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>Integer and fractional literals mean
833 "<literal>fromInteger 1</literal>" and
834 "<literal>fromRational 3.2</literal>", not the
835 Prelude-qualified versions; both in expressions and in
837 <para>However, the standard Prelude <literal>Eq</literal> class
838 is still used for the equality test necessary for literal patterns.</para>
842 <para>Negation (e.g. "<literal>- (f x)</literal>")
843 means "<literal>negate (f x)</literal>" (not
844 <literal>Prelude.negate</literal>).</para>
848 <para>In an n+k pattern, the standard Prelude
849 <literal>Ord</literal> class is still used for comparison,
850 but the necessary subtraction uses whatever
851 "<literal>(-)</literal>" is in scope (not
852 "<literal>Prelude.(-)</literal>").</para>
856 <para>"Do" notation is translated using whatever
857 functions <literal>(>>=)</literal>,
858 <literal>(>>)</literal>, <literal>fail</literal>, and
859 <literal>return</literal>, are in scope (not the Prelude
860 versions). List comprehensions, and parallel array
861 comprehensions, are unaffected. </para></listitem>
864 <para>Similarly recursive do notation (see
865 <xref linkend="mdo-notation"/>) uses whatever
866 <literal>mfix</literal> function is in scope, and arrow
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.</para>
875 <para>The functions with these names that GHC finds in scope
876 must have types matching those of the originals, namely:
878 fromInteger :: Integer -> N
879 fromRational :: Rational -> N
882 (>>=) :: forall a b. M a -> (a -> M b) -> M b
883 (>>) :: forall a b. M a -> M b -> M b
884 return :: forall a. a -> M a
885 fail :: forall a. String -> M a
887 (Here <literal>N</literal> may be any type,
888 and <literal>M</literal> any type constructor.)</para>
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 Laufer (I believe, thought doubtless someone will
1096 correct me), and implemented in Hope+. It's been in Lennart
1097 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1098 proved very useful. Here's the idea. Consider the declaration:
1104 data Foo = forall a. MkFoo a (a -> Bool)
1111 The data type <literal>Foo</literal> has two constructors with types:
1117 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1124 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1125 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1126 For example, the following expression is fine:
1132 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1138 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1139 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1140 isUpper</function> packages a character with a compatible function. These
1141 two things are each of type <literal>Foo</literal> and can be put in a list.
1145 What can we do with a value of type <literal>Foo</literal>?. In particular,
1146 what happens when we pattern-match on <function>MkFoo</function>?
1152 f (MkFoo val fn) = ???
1158 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1159 are compatible, the only (useful) thing we can do with them is to
1160 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1167 f (MkFoo val fn) = fn val
1173 What this allows us to do is to package heterogenous values
1174 together with a bunch of functions that manipulate them, and then treat
1175 that collection of packages in a uniform manner. You can express
1176 quite a bit of object-oriented-like programming this way.
1179 <sect4 id="existential">
1180 <title>Why existential?
1184 What has this to do with <emphasis>existential</emphasis> quantification?
1185 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1191 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1197 But Haskell programmers can safely think of the ordinary
1198 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1199 adding a new existential quantification construct.
1205 <title>Type classes</title>
1208 An easy extension (implemented in <command>hbc</command>) is to allow
1209 arbitrary contexts before the constructor. For example:
1215 data Baz = forall a. Eq a => Baz1 a a
1216 | forall b. Show b => Baz2 b (b -> b)
1222 The two constructors have the types you'd expect:
1228 Baz1 :: forall a. Eq a => a -> a -> Baz
1229 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1235 But when pattern matching on <function>Baz1</function> the matched values can be compared
1236 for equality, and when pattern matching on <function>Baz2</function> the first matched
1237 value can be converted to a string (as well as applying the function to it).
1238 So this program is legal:
1245 f (Baz1 p q) | p == q = "Yes"
1247 f (Baz2 v fn) = show (fn v)
1253 Operationally, in a dictionary-passing implementation, the
1254 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1255 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1256 extract it on pattern matching.
1260 Notice the way that the syntax fits smoothly with that used for
1261 universal quantification earlier.
1267 <title>Restrictions</title>
1270 There are several restrictions on the ways in which existentially-quantified
1271 constructors can be use.
1280 When pattern matching, each pattern match introduces a new,
1281 distinct, type for each existential type variable. These types cannot
1282 be unified with any other type, nor can they escape from the scope of
1283 the pattern match. For example, these fragments are incorrect:
1291 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1292 is the result of <function>f1</function>. One way to see why this is wrong is to
1293 ask what type <function>f1</function> has:
1297 f1 :: Foo -> a -- Weird!
1301 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1306 f1 :: forall a. Foo -> a -- Wrong!
1310 The original program is just plain wrong. Here's another sort of error
1314 f2 (Baz1 a b) (Baz1 p q) = a==q
1318 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1319 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1320 from the two <function>Baz1</function> constructors.
1328 You can't pattern-match on an existentially quantified
1329 constructor in a <literal>let</literal> or <literal>where</literal> group of
1330 bindings. So this is illegal:
1334 f3 x = a==b where { Baz1 a b = x }
1337 Instead, use a <literal>case</literal> expression:
1340 f3 x = case x of Baz1 a b -> a==b
1343 In general, you can only pattern-match
1344 on an existentially-quantified constructor in a <literal>case</literal> expression or
1345 in the patterns of a function definition.
1347 The reason for this restriction is really an implementation one.
1348 Type-checking binding groups is already a nightmare without
1349 existentials complicating the picture. Also an existential pattern
1350 binding at the top level of a module doesn't make sense, because it's
1351 not clear how to prevent the existentially-quantified type "escaping".
1352 So for now, there's a simple-to-state restriction. We'll see how
1360 You can't use existential quantification for <literal>newtype</literal>
1361 declarations. So this is illegal:
1365 newtype T = forall a. Ord a => MkT a
1369 Reason: a value of type <literal>T</literal> must be represented as a
1370 pair of a dictionary for <literal>Ord t</literal> and a value of type
1371 <literal>t</literal>. That contradicts the idea that
1372 <literal>newtype</literal> should have no concrete representation.
1373 You can get just the same efficiency and effect by using
1374 <literal>data</literal> instead of <literal>newtype</literal>. If
1375 there is no overloading involved, then there is more of a case for
1376 allowing an existentially-quantified <literal>newtype</literal>,
1377 because the <literal>data</literal> version does carry an
1378 implementation cost, but single-field existentially quantified
1379 constructors aren't much use. So the simple restriction (no
1380 existential stuff on <literal>newtype</literal>) stands, unless there
1381 are convincing reasons to change it.
1389 You can't use <literal>deriving</literal> to define instances of a
1390 data type with existentially quantified data constructors.
1392 Reason: in most cases it would not make sense. For example:#
1395 data T = forall a. MkT [a] deriving( Eq )
1398 To derive <literal>Eq</literal> in the standard way we would need to have equality
1399 between the single component of two <function>MkT</function> constructors:
1403 (MkT a) == (MkT b) = ???
1406 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1407 It's just about possible to imagine examples in which the derived instance
1408 would make sense, but it seems altogether simpler simply to prohibit such
1409 declarations. Define your own instances!
1424 <sect2 id="multi-param-type-classes">
1425 <title>Class declarations</title>
1428 This section documents GHC's implementation of multi-parameter type
1429 classes. There's lots of background in the paper <ulink
1430 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1431 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1432 Jones, Erik Meijer).
1435 There are the following constraints on class declarations:
1440 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1444 class Collection c a where
1445 union :: c a -> c a -> c a
1456 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1457 of "acyclic" involves only the superclass relationships. For example,
1463 op :: D b => a -> b -> b
1466 class C a => D a where { ... }
1470 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1471 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1472 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1479 <emphasis>There are no restrictions on the context in a class declaration
1480 (which introduces superclasses), except that the class hierarchy must
1481 be acyclic</emphasis>. So these class declarations are OK:
1485 class Functor (m k) => FiniteMap m k where
1488 class (Monad m, Monad (t m)) => Transform t m where
1489 lift :: m a -> (t m) a
1499 <emphasis>All of the class type variables must be reachable (in the sense
1500 mentioned in <xref linkend="type-restrictions"/>)
1501 from the free variables of each method type
1502 </emphasis>. For example:
1506 class Coll s a where
1508 insert :: s -> a -> s
1512 is not OK, because the type of <literal>empty</literal> doesn't mention
1513 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1514 types, and has the same motivation.
1516 Sometimes, offending class declarations exhibit misunderstandings. For
1517 example, <literal>Coll</literal> might be rewritten
1521 class Coll s a where
1523 insert :: s a -> a -> s a
1527 which makes the connection between the type of a collection of
1528 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1529 Occasionally this really doesn't work, in which case you can split the
1537 class CollE s => Coll s a where
1538 insert :: s -> a -> s
1548 <sect3 id="class-method-types">
1549 <title>Class method types</title>
1551 Haskell 98 prohibits class method types to mention constraints on the
1552 class type variable, thus:
1555 fromList :: [a] -> s a
1556 elem :: Eq a => a -> s a -> Bool
1558 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1559 contains the constraint <literal>Eq a</literal>, constrains only the
1560 class type variable (in this case <literal>a</literal>).
1563 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1570 <sect2 id="type-restrictions">
1571 <title>Type signatures</title>
1573 <sect3><title>The context of a type signature</title>
1575 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1576 the form <emphasis>(class type-variable)</emphasis> or
1577 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1578 these type signatures are perfectly OK
1581 g :: Ord (T a ()) => ...
1585 GHC imposes the following restrictions on the constraints in a type signature.
1589 forall tv1..tvn (c1, ...,cn) => type
1592 (Here, we write the "foralls" explicitly, although the Haskell source
1593 language omits them; in Haskell 98, all the free type variables of an
1594 explicit source-language type signature are universally quantified,
1595 except for the class type variables in a class declaration. However,
1596 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1605 <emphasis>Each universally quantified type variable
1606 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1608 A type variable <literal>a</literal> is "reachable" if it it appears
1609 in the same constraint as either a type variable free in in
1610 <literal>type</literal>, or another reachable type variable.
1611 A value with a type that does not obey
1612 this reachability restriction cannot be used without introducing
1613 ambiguity; that is why the type is rejected.
1614 Here, for example, is an illegal type:
1618 forall a. Eq a => Int
1622 When a value with this type was used, the constraint <literal>Eq tv</literal>
1623 would be introduced where <literal>tv</literal> is a fresh type variable, and
1624 (in the dictionary-translation implementation) the value would be
1625 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1626 can never know which instance of <literal>Eq</literal> to use because we never
1627 get any more information about <literal>tv</literal>.
1631 that the reachability condition is weaker than saying that <literal>a</literal> is
1632 functionally dependent on a type variable free in
1633 <literal>type</literal> (see <xref
1634 linkend="functional-dependencies"/>). The reason for this is there
1635 might be a "hidden" dependency, in a superclass perhaps. So
1636 "reachable" is a conservative approximation to "functionally dependent".
1637 For example, consider:
1639 class C a b | a -> b where ...
1640 class C a b => D a b where ...
1641 f :: forall a b. D a b => a -> a
1643 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1644 but that is not immediately apparent from <literal>f</literal>'s type.
1650 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1651 universally quantified type variables <literal>tvi</literal></emphasis>.
1653 For example, this type is OK because <literal>C a b</literal> mentions the
1654 universally quantified type variable <literal>b</literal>:
1658 forall a. C a b => burble
1662 The next type is illegal because the constraint <literal>Eq b</literal> does not
1663 mention <literal>a</literal>:
1667 forall a. Eq b => burble
1671 The reason for this restriction is milder than the other one. The
1672 excluded types are never useful or necessary (because the offending
1673 context doesn't need to be witnessed at this point; it can be floated
1674 out). Furthermore, floating them out increases sharing. Lastly,
1675 excluding them is a conservative choice; it leaves a patch of
1676 territory free in case we need it later.
1687 <title>For-all hoisting</title>
1689 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1690 end of an arrow, thus:
1692 type Discard a = forall b. a -> b -> a
1694 g :: Int -> Discard Int
1697 Simply expanding the type synonym would give
1699 g :: Int -> (forall b. Int -> b -> Int)
1701 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1703 g :: forall b. Int -> Int -> b -> Int
1705 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1706 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1707 performs the transformation:</emphasis>
1709 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1711 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1713 (In fact, GHC tries to retain as much synonym information as possible for use in
1714 error messages, but that is a usability issue.) This rule applies, of course, whether
1715 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1716 valid way to write <literal>g</literal>'s type signature:
1718 g :: Int -> Int -> forall b. b -> Int
1722 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1725 type Foo a = (?x::Int) => Bool -> a
1730 g :: (?x::Int) => Bool -> Bool -> Int
1738 <sect2 id="instance-decls">
1739 <title>Instance declarations</title>
1741 <sect3 id="instance-overlap">
1742 <title>Overlapping instances</title>
1744 In general, <emphasis>GHC requires that that it be unambiguous which instance
1746 should be used to resolve a type-class constraint</emphasis>. This behaviour
1747 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1748 <indexterm><primary>-fallow-overlapping-instances
1749 </primary></indexterm>
1750 and <option>-fallow-incoherent-instances</option>
1751 <indexterm><primary>-fallow-incoherent-instances
1752 </primary></indexterm>, as this section discusses.</para>
1754 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1755 it tries to match every instance declaration against the
1757 by instantiating the head of the instance declaration. For example, consider
1760 instance context1 => C Int a where ... -- (A)
1761 instance context2 => C a Bool where ... -- (B)
1762 instance context3 => C Int [a] where ... -- (C)
1763 instance context4 => C Int [Int] where ... -- (D)
1765 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>, but (C) and (D) do not. When matching, GHC takes
1766 no account of the context of the instance declaration
1767 (<literal>context1</literal> etc).
1768 GHC's default behaviour is that <emphasis>exactly one instance must match the
1769 constraint it is trying to resolve</emphasis>.
1770 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1771 including both declarations (A) and (B), say); an error is only reported if a
1772 particular constraint matches more than one.
1776 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1777 more than one instance to match, provided there is a most specific one. For
1778 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1779 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1780 most-specific match, the program is rejected.
1783 However, GHC is conservative about committing to an overlapping instance. For example:
1788 Suppose that from the RHS of <literal>f</literal> we get the constraint
1789 <literal>C Int [b]</literal>. But
1790 GHC does not commit to instance (C), because in a particular
1791 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1792 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1793 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1794 GHC will instead pick (C), without complaining about
1795 the problem of subsequent instantiations.
1798 Because overlaps are checked and reported lazily, as described above, you need
1799 the <option>-fallow-overlapping-instances</option> in the module that <emphasis>calls</emphasis>
1800 the overloaded function, rather than in the module that <emphasis>defines</emphasis> it.</para>
1805 <title>Type synonyms in the instance head</title>
1808 <emphasis>Unlike Haskell 98, instance heads may use type
1809 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1810 As always, using a type synonym is just shorthand for
1811 writing the RHS of the type synonym definition. For example:
1815 type Point = (Int,Int)
1816 instance C Point where ...
1817 instance C [Point] where ...
1821 is legal. However, if you added
1825 instance C (Int,Int) where ...
1829 as well, then the compiler will complain about the overlapping
1830 (actually, identical) instance declarations. As always, type synonyms
1831 must be fully applied. You cannot, for example, write:
1836 instance Monad P where ...
1840 This design decision is independent of all the others, and easily
1841 reversed, but it makes sense to me.
1846 <sect3 id="undecidable-instances">
1847 <title>Undecidable instances</title>
1849 <para>An instance declaration must normally obey the following rules:
1851 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1852 an instance declaration <emphasis>must not</emphasis> be a type variable.
1853 For example, these are OK:
1856 instance C Int a where ...
1858 instance D (Int, Int) where ...
1860 instance E [[a]] where ...
1864 instance F a where ...
1866 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1867 For example, this is OK:
1869 instance Stateful (ST s) (MutVar s) where ...
1876 <para>All of the types in the <emphasis>context</emphasis> of
1877 an instance declaration <emphasis>must</emphasis> be type variables.
1880 instance C a b => Eq (a,b) where ...
1884 instance C Int b => Foo b where ...
1890 These restrictions ensure that
1891 context reduction terminates: each reduction step removes one type
1892 constructor. For example, the following would make the type checker
1893 loop if it wasn't excluded:
1895 instance C a => C a where ...
1897 There are two situations in which the rule is a bit of a pain. First,
1898 if one allows overlapping instance declarations then it's quite
1899 convenient to have a "default instance" declaration that applies if
1900 something more specific does not:
1909 Second, sometimes you might want to use the following to get the
1910 effect of a "class synonym":
1914 class (C1 a, C2 a, C3 a) => C a where { }
1916 instance (C1 a, C2 a, C3 a) => C a where { }
1920 This allows you to write shorter signatures:
1932 f :: (C1 a, C2 a, C3 a) => ...
1936 Voluminous correspondence on the Haskell mailing list has convinced me
1937 that it's worth experimenting with more liberal rules. If you use
1938 the experimental flag <option>-fallow-undecidable-instances</option>
1939 <indexterm><primary>-fallow-undecidable-instances
1940 option</primary></indexterm>, you can use arbitrary
1941 types in both an instance context and instance head. Termination is ensured by having a
1942 fixed-depth recursion stack. If you exceed the stack depth you get a
1943 sort of backtrace, and the opportunity to increase the stack depth
1944 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1947 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1948 allowing these idioms interesting idioms.
1955 <sect2 id="implicit-parameters">
1956 <title>Implicit parameters</title>
1958 <para> Implicit parameters are implemented as described in
1959 "Implicit parameters: dynamic scoping with static types",
1960 J Lewis, MB Shields, E Meijer, J Launchbury,
1961 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1965 <para>(Most of the following, stil rather incomplete, documentation is
1966 due to Jeff Lewis.)</para>
1968 <para>Implicit parameter support is enabled with the option
1969 <option>-fimplicit-params</option>.</para>
1972 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1973 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1974 context. In Haskell, all variables are statically bound. Dynamic
1975 binding of variables is a notion that goes back to Lisp, but was later
1976 discarded in more modern incarnations, such as Scheme. Dynamic binding
1977 can be very confusing in an untyped language, and unfortunately, typed
1978 languages, in particular Hindley-Milner typed languages like Haskell,
1979 only support static scoping of variables.
1982 However, by a simple extension to the type class system of Haskell, we
1983 can support dynamic binding. Basically, we express the use of a
1984 dynamically bound variable as a constraint on the type. These
1985 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1986 function uses a dynamically-bound variable <literal>?x</literal>
1987 of type <literal>t'</literal>". For
1988 example, the following expresses the type of a sort function,
1989 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1991 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1993 The dynamic binding constraints are just a new form of predicate in the type class system.
1996 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1997 where <literal>x</literal> is
1998 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1999 Use of this construct also introduces a new
2000 dynamic-binding constraint in the type of the expression.
2001 For example, the following definition
2002 shows how we can define an implicitly parameterized sort function in
2003 terms of an explicitly parameterized <literal>sortBy</literal> function:
2005 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2007 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2013 <title>Implicit-parameter type constraints</title>
2015 Dynamic binding constraints behave just like other type class
2016 constraints in that they are automatically propagated. Thus, when a
2017 function is used, its implicit parameters are inherited by the
2018 function that called it. For example, our <literal>sort</literal> function might be used
2019 to pick out the least value in a list:
2021 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2022 least xs = fst (sort xs)
2024 Without lifting a finger, the <literal>?cmp</literal> parameter is
2025 propagated to become a parameter of <literal>least</literal> as well. With explicit
2026 parameters, the default is that parameters must always be explicit
2027 propagated. With implicit parameters, the default is to always
2031 An implicit-parameter type constraint differs from other type class constraints in the
2032 following way: All uses of a particular implicit parameter must have
2033 the same type. This means that the type of <literal>(?x, ?x)</literal>
2034 is <literal>(?x::a) => (a,a)</literal>, and not
2035 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2039 <para> You can't have an implicit parameter in the context of a class or instance
2040 declaration. For example, both these declarations are illegal:
2042 class (?x::Int) => C a where ...
2043 instance (?x::a) => Foo [a] where ...
2045 Reason: exactly which implicit parameter you pick up depends on exactly where
2046 you invoke a function. But the ``invocation'' of instance declarations is done
2047 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2048 Easiest thing is to outlaw the offending types.</para>
2050 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2052 f :: (?x :: [a]) => Int -> Int
2055 g :: (Read a, Show a) => String -> String
2058 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2059 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2060 quite unambiguous, and fixes the type <literal>a</literal>.
2065 <title>Implicit-parameter bindings</title>
2068 An implicit parameter is <emphasis>bound</emphasis> using the standard
2069 <literal>let</literal> or <literal>where</literal> binding forms.
2070 For example, we define the <literal>min</literal> function by binding
2071 <literal>cmp</literal>.
2074 min = let ?cmp = (<=) in least
2078 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2079 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2080 (including in a list comprehension, or do-notation, or pattern guards),
2081 or a <literal>where</literal> clause.
2082 Note the following points:
2085 An implicit-parameter binding group must be a
2086 collection of simple bindings to implicit-style variables (no
2087 function-style bindings, and no type signatures); these bindings are
2088 neither polymorphic or recursive.
2091 You may not mix implicit-parameter bindings with ordinary bindings in a
2092 single <literal>let</literal>
2093 expression; use two nested <literal>let</literal>s instead.
2094 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2098 You may put multiple implicit-parameter bindings in a
2099 single binding group; but they are <emphasis>not</emphasis> treated
2100 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2101 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2102 parameter. The bindings are not nested, and may be re-ordered without changing
2103 the meaning of the program.
2104 For example, consider:
2106 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2108 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2109 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2111 f :: (?x::Int) => Int -> Int
2119 <sect3><title>Implicit parameters and polymorphic recursion</title>
2122 Consider these two definitions:
2125 len1 xs = let ?acc = 0 in len_acc1 xs
2128 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2133 len2 xs = let ?acc = 0 in len_acc2 xs
2135 len_acc2 :: (?acc :: Int) => [a] -> Int
2137 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2139 The only difference between the two groups is that in the second group
2140 <literal>len_acc</literal> is given a type signature.
2141 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2142 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2143 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2144 has a type signature, the recursive call is made to the
2145 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2146 as an implicit parameter. So we get the following results in GHCi:
2153 Adding a type signature dramatically changes the result! This is a rather
2154 counter-intuitive phenomenon, worth watching out for.
2158 <sect3><title>Implicit parameters and monomorphism</title>
2160 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2161 Haskell Report) to implicit parameters. For example, consider:
2169 Since the binding for <literal>y</literal> falls under the Monomorphism
2170 Restriction it is not generalised, so the type of <literal>y</literal> is
2171 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2172 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2173 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2174 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2175 <literal>y</literal> in the body of the <literal>let</literal> will see the
2176 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2177 <literal>14</literal>.
2182 <sect2 id="linear-implicit-parameters">
2183 <title>Linear implicit parameters</title>
2185 Linear implicit parameters are an idea developed by Koen Claessen,
2186 Mark Shields, and Simon PJ. They address the long-standing
2187 problem that monads seem over-kill for certain sorts of problem, notably:
2190 <listitem> <para> distributing a supply of unique names </para> </listitem>
2191 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2192 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2196 Linear implicit parameters are just like ordinary implicit parameters,
2197 except that they are "linear" -- that is, they cannot be copied, and
2198 must be explicitly "split" instead. Linear implicit parameters are
2199 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2200 (The '/' in the '%' suggests the split!)
2205 import GHC.Exts( Splittable )
2207 data NameSupply = ...
2209 splitNS :: NameSupply -> (NameSupply, NameSupply)
2210 newName :: NameSupply -> Name
2212 instance Splittable NameSupply where
2216 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2217 f env (Lam x e) = Lam x' (f env e)
2220 env' = extend env x x'
2221 ...more equations for f...
2223 Notice that the implicit parameter %ns is consumed
2225 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2226 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2230 So the translation done by the type checker makes
2231 the parameter explicit:
2233 f :: NameSupply -> Env -> Expr -> Expr
2234 f ns env (Lam x e) = Lam x' (f ns1 env e)
2236 (ns1,ns2) = splitNS ns
2238 env = extend env x x'
2240 Notice the call to 'split' introduced by the type checker.
2241 How did it know to use 'splitNS'? Because what it really did
2242 was to introduce a call to the overloaded function 'split',
2243 defined by the class <literal>Splittable</literal>:
2245 class Splittable a where
2248 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2249 split for name supplies. But we can simply write
2255 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2257 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2258 <literal>GHC.Exts</literal>.
2263 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2264 are entirely distinct implicit parameters: you
2265 can use them together and they won't intefere with each other. </para>
2268 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2270 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2271 in the context of a class or instance declaration. </para></listitem>
2275 <sect3><title>Warnings</title>
2278 The monomorphism restriction is even more important than usual.
2279 Consider the example above:
2281 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2282 f env (Lam x e) = Lam x' (f env e)
2285 env' = extend env x x'
2287 If we replaced the two occurrences of x' by (newName %ns), which is
2288 usually a harmless thing to do, we get:
2290 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2291 f env (Lam x e) = Lam (newName %ns) (f env e)
2293 env' = extend env x (newName %ns)
2295 But now the name supply is consumed in <emphasis>three</emphasis> places
2296 (the two calls to newName,and the recursive call to f), so
2297 the result is utterly different. Urk! We don't even have
2301 Well, this is an experimental change. With implicit
2302 parameters we have already lost beta reduction anyway, and
2303 (as John Launchbury puts it) we can't sensibly reason about
2304 Haskell programs without knowing their typing.
2309 <sect3><title>Recursive functions</title>
2310 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2313 foo :: %x::T => Int -> [Int]
2315 foo n = %x : foo (n-1)
2317 where T is some type in class Splittable.</para>
2319 Do you get a list of all the same T's or all different T's
2320 (assuming that split gives two distinct T's back)?
2322 If you supply the type signature, taking advantage of polymorphic
2323 recursion, you get what you'd probably expect. Here's the
2324 translated term, where the implicit param is made explicit:
2327 foo x n = let (x1,x2) = split x
2328 in x1 : foo x2 (n-1)
2330 But if you don't supply a type signature, GHC uses the Hindley
2331 Milner trick of using a single monomorphic instance of the function
2332 for the recursive calls. That is what makes Hindley Milner type inference
2333 work. So the translation becomes
2337 foom n = x : foom (n-1)
2341 Result: 'x' is not split, and you get a list of identical T's. So the
2342 semantics of the program depends on whether or not foo has a type signature.
2345 You may say that this is a good reason to dislike linear implicit parameters
2346 and you'd be right. That is why they are an experimental feature.
2352 <sect2 id="functional-dependencies">
2353 <title>Functional dependencies
2356 <para> Functional dependencies are implemented as described by Mark Jones
2357 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2358 In Proceedings of the 9th European Symposium on Programming,
2359 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2363 Functional dependencies are introduced by a vertical bar in the syntax of a
2364 class declaration; e.g.
2366 class (Monad m) => MonadState s m | m -> s where ...
2368 class Foo a b c | a b -> c where ...
2370 There should be more documentation, but there isn't (yet). Yell if you need it.
2376 <sect2 id="sec-kinding">
2377 <title>Explicitly-kinded quantification</title>
2380 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2381 to give the kind explicitly as (machine-checked) documentation,
2382 just as it is nice to give a type signature for a function. On some occasions,
2383 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2384 John Hughes had to define the data type:
2386 data Set cxt a = Set [a]
2387 | Unused (cxt a -> ())
2389 The only use for the <literal>Unused</literal> constructor was to force the correct
2390 kind for the type variable <literal>cxt</literal>.
2393 GHC now instead allows you to specify the kind of a type variable directly, wherever
2394 a type variable is explicitly bound. Namely:
2396 <listitem><para><literal>data</literal> declarations:
2398 data Set (cxt :: * -> *) a = Set [a]
2399 </screen></para></listitem>
2400 <listitem><para><literal>type</literal> declarations:
2402 type T (f :: * -> *) = f Int
2403 </screen></para></listitem>
2404 <listitem><para><literal>class</literal> declarations:
2406 class (Eq a) => C (f :: * -> *) a where ...
2407 </screen></para></listitem>
2408 <listitem><para><literal>forall</literal>'s in type signatures:
2410 f :: forall (cxt :: * -> *). Set cxt Int
2411 </screen></para></listitem>
2416 The parentheses are required. Some of the spaces are required too, to
2417 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2418 will get a parse error, because "<literal>::*->*</literal>" is a
2419 single lexeme in Haskell.
2423 As part of the same extension, you can put kind annotations in types
2426 f :: (Int :: *) -> Int
2427 g :: forall a. a -> (a :: *)
2431 atype ::= '(' ctype '::' kind ')
2433 The parentheses are required.
2438 <sect2 id="universal-quantification">
2439 <title>Arbitrary-rank polymorphism
2443 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2444 allows us to say exactly what this means. For example:
2452 g :: forall b. (b -> b)
2454 The two are treated identically.
2458 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2459 explicit universal quantification in
2461 For example, all the following types are legal:
2463 f1 :: forall a b. a -> b -> a
2464 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2466 f2 :: (forall a. a->a) -> Int -> Int
2467 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2469 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2471 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2472 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2473 The <literal>forall</literal> makes explicit the universal quantification that
2474 is implicitly added by Haskell.
2477 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2478 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2479 shows, the polymorphic type on the left of the function arrow can be overloaded.
2482 The function <literal>f3</literal> has a rank-3 type;
2483 it has rank-2 types on the left of a function arrow.
2486 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2487 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2488 that restriction has now been lifted.)
2489 In particular, a forall-type (also called a "type scheme"),
2490 including an operational type class context, is legal:
2492 <listitem> <para> On the left of a function arrow </para> </listitem>
2493 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2494 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2495 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2496 field type signatures.</para> </listitem>
2497 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2498 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2500 There is one place you cannot put a <literal>forall</literal>:
2501 you cannot instantiate a type variable with a forall-type. So you cannot
2502 make a forall-type the argument of a type constructor. So these types are illegal:
2504 x1 :: [forall a. a->a]
2505 x2 :: (forall a. a->a, Int)
2506 x3 :: Maybe (forall a. a->a)
2508 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2509 a type variable any more!
2518 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2519 the types of the constructor arguments. Here are several examples:
2525 data T a = T1 (forall b. b -> b -> b) a
2527 data MonadT m = MkMonad { return :: forall a. a -> m a,
2528 bind :: forall a b. m a -> (a -> m b) -> m b
2531 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2537 The constructors have rank-2 types:
2543 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2544 MkMonad :: forall m. (forall a. a -> m a)
2545 -> (forall a b. m a -> (a -> m b) -> m b)
2547 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2553 Notice that you don't need to use a <literal>forall</literal> if there's an
2554 explicit context. For example in the first argument of the
2555 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2556 prefixed to the argument type. The implicit <literal>forall</literal>
2557 quantifies all type variables that are not already in scope, and are
2558 mentioned in the type quantified over.
2562 As for type signatures, implicit quantification happens for non-overloaded
2563 types too. So if you write this:
2566 data T a = MkT (Either a b) (b -> b)
2569 it's just as if you had written this:
2572 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2575 That is, since the type variable <literal>b</literal> isn't in scope, it's
2576 implicitly universally quantified. (Arguably, it would be better
2577 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2578 where that is what is wanted. Feedback welcomed.)
2582 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2583 the constructor to suitable values, just as usual. For example,
2594 a3 = MkSwizzle reverse
2597 a4 = let r x = Just x
2604 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2605 mkTs f x y = [T1 f x, T1 f y]
2611 The type of the argument can, as usual, be more general than the type
2612 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2613 does not need the <literal>Ord</literal> constraint.)
2617 When you use pattern matching, the bound variables may now have
2618 polymorphic types. For example:
2624 f :: T a -> a -> (a, Char)
2625 f (T1 w k) x = (w k x, w 'c' 'd')
2627 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2628 g (MkSwizzle s) xs f = s (map f (s xs))
2630 h :: MonadT m -> [m a] -> m [a]
2631 h m [] = return m []
2632 h m (x:xs) = bind m x $ \y ->
2633 bind m (h m xs) $ \ys ->
2640 In the function <function>h</function> we use the record selectors <literal>return</literal>
2641 and <literal>bind</literal> to extract the polymorphic bind and return functions
2642 from the <literal>MonadT</literal> data structure, rather than using pattern
2648 <title>Type inference</title>
2651 In general, type inference for arbitrary-rank types is undecidable.
2652 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2653 to get a decidable algorithm by requiring some help from the programmer.
2654 We do not yet have a formal specification of "some help" but the rule is this:
2657 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2658 provides an explicit polymorphic type for x, or GHC's type inference will assume
2659 that x's type has no foralls in it</emphasis>.
2662 What does it mean to "provide" an explicit type for x? You can do that by
2663 giving a type signature for x directly, using a pattern type signature
2664 (<xref linkend="scoped-type-variables"/>), thus:
2666 \ f :: (forall a. a->a) -> (f True, f 'c')
2668 Alternatively, you can give a type signature to the enclosing
2669 context, which GHC can "push down" to find the type for the variable:
2671 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2673 Here the type signature on the expression can be pushed inwards
2674 to give a type signature for f. Similarly, and more commonly,
2675 one can give a type signature for the function itself:
2677 h :: (forall a. a->a) -> (Bool,Char)
2678 h f = (f True, f 'c')
2680 You don't need to give a type signature if the lambda bound variable
2681 is a constructor argument. Here is an example we saw earlier:
2683 f :: T a -> a -> (a, Char)
2684 f (T1 w k) x = (w k x, w 'c' 'd')
2686 Here we do not need to give a type signature to <literal>w</literal>, because
2687 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2694 <sect3 id="implicit-quant">
2695 <title>Implicit quantification</title>
2698 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2699 user-written types, if and only if there is no explicit <literal>forall</literal>,
2700 GHC finds all the type variables mentioned in the type that are not already
2701 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2705 f :: forall a. a -> a
2712 h :: forall b. a -> b -> b
2718 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2721 f :: (a -> a) -> Int
2723 f :: forall a. (a -> a) -> Int
2725 f :: (forall a. a -> a) -> Int
2728 g :: (Ord a => a -> a) -> Int
2729 -- MEANS the illegal type
2730 g :: forall a. (Ord a => a -> a) -> Int
2732 g :: (forall a. Ord a => a -> a) -> Int
2734 The latter produces an illegal type, which you might think is silly,
2735 but at least the rule is simple. If you want the latter type, you
2736 can write your for-alls explicitly. Indeed, doing so is strongly advised
2745 <sect2 id="scoped-type-variables">
2746 <title>Scoped type variables
2750 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2752 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2753 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2754 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2758 f (xs::[a]) = ys ++ ys
2763 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2764 This brings the type variable <literal>a</literal> into scope; it scopes over
2765 all the patterns and right hand sides for this equation for <function>f</function>.
2766 In particular, it is in scope at the type signature for <varname>y</varname>.
2770 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2771 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2772 implicitly universally quantified. (If there are no type variables in
2773 scope, all type variables mentioned in the signature are universally
2774 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2775 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2776 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2777 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2778 it becomes possible to do so.
2782 Scoped type variables are implemented in both GHC and Hugs. Where the
2783 implementations differ from the specification below, those differences
2788 So much for the basic idea. Here are the details.
2792 <title>What a scoped type variable means</title>
2794 A lexically-scoped type variable is simply
2795 the name for a type. The restriction it expresses is that all occurrences
2796 of the same name mean the same type. For example:
2798 f :: [Int] -> Int -> Int
2799 f (xs::[a]) (y::a) = (head xs + y) :: a
2801 The pattern type signatures on the left hand side of
2802 <literal>f</literal> express the fact that <literal>xs</literal>
2803 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2804 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2805 specifies that this expression must have the same type <literal>a</literal>.
2806 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2807 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2808 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2809 rules, which specified that a pattern-bound type variable should be universally quantified.)
2810 For example, all of these are legal:</para>
2813 t (x::a) (y::a) = x+y*2
2815 f (x::a) (y::b) = [x,y] -- a unifies with b
2817 g (x::a) = x + 1::Int -- a unifies with Int
2819 h x = let k (y::a) = [x,y] -- a is free in the
2820 in k x -- environment
2822 k (x::a) True = ... -- a unifies with Int
2823 k (x::Int) False = ...
2826 w (x::a) = x -- a unifies with [b]
2832 <title>Scope and implicit quantification</title>
2840 All the type variables mentioned in a pattern,
2841 that are not already in scope,
2842 are brought into scope by the pattern. We describe this set as
2843 the <emphasis>type variables bound by the pattern</emphasis>.
2846 f (x::a) = let g (y::(a,b)) = fst y
2850 The pattern <literal>(x::a)</literal> brings the type variable
2851 <literal>a</literal> into scope, as well as the term
2852 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2853 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2854 and brings into scope the type variable <literal>b</literal>.
2860 The type variable(s) bound by the pattern have the same scope
2861 as the term variable(s) bound by the pattern. For example:
2864 f (x::a) = <...rhs of f...>
2865 (p::b, q::b) = (1,2)
2866 in <...body of let...>
2868 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2869 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2870 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2871 just like <literal>p</literal> and <literal>q</literal> do.
2872 Indeed, the newly bound type variables also scope over any ordinary, separate
2873 type signatures in the <literal>let</literal> group.
2880 The type variables bound by the pattern may be
2881 mentioned in ordinary type signatures or pattern
2882 type signatures anywhere within their scope.
2889 In ordinary type signatures, any type variable mentioned in the
2890 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2898 Ordinary type signatures do not bring any new type variables
2899 into scope (except in the type signature itself!). So this is illegal:
2906 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2907 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2908 and that is an incorrect typing.
2915 The pattern type signature is a monotype:
2920 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2924 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2925 not to type schemes.
2929 There is no implicit universal quantification on pattern type signatures (in contrast to
2930 ordinary type signatures).
2940 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2941 scope over the methods defined in the <literal>where</literal> part. For example:
2955 (Not implemented in Hugs yet, Dec 98).
2965 <sect3 id="decl-type-sigs">
2966 <title>Declaration type signatures</title>
2967 <para>A declaration type signature that has <emphasis>explicit</emphasis>
2968 quantification (using <literal>forall</literal>) brings into scope the
2969 explicitly-quantified
2970 type variables, in the definition of the named function(s). For example:
2972 f :: forall a. [a] -> [a]
2973 f (x:xs) = xs ++ [ x :: a ]
2975 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
2976 the definition of "<literal>f</literal>".
2978 <para>This only happens if the quantification in <literal>f</literal>'s type
2979 signature is explicit. For example:
2982 g (x:xs) = xs ++ [ x :: a ]
2984 This program will be rejected, because "<literal>a</literal>" does not scope
2985 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
2986 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
2987 quantification rules.
2991 <sect3 id="pattern-type-sigs">
2992 <title>Where a pattern type signature can occur</title>
2995 A pattern type signature can occur in any pattern. For example:
3000 A pattern type signature can be on an arbitrary sub-pattern, not
3005 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3014 Pattern type signatures, including the result part, can be used
3015 in lambda abstractions:
3018 (\ (x::a, y) :: a -> x)
3025 Pattern type signatures, including the result part, can be used
3026 in <literal>case</literal> expressions:
3029 case e of { ((x::a, y) :: (a,b)) -> x }
3032 Note that the <literal>-></literal> symbol in a case alternative
3033 leads to difficulties when parsing a type signature in the pattern: in
3034 the absence of the extra parentheses in the example above, the parser
3035 would try to interpret the <literal>-></literal> as a function
3036 arrow and give a parse error later.
3044 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3045 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3046 token or a parenthesised type of some sort). To see why,
3047 consider how one would parse this:
3061 Pattern type signatures can bind existential type variables.
3066 data T = forall a. MkT [a]
3069 f (MkT [t::a]) = MkT t3
3082 Pattern type signatures
3083 can be used in pattern bindings:
3086 f x = let (y, z::a) = x in ...
3087 f1 x = let (y, z::Int) = x in ...
3088 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3089 f3 :: (b->b) = \x -> x
3092 In all such cases, the binding is not generalised over the pattern-bound
3093 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3094 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3095 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3096 In contrast, the binding
3101 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3102 in <literal>f4</literal>'s scope.
3108 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3109 type signatures. The two can be used independently or together.</para>
3113 <sect3 id="result-type-sigs">
3114 <title>Result type signatures</title>
3117 The result type of a function can be given a signature, thus:
3121 f (x::a) :: [a] = [x,x,x]
3125 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3126 result type. Sometimes this is the only way of naming the type variable
3131 f :: Int -> [a] -> [a]
3132 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3133 in \xs -> map g (reverse xs `zip` xs)
3138 The type variables bound in a result type signature scope over the right hand side
3139 of the definition. However, consider this corner-case:
3141 rev1 :: [a] -> [a] = \xs -> reverse xs
3143 foo ys = rev (ys::[a])
3145 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3146 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3147 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3148 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3149 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3152 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3153 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3157 rev1 :: [a] -> [a] = \xs -> reverse xs
3162 Result type signatures are not yet implemented in Hugs.
3169 <sect2 id="deriving-typeable">
3170 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3173 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3174 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3175 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3176 classes <literal>Eq</literal>, <literal>Ord</literal>,
3177 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3180 GHC extends this list with two more classes that may be automatically derived
3181 (provided the <option>-fglasgow-exts</option> flag is specified):
3182 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3183 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3184 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3188 <sect2 id="newtype-deriving">
3189 <title>Generalised derived instances for newtypes</title>
3192 When you define an abstract type using <literal>newtype</literal>, you may want
3193 the new type to inherit some instances from its representation. In
3194 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3195 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3196 other classes you have to write an explicit instance declaration. For
3197 example, if you define
3200 newtype Dollars = Dollars Int
3203 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3204 explicitly define an instance of <literal>Num</literal>:
3207 instance Num Dollars where
3208 Dollars a + Dollars b = Dollars (a+b)
3211 All the instance does is apply and remove the <literal>newtype</literal>
3212 constructor. It is particularly galling that, since the constructor
3213 doesn't appear at run-time, this instance declaration defines a
3214 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3215 dictionary, only slower!
3219 <sect3> <title> Generalising the deriving clause </title>
3221 GHC now permits such instances to be derived instead, so one can write
3223 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3226 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3227 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3228 derives an instance declaration of the form
3231 instance Num Int => Num Dollars
3234 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3238 We can also derive instances of constructor classes in a similar
3239 way. For example, suppose we have implemented state and failure monad
3240 transformers, such that
3243 instance Monad m => Monad (State s m)
3244 instance Monad m => Monad (Failure m)
3246 In Haskell 98, we can define a parsing monad by
3248 type Parser tok m a = State [tok] (Failure m) a
3251 which is automatically a monad thanks to the instance declarations
3252 above. With the extension, we can make the parser type abstract,
3253 without needing to write an instance of class <literal>Monad</literal>, via
3256 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3259 In this case the derived instance declaration is of the form
3261 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3264 Notice that, since <literal>Monad</literal> is a constructor class, the
3265 instance is a <emphasis>partial application</emphasis> of the new type, not the
3266 entire left hand side. We can imagine that the type declaration is
3267 ``eta-converted'' to generate the context of the instance
3272 We can even derive instances of multi-parameter classes, provided the
3273 newtype is the last class parameter. In this case, a ``partial
3274 application'' of the class appears in the <literal>deriving</literal>
3275 clause. For example, given the class
3278 class StateMonad s m | m -> s where ...
3279 instance Monad m => StateMonad s (State s m) where ...
3281 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3283 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3284 deriving (Monad, StateMonad [tok])
3287 The derived instance is obtained by completing the application of the
3288 class to the new type:
3291 instance StateMonad [tok] (State [tok] (Failure m)) =>
3292 StateMonad [tok] (Parser tok m)
3297 As a result of this extension, all derived instances in newtype
3298 declarations are treated uniformly (and implemented just by reusing
3299 the dictionary for the representation type), <emphasis>except</emphasis>
3300 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3301 the newtype and its representation.
3305 <sect3> <title> A more precise specification </title>
3307 Derived instance declarations are constructed as follows. Consider the
3308 declaration (after expansion of any type synonyms)
3311 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3317 <literal>S</literal> is a type constructor,
3320 The <literal>t1...tk</literal> are types,
3323 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3324 the <literal>ti</literal>, and
3327 The <literal>ci</literal> are partial applications of
3328 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3329 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3332 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3333 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3334 should not "look through" the type or its constructor. You can still
3335 derive these classes for a newtype, but it happens in the usual way, not
3336 via this new mechanism.
3339 Then, for each <literal>ci</literal>, the derived instance
3342 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3344 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3345 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3349 As an example which does <emphasis>not</emphasis> work, consider
3351 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3353 Here we cannot derive the instance
3355 instance Monad (State s m) => Monad (NonMonad m)
3358 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3359 and so cannot be "eta-converted" away. It is a good thing that this
3360 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3361 not, in fact, a monad --- for the same reason. Try defining
3362 <literal>>>=</literal> with the correct type: you won't be able to.
3366 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3367 important, since we can only derive instances for the last one. If the
3368 <literal>StateMonad</literal> class above were instead defined as
3371 class StateMonad m s | m -> s where ...
3374 then we would not have been able to derive an instance for the
3375 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3376 classes usually have one "main" parameter for which deriving new
3377 instances is most interesting.
3379 <para>Lastly, all of this applies only for classes other than
3380 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3381 and <literal>Data</literal>, for which the built-in derivation applies (section
3382 4.3.3. of the Haskell Report).
3383 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3384 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3385 the standard method is used or the one described here.)
3393 <!-- ==================== End of type system extensions ================= -->
3395 <!-- ====================== Generalised algebraic data types ======================= -->
3398 <title>Generalised Algebraic Data Types</title>
3400 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3401 to give the type signatures of constructors explicitly. For example:
3404 Lit :: Int -> Term Int
3405 Succ :: Term Int -> Term Int
3406 IsZero :: Term Int -> Term Bool
3407 If :: Term Bool -> Term a -> Term a -> Term a
3408 Pair :: Term a -> Term b -> Term (a,b)
3410 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3411 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3412 for these <literal>Terms</literal>:
3416 eval (Succ t) = 1 + eval t
3417 eval (IsZero i) = eval i == 0
3418 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3419 eval (Pair e1 e2) = (eval e2, eval e2)
3421 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3423 <para> The extensions to GHC are these:
3426 Data type declarations have a 'where' form, as exemplified above. The type signature of
3427 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3428 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3429 have no scope. Indeed, one can write a kind signature instead:
3431 data Term :: * -> * where ...
3433 or even a mixture of the two:
3435 data Foo a :: (* -> *) -> * where ...
3437 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3440 data Foo a (b :: * -> *) where ...
3445 There are no restrictions on the type of the data constructor, except that the result
3446 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3447 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3451 You cannot use a <literal>deriving</literal> clause on a GADT-style data type declaration,
3452 nor can you use record syntax. (It's not clear what these constructs would mean. For example,
3453 the record selectors might ill-typed.) However, you can use strictness annotations, in the obvious places
3454 in the constructor type:
3457 Lit :: !Int -> Term Int
3458 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3459 Pair :: Term a -> Term b -> Term (a,b)
3464 Pattern matching causes type refinement. For example, in the right hand side of the equation
3469 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3470 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3471 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3473 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3474 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3475 occur. However, the refinement is quite general. For example, if we had:
3477 eval :: Term a -> a -> a
3478 eval (Lit i) j = i+j
3480 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3481 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3482 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3488 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3490 data T a = forall b. MkT b (b->a)
3491 data T' a where { MKT :: b -> (b->a) -> T a }
3496 <!-- ====================== End of Generalised algebraic data types ======================= -->
3498 <!-- ====================== TEMPLATE HASKELL ======================= -->
3500 <sect1 id="template-haskell">
3501 <title>Template Haskell</title>
3503 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3504 Template Haskell at <ulink url="http://www.haskell.org/th/">
3505 http://www.haskell.org/th/</ulink>, while
3507 the main technical innovations is discussed in "<ulink
3508 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3509 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3510 The details of the Template Haskell design are still in flux. Make sure you
3511 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3512 (search for the type ExpQ).
3513 [Temporary: many changes to the original design are described in
3514 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3515 Not all of these changes are in GHC 6.2.]
3518 <para> The first example from that paper is set out below as a worked example to help get you started.
3522 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3523 Tim Sheard is going to expand it.)
3527 <title>Syntax</title>
3529 <para> Template Haskell has the following new syntactic
3530 constructions. You need to use the flag
3531 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3532 </indexterm>to switch these syntactic extensions on
3533 (<option>-fth</option> is currently implied by
3534 <option>-fglasgow-exts</option>, but you are encouraged to
3535 specify it explicitly).</para>
3539 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3540 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3541 There must be no space between the "$" and the identifier or parenthesis. This use
3542 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3543 of "." as an infix operator. If you want the infix operator, put spaces around it.
3545 <para> A splice can occur in place of
3547 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3548 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3549 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3551 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3552 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3558 A expression quotation is written in Oxford brackets, thus:
3560 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3561 the quotation has type <literal>Expr</literal>.</para></listitem>
3562 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3563 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3564 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3565 the quotation has type <literal>Type</literal>.</para></listitem>
3566 </itemizedlist></para></listitem>
3569 Reification is written thus:
3571 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3572 has type <literal>Dec</literal>. </para></listitem>
3573 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3574 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3575 <listitem><para> Still to come: fixities </para></listitem>
3577 </itemizedlist></para>
3584 <sect2> <title> Using Template Haskell </title>
3588 The data types and monadic constructor functions for Template Haskell are in the library
3589 <literal>Language.Haskell.THSyntax</literal>.
3593 You can only run a function at compile time if it is imported from another module. That is,
3594 you can't define a function in a module, and call it from within a splice in the same module.
3595 (It would make sense to do so, but it's hard to implement.)
3599 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3602 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3603 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3604 compiles and runs a program, and then looks at the result. So it's important that
3605 the program it compiles produces results whose representations are identical to
3606 those of the compiler itself.
3610 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3611 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3616 <sect2> <title> A Template Haskell Worked Example </title>
3617 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3618 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3625 -- Import our template "pr"
3626 import Printf ( pr )
3628 -- The splice operator $ takes the Haskell source code
3629 -- generated at compile time by "pr" and splices it into
3630 -- the argument of "putStrLn".
3631 main = putStrLn ( $(pr "Hello") )
3637 -- Skeletal printf from the paper.
3638 -- It needs to be in a separate module to the one where
3639 -- you intend to use it.
3641 -- Import some Template Haskell syntax
3642 import Language.Haskell.TH
3644 -- Describe a format string
3645 data Format = D | S | L String
3647 -- Parse a format string. This is left largely to you
3648 -- as we are here interested in building our first ever
3649 -- Template Haskell program and not in building printf.
3650 parse :: String -> [Format]
3653 -- Generate Haskell source code from a parsed representation
3654 -- of the format string. This code will be spliced into
3655 -- the module which calls "pr", at compile time.
3656 gen :: [Format] -> ExpQ
3657 gen [D] = [| \n -> show n |]
3658 gen [S] = [| \s -> s |]
3659 gen [L s] = stringE s
3661 -- Here we generate the Haskell code for the splice
3662 -- from an input format string.
3663 pr :: String -> ExpQ
3664 pr s = gen (parse s)
3667 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3670 $ ghc --make -fth main.hs -o main.exe
3673 <para>Run "main.exe" and here is your output:</para>
3684 <!-- ===================== Arrow notation =================== -->
3686 <sect1 id="arrow-notation">
3687 <title>Arrow notation
3690 <para>Arrows are a generalization of monads introduced by John Hughes.
3691 For more details, see
3696 “Generalising Monads to Arrows”,
3697 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3698 pp67–111, May 2000.
3704 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3705 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3711 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3712 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3718 and the arrows web page at
3719 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3720 With the <option>-farrows</option> flag, GHC supports the arrow
3721 notation described in the second of these papers.
3722 What follows is a brief introduction to the notation;
3723 it won't make much sense unless you've read Hughes's paper.
3724 This notation is translated to ordinary Haskell,
3725 using combinators from the
3726 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3730 <para>The extension adds a new kind of expression for defining arrows:
3732 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3733 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3735 where <literal>proc</literal> is a new keyword.
3736 The variables of the pattern are bound in the body of the
3737 <literal>proc</literal>-expression,
3738 which is a new sort of thing called a <firstterm>command</firstterm>.
3739 The syntax of commands is as follows:
3741 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3742 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3743 | <replaceable>cmd</replaceable><superscript>0</superscript>
3745 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3746 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3747 infix operators as for expressions, and
3749 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3750 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3751 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3752 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3753 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3754 | <replaceable>fcmd</replaceable>
3756 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3757 | ( <replaceable>cmd</replaceable> )
3758 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3760 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3761 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3762 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3763 | <replaceable>cmd</replaceable>
3765 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3766 except that the bodies are commands instead of expressions.
3770 Commands produce values, but (like monadic computations)
3771 may yield more than one value,
3772 or none, and may do other things as well.
3773 For the most part, familiarity with monadic notation is a good guide to
3775 However the values of expressions, even monadic ones,
3776 are determined by the values of the variables they contain;
3777 this is not necessarily the case for commands.
3781 A simple example of the new notation is the expression
3783 proc x -> f -< x+1
3785 We call this a <firstterm>procedure</firstterm> or
3786 <firstterm>arrow abstraction</firstterm>.
3787 As with a lambda expression, the variable <literal>x</literal>
3788 is a new variable bound within the <literal>proc</literal>-expression.
3789 It refers to the input to the arrow.
3790 In the above example, <literal>-<</literal> is not an identifier but an
3791 new reserved symbol used for building commands from an expression of arrow
3792 type and an expression to be fed as input to that arrow.
3793 (The weird look will make more sense later.)
3794 It may be read as analogue of application for arrows.
3795 The above example is equivalent to the Haskell expression
3797 arr (\ x -> x+1) >>> f
3799 That would make no sense if the expression to the left of
3800 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3801 More generally, the expression to the left of <literal>-<</literal>
3802 may not involve any <firstterm>local variable</firstterm>,
3803 i.e. a variable bound in the current arrow abstraction.
3804 For such a situation there is a variant <literal>-<<</literal>, as in
3806 proc x -> f x -<< x+1
3808 which is equivalent to
3810 arr (\ x -> (f, x+1)) >>> app
3812 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3814 Such an arrow is equivalent to a monad, so if you're using this form
3815 you may find a monadic formulation more convenient.
3819 <title>do-notation for commands</title>
3822 Another form of command is a form of <literal>do</literal>-notation.
3823 For example, you can write
3832 You can read this much like ordinary <literal>do</literal>-notation,
3833 but with commands in place of monadic expressions.
3834 The first line sends the value of <literal>x+1</literal> as an input to
3835 the arrow <literal>f</literal>, and matches its output against
3836 <literal>y</literal>.
3837 In the next line, the output is discarded.
3838 The arrow <function>returnA</function> is defined in the
3839 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3840 module as <literal>arr id</literal>.
3841 The above example is treated as an abbreviation for
3843 arr (\ x -> (x, x)) >>>
3844 first (arr (\ x -> x+1) >>> f) >>>
3845 arr (\ (y, x) -> (y, (x, y))) >>>
3846 first (arr (\ y -> 2*y) >>> g) >>>
3848 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3849 first (arr (\ (x, z) -> x*z) >>> h) >>>
3850 arr (\ (t, z) -> t+z) >>>
3853 Note that variables not used later in the composition are projected out.
3854 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3856 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3857 module, this reduces to
3859 arr (\ x -> (x+1, x)) >>>
3861 arr (\ (y, x) -> (2*y, (x, y))) >>>
3863 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3865 arr (\ (t, z) -> t+z)
3867 which is what you might have written by hand.
3868 With arrow notation, GHC keeps track of all those tuples of variables for you.
3872 Note that although the above translation suggests that
3873 <literal>let</literal>-bound variables like <literal>z</literal> must be
3874 monomorphic, the actual translation produces Core,
3875 so polymorphic variables are allowed.
3879 It's also possible to have mutually recursive bindings,
3880 using the new <literal>rec</literal> keyword, as in the following example:
3882 counter :: ArrowCircuit a => a Bool Int
3883 counter = proc reset -> do
3884 rec output <- returnA -< if reset then 0 else next
3885 next <- delay 0 -< output+1
3886 returnA -< output
3888 The translation of such forms uses the <function>loop</function> combinator,
3889 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3895 <title>Conditional commands</title>
3898 In the previous example, we used a conditional expression to construct the
3900 Sometimes we want to conditionally execute different commands, as in
3907 which is translated to
3909 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3910 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3912 Since the translation uses <function>|||</function>,
3913 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3917 There are also <literal>case</literal> commands, like
3923 y <- h -< (x1, x2)
3927 The syntax is the same as for <literal>case</literal> expressions,
3928 except that the bodies of the alternatives are commands rather than expressions.
3929 The translation is similar to that of <literal>if</literal> commands.
3935 <title>Defining your own control structures</title>
3938 As we're seen, arrow notation provides constructs,
3939 modelled on those for expressions,
3940 for sequencing, value recursion and conditionals.
3941 But suitable combinators,
3942 which you can define in ordinary Haskell,
3943 may also be used to build new commands out of existing ones.
3944 The basic idea is that a command defines an arrow from environments to values.
3945 These environments assign values to the free local variables of the command.
3946 Thus combinators that produce arrows from arrows
3947 may also be used to build commands from commands.
3948 For example, the <literal>ArrowChoice</literal> class includes a combinator
3950 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3952 so we can use it to build commands:
3954 expr' = proc x -> do
3957 symbol Plus -< ()
3958 y <- term -< ()
3961 symbol Minus -< ()
3962 y <- term -< ()
3965 (The <literal>do</literal> on the first line is needed to prevent the first
3966 <literal><+> ...</literal> from being interpreted as part of the
3967 expression on the previous line.)
3968 This is equivalent to
3970 expr' = (proc x -> returnA -< x)
3971 <+> (proc x -> do
3972 symbol Plus -< ()
3973 y <- term -< ()
3975 <+> (proc x -> do
3976 symbol Minus -< ()
3977 y <- term -< ()
3980 It is essential that this operator be polymorphic in <literal>e</literal>
3981 (representing the environment input to the command
3982 and thence to its subcommands)
3983 and satisfy the corresponding naturality property
3985 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3987 at least for strict <literal>k</literal>.
3988 (This should be automatic if you're not using <function>seq</function>.)
3989 This ensures that environments seen by the subcommands are environments
3990 of the whole command,
3991 and also allows the translation to safely trim these environments.
3992 The operator must also not use any variable defined within the current
3997 We could define our own operator
3999 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4000 untilA body cond = proc x ->
4001 if cond x then returnA -< ()
4004 untilA body cond -< x
4006 and use it in the same way.
4007 Of course this infix syntax only makes sense for binary operators;
4008 there is also a more general syntax involving special brackets:
4012 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4019 <title>Primitive constructs</title>
4022 Some operators will need to pass additional inputs to their subcommands.
4023 For example, in an arrow type supporting exceptions,
4024 the operator that attaches an exception handler will wish to pass the
4025 exception that occurred to the handler.
4026 Such an operator might have a type
4028 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4030 where <literal>Ex</literal> is the type of exceptions handled.
4031 You could then use this with arrow notation by writing a command
4033 body `handleA` \ ex -> handler
4035 so that if an exception is raised in the command <literal>body</literal>,
4036 the variable <literal>ex</literal> is bound to the value of the exception
4037 and the command <literal>handler</literal>,
4038 which typically refers to <literal>ex</literal>, is entered.
4039 Though the syntax here looks like a functional lambda,
4040 we are talking about commands, and something different is going on.
4041 The input to the arrow represented by a command consists of values for
4042 the free local variables in the command, plus a stack of anonymous values.
4043 In all the prior examples, this stack was empty.
4044 In the second argument to <function>handleA</function>,
4045 this stack consists of one value, the value of the exception.
4046 The command form of lambda merely gives this value a name.
4051 the values on the stack are paired to the right of the environment.
4052 So operators like <function>handleA</function> that pass
4053 extra inputs to their subcommands can be designed for use with the notation
4054 by pairing the values with the environment in this way.
4055 More precisely, the type of each argument of the operator (and its result)
4056 should have the form
4058 a (...(e,t1), ... tn) t
4060 where <replaceable>e</replaceable> is a polymorphic variable
4061 (representing the environment)
4062 and <replaceable>ti</replaceable> are the types of the values on the stack,
4063 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4064 The polymorphic variable <replaceable>e</replaceable> must not occur in
4065 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4066 <replaceable>t</replaceable>.
4067 However the arrows involved need not be the same.
4068 Here are some more examples of suitable operators:
4070 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4071 runReader :: ... => a e c -> a' (e,State) c
4072 runState :: ... => a e c -> a' (e,State) (c,State)
4074 We can supply the extra input required by commands built with the last two
4075 by applying them to ordinary expressions, as in
4079 (|runReader (do { ... })|) s
4081 which adds <literal>s</literal> to the stack of inputs to the command
4082 built using <function>runReader</function>.
4086 The command versions of lambda abstraction and application are analogous to
4087 the expression versions.
4088 In particular, the beta and eta rules describe equivalences of commands.
4089 These three features (operators, lambda abstraction and application)
4090 are the core of the notation; everything else can be built using them,
4091 though the results would be somewhat clumsy.
4092 For example, we could simulate <literal>do</literal>-notation by defining
4094 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4095 u `bind` f = returnA &&& u >>> f
4097 bind_ :: Arrow a => a e b -> a e c -> a e c
4098 u `bind_` f = u `bind` (arr fst >>> f)
4100 We could simulate <literal>if</literal> by defining
4102 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4103 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4110 <title>Differences with the paper</title>
4115 <para>Instead of a single form of arrow application (arrow tail) with two
4116 translations, the implementation provides two forms
4117 <quote><literal>-<</literal></quote> (first-order)
4118 and <quote><literal>-<<</literal></quote> (higher-order).
4123 <para>User-defined operators are flagged with banana brackets instead of
4124 a new <literal>form</literal> keyword.
4133 <title>Portability</title>
4136 Although only GHC implements arrow notation directly,
4137 there is also a preprocessor
4139 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4140 that translates arrow notation into Haskell 98
4141 for use with other Haskell systems.
4142 You would still want to check arrow programs with GHC;
4143 tracing type errors in the preprocessor output is not easy.
4144 Modules intended for both GHC and the preprocessor must observe some
4145 additional restrictions:
4150 The module must import
4151 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4157 The preprocessor cannot cope with other Haskell extensions.
4158 These would have to go in separate modules.
4164 Because the preprocessor targets Haskell (rather than Core),
4165 <literal>let</literal>-bound variables are monomorphic.
4176 <!-- ==================== ASSERTIONS ================= -->
4178 <sect1 id="sec-assertions">
4180 <indexterm><primary>Assertions</primary></indexterm>
4184 If you want to make use of assertions in your standard Haskell code, you
4185 could define a function like the following:
4191 assert :: Bool -> a -> a
4192 assert False x = error "assertion failed!"
4199 which works, but gives you back a less than useful error message --
4200 an assertion failed, but which and where?
4204 One way out is to define an extended <function>assert</function> function which also
4205 takes a descriptive string to include in the error message and
4206 perhaps combine this with the use of a pre-processor which inserts
4207 the source location where <function>assert</function> was used.
4211 Ghc offers a helping hand here, doing all of this for you. For every
4212 use of <function>assert</function> in the user's source:
4218 kelvinToC :: Double -> Double
4219 kelvinToC k = assert (k >= 0.0) (k+273.15)
4225 Ghc will rewrite this to also include the source location where the
4232 assert pred val ==> assertError "Main.hs|15" pred val
4238 The rewrite is only performed by the compiler when it spots
4239 applications of <function>Control.Exception.assert</function>, so you
4240 can still define and use your own versions of
4241 <function>assert</function>, should you so wish. If not, import
4242 <literal>Control.Exception</literal> to make use
4243 <function>assert</function> in your code.
4247 To have the compiler ignore uses of assert, use the compiler option
4248 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4249 option</primary></indexterm> That is, expressions of the form
4250 <literal>assert pred e</literal> will be rewritten to
4251 <literal>e</literal>.
4255 Assertion failures can be caught, see the documentation for the
4256 <literal>Control.Exception</literal> library for the details.
4262 <!-- =============================== PRAGMAS =========================== -->
4264 <sect1 id="pragmas">
4265 <title>Pragmas</title>
4267 <indexterm><primary>pragma</primary></indexterm>
4269 <para>GHC supports several pragmas, or instructions to the
4270 compiler placed in the source code. Pragmas don't normally affect
4271 the meaning of the program, but they might affect the efficiency
4272 of the generated code.</para>
4274 <para>Pragmas all take the form
4276 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4278 where <replaceable>word</replaceable> indicates the type of
4279 pragma, and is followed optionally by information specific to that
4280 type of pragma. Case is ignored in
4281 <replaceable>word</replaceable>. The various values for
4282 <replaceable>word</replaceable> that GHC understands are described
4283 in the following sections; any pragma encountered with an
4284 unrecognised <replaceable>word</replaceable> is (silently)
4287 <sect2 id="deprecated-pragma">
4288 <title>DEPRECATED pragma</title>
4289 <indexterm><primary>DEPRECATED</primary>
4292 <para>The DEPRECATED pragma lets you specify that a particular
4293 function, class, or type, is deprecated. There are two
4298 <para>You can deprecate an entire module thus:</para>
4300 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4303 <para>When you compile any module that import
4304 <literal>Wibble</literal>, GHC will print the specified
4309 <para>You can deprecate a function, class, or type, with the
4310 following top-level declaration:</para>
4312 {-# DEPRECATED f, C, T "Don't use these" #-}
4314 <para>When you compile any module that imports and uses any
4315 of the specified entities, GHC will print the specified
4319 Any use of the deprecated item, or of anything from a deprecated
4320 module, will be flagged with an appropriate message. However,
4321 deprecations are not reported for
4322 (a) uses of a deprecated function within its defining module, and
4323 (b) uses of a deprecated function in an export list.
4324 The latter reduces spurious complaints within a library
4325 in which one module gathers together and re-exports
4326 the exports of several others.
4328 <para>You can suppress the warnings with the flag
4329 <option>-fno-warn-deprecations</option>.</para>
4332 <sect2 id="include-pragma">
4333 <title>INCLUDE pragma</title>
4335 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4336 of C header files that should be <literal>#include</literal>'d into
4337 the C source code generated by the compiler for the current module (if
4338 compiling via C). For example:</para>
4341 {-# INCLUDE "foo.h" #-}
4342 {-# INCLUDE <stdio.h> #-}</programlisting>
4344 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4345 your source file with any <literal>OPTIONS_GHC</literal>
4348 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4349 to the <option>-#include</option> option (<xref
4350 linkend="options-C-compiler" />), because the
4351 <literal>INCLUDE</literal> pragma is understood by other
4352 compilers. Yet another alternative is to add the include file to each
4353 <literal>foreign import</literal> declaration in your code, but we
4354 don't recommend using this approach with GHC.</para>
4357 <sect2 id="inline-noinline-pragma">
4358 <title>INLINE and NOINLINE pragmas</title>
4360 <para>These pragmas control the inlining of function
4363 <sect3 id="inline-pragma">
4364 <title>INLINE pragma</title>
4365 <indexterm><primary>INLINE</primary></indexterm>
4367 <para>GHC (with <option>-O</option>, as always) tries to
4368 inline (or “unfold”) functions/values that are
4369 “small enough,” thus avoiding the call overhead
4370 and possibly exposing other more-wonderful optimisations.
4371 Normally, if GHC decides a function is “too
4372 expensive” to inline, it will not do so, nor will it
4373 export that unfolding for other modules to use.</para>
4375 <para>The sledgehammer you can bring to bear is the
4376 <literal>INLINE</literal><indexterm><primary>INLINE
4377 pragma</primary></indexterm> pragma, used thusly:</para>
4380 key_function :: Int -> String -> (Bool, Double)
4382 #ifdef __GLASGOW_HASKELL__
4383 {-# INLINE key_function #-}
4387 <para>(You don't need to do the C pre-processor carry-on
4388 unless you're going to stick the code through HBC—it
4389 doesn't like <literal>INLINE</literal> pragmas.)</para>
4391 <para>The major effect of an <literal>INLINE</literal> pragma
4392 is to declare a function's “cost” to be very low.
4393 The normal unfolding machinery will then be very keen to
4396 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4397 function can be put anywhere its type signature could be
4400 <para><literal>INLINE</literal> pragmas are a particularly
4402 <literal>then</literal>/<literal>return</literal> (or
4403 <literal>bind</literal>/<literal>unit</literal>) functions in
4404 a monad. For example, in GHC's own
4405 <literal>UniqueSupply</literal> monad code, we have:</para>
4408 #ifdef __GLASGOW_HASKELL__
4409 {-# INLINE thenUs #-}
4410 {-# INLINE returnUs #-}
4414 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4415 linkend="noinline-pragma"/>).</para>
4418 <sect3 id="noinline-pragma">
4419 <title>NOINLINE pragma</title>
4421 <indexterm><primary>NOINLINE</primary></indexterm>
4422 <indexterm><primary>NOTINLINE</primary></indexterm>
4424 <para>The <literal>NOINLINE</literal> pragma does exactly what
4425 you'd expect: it stops the named function from being inlined
4426 by the compiler. You shouldn't ever need to do this, unless
4427 you're very cautious about code size.</para>
4429 <para><literal>NOTINLINE</literal> is a synonym for
4430 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4431 specified by Haskell 98 as the standard way to disable
4432 inlining, so it should be used if you want your code to be
4436 <sect3 id="phase-control">
4437 <title>Phase control</title>
4439 <para> Sometimes you want to control exactly when in GHC's
4440 pipeline the INLINE pragma is switched on. Inlining happens
4441 only during runs of the <emphasis>simplifier</emphasis>. Each
4442 run of the simplifier has a different <emphasis>phase
4443 number</emphasis>; the phase number decreases towards zero.
4444 If you use <option>-dverbose-core2core</option> you'll see the
4445 sequence of phase numbers for successive runs of the
4446 simplifier. In an INLINE pragma you can optionally specify a
4447 phase number, thus:</para>
4451 <para>You can say "inline <literal>f</literal> in Phase 2
4452 and all subsequent phases":
4454 {-# INLINE [2] f #-}
4460 <para>You can say "inline <literal>g</literal> in all
4461 phases up to, but not including, Phase 3":
4463 {-# INLINE [~3] g #-}
4469 <para>If you omit the phase indicator, you mean "inline in
4474 <para>You can use a phase number on a NOINLINE pragma too:</para>
4478 <para>You can say "do not inline <literal>f</literal>
4479 until Phase 2; in Phase 2 and subsequently behave as if
4480 there was no pragma at all":
4482 {-# NOINLINE [2] f #-}
4488 <para>You can say "do not inline <literal>g</literal> in
4489 Phase 3 or any subsequent phase; before that, behave as if
4490 there was no pragma":
4492 {-# NOINLINE [~3] g #-}
4498 <para>If you omit the phase indicator, you mean "never
4499 inline this function".</para>
4503 <para>The same phase-numbering control is available for RULES
4504 (<xref linkend="rewrite-rules"/>).</para>
4508 <sect2 id="line-pragma">
4509 <title>LINE pragma</title>
4511 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4512 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4513 <para>This pragma is similar to C's <literal>#line</literal>
4514 pragma, and is mainly for use in automatically generated Haskell
4515 code. It lets you specify the line number and filename of the
4516 original code; for example</para>
4519 {-# LINE 42 "Foo.vhs" #-}
4522 <para>if you'd generated the current file from something called
4523 <filename>Foo.vhs</filename> and this line corresponds to line
4524 42 in the original. GHC will adjust its error messages to refer
4525 to the line/file named in the <literal>LINE</literal>
4529 <sect2 id="options-pragma">
4530 <title>OPTIONS_GHC pragma</title>
4531 <indexterm><primary>OPTIONS_GHC</primary>
4533 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4536 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4537 additional options that are given to the compiler when compiling
4538 this source file. See <xref linkend="source-file-options"/> for
4541 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4542 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4546 <title>RULES pragma</title>
4548 <para>The RULES pragma lets you specify rewrite rules. It is
4549 described in <xref linkend="rewrite-rules"/>.</para>
4552 <sect2 id="specialize-pragma">
4553 <title>SPECIALIZE pragma</title>
4555 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4556 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4557 <indexterm><primary>overloading, death to</primary></indexterm>
4559 <para>(UK spelling also accepted.) For key overloaded
4560 functions, you can create extra versions (NB: more code space)
4561 specialised to particular types. Thus, if you have an
4562 overloaded function:</para>
4565 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4568 <para>If it is heavily used on lists with
4569 <literal>Widget</literal> keys, you could specialise it as
4573 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4576 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4577 be put anywhere its type signature could be put.</para>
4579 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4580 (a) a specialised version of the function and (b) a rewrite rule
4581 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4582 un-specialised function into a call to the specialised one.</para>
4584 <para>In earlier versions of GHC, it was possible to provide your own
4585 specialised function for a given type:
4588 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4591 This feature has been removed, as it is now subsumed by the
4592 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4596 <sect2 id="specialize-instance-pragma">
4597 <title>SPECIALIZE instance pragma
4601 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4602 <indexterm><primary>overloading, death to</primary></indexterm>
4603 Same idea, except for instance declarations. For example:
4606 instance (Eq a) => Eq (Foo a) where {
4607 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4611 The pragma must occur inside the <literal>where</literal> part
4612 of the instance declaration.
4615 Compatible with HBC, by the way, except perhaps in the placement
4621 <sect2 id="unpack-pragma">
4622 <title>UNPACK pragma</title>
4624 <indexterm><primary>UNPACK</primary></indexterm>
4626 <para>The <literal>UNPACK</literal> indicates to the compiler
4627 that it should unpack the contents of a constructor field into
4628 the constructor itself, removing a level of indirection. For
4632 data T = T {-# UNPACK #-} !Float
4633 {-# UNPACK #-} !Float
4636 <para>will create a constructor <literal>T</literal> containing
4637 two unboxed floats. This may not always be an optimisation: if
4638 the <function>T</function> constructor is scrutinised and the
4639 floats passed to a non-strict function for example, they will
4640 have to be reboxed (this is done automatically by the
4643 <para>Unpacking constructor fields should only be used in
4644 conjunction with <option>-O</option>, in order to expose
4645 unfoldings to the compiler so the reboxing can be removed as
4646 often as possible. For example:</para>
4650 f (T f1 f2) = f1 + f2
4653 <para>The compiler will avoid reboxing <function>f1</function>
4654 and <function>f2</function> by inlining <function>+</function>
4655 on floats, but only when <option>-O</option> is on.</para>
4657 <para>Any single-constructor data is eligible for unpacking; for
4661 data T = T {-# UNPACK #-} !(Int,Int)
4664 <para>will store the two <literal>Int</literal>s directly in the
4665 <function>T</function> constructor, by flattening the pair.
4666 Multi-level unpacking is also supported:</para>
4669 data T = T {-# UNPACK #-} !S
4670 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4673 <para>will store two unboxed <literal>Int#</literal>s
4674 directly in the <function>T</function> constructor. The
4675 unpacker can see through newtypes, too.</para>
4677 <para>If a field cannot be unpacked, you will not get a warning,
4678 so it might be an idea to check the generated code with
4679 <option>-ddump-simpl</option>.</para>
4681 <para>See also the <option>-funbox-strict-fields</option> flag,
4682 which essentially has the effect of adding
4683 <literal>{-# UNPACK #-}</literal> to every strict
4684 constructor field.</para>
4689 <!-- ======================= REWRITE RULES ======================== -->
4691 <sect1 id="rewrite-rules">
4692 <title>Rewrite rules
4694 <indexterm><primary>RULES pragma</primary></indexterm>
4695 <indexterm><primary>pragma, RULES</primary></indexterm>
4696 <indexterm><primary>rewrite rules</primary></indexterm></title>
4699 The programmer can specify rewrite rules as part of the source program
4700 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4701 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4702 and (b) the <option>-frules-off</option> flag
4703 (<xref linkend="options-f"/>) is not specified.
4711 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4718 <title>Syntax</title>
4721 From a syntactic point of view:
4727 There may be zero or more rules in a <literal>RULES</literal> pragma.
4734 Each rule has a name, enclosed in double quotes. The name itself has
4735 no significance at all. It is only used when reporting how many times the rule fired.
4741 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4742 immediately after the name of the rule. Thus:
4745 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4748 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4749 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4758 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4759 is set, so you must lay out your rules starting in the same column as the
4760 enclosing definitions.
4767 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4768 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4769 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4770 by spaces, just like in a type <literal>forall</literal>.
4776 A pattern variable may optionally have a type signature.
4777 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4778 For example, here is the <literal>foldr/build</literal> rule:
4781 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4782 foldr k z (build g) = g k z
4785 Since <function>g</function> has a polymorphic type, it must have a type signature.
4792 The left hand side of a rule must consist of a top-level variable applied
4793 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4796 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4797 "wrong2" forall f. f True = True
4800 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4807 A rule does not need to be in the same module as (any of) the
4808 variables it mentions, though of course they need to be in scope.
4814 Rules are automatically exported from a module, just as instance declarations are.
4825 <title>Semantics</title>
4828 From a semantic point of view:
4834 Rules are only applied if you use the <option>-O</option> flag.
4840 Rules are regarded as left-to-right rewrite rules.
4841 When GHC finds an expression that is a substitution instance of the LHS
4842 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4843 By "a substitution instance" we mean that the LHS can be made equal to the
4844 expression by substituting for the pattern variables.
4851 The LHS and RHS of a rule are typechecked, and must have the
4859 GHC makes absolutely no attempt to verify that the LHS and RHS
4860 of a rule have the same meaning. That is undecidable in general, and
4861 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4868 GHC makes no attempt to make sure that the rules are confluent or
4869 terminating. For example:
4872 "loop" forall x,y. f x y = f y x
4875 This rule will cause the compiler to go into an infinite loop.
4882 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4888 GHC currently uses a very simple, syntactic, matching algorithm
4889 for matching a rule LHS with an expression. It seeks a substitution
4890 which makes the LHS and expression syntactically equal modulo alpha
4891 conversion. The pattern (rule), but not the expression, is eta-expanded if
4892 necessary. (Eta-expanding the expression can lead to laziness bugs.)
4893 But not beta conversion (that's called higher-order matching).
4897 Matching is carried out on GHC's intermediate language, which includes
4898 type abstractions and applications. So a rule only matches if the
4899 types match too. See <xref linkend="rule-spec"/> below.
4905 GHC keeps trying to apply the rules as it optimises the program.
4906 For example, consider:
4915 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4916 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4917 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4918 not be substituted, and the rule would not fire.
4925 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4926 that appears on the LHS of a rule</emphasis>, because once you have substituted
4927 for something you can't match against it (given the simple minded
4928 matching). So if you write the rule
4931 "map/map" forall f,g. map f . map g = map (f.g)
4934 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4935 It will only match something written with explicit use of ".".
4936 Well, not quite. It <emphasis>will</emphasis> match the expression
4942 where <function>wibble</function> is defined:
4945 wibble f g = map f . map g
4948 because <function>wibble</function> will be inlined (it's small).
4950 Later on in compilation, GHC starts inlining even things on the
4951 LHS of rules, but still leaves the rules enabled. This inlining
4952 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4959 All rules are implicitly exported from the module, and are therefore
4960 in force in any module that imports the module that defined the rule, directly
4961 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4962 in force when compiling A.) The situation is very similar to that for instance
4974 <title>List fusion</title>
4977 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4978 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4979 intermediate list should be eliminated entirely.
4983 The following are good producers:
4995 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5001 Explicit lists (e.g. <literal>[True, False]</literal>)
5007 The cons constructor (e.g <literal>3:4:[]</literal>)
5013 <function>++</function>
5019 <function>map</function>
5025 <function>filter</function>
5031 <function>iterate</function>, <function>repeat</function>
5037 <function>zip</function>, <function>zipWith</function>
5046 The following are good consumers:
5058 <function>array</function> (on its second argument)
5064 <function>length</function>
5070 <function>++</function> (on its first argument)
5076 <function>foldr</function>
5082 <function>map</function>
5088 <function>filter</function>
5094 <function>concat</function>
5100 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5106 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5107 will fuse with one but not the other)
5113 <function>partition</function>
5119 <function>head</function>
5125 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5131 <function>sequence_</function>
5137 <function>msum</function>
5143 <function>sortBy</function>
5152 So, for example, the following should generate no intermediate lists:
5155 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5161 This list could readily be extended; if there are Prelude functions that you use
5162 a lot which are not included, please tell us.
5166 If you want to write your own good consumers or producers, look at the
5167 Prelude definitions of the above functions to see how to do so.
5172 <sect2 id="rule-spec">
5173 <title>Specialisation
5177 Rewrite rules can be used to get the same effect as a feature
5178 present in earlier versions of GHC.
5179 For example, suppose that:
5182 genericLookup :: Ord a => Table a b -> a -> b
5183 intLookup :: Table Int b -> Int -> b
5186 where <function>intLookup</function> is an implementation of
5187 <function>genericLookup</function> that works very fast for
5188 keys of type <literal>Int</literal>. You might wish
5189 to tell GHC to use <function>intLookup</function> instead of
5190 <function>genericLookup</function> whenever the latter was called with
5191 type <literal>Table Int b -> Int -> b</literal>.
5192 It used to be possible to write
5195 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5198 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5201 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5204 This slightly odd-looking rule instructs GHC to replace
5205 <function>genericLookup</function> by <function>intLookup</function>
5206 <emphasis>whenever the types match</emphasis>.
5207 What is more, this rule does not need to be in the same
5208 file as <function>genericLookup</function>, unlike the
5209 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5210 have an original definition available to specialise).
5213 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5214 <function>intLookup</function> really behaves as a specialised version
5215 of <function>genericLookup</function>!!!</para>
5217 <para>An example in which using <literal>RULES</literal> for
5218 specialisation will Win Big:
5221 toDouble :: Real a => a -> Double
5222 toDouble = fromRational . toRational
5224 {-# RULES "toDouble/Int" toDouble = i2d #-}
5225 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5228 The <function>i2d</function> function is virtually one machine
5229 instruction; the default conversion—via an intermediate
5230 <literal>Rational</literal>—is obscenely expensive by
5237 <title>Controlling what's going on</title>
5245 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5251 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5252 If you add <option>-dppr-debug</option> you get a more detailed listing.
5258 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5261 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5262 {-# INLINE build #-}
5266 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5267 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5268 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5269 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5276 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5277 see how to write rules that will do fusion and yet give an efficient
5278 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5288 <sect2 id="core-pragma">
5289 <title>CORE pragma</title>
5291 <indexterm><primary>CORE pragma</primary></indexterm>
5292 <indexterm><primary>pragma, CORE</primary></indexterm>
5293 <indexterm><primary>core, annotation</primary></indexterm>
5296 The external core format supports <quote>Note</quote> annotations;
5297 the <literal>CORE</literal> pragma gives a way to specify what these
5298 should be in your Haskell source code. Syntactically, core
5299 annotations are attached to expressions and take a Haskell string
5300 literal as an argument. The following function definition shows an
5304 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5307 Semantically, this is equivalent to:
5315 However, when external for is generated (via
5316 <option>-fext-core</option>), there will be Notes attached to the
5317 expressions <function>show</function> and <varname>x</varname>.
5318 The core function declaration for <function>f</function> is:
5322 f :: %forall a . GHCziShow.ZCTShow a ->
5323 a -> GHCziBase.ZMZN GHCziBase.Char =
5324 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5326 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5328 (tpl1::GHCziBase.Int ->
5330 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5332 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5333 (tpl3::GHCziBase.ZMZN a ->
5334 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5342 Here, we can see that the function <function>show</function> (which
5343 has been expanded out to a case expression over the Show dictionary)
5344 has a <literal>%note</literal> attached to it, as does the
5345 expression <varname>eta</varname> (which used to be called
5346 <varname>x</varname>).
5353 <sect1 id="generic-classes">
5354 <title>Generic classes</title>
5356 <para>(Note: support for generic classes is currently broken in
5360 The ideas behind this extension are described in detail in "Derivable type classes",
5361 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5362 An example will give the idea:
5370 fromBin :: [Int] -> (a, [Int])
5372 toBin {| Unit |} Unit = []
5373 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5374 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5375 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5377 fromBin {| Unit |} bs = (Unit, bs)
5378 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5379 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5380 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5381 (y,bs'') = fromBin bs'
5384 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5385 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5386 which are defined thus in the library module <literal>Generics</literal>:
5390 data a :+: b = Inl a | Inr b
5391 data a :*: b = a :*: b
5394 Now you can make a data type into an instance of Bin like this:
5396 instance (Bin a, Bin b) => Bin (a,b)
5397 instance Bin a => Bin [a]
5399 That is, just leave off the "where" clause. Of course, you can put in the
5400 where clause and over-ride whichever methods you please.
5404 <title> Using generics </title>
5405 <para>To use generics you need to</para>
5408 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5409 <option>-fgenerics</option> (to generate extra per-data-type code),
5410 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5414 <para>Import the module <literal>Generics</literal> from the
5415 <literal>lang</literal> package. This import brings into
5416 scope the data types <literal>Unit</literal>,
5417 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5418 don't need this import if you don't mention these types
5419 explicitly; for example, if you are simply giving instance
5420 declarations.)</para>
5425 <sect2> <title> Changes wrt the paper </title>
5427 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5428 can be written infix (indeed, you can now use
5429 any operator starting in a colon as an infix type constructor). Also note that
5430 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5431 Finally, note that the syntax of the type patterns in the class declaration
5432 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5433 alone would ambiguous when they appear on right hand sides (an extension we
5434 anticipate wanting).
5438 <sect2> <title>Terminology and restrictions</title>
5440 Terminology. A "generic default method" in a class declaration
5441 is one that is defined using type patterns as above.
5442 A "polymorphic default method" is a default method defined as in Haskell 98.
5443 A "generic class declaration" is a class declaration with at least one
5444 generic default method.
5452 Alas, we do not yet implement the stuff about constructor names and
5459 A generic class can have only one parameter; you can't have a generic
5460 multi-parameter class.
5466 A default method must be defined entirely using type patterns, or entirely
5467 without. So this is illegal:
5470 op :: a -> (a, Bool)
5471 op {| Unit |} Unit = (Unit, True)
5474 However it is perfectly OK for some methods of a generic class to have
5475 generic default methods and others to have polymorphic default methods.
5481 The type variable(s) in the type pattern for a generic method declaration
5482 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:
5486 op {| p :*: q |} (x :*: y) = op (x :: p)
5494 The type patterns in a generic default method must take one of the forms:
5500 where "a" and "b" are type variables. Furthermore, all the type patterns for
5501 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5502 must use the same type variables. So this is illegal:
5506 op {| a :+: b |} (Inl x) = True
5507 op {| p :+: q |} (Inr y) = False
5509 The type patterns must be identical, even in equations for different methods of the class.
5510 So this too is illegal:
5514 op1 {| a :*: b |} (x :*: y) = True
5517 op2 {| p :*: q |} (x :*: y) = False
5519 (The reason for this restriction is that we gather all the equations for a particular type consructor
5520 into a single generic instance declaration.)
5526 A generic method declaration must give a case for each of the three type constructors.
5532 The type for a generic method can be built only from:
5534 <listitem> <para> Function arrows </para> </listitem>
5535 <listitem> <para> Type variables </para> </listitem>
5536 <listitem> <para> Tuples </para> </listitem>
5537 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5539 Here are some example type signatures for generic methods:
5542 op2 :: Bool -> (a,Bool)
5543 op3 :: [Int] -> a -> a
5546 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5550 This restriction is an implementation restriction: we just havn't got around to
5551 implementing the necessary bidirectional maps over arbitrary type constructors.
5552 It would be relatively easy to add specific type constructors, such as Maybe and list,
5553 to the ones that are allowed.</para>
5558 In an instance declaration for a generic class, the idea is that the compiler
5559 will fill in the methods for you, based on the generic templates. However it can only
5564 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5569 No constructor of the instance type has unboxed fields.
5573 (Of course, these things can only arise if you are already using GHC extensions.)
5574 However, you can still give an instance declarations for types which break these rules,
5575 provided you give explicit code to override any generic default methods.
5583 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5584 what the compiler does with generic declarations.
5589 <sect2> <title> Another example </title>
5591 Just to finish with, here's another example I rather like:
5595 nCons {| Unit |} _ = 1
5596 nCons {| a :*: b |} _ = 1
5597 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5600 tag {| Unit |} _ = 1
5601 tag {| a :*: b |} _ = 1
5602 tag {| a :+: b |} (Inl x) = tag x
5603 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5612 ;;; Local Variables: ***
5614 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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