939 Such an arrow is equivalent to a monad, so if you're using this form
3940 you may find a monadic formulation more convenient.
3944 <title>do-notation for commands</title>
3947 Another form of command is a form of <literal>do</literal>-notation.
3948 For example, you can write
3957 You can read this much like ordinary <literal>do</literal>-notation,
3958 but with commands in place of monadic expressions.
3959 The first line sends the value of <literal>x+1</literal> as an input to
3960 the arrow <literal>f</literal>, and matches its output against
3961 <literal>y</literal>.
3962 In the next line, the output is discarded.
3963 The arrow <function>returnA</function> is defined in the
3964 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3965 module as <literal>arr id</literal>.
3966 The above example is treated as an abbreviation for
3968 arr (\ x -> (x, x)) >>>
3969 first (arr (\ x -> x+1) >>> f) >>>
3970 arr (\ (y, x) -> (y, (x, y))) >>>
3971 first (arr (\ y -> 2*y) >>> g) >>>
3973 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3974 first (arr (\ (x, z) -> x*z) >>> h) >>>
3975 arr (\ (t, z) -> t+z) >>>
3978 Note that variables not used later in the composition are projected out.
3979 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3981 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3982 module, this reduces to
3984 arr (\ x -> (x+1, x)) >>>
3986 arr (\ (y, x) -> (2*y, (x, y))) >>>
3988 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3990 arr (\ (t, z) -> t+z)
3992 which is what you might have written by hand.
3993 With arrow notation, GHC keeps track of all those tuples of variables for you.
3997 Note that although the above translation suggests that
3998 <literal>let</literal>-bound variables like <literal>z</literal> must be
3999 monomorphic, the actual translation produces Core,
4000 so polymorphic variables are allowed.
4004 It's also possible to have mutually recursive bindings,
4005 using the new <literal>rec</literal> keyword, as in the following example:
4007 counter :: ArrowCircuit a => a Bool Int
4008 counter = proc reset -> do
4009 rec output <- returnA -< if reset then 0 else next
4010 next <- delay 0 -< output+1
4011 returnA -< output
4013 The translation of such forms uses the <function>loop</function> combinator,
4014 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4020 <title>Conditional commands</title>
4023 In the previous example, we used a conditional expression to construct the
4025 Sometimes we want to conditionally execute different commands, as in
4032 which is translated to
4034 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4035 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4037 Since the translation uses <function>|||</function>,
4038 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4042 There are also <literal>case</literal> commands, like
4048 y <- h -< (x1, x2)
4052 The syntax is the same as for <literal>case</literal> expressions,
4053 except that the bodies of the alternatives are commands rather than expressions.
4054 The translation is similar to that of <literal>if</literal> commands.
4060 <title>Defining your own control structures</title>
4063 As we're seen, arrow notation provides constructs,
4064 modelled on those for expressions,
4065 for sequencing, value recursion and conditionals.
4066 But suitable combinators,
4067 which you can define in ordinary Haskell,
4068 may also be used to build new commands out of existing ones.
4069 The basic idea is that a command defines an arrow from environments to values.
4070 These environments assign values to the free local variables of the command.
4071 Thus combinators that produce arrows from arrows
4072 may also be used to build commands from commands.
4073 For example, the <literal>ArrowChoice</literal> class includes a combinator
4075 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4077 so we can use it to build commands:
4079 expr' = proc x -> do
4082 symbol Plus -< ()
4083 y <- term -< ()
4086 symbol Minus -< ()
4087 y <- term -< ()
4090 (The <literal>do</literal> on the first line is needed to prevent the first
4091 <literal><+> ...</literal> from being interpreted as part of the
4092 expression on the previous line.)
4093 This is equivalent to
4095 expr' = (proc x -> returnA -< x)
4096 <+> (proc x -> do
4097 symbol Plus -< ()
4098 y <- term -< ()
4100 <+> (proc x -> do
4101 symbol Minus -< ()
4102 y <- term -< ()
4105 It is essential that this operator be polymorphic in <literal>e</literal>
4106 (representing the environment input to the command
4107 and thence to its subcommands)
4108 and satisfy the corresponding naturality property
4110 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4112 at least for strict <literal>k</literal>.
4113 (This should be automatic if you're not using <function>seq</function>.)
4114 This ensures that environments seen by the subcommands are environments
4115 of the whole command,
4116 and also allows the translation to safely trim these environments.
4117 The operator must also not use any variable defined within the current
4122 We could define our own operator
4124 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4125 untilA body cond = proc x ->
4126 if cond x then returnA -< ()
4129 untilA body cond -< x
4131 and use it in the same way.
4132 Of course this infix syntax only makes sense for binary operators;
4133 there is also a more general syntax involving special brackets:
4137 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4144 <title>Primitive constructs</title>
4147 Some operators will need to pass additional inputs to their subcommands.
4148 For example, in an arrow type supporting exceptions,
4149 the operator that attaches an exception handler will wish to pass the
4150 exception that occurred to the handler.
4151 Such an operator might have a type
4153 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4155 where <literal>Ex</literal> is the type of exceptions handled.
4156 You could then use this with arrow notation by writing a command
4158 body `handleA` \ ex -> handler
4160 so that if an exception is raised in the command <literal>body</literal>,
4161 the variable <literal>ex</literal> is bound to the value of the exception
4162 and the command <literal>handler</literal>,
4163 which typically refers to <literal>ex</literal>, is entered.
4164 Though the syntax here looks like a functional lambda,
4165 we are talking about commands, and something different is going on.
4166 The input to the arrow represented by a command consists of values for
4167 the free local variables in the command, plus a stack of anonymous values.
4168 In all the prior examples, this stack was empty.
4169 In the second argument to <function>handleA</function>,
4170 this stack consists of one value, the value of the exception.
4171 The command form of lambda merely gives this value a name.
4176 the values on the stack are paired to the right of the environment.
4177 So operators like <function>handleA</function> that pass
4178 extra inputs to their subcommands can be designed for use with the notation
4179 by pairing the values with the environment in this way.
4180 More precisely, the type of each argument of the operator (and its result)
4181 should have the form
4183 a (...(e,t1), ... tn) t
4185 where <replaceable>e</replaceable> is a polymorphic variable
4186 (representing the environment)
4187 and <replaceable>ti</replaceable> are the types of the values on the stack,
4188 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4189 The polymorphic variable <replaceable>e</replaceable> must not occur in
4190 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4191 <replaceable>t</replaceable>.
4192 However the arrows involved need not be the same.
4193 Here are some more examples of suitable operators:
4195 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4196 runReader :: ... => a e c -> a' (e,State) c
4197 runState :: ... => a e c -> a' (e,State) (c,State)
4199 We can supply the extra input required by commands built with the last two
4200 by applying them to ordinary expressions, as in
4204 (|runReader (do { ... })|) s
4206 which adds <literal>s</literal> to the stack of inputs to the command
4207 built using <function>runReader</function>.
4211 The command versions of lambda abstraction and application are analogous to
4212 the expression versions.
4213 In particular, the beta and eta rules describe equivalences of commands.
4214 These three features (operators, lambda abstraction and application)
4215 are the core of the notation; everything else can be built using them,
4216 though the results would be somewhat clumsy.
4217 For example, we could simulate <literal>do</literal>-notation by defining
4219 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4220 u `bind` f = returnA &&& u >>> f
4222 bind_ :: Arrow a => a e b -> a e c -> a e c
4223 u `bind_` f = u `bind` (arr fst >>> f)
4225 We could simulate <literal>if</literal> by defining
4227 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4228 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4235 <title>Differences with the paper</title>
4240 <para>Instead of a single form of arrow application (arrow tail) with two
4241 translations, the implementation provides two forms
4242 <quote><literal>-<</literal></quote> (first-order)
4243 and <quote><literal>-<<</literal></quote> (higher-order).
4248 <para>User-defined operators are flagged with banana brackets instead of
4249 a new <literal>form</literal> keyword.
4258 <title>Portability</title>
4261 Although only GHC implements arrow notation directly,
4262 there is also a preprocessor
4264 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4265 that translates arrow notation into Haskell 98
4266 for use with other Haskell systems.
4267 You would still want to check arrow programs with GHC;
4268 tracing type errors in the preprocessor output is not easy.
4269 Modules intended for both GHC and the preprocessor must observe some
4270 additional restrictions:
4275 The module must import
4276 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4282 The preprocessor cannot cope with other Haskell extensions.
4283 These would have to go in separate modules.
4289 Because the preprocessor targets Haskell (rather than Core),
4290 <literal>let</literal>-bound variables are monomorphic.
4301 <!-- ==================== ASSERTIONS ================= -->
4303 <sect1 id="sec-assertions">
4305 <indexterm><primary>Assertions</primary></indexterm>
4309 If you want to make use of assertions in your standard Haskell code, you
4310 could define a function like the following:
4316 assert :: Bool -> a -> a
4317 assert False x = error "assertion failed!"
4324 which works, but gives you back a less than useful error message --
4325 an assertion failed, but which and where?
4329 One way out is to define an extended <function>assert</function> function which also
4330 takes a descriptive string to include in the error message and
4331 perhaps combine this with the use of a pre-processor which inserts
4332 the source location where <function>assert</function> was used.
4336 Ghc offers a helping hand here, doing all of this for you. For every
4337 use of <function>assert</function> in the user's source:
4343 kelvinToC :: Double -> Double
4344 kelvinToC k = assert (k >= 0.0) (k+273.15)
4350 Ghc will rewrite this to also include the source location where the
4357 assert pred val ==> assertError "Main.hs|15" pred val
4363 The rewrite is only performed by the compiler when it spots
4364 applications of <function>Control.Exception.assert</function>, so you
4365 can still define and use your own versions of
4366 <function>assert</function>, should you so wish. If not, import
4367 <literal>Control.Exception</literal> to make use
4368 <function>assert</function> in your code.
4372 GHC ignores assertions when optimisation is turned on with the
4373 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4374 <literal>assert pred e</literal> will be rewritten to
4375 <literal>e</literal>. You can also disable assertions using the
4376 <option>-fignore-asserts</option>
4377 option<indexterm><primary><option>-fignore-asserts</option></primary>
4378 </indexterm>.</para>
4381 Assertion failures can be caught, see the documentation for the
4382 <literal>Control.Exception</literal> library for the details.
4388 <!-- =============================== PRAGMAS =========================== -->
4390 <sect1 id="pragmas">
4391 <title>Pragmas</title>
4393 <indexterm><primary>pragma</primary></indexterm>
4395 <para>GHC supports several pragmas, or instructions to the
4396 compiler placed in the source code. Pragmas don't normally affect
4397 the meaning of the program, but they might affect the efficiency
4398 of the generated code.</para>
4400 <para>Pragmas all take the form
4402 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4404 where <replaceable>word</replaceable> indicates the type of
4405 pragma, and is followed optionally by information specific to that
4406 type of pragma. Case is ignored in
4407 <replaceable>word</replaceable>. The various values for
4408 <replaceable>word</replaceable> that GHC understands are described
4409 in the following sections; any pragma encountered with an
4410 unrecognised <replaceable>word</replaceable> is (silently)
4413 <sect2 id="deprecated-pragma">
4414 <title>DEPRECATED pragma</title>
4415 <indexterm><primary>DEPRECATED</primary>
4418 <para>The DEPRECATED pragma lets you specify that a particular
4419 function, class, or type, is deprecated. There are two
4424 <para>You can deprecate an entire module thus:</para>
4426 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4429 <para>When you compile any module that import
4430 <literal>Wibble</literal>, GHC will print the specified
4435 <para>You can deprecate a function, class, type, or data constructor, with the
4436 following top-level declaration:</para>
4438 {-# DEPRECATED f, C, T "Don't use these" #-}
4440 <para>When you compile any module that imports and uses any
4441 of the specified entities, GHC will print the specified
4443 <para> You can only depecate entities declared at top level in the module
4444 being compiled, and you can only use unqualified names in the list of
4445 entities being deprecated. A capitalised name, such as <literal>T</literal>
4446 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4447 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4448 both are in scope. If both are in scope, there is currently no way to deprecate
4449 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4452 Any use of the deprecated item, or of anything from a deprecated
4453 module, will be flagged with an appropriate message. However,
4454 deprecations are not reported for
4455 (a) uses of a deprecated function within its defining module, and
4456 (b) uses of a deprecated function in an export list.
4457 The latter reduces spurious complaints within a library
4458 in which one module gathers together and re-exports
4459 the exports of several others.
4461 <para>You can suppress the warnings with the flag
4462 <option>-fno-warn-deprecations</option>.</para>
4465 <sect2 id="include-pragma">
4466 <title>INCLUDE pragma</title>
4468 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4469 of C header files that should be <literal>#include</literal>'d into
4470 the C source code generated by the compiler for the current module (if
4471 compiling via C). For example:</para>
4474 {-# INCLUDE "foo.h" #-}
4475 {-# INCLUDE <stdio.h> #-}</programlisting>
4477 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4478 your source file with any <literal>OPTIONS_GHC</literal>
4481 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4482 to the <option>-#include</option> option (<xref
4483 linkend="options-C-compiler" />), because the
4484 <literal>INCLUDE</literal> pragma is understood by other
4485 compilers. Yet another alternative is to add the include file to each
4486 <literal>foreign import</literal> declaration in your code, but we
4487 don't recommend using this approach with GHC.</para>
4490 <sect2 id="inline-noinline-pragma">
4491 <title>INLINE and NOINLINE pragmas</title>
4493 <para>These pragmas control the inlining of function
4496 <sect3 id="inline-pragma">
4497 <title>INLINE pragma</title>
4498 <indexterm><primary>INLINE</primary></indexterm>
4500 <para>GHC (with <option>-O</option>, as always) tries to
4501 inline (or “unfold”) functions/values that are
4502 “small enough,” thus avoiding the call overhead
4503 and possibly exposing other more-wonderful optimisations.
4504 Normally, if GHC decides a function is “too
4505 expensive” to inline, it will not do so, nor will it
4506 export that unfolding for other modules to use.</para>
4508 <para>The sledgehammer you can bring to bear is the
4509 <literal>INLINE</literal><indexterm><primary>INLINE
4510 pragma</primary></indexterm> pragma, used thusly:</para>
4513 key_function :: Int -> String -> (Bool, Double)
4515 #ifdef __GLASGOW_HASKELL__
4516 {-# INLINE key_function #-}
4520 <para>(You don't need to do the C pre-processor carry-on
4521 unless you're going to stick the code through HBC—it
4522 doesn't like <literal>INLINE</literal> pragmas.)</para>
4524 <para>The major effect of an <literal>INLINE</literal> pragma
4525 is to declare a function's “cost” to be very low.
4526 The normal unfolding machinery will then be very keen to
4529 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4530 function can be put anywhere its type signature could be
4533 <para><literal>INLINE</literal> pragmas are a particularly
4535 <literal>then</literal>/<literal>return</literal> (or
4536 <literal>bind</literal>/<literal>unit</literal>) functions in
4537 a monad. For example, in GHC's own
4538 <literal>UniqueSupply</literal> monad code, we have:</para>
4541 #ifdef __GLASGOW_HASKELL__
4542 {-# INLINE thenUs #-}
4543 {-# INLINE returnUs #-}
4547 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4548 linkend="noinline-pragma"/>).</para>
4551 <sect3 id="noinline-pragma">
4552 <title>NOINLINE pragma</title>
4554 <indexterm><primary>NOINLINE</primary></indexterm>
4555 <indexterm><primary>NOTINLINE</primary></indexterm>
4557 <para>The <literal>NOINLINE</literal> pragma does exactly what
4558 you'd expect: it stops the named function from being inlined
4559 by the compiler. You shouldn't ever need to do this, unless
4560 you're very cautious about code size.</para>
4562 <para><literal>NOTINLINE</literal> is a synonym for
4563 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4564 specified by Haskell 98 as the standard way to disable
4565 inlining, so it should be used if you want your code to be
4569 <sect3 id="phase-control">
4570 <title>Phase control</title>
4572 <para> Sometimes you want to control exactly when in GHC's
4573 pipeline the INLINE pragma is switched on. Inlining happens
4574 only during runs of the <emphasis>simplifier</emphasis>. Each
4575 run of the simplifier has a different <emphasis>phase
4576 number</emphasis>; the phase number decreases towards zero.
4577 If you use <option>-dverbose-core2core</option> you'll see the
4578 sequence of phase numbers for successive runs of the
4579 simplifier. In an INLINE pragma you can optionally specify a
4580 phase number, thus:</para>
4584 <para>You can say "inline <literal>f</literal> in Phase 2
4585 and all subsequent phases":
4587 {-# INLINE [2] f #-}
4593 <para>You can say "inline <literal>g</literal> in all
4594 phases up to, but not including, Phase 3":
4596 {-# INLINE [~3] g #-}
4602 <para>If you omit the phase indicator, you mean "inline in
4607 <para>You can use a phase number on a NOINLINE pragma too:</para>
4611 <para>You can say "do not inline <literal>f</literal>
4612 until Phase 2; in Phase 2 and subsequently behave as if
4613 there was no pragma at all":
4615 {-# NOINLINE [2] f #-}
4621 <para>You can say "do not inline <literal>g</literal> in
4622 Phase 3 or any subsequent phase; before that, behave as if
4623 there was no pragma":
4625 {-# NOINLINE [~3] g #-}
4631 <para>If you omit the phase indicator, you mean "never
4632 inline this function".</para>
4636 <para>The same phase-numbering control is available for RULES
4637 (<xref linkend="rewrite-rules"/>).</para>
4641 <sect2 id="line-pragma">
4642 <title>LINE pragma</title>
4644 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4645 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4646 <para>This pragma is similar to C's <literal>#line</literal>
4647 pragma, and is mainly for use in automatically generated Haskell
4648 code. It lets you specify the line number and filename of the
4649 original code; for example</para>
4652 {-# LINE 42 "Foo.vhs" #-}
4655 <para>if you'd generated the current file from something called
4656 <filename>Foo.vhs</filename> and this line corresponds to line
4657 42 in the original. GHC will adjust its error messages to refer
4658 to the line/file named in the <literal>LINE</literal>
4662 <sect2 id="options-pragma">
4663 <title>OPTIONS_GHC pragma</title>
4664 <indexterm><primary>OPTIONS_GHC</primary>
4666 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4669 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4670 additional options that are given to the compiler when compiling
4671 this source file. See <xref linkend="source-file-options"/> for
4674 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4675 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4679 <title>RULES pragma</title>
4681 <para>The RULES pragma lets you specify rewrite rules. It is
4682 described in <xref linkend="rewrite-rules"/>.</para>
4685 <sect2 id="specialize-pragma">
4686 <title>SPECIALIZE pragma</title>
4688 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4689 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4690 <indexterm><primary>overloading, death to</primary></indexterm>
4692 <para>(UK spelling also accepted.) For key overloaded
4693 functions, you can create extra versions (NB: more code space)
4694 specialised to particular types. Thus, if you have an
4695 overloaded function:</para>
4698 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4701 <para>If it is heavily used on lists with
4702 <literal>Widget</literal> keys, you could specialise it as
4706 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4709 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4710 be put anywhere its type signature could be put.</para>
4712 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4713 (a) a specialised version of the function and (b) a rewrite rule
4714 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4715 un-specialised function into a call to the specialised one.</para>
4717 <para>The type in a SPECIALIZE pragma can be any type that is less
4718 polymorphic than the type of the original function. In concrete terms,
4719 if the original function is <literal>f</literal> then the pragma
4721 {-# SPECIALIZE f :: <type> #-}
4723 is valid if and only if the defintion
4725 f_spec :: <type>
4728 is valid. Here are some examples (where we only give the type signature
4729 for the original function, not its code):
4731 f :: Eq a => a -> b -> b
4732 {-# SPECIALISE g :: Int -> b -> b #-}
4734 g :: (Eq a, Ix b) => a -> b -> b
4735 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
4737 h :: Eq a => a -> a -> a
4738 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
4740 The last of these examples will generate a
4741 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
4742 well. If you use this kind of specialisation, let us know how well it works.
4745 <para>Note: In earlier versions of GHC, it was possible to provide your own
4746 specialised function for a given type:
4749 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4752 This feature has been removed, as it is now subsumed by the
4753 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4757 <sect2 id="specialize-instance-pragma">
4758 <title>SPECIALIZE instance pragma
4762 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4763 <indexterm><primary>overloading, death to</primary></indexterm>
4764 Same idea, except for instance declarations. For example:
4767 instance (Eq a) => Eq (Foo a) where {
4768 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4772 The pragma must occur inside the <literal>where</literal> part
4773 of the instance declaration.
4776 Compatible with HBC, by the way, except perhaps in the placement
4782 <sect2 id="unpack-pragma">
4783 <title>UNPACK pragma</title>
4785 <indexterm><primary>UNPACK</primary></indexterm>
4787 <para>The <literal>UNPACK</literal> indicates to the compiler
4788 that it should unpack the contents of a constructor field into
4789 the constructor itself, removing a level of indirection. For
4793 data T = T {-# UNPACK #-} !Float
4794 {-# UNPACK #-} !Float
4797 <para>will create a constructor <literal>T</literal> containing
4798 two unboxed floats. This may not always be an optimisation: if
4799 the <function>T</function> constructor is scrutinised and the
4800 floats passed to a non-strict function for example, they will
4801 have to be reboxed (this is done automatically by the
4804 <para>Unpacking constructor fields should only be used in
4805 conjunction with <option>-O</option>, in order to expose
4806 unfoldings to the compiler so the reboxing can be removed as
4807 often as possible. For example:</para>
4811 f (T f1 f2) = f1 + f2
4814 <para>The compiler will avoid reboxing <function>f1</function>
4815 and <function>f2</function> by inlining <function>+</function>
4816 on floats, but only when <option>-O</option> is on.</para>
4818 <para>Any single-constructor data is eligible for unpacking; for
4822 data T = T {-# UNPACK #-} !(Int,Int)
4825 <para>will store the two <literal>Int</literal>s directly in the
4826 <function>T</function> constructor, by flattening the pair.
4827 Multi-level unpacking is also supported:</para>
4830 data T = T {-# UNPACK #-} !S
4831 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4834 <para>will store two unboxed <literal>Int#</literal>s
4835 directly in the <function>T</function> constructor. The
4836 unpacker can see through newtypes, too.</para>
4838 <para>If a field cannot be unpacked, you will not get a warning,
4839 so it might be an idea to check the generated code with
4840 <option>-ddump-simpl</option>.</para>
4842 <para>See also the <option>-funbox-strict-fields</option> flag,
4843 which essentially has the effect of adding
4844 <literal>{-# UNPACK #-}</literal> to every strict
4845 constructor field.</para>
4850 <!-- ======================= REWRITE RULES ======================== -->
4852 <sect1 id="rewrite-rules">
4853 <title>Rewrite rules
4855 <indexterm><primary>RULES pragma</primary></indexterm>
4856 <indexterm><primary>pragma, RULES</primary></indexterm>
4857 <indexterm><primary>rewrite rules</primary></indexterm></title>
4860 The programmer can specify rewrite rules as part of the source program
4861 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4862 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4863 and (b) the <option>-frules-off</option> flag
4864 (<xref linkend="options-f"/>) is not specified.
4872 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4879 <title>Syntax</title>
4882 From a syntactic point of view:
4888 There may be zero or more rules in a <literal>RULES</literal> pragma.
4895 Each rule has a name, enclosed in double quotes. The name itself has
4896 no significance at all. It is only used when reporting how many times the rule fired.
4902 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4903 immediately after the name of the rule. Thus:
4906 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4909 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4910 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4919 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4920 is set, so you must lay out your rules starting in the same column as the
4921 enclosing definitions.
4928 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4929 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4930 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4931 by spaces, just like in a type <literal>forall</literal>.
4937 A pattern variable may optionally have a type signature.
4938 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4939 For example, here is the <literal>foldr/build</literal> rule:
4942 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4943 foldr k z (build g) = g k z
4946 Since <function>g</function> has a polymorphic type, it must have a type signature.
4953 The left hand side of a rule must consist of a top-level variable applied
4954 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4957 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4958 "wrong2" forall f. f True = True
4961 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4968 A rule does not need to be in the same module as (any of) the
4969 variables it mentions, though of course they need to be in scope.
4975 Rules are automatically exported from a module, just as instance declarations are.
4986 <title>Semantics</title>
4989 From a semantic point of view:
4995 Rules are only applied if you use the <option>-O</option> flag.
5001 Rules are regarded as left-to-right rewrite rules.
5002 When GHC finds an expression that is a substitution instance of the LHS
5003 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5004 By "a substitution instance" we mean that the LHS can be made equal to the
5005 expression by substituting for the pattern variables.
5012 The LHS and RHS of a rule are typechecked, and must have the
5020 GHC makes absolutely no attempt to verify that the LHS and RHS
5021 of a rule have the same meaning. That is undecidable in general, and
5022 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5029 GHC makes no attempt to make sure that the rules are confluent or
5030 terminating. For example:
5033 "loop" forall x,y. f x y = f y x
5036 This rule will cause the compiler to go into an infinite loop.
5043 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5049 GHC currently uses a very simple, syntactic, matching algorithm
5050 for matching a rule LHS with an expression. It seeks a substitution
5051 which makes the LHS and expression syntactically equal modulo alpha
5052 conversion. The pattern (rule), but not the expression, is eta-expanded if
5053 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5054 But not beta conversion (that's called higher-order matching).
5058 Matching is carried out on GHC's intermediate language, which includes
5059 type abstractions and applications. So a rule only matches if the
5060 types match too. See <xref linkend="rule-spec"/> below.
5066 GHC keeps trying to apply the rules as it optimises the program.
5067 For example, consider:
5076 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5077 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5078 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5079 not be substituted, and the rule would not fire.
5086 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5087 that appears on the LHS of a rule</emphasis>, because once you have substituted
5088 for something you can't match against it (given the simple minded
5089 matching). So if you write the rule
5092 "map/map" forall f,g. map f . map g = map (f.g)
5095 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5096 It will only match something written with explicit use of ".".
5097 Well, not quite. It <emphasis>will</emphasis> match the expression
5103 where <function>wibble</function> is defined:
5106 wibble f g = map f . map g
5109 because <function>wibble</function> will be inlined (it's small).
5111 Later on in compilation, GHC starts inlining even things on the
5112 LHS of rules, but still leaves the rules enabled. This inlining
5113 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5120 All rules are implicitly exported from the module, and are therefore
5121 in force in any module that imports the module that defined the rule, directly
5122 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5123 in force when compiling A.) The situation is very similar to that for instance
5135 <title>List fusion</title>
5138 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5139 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5140 intermediate list should be eliminated entirely.
5144 The following are good producers:
5156 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5162 Explicit lists (e.g. <literal>[True, False]</literal>)
5168 The cons constructor (e.g <literal>3:4:[]</literal>)
5174 <function>++</function>
5180 <function>map</function>
5186 <function>filter</function>
5192 <function>iterate</function>, <function>repeat</function>
5198 <function>zip</function>, <function>zipWith</function>
5207 The following are good consumers:
5219 <function>array</function> (on its second argument)
5225 <function>length</function>
5231 <function>++</function> (on its first argument)
5237 <function>foldr</function>
5243 <function>map</function>
5249 <function>filter</function>
5255 <function>concat</function>
5261 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5267 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5268 will fuse with one but not the other)
5274 <function>partition</function>
5280 <function>head</function>
5286 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5292 <function>sequence_</function>
5298 <function>msum</function>
5304 <function>sortBy</function>
5313 So, for example, the following should generate no intermediate lists:
5316 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5322 This list could readily be extended; if there are Prelude functions that you use
5323 a lot which are not included, please tell us.
5327 If you want to write your own good consumers or producers, look at the
5328 Prelude definitions of the above functions to see how to do so.
5333 <sect2 id="rule-spec">
5334 <title>Specialisation
5338 Rewrite rules can be used to get the same effect as a feature
5339 present in earlier versions of GHC.
5340 For example, suppose that:
5343 genericLookup :: Ord a => Table a b -> a -> b
5344 intLookup :: Table Int b -> Int -> b
5347 where <function>intLookup</function> is an implementation of
5348 <function>genericLookup</function> that works very fast for
5349 keys of type <literal>Int</literal>. You might wish
5350 to tell GHC to use <function>intLookup</function> instead of
5351 <function>genericLookup</function> whenever the latter was called with
5352 type <literal>Table Int b -> Int -> b</literal>.
5353 It used to be possible to write
5356 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5359 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5362 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5365 This slightly odd-looking rule instructs GHC to replace
5366 <function>genericLookup</function> by <function>intLookup</function>
5367 <emphasis>whenever the types match</emphasis>.
5368 What is more, this rule does not need to be in the same
5369 file as <function>genericLookup</function>, unlike the
5370 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5371 have an original definition available to specialise).
5374 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5375 <function>intLookup</function> really behaves as a specialised version
5376 of <function>genericLookup</function>!!!</para>
5378 <para>An example in which using <literal>RULES</literal> for
5379 specialisation will Win Big:
5382 toDouble :: Real a => a -> Double
5383 toDouble = fromRational . toRational
5385 {-# RULES "toDouble/Int" toDouble = i2d #-}
5386 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5389 The <function>i2d</function> function is virtually one machine
5390 instruction; the default conversion—via an intermediate
5391 <literal>Rational</literal>—is obscenely expensive by
5398 <title>Controlling what's going on</title>
5406 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5412 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5413 If you add <option>-dppr-debug</option> you get a more detailed listing.
5419 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5422 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5423 {-# INLINE build #-}
5427 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5428 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5429 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5430 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5437 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5438 see how to write rules that will do fusion and yet give an efficient
5439 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5449 <sect2 id="core-pragma">
5450 <title>CORE pragma</title>
5452 <indexterm><primary>CORE pragma</primary></indexterm>
5453 <indexterm><primary>pragma, CORE</primary></indexterm>
5454 <indexterm><primary>core, annotation</primary></indexterm>
5457 The external core format supports <quote>Note</quote> annotations;
5458 the <literal>CORE</literal> pragma gives a way to specify what these
5459 should be in your Haskell source code. Syntactically, core
5460 annotations are attached to expressions and take a Haskell string
5461 literal as an argument. The following function definition shows an
5465 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5468 Semantically, this is equivalent to:
5476 However, when external for is generated (via
5477 <option>-fext-core</option>), there will be Notes attached to the
5478 expressions <function>show</function> and <varname>x</varname>.
5479 The core function declaration for <function>f</function> is:
5483 f :: %forall a . GHCziShow.ZCTShow a ->
5484 a -> GHCziBase.ZMZN GHCziBase.Char =
5485 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5487 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5489 (tpl1::GHCziBase.Int ->
5491 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5493 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5494 (tpl3::GHCziBase.ZMZN a ->
5495 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5503 Here, we can see that the function <function>show</function> (which
5504 has been expanded out to a case expression over the Show dictionary)
5505 has a <literal>%note</literal> attached to it, as does the
5506 expression <varname>eta</varname> (which used to be called
5507 <varname>x</varname>).
5514 <sect1 id="generic-classes">
5515 <title>Generic classes</title>
5517 <para>(Note: support for generic classes is currently broken in
5521 The ideas behind this extension are described in detail in "Derivable type classes",
5522 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5523 An example will give the idea:
5531 fromBin :: [Int] -> (a, [Int])
5533 toBin {| Unit |} Unit = []
5534 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5535 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5536 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5538 fromBin {| Unit |} bs = (Unit, bs)
5539 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5540 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5541 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5542 (y,bs'') = fromBin bs'
5545 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5546 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5547 which are defined thus in the library module <literal>Generics</literal>:
5551 data a :+: b = Inl a | Inr b
5552 data a :*: b = a :*: b
5555 Now you can make a data type into an instance of Bin like this:
5557 instance (Bin a, Bin b) => Bin (a,b)
5558 instance Bin a => Bin [a]
5560 That is, just leave off the "where" clause. Of course, you can put in the
5561 where clause and over-ride whichever methods you please.
5565 <title> Using generics </title>
5566 <para>To use generics you need to</para>
5569 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5570 <option>-fgenerics</option> (to generate extra per-data-type code),
5571 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5575 <para>Import the module <literal>Generics</literal> from the
5576 <literal>lang</literal> package. This import brings into
5577 scope the data types <literal>Unit</literal>,
5578 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5579 don't need this import if you don't mention these types
5580 explicitly; for example, if you are simply giving instance
5581 declarations.)</para>
5586 <sect2> <title> Changes wrt the paper </title>
5588 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5589 can be written infix (indeed, you can now use
5590 any operator starting in a colon as an infix type constructor). Also note that
5591 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5592 Finally, note that the syntax of the type patterns in the class declaration
5593 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5594 alone would ambiguous when they appear on right hand sides (an extension we
5595 anticipate wanting).
5599 <sect2> <title>Terminology and restrictions</title>
5601 Terminology. A "generic default method" in a class declaration
5602 is one that is defined using type patterns as above.
5603 A "polymorphic default method" is a default method defined as in Haskell 98.
5604 A "generic class declaration" is a class declaration with at least one
5605 generic default method.
5613 Alas, we do not yet implement the stuff about constructor names and
5620 A generic class can have only one parameter; you can't have a generic
5621 multi-parameter class.
5627 A default method must be defined entirely using type patterns, or entirely
5628 without. So this is illegal:
5631 op :: a -> (a, Bool)
5632 op {| Unit |} Unit = (Unit, True)
5635 However it is perfectly OK for some methods of a generic class to have
5636 generic default methods and others to have polymorphic default methods.
5642 The type variable(s) in the type pattern for a generic method declaration
5643 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:
5647 op {| p :*: q |} (x :*: y) = op (x :: p)
5655 The type patterns in a generic default method must take one of the forms:
5661 where "a" and "b" are type variables. Furthermore, all the type patterns for
5662 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5663 must use the same type variables. So this is illegal:
5667 op {| a :+: b |} (Inl x) = True
5668 op {| p :+: q |} (Inr y) = False
5670 The type patterns must be identical, even in equations for different methods of the class.
5671 So this too is illegal:
5675 op1 {| a :*: b |} (x :*: y) = True
5678 op2 {| p :*: q |} (x :*: y) = False
5680 (The reason for this restriction is that we gather all the equations for a particular type consructor
5681 into a single generic instance declaration.)
5687 A generic method declaration must give a case for each of the three type constructors.
5693 The type for a generic method can be built only from:
5695 <listitem> <para> Function arrows </para> </listitem>
5696 <listitem> <para> Type variables </para> </listitem>
5697 <listitem> <para> Tuples </para> </listitem>
5698 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5700 Here are some example type signatures for generic methods:
5703 op2 :: Bool -> (a,Bool)
5704 op3 :: [Int] -> a -> a
5707 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5711 This restriction is an implementation restriction: we just havn't got around to
5712 implementing the necessary bidirectional maps over arbitrary type constructors.
5713 It would be relatively easy to add specific type constructors, such as Maybe and list,
5714 to the ones that are allowed.</para>
5719 In an instance declaration for a generic class, the idea is that the compiler
5720 will fill in the methods for you, based on the generic templates. However it can only
5725 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5730 No constructor of the instance type has unboxed fields.
5734 (Of course, these things can only arise if you are already using GHC extensions.)
5735 However, you can still give an instance declarations for types which break these rules,
5736 provided you give explicit code to override any generic default methods.
5744 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5745 what the compiler does with generic declarations.
5750 <sect2> <title> Another example </title>
5752 Just to finish with, here's another example I rather like:
5756 nCons {| Unit |} _ = 1
5757 nCons {| a :*: b |} _ = 1
5758 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5761 tag {| Unit |} _ = 1
5762 tag {| a :*: b |} _ = 1
5763 tag {| a :+: b |} (Inl x) = tag x
5764 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5773 ;;; Local Variables: ***
5775 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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