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 and classes</title>
931 GHC allows type constructors and classes to be operators, and to be written infix, very much
932 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
959 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
960 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
963 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
964 one cannot distinguish between the two in a fixity declaration; a fixity declaration
965 sets the fixity for a data constructor and the corresponding type constructor. For example:
969 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
970 and similarly for <literal>:*:</literal>.
971 <literal>Int `a` Bool</literal>.
974 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
977 The only thing that differs between operators in types and operators in expressions is that
978 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
979 are not allowed in types. Reason: the uniform thing to do would be to make them type
980 variables, but that's not very useful. A less uniform but more useful thing would be to
981 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
982 lists. So for now we just exclude them.
989 <sect3 id="type-synonyms">
990 <title>Liberalised type synonyms</title>
993 Type synonyms are like macros at the type level, and
994 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
995 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
997 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
998 in a type synonym, thus:
1000 type Discard a = forall b. Show b => a -> b -> (a, String)
1005 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1012 You can write an unboxed tuple in a type synonym:
1014 type Pr = (# Int, Int #)
1022 You can apply a type synonym to a forall type:
1024 type Foo a = a -> a -> Bool
1026 f :: Foo (forall b. b->b)
1028 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1030 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1035 You can apply a type synonym to a partially applied type synonym:
1037 type Generic i o = forall x. i x -> o x
1040 foo :: Generic Id []
1042 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1044 foo :: forall x. x -> [x]
1052 GHC currently does kind checking before expanding synonyms (though even that
1056 After expanding type synonyms, GHC does validity checking on types, looking for
1057 the following mal-formedness which isn't detected simply by kind checking:
1060 Type constructor applied to a type involving for-alls.
1063 Unboxed tuple on left of an arrow.
1066 Partially-applied type synonym.
1070 this will be rejected:
1072 type Pr = (# Int, Int #)
1077 because GHC does not allow unboxed tuples on the left of a function arrow.
1082 <sect3 id="existential-quantification">
1083 <title>Existentially quantified data constructors
1087 The idea of using existential quantification in data type declarations
1088 was suggested by Laufer (I believe, thought doubtless someone will
1089 correct me), and implemented in Hope+. It's been in Lennart
1090 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1091 proved very useful. Here's the idea. Consider the declaration:
1097 data Foo = forall a. MkFoo a (a -> Bool)
1104 The data type <literal>Foo</literal> has two constructors with types:
1110 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1117 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1118 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1119 For example, the following expression is fine:
1125 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1131 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1132 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1133 isUpper</function> packages a character with a compatible function. These
1134 two things are each of type <literal>Foo</literal> and can be put in a list.
1138 What can we do with a value of type <literal>Foo</literal>?. In particular,
1139 what happens when we pattern-match on <function>MkFoo</function>?
1145 f (MkFoo val fn) = ???
1151 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1152 are compatible, the only (useful) thing we can do with them is to
1153 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1160 f (MkFoo val fn) = fn val
1166 What this allows us to do is to package heterogenous values
1167 together with a bunch of functions that manipulate them, and then treat
1168 that collection of packages in a uniform manner. You can express
1169 quite a bit of object-oriented-like programming this way.
1172 <sect4 id="existential">
1173 <title>Why existential?
1177 What has this to do with <emphasis>existential</emphasis> quantification?
1178 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1184 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1190 But Haskell programmers can safely think of the ordinary
1191 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1192 adding a new existential quantification construct.
1198 <title>Type classes</title>
1201 An easy extension (implemented in <command>hbc</command>) is to allow
1202 arbitrary contexts before the constructor. For example:
1208 data Baz = forall a. Eq a => Baz1 a a
1209 | forall b. Show b => Baz2 b (b -> b)
1215 The two constructors have the types you'd expect:
1221 Baz1 :: forall a. Eq a => a -> a -> Baz
1222 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1228 But when pattern matching on <function>Baz1</function> the matched values can be compared
1229 for equality, and when pattern matching on <function>Baz2</function> the first matched
1230 value can be converted to a string (as well as applying the function to it).
1231 So this program is legal:
1238 f (Baz1 p q) | p == q = "Yes"
1240 f (Baz2 v fn) = show (fn v)
1246 Operationally, in a dictionary-passing implementation, the
1247 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1248 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1249 extract it on pattern matching.
1253 Notice the way that the syntax fits smoothly with that used for
1254 universal quantification earlier.
1260 <title>Restrictions</title>
1263 There are several restrictions on the ways in which existentially-quantified
1264 constructors can be use.
1273 When pattern matching, each pattern match introduces a new,
1274 distinct, type for each existential type variable. These types cannot
1275 be unified with any other type, nor can they escape from the scope of
1276 the pattern match. For example, these fragments are incorrect:
1284 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1285 is the result of <function>f1</function>. One way to see why this is wrong is to
1286 ask what type <function>f1</function> has:
1290 f1 :: Foo -> a -- Weird!
1294 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1299 f1 :: forall a. Foo -> a -- Wrong!
1303 The original program is just plain wrong. Here's another sort of error
1307 f2 (Baz1 a b) (Baz1 p q) = a==q
1311 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1312 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1313 from the two <function>Baz1</function> constructors.
1321 You can't pattern-match on an existentially quantified
1322 constructor in a <literal>let</literal> or <literal>where</literal> group of
1323 bindings. So this is illegal:
1327 f3 x = a==b where { Baz1 a b = x }
1330 Instead, use a <literal>case</literal> expression:
1333 f3 x = case x of Baz1 a b -> a==b
1336 In general, you can only pattern-match
1337 on an existentially-quantified constructor in a <literal>case</literal> expression or
1338 in the patterns of a function definition.
1340 The reason for this restriction is really an implementation one.
1341 Type-checking binding groups is already a nightmare without
1342 existentials complicating the picture. Also an existential pattern
1343 binding at the top level of a module doesn't make sense, because it's
1344 not clear how to prevent the existentially-quantified type "escaping".
1345 So for now, there's a simple-to-state restriction. We'll see how
1353 You can't use existential quantification for <literal>newtype</literal>
1354 declarations. So this is illegal:
1358 newtype T = forall a. Ord a => MkT a
1362 Reason: a value of type <literal>T</literal> must be represented as a
1363 pair of a dictionary for <literal>Ord t</literal> and a value of type
1364 <literal>t</literal>. That contradicts the idea that
1365 <literal>newtype</literal> should have no concrete representation.
1366 You can get just the same efficiency and effect by using
1367 <literal>data</literal> instead of <literal>newtype</literal>. If
1368 there is no overloading involved, then there is more of a case for
1369 allowing an existentially-quantified <literal>newtype</literal>,
1370 because the <literal>data</literal> version does carry an
1371 implementation cost, but single-field existentially quantified
1372 constructors aren't much use. So the simple restriction (no
1373 existential stuff on <literal>newtype</literal>) stands, unless there
1374 are convincing reasons to change it.
1382 You can't use <literal>deriving</literal> to define instances of a
1383 data type with existentially quantified data constructors.
1385 Reason: in most cases it would not make sense. For example:#
1388 data T = forall a. MkT [a] deriving( Eq )
1391 To derive <literal>Eq</literal> in the standard way we would need to have equality
1392 between the single component of two <function>MkT</function> constructors:
1396 (MkT a) == (MkT b) = ???
1399 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1400 It's just about possible to imagine examples in which the derived instance
1401 would make sense, but it seems altogether simpler simply to prohibit such
1402 declarations. Define your own instances!
1417 <sect2 id="multi-param-type-classes">
1418 <title>Class declarations</title>
1421 This section documents GHC's implementation of multi-parameter type
1422 classes. There's lots of background in the paper <ulink
1423 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1424 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1425 Jones, Erik Meijer).
1428 There are the following constraints on class declarations:
1433 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1437 class Collection c a where
1438 union :: c a -> c a -> c a
1449 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1450 of "acyclic" involves only the superclass relationships. For example,
1456 op :: D b => a -> b -> b
1459 class C a => D a where { ... }
1463 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1464 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1465 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1472 <emphasis>There are no restrictions on the context in a class declaration
1473 (which introduces superclasses), except that the class hierarchy must
1474 be acyclic</emphasis>. So these class declarations are OK:
1478 class Functor (m k) => FiniteMap m k where
1481 class (Monad m, Monad (t m)) => Transform t m where
1482 lift :: m a -> (t m) a
1492 <emphasis>All of the class type variables must be reachable (in the sense
1493 mentioned in <xref linkend="type-restrictions"/>)
1494 from the free variables of each method type
1495 </emphasis>. For example:
1499 class Coll s a where
1501 insert :: s -> a -> s
1505 is not OK, because the type of <literal>empty</literal> doesn't mention
1506 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1507 types, and has the same motivation.
1509 Sometimes, offending class declarations exhibit misunderstandings. For
1510 example, <literal>Coll</literal> might be rewritten
1514 class Coll s a where
1516 insert :: s a -> a -> s a
1520 which makes the connection between the type of a collection of
1521 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1522 Occasionally this really doesn't work, in which case you can split the
1530 class CollE s => Coll s a where
1531 insert :: s -> a -> s
1541 <sect3 id="class-method-types">
1542 <title>Class method types</title>
1544 Haskell 98 prohibits class method types to mention constraints on the
1545 class type variable, thus:
1548 fromList :: [a] -> s a
1549 elem :: Eq a => a -> s a -> Bool
1551 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1552 contains the constraint <literal>Eq a</literal>, constrains only the
1553 class type variable (in this case <literal>a</literal>).
1556 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1563 <sect2 id="type-restrictions">
1564 <title>Type signatures</title>
1566 <sect3><title>The context of a type signature</title>
1568 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1569 the form <emphasis>(class type-variable)</emphasis> or
1570 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1571 these type signatures are perfectly OK
1574 g :: Ord (T a ()) => ...
1578 GHC imposes the following restrictions on the constraints in a type signature.
1582 forall tv1..tvn (c1, ...,cn) => type
1585 (Here, we write the "foralls" explicitly, although the Haskell source
1586 language omits them; in Haskell 98, all the free type variables of an
1587 explicit source-language type signature are universally quantified,
1588 except for the class type variables in a class declaration. However,
1589 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1598 <emphasis>Each universally quantified type variable
1599 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1601 A type variable <literal>a</literal> is "reachable" if it it appears
1602 in the same constraint as either a type variable free in in
1603 <literal>type</literal>, or another reachable type variable.
1604 A value with a type that does not obey
1605 this reachability restriction cannot be used without introducing
1606 ambiguity; that is why the type is rejected.
1607 Here, for example, is an illegal type:
1611 forall a. Eq a => Int
1615 When a value with this type was used, the constraint <literal>Eq tv</literal>
1616 would be introduced where <literal>tv</literal> is a fresh type variable, and
1617 (in the dictionary-translation implementation) the value would be
1618 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1619 can never know which instance of <literal>Eq</literal> to use because we never
1620 get any more information about <literal>tv</literal>.
1624 that the reachability condition is weaker than saying that <literal>a</literal> is
1625 functionally dependent on a type variable free in
1626 <literal>type</literal> (see <xref
1627 linkend="functional-dependencies"/>). The reason for this is there
1628 might be a "hidden" dependency, in a superclass perhaps. So
1629 "reachable" is a conservative approximation to "functionally dependent".
1630 For example, consider:
1632 class C a b | a -> b where ...
1633 class C a b => D a b where ...
1634 f :: forall a b. D a b => a -> a
1636 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1637 but that is not immediately apparent from <literal>f</literal>'s type.
1643 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1644 universally quantified type variables <literal>tvi</literal></emphasis>.
1646 For example, this type is OK because <literal>C a b</literal> mentions the
1647 universally quantified type variable <literal>b</literal>:
1651 forall a. C a b => burble
1655 The next type is illegal because the constraint <literal>Eq b</literal> does not
1656 mention <literal>a</literal>:
1660 forall a. Eq b => burble
1664 The reason for this restriction is milder than the other one. The
1665 excluded types are never useful or necessary (because the offending
1666 context doesn't need to be witnessed at this point; it can be floated
1667 out). Furthermore, floating them out increases sharing. Lastly,
1668 excluding them is a conservative choice; it leaves a patch of
1669 territory free in case we need it later.
1680 <title>For-all hoisting</title>
1682 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1683 end of an arrow, thus:
1685 type Discard a = forall b. a -> b -> a
1687 g :: Int -> Discard Int
1690 Simply expanding the type synonym would give
1692 g :: Int -> (forall b. Int -> b -> Int)
1694 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1696 g :: forall b. Int -> Int -> b -> Int
1698 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1699 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1700 performs the transformation:</emphasis>
1702 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1704 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1706 (In fact, GHC tries to retain as much synonym information as possible for use in
1707 error messages, but that is a usability issue.) This rule applies, of course, whether
1708 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1709 valid way to write <literal>g</literal>'s type signature:
1711 g :: Int -> Int -> forall b. b -> Int
1715 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1718 type Foo a = (?x::Int) => Bool -> a
1723 g :: (?x::Int) => Bool -> Bool -> Int
1731 <sect2 id="instance-decls">
1732 <title>Instance declarations</title>
1734 <sect3 id="instance-overlap">
1735 <title>Overlapping instances</title>
1737 In general, <emphasis>GHC requires that that it be unambiguous which instance
1739 should be used to resolve a type-class constraint</emphasis>. This behaviour
1740 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1741 <indexterm><primary>-fallow-overlapping-instances
1742 </primary></indexterm>
1743 and <option>-fallow-incoherent-instances</option>
1744 <indexterm><primary>-fallow-incoherent-instances
1745 </primary></indexterm>, as this section discusses.</para>
1747 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1748 it tries to match every instance declaration against the
1750 by instantiating the head of the instance declaration. For example, consider
1753 instance context1 => C Int a where ... -- (A)
1754 instance context2 => C a Bool where ... -- (B)
1755 instance context3 => C Int [a] where ... -- (C)
1756 instance context4 => C Int [Int] where ... -- (D)
1758 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>, but (C) and (D) do not. When matching, GHC takes
1759 no account of the context of the instance declaration
1760 (<literal>context1</literal> etc).
1761 GHC's default behaviour is that <emphasis>exactly one instance must match the
1762 constraint it is trying to resolve</emphasis>.
1763 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1764 including both declarations (A) and (B), say); an error is only reported if a
1765 particular constraint matches more than one.
1769 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1770 more than one instance to match, provided there is a most specific one. For
1771 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1772 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1773 most-specific match, the program is rejected.
1776 However, GHC is conservative about committing to an overlapping instance. For example:
1781 Suppose that from the RHS of <literal>f</literal> we get the constraint
1782 <literal>C Int [b]</literal>. But
1783 GHC does not commit to instance (C), because in a particular
1784 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1785 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1786 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1787 GHC will instead pick (C), without complaining about
1788 the problem of subsequent instantiations.
1791 Because overlaps are checked and reported lazily, as described above, you need
1792 the <option>-fallow-overlapping-instances</option> in the module that <emphasis>calls</emphasis>
1793 the overloaded function, rather than in the module that <emphasis>defines</emphasis> it.</para>
1798 <title>Type synonyms in the instance head</title>
1801 <emphasis>Unlike Haskell 98, instance heads may use type
1802 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1803 As always, using a type synonym is just shorthand for
1804 writing the RHS of the type synonym definition. For example:
1808 type Point = (Int,Int)
1809 instance C Point where ...
1810 instance C [Point] where ...
1814 is legal. However, if you added
1818 instance C (Int,Int) where ...
1822 as well, then the compiler will complain about the overlapping
1823 (actually, identical) instance declarations. As always, type synonyms
1824 must be fully applied. You cannot, for example, write:
1829 instance Monad P where ...
1833 This design decision is independent of all the others, and easily
1834 reversed, but it makes sense to me.
1839 <sect3 id="undecidable-instances">
1840 <title>Undecidable instances</title>
1842 <para>An instance declaration must normally obey the following rules:
1844 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1845 an instance declaration <emphasis>must not</emphasis> be a type variable.
1846 For example, these are OK:
1849 instance C Int a where ...
1851 instance D (Int, Int) where ...
1853 instance E [[a]] where ...
1857 instance F a where ...
1859 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1860 For example, this is OK:
1862 instance Stateful (ST s) (MutVar s) where ...
1869 <para>All of the types in the <emphasis>context</emphasis> of
1870 an instance declaration <emphasis>must</emphasis> be type variables.
1873 instance C a b => Eq (a,b) where ...
1877 instance C Int b => Foo b where ...
1883 These restrictions ensure that
1884 context reduction terminates: each reduction step removes one type
1885 constructor. For example, the following would make the type checker
1886 loop if it wasn't excluded:
1888 instance C a => C a where ...
1890 There are two situations in which the rule is a bit of a pain. First,
1891 if one allows overlapping instance declarations then it's quite
1892 convenient to have a "default instance" declaration that applies if
1893 something more specific does not:
1902 Second, sometimes you might want to use the following to get the
1903 effect of a "class synonym":
1907 class (C1 a, C2 a, C3 a) => C a where { }
1909 instance (C1 a, C2 a, C3 a) => C a where { }
1913 This allows you to write shorter signatures:
1925 f :: (C1 a, C2 a, C3 a) => ...
1929 Voluminous correspondence on the Haskell mailing list has convinced me
1930 that it's worth experimenting with more liberal rules. If you use
1931 the experimental flag <option>-fallow-undecidable-instances</option>
1932 <indexterm><primary>-fallow-undecidable-instances
1933 option</primary></indexterm>, you can use arbitrary
1934 types in both an instance context and instance head. Termination is ensured by having a
1935 fixed-depth recursion stack. If you exceed the stack depth you get a
1936 sort of backtrace, and the opportunity to increase the stack depth
1937 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1940 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1941 allowing these idioms interesting idioms.
1948 <sect2 id="implicit-parameters">
1949 <title>Implicit parameters</title>
1951 <para> Implicit parameters are implemented as described in
1952 "Implicit parameters: dynamic scoping with static types",
1953 J Lewis, MB Shields, E Meijer, J Launchbury,
1954 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1958 <para>(Most of the following, stil rather incomplete, documentation is
1959 due to Jeff Lewis.)</para>
1961 <para>Implicit parameter support is enabled with the option
1962 <option>-fimplicit-params</option>.</para>
1965 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1966 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1967 context. In Haskell, all variables are statically bound. Dynamic
1968 binding of variables is a notion that goes back to Lisp, but was later
1969 discarded in more modern incarnations, such as Scheme. Dynamic binding
1970 can be very confusing in an untyped language, and unfortunately, typed
1971 languages, in particular Hindley-Milner typed languages like Haskell,
1972 only support static scoping of variables.
1975 However, by a simple extension to the type class system of Haskell, we
1976 can support dynamic binding. Basically, we express the use of a
1977 dynamically bound variable as a constraint on the type. These
1978 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1979 function uses a dynamically-bound variable <literal>?x</literal>
1980 of type <literal>t'</literal>". For
1981 example, the following expresses the type of a sort function,
1982 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1984 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1986 The dynamic binding constraints are just a new form of predicate in the type class system.
1989 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1990 where <literal>x</literal> is
1991 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1992 Use of this construct also introduces a new
1993 dynamic-binding constraint in the type of the expression.
1994 For example, the following definition
1995 shows how we can define an implicitly parameterized sort function in
1996 terms of an explicitly parameterized <literal>sortBy</literal> function:
1998 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2000 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2006 <title>Implicit-parameter type constraints</title>
2008 Dynamic binding constraints behave just like other type class
2009 constraints in that they are automatically propagated. Thus, when a
2010 function is used, its implicit parameters are inherited by the
2011 function that called it. For example, our <literal>sort</literal> function might be used
2012 to pick out the least value in a list:
2014 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2015 least xs = fst (sort xs)
2017 Without lifting a finger, the <literal>?cmp</literal> parameter is
2018 propagated to become a parameter of <literal>least</literal> as well. With explicit
2019 parameters, the default is that parameters must always be explicit
2020 propagated. With implicit parameters, the default is to always
2024 An implicit-parameter type constraint differs from other type class constraints in the
2025 following way: All uses of a particular implicit parameter must have
2026 the same type. This means that the type of <literal>(?x, ?x)</literal>
2027 is <literal>(?x::a) => (a,a)</literal>, and not
2028 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2032 <para> You can't have an implicit parameter in the context of a class or instance
2033 declaration. For example, both these declarations are illegal:
2035 class (?x::Int) => C a where ...
2036 instance (?x::a) => Foo [a] where ...
2038 Reason: exactly which implicit parameter you pick up depends on exactly where
2039 you invoke a function. But the ``invocation'' of instance declarations is done
2040 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2041 Easiest thing is to outlaw the offending types.</para>
2043 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2045 f :: (?x :: [a]) => Int -> Int
2048 g :: (Read a, Show a) => String -> String
2051 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2052 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2053 quite unambiguous, and fixes the type <literal>a</literal>.
2058 <title>Implicit-parameter bindings</title>
2061 An implicit parameter is <emphasis>bound</emphasis> using the standard
2062 <literal>let</literal> or <literal>where</literal> binding forms.
2063 For example, we define the <literal>min</literal> function by binding
2064 <literal>cmp</literal>.
2067 min = let ?cmp = (<=) in least
2071 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2072 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2073 (including in a list comprehension, or do-notation, or pattern guards),
2074 or a <literal>where</literal> clause.
2075 Note the following points:
2078 An implicit-parameter binding group must be a
2079 collection of simple bindings to implicit-style variables (no
2080 function-style bindings, and no type signatures); these bindings are
2081 neither polymorphic or recursive.
2084 You may not mix implicit-parameter bindings with ordinary bindings in a
2085 single <literal>let</literal>
2086 expression; use two nested <literal>let</literal>s instead.
2087 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2091 You may put multiple implicit-parameter bindings in a
2092 single binding group; but they are <emphasis>not</emphasis> treated
2093 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2094 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2095 parameter. The bindings are not nested, and may be re-ordered without changing
2096 the meaning of the program.
2097 For example, consider:
2099 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2101 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2102 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2104 f :: (?x::Int) => Int -> Int
2112 <sect3><title>Implicit parameters and polymorphic recursion</title>
2115 Consider these two definitions:
2118 len1 xs = let ?acc = 0 in len_acc1 xs
2121 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2126 len2 xs = let ?acc = 0 in len_acc2 xs
2128 len_acc2 :: (?acc :: Int) => [a] -> Int
2130 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2132 The only difference between the two groups is that in the second group
2133 <literal>len_acc</literal> is given a type signature.
2134 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2135 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2136 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2137 has a type signature, the recursive call is made to the
2138 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2139 as an implicit parameter. So we get the following results in GHCi:
2146 Adding a type signature dramatically changes the result! This is a rather
2147 counter-intuitive phenomenon, worth watching out for.
2151 <sect3><title>Implicit parameters and monomorphism</title>
2153 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2154 Haskell Report) to implicit parameters. For example, consider:
2162 Since the binding for <literal>y</literal> falls under the Monomorphism
2163 Restriction it is not generalised, so the type of <literal>y</literal> is
2164 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2165 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2166 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2167 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2168 <literal>y</literal> in the body of the <literal>let</literal> will see the
2169 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2170 <literal>14</literal>.
2175 <sect2 id="linear-implicit-parameters">
2176 <title>Linear implicit parameters</title>
2178 Linear implicit parameters are an idea developed by Koen Claessen,
2179 Mark Shields, and Simon PJ. They address the long-standing
2180 problem that monads seem over-kill for certain sorts of problem, notably:
2183 <listitem> <para> distributing a supply of unique names </para> </listitem>
2184 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2185 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2189 Linear implicit parameters are just like ordinary implicit parameters,
2190 except that they are "linear" -- that is, they cannot be copied, and
2191 must be explicitly "split" instead. Linear implicit parameters are
2192 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2193 (The '/' in the '%' suggests the split!)
2198 import GHC.Exts( Splittable )
2200 data NameSupply = ...
2202 splitNS :: NameSupply -> (NameSupply, NameSupply)
2203 newName :: NameSupply -> Name
2205 instance Splittable NameSupply where
2209 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2210 f env (Lam x e) = Lam x' (f env e)
2213 env' = extend env x x'
2214 ...more equations for f...
2216 Notice that the implicit parameter %ns is consumed
2218 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2219 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2223 So the translation done by the type checker makes
2224 the parameter explicit:
2226 f :: NameSupply -> Env -> Expr -> Expr
2227 f ns env (Lam x e) = Lam x' (f ns1 env e)
2229 (ns1,ns2) = splitNS ns
2231 env = extend env x x'
2233 Notice the call to 'split' introduced by the type checker.
2234 How did it know to use 'splitNS'? Because what it really did
2235 was to introduce a call to the overloaded function 'split',
2236 defined by the class <literal>Splittable</literal>:
2238 class Splittable a where
2241 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2242 split for name supplies. But we can simply write
2248 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2250 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2251 <literal>GHC.Exts</literal>.
2256 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2257 are entirely distinct implicit parameters: you
2258 can use them together and they won't intefere with each other. </para>
2261 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2263 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2264 in the context of a class or instance declaration. </para></listitem>
2268 <sect3><title>Warnings</title>
2271 The monomorphism restriction is even more important than usual.
2272 Consider the example above:
2274 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2275 f env (Lam x e) = Lam x' (f env e)
2278 env' = extend env x x'
2280 If we replaced the two occurrences of x' by (newName %ns), which is
2281 usually a harmless thing to do, we get:
2283 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2284 f env (Lam x e) = Lam (newName %ns) (f env e)
2286 env' = extend env x (newName %ns)
2288 But now the name supply is consumed in <emphasis>three</emphasis> places
2289 (the two calls to newName,and the recursive call to f), so
2290 the result is utterly different. Urk! We don't even have
2294 Well, this is an experimental change. With implicit
2295 parameters we have already lost beta reduction anyway, and
2296 (as John Launchbury puts it) we can't sensibly reason about
2297 Haskell programs without knowing their typing.
2302 <sect3><title>Recursive functions</title>
2303 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2306 foo :: %x::T => Int -> [Int]
2308 foo n = %x : foo (n-1)
2310 where T is some type in class Splittable.</para>
2312 Do you get a list of all the same T's or all different T's
2313 (assuming that split gives two distinct T's back)?
2315 If you supply the type signature, taking advantage of polymorphic
2316 recursion, you get what you'd probably expect. Here's the
2317 translated term, where the implicit param is made explicit:
2320 foo x n = let (x1,x2) = split x
2321 in x1 : foo x2 (n-1)
2323 But if you don't supply a type signature, GHC uses the Hindley
2324 Milner trick of using a single monomorphic instance of the function
2325 for the recursive calls. That is what makes Hindley Milner type inference
2326 work. So the translation becomes
2330 foom n = x : foom (n-1)
2334 Result: 'x' is not split, and you get a list of identical T's. So the
2335 semantics of the program depends on whether or not foo has a type signature.
2338 You may say that this is a good reason to dislike linear implicit parameters
2339 and you'd be right. That is why they are an experimental feature.
2345 <sect2 id="functional-dependencies">
2346 <title>Functional dependencies
2349 <para> Functional dependencies are implemented as described by Mark Jones
2350 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2351 In Proceedings of the 9th European Symposium on Programming,
2352 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2356 Functional dependencies are introduced by a vertical bar in the syntax of a
2357 class declaration; e.g.
2359 class (Monad m) => MonadState s m | m -> s where ...
2361 class Foo a b c | a b -> c where ...
2363 There should be more documentation, but there isn't (yet). Yell if you need it.
2369 <sect2 id="sec-kinding">
2370 <title>Explicitly-kinded quantification</title>
2373 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2374 to give the kind explicitly as (machine-checked) documentation,
2375 just as it is nice to give a type signature for a function. On some occasions,
2376 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2377 John Hughes had to define the data type:
2379 data Set cxt a = Set [a]
2380 | Unused (cxt a -> ())
2382 The only use for the <literal>Unused</literal> constructor was to force the correct
2383 kind for the type variable <literal>cxt</literal>.
2386 GHC now instead allows you to specify the kind of a type variable directly, wherever
2387 a type variable is explicitly bound. Namely:
2389 <listitem><para><literal>data</literal> declarations:
2391 data Set (cxt :: * -> *) a = Set [a]
2392 </screen></para></listitem>
2393 <listitem><para><literal>type</literal> declarations:
2395 type T (f :: * -> *) = f Int
2396 </screen></para></listitem>
2397 <listitem><para><literal>class</literal> declarations:
2399 class (Eq a) => C (f :: * -> *) a where ...
2400 </screen></para></listitem>
2401 <listitem><para><literal>forall</literal>'s in type signatures:
2403 f :: forall (cxt :: * -> *). Set cxt Int
2404 </screen></para></listitem>
2409 The parentheses are required. Some of the spaces are required too, to
2410 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2411 will get a parse error, because "<literal>::*->*</literal>" is a
2412 single lexeme in Haskell.
2416 As part of the same extension, you can put kind annotations in types
2419 f :: (Int :: *) -> Int
2420 g :: forall a. a -> (a :: *)
2424 atype ::= '(' ctype '::' kind ')
2426 The parentheses are required.
2431 <sect2 id="universal-quantification">
2432 <title>Arbitrary-rank polymorphism
2436 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2437 allows us to say exactly what this means. For example:
2445 g :: forall b. (b -> b)
2447 The two are treated identically.
2451 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2452 explicit universal quantification in
2454 For example, all the following types are legal:
2456 f1 :: forall a b. a -> b -> a
2457 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2459 f2 :: (forall a. a->a) -> Int -> Int
2460 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2462 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2464 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2465 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2466 The <literal>forall</literal> makes explicit the universal quantification that
2467 is implicitly added by Haskell.
2470 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2471 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2472 shows, the polymorphic type on the left of the function arrow can be overloaded.
2475 The function <literal>f3</literal> has a rank-3 type;
2476 it has rank-2 types on the left of a function arrow.
2479 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2480 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2481 that restriction has now been lifted.)
2482 In particular, a forall-type (also called a "type scheme"),
2483 including an operational type class context, is legal:
2485 <listitem> <para> On the left of a function arrow </para> </listitem>
2486 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2487 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2488 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2489 field type signatures.</para> </listitem>
2490 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2491 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2493 There is one place you cannot put a <literal>forall</literal>:
2494 you cannot instantiate a type variable with a forall-type. So you cannot
2495 make a forall-type the argument of a type constructor. So these types are illegal:
2497 x1 :: [forall a. a->a]
2498 x2 :: (forall a. a->a, Int)
2499 x3 :: Maybe (forall a. a->a)
2501 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2502 a type variable any more!
2511 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2512 the types of the constructor arguments. Here are several examples:
2518 data T a = T1 (forall b. b -> b -> b) a
2520 data MonadT m = MkMonad { return :: forall a. a -> m a,
2521 bind :: forall a b. m a -> (a -> m b) -> m b
2524 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2530 The constructors have rank-2 types:
2536 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2537 MkMonad :: forall m. (forall a. a -> m a)
2538 -> (forall a b. m a -> (a -> m b) -> m b)
2540 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2546 Notice that you don't need to use a <literal>forall</literal> if there's an
2547 explicit context. For example in the first argument of the
2548 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2549 prefixed to the argument type. The implicit <literal>forall</literal>
2550 quantifies all type variables that are not already in scope, and are
2551 mentioned in the type quantified over.
2555 As for type signatures, implicit quantification happens for non-overloaded
2556 types too. So if you write this:
2559 data T a = MkT (Either a b) (b -> b)
2562 it's just as if you had written this:
2565 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2568 That is, since the type variable <literal>b</literal> isn't in scope, it's
2569 implicitly universally quantified. (Arguably, it would be better
2570 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2571 where that is what is wanted. Feedback welcomed.)
2575 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2576 the constructor to suitable values, just as usual. For example,
2587 a3 = MkSwizzle reverse
2590 a4 = let r x = Just x
2597 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2598 mkTs f x y = [T1 f x, T1 f y]
2604 The type of the argument can, as usual, be more general than the type
2605 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2606 does not need the <literal>Ord</literal> constraint.)
2610 When you use pattern matching, the bound variables may now have
2611 polymorphic types. For example:
2617 f :: T a -> a -> (a, Char)
2618 f (T1 w k) x = (w k x, w 'c' 'd')
2620 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2621 g (MkSwizzle s) xs f = s (map f (s xs))
2623 h :: MonadT m -> [m a] -> m [a]
2624 h m [] = return m []
2625 h m (x:xs) = bind m x $ \y ->
2626 bind m (h m xs) $ \ys ->
2633 In the function <function>h</function> we use the record selectors <literal>return</literal>
2634 and <literal>bind</literal> to extract the polymorphic bind and return functions
2635 from the <literal>MonadT</literal> data structure, rather than using pattern
2641 <title>Type inference</title>
2644 In general, type inference for arbitrary-rank types is undecidable.
2645 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2646 to get a decidable algorithm by requiring some help from the programmer.
2647 We do not yet have a formal specification of "some help" but the rule is this:
2650 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2651 provides an explicit polymorphic type for x, or GHC's type inference will assume
2652 that x's type has no foralls in it</emphasis>.
2655 What does it mean to "provide" an explicit type for x? You can do that by
2656 giving a type signature for x directly, using a pattern type signature
2657 (<xref linkend="scoped-type-variables"/>), thus:
2659 \ f :: (forall a. a->a) -> (f True, f 'c')
2661 Alternatively, you can give a type signature to the enclosing
2662 context, which GHC can "push down" to find the type for the variable:
2664 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2666 Here the type signature on the expression can be pushed inwards
2667 to give a type signature for f. Similarly, and more commonly,
2668 one can give a type signature for the function itself:
2670 h :: (forall a. a->a) -> (Bool,Char)
2671 h f = (f True, f 'c')
2673 You don't need to give a type signature if the lambda bound variable
2674 is a constructor argument. Here is an example we saw earlier:
2676 f :: T a -> a -> (a, Char)
2677 f (T1 w k) x = (w k x, w 'c' 'd')
2679 Here we do not need to give a type signature to <literal>w</literal>, because
2680 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2687 <sect3 id="implicit-quant">
2688 <title>Implicit quantification</title>
2691 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2692 user-written types, if and only if there is no explicit <literal>forall</literal>,
2693 GHC finds all the type variables mentioned in the type that are not already
2694 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2698 f :: forall a. a -> a
2705 h :: forall b. a -> b -> b
2711 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2714 f :: (a -> a) -> Int
2716 f :: forall a. (a -> a) -> Int
2718 f :: (forall a. a -> a) -> Int
2721 g :: (Ord a => a -> a) -> Int
2722 -- MEANS the illegal type
2723 g :: forall a. (Ord a => a -> a) -> Int
2725 g :: (forall a. Ord a => a -> a) -> Int
2727 The latter produces an illegal type, which you might think is silly,
2728 but at least the rule is simple. If you want the latter type, you
2729 can write your for-alls explicitly. Indeed, doing so is strongly advised
2738 <sect2 id="scoped-type-variables">
2739 <title>Scoped type variables
2743 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2745 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2746 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2747 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2751 f (xs::[a]) = ys ++ ys
2756 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2757 This brings the type variable <literal>a</literal> into scope; it scopes over
2758 all the patterns and right hand sides for this equation for <function>f</function>.
2759 In particular, it is in scope at the type signature for <varname>y</varname>.
2763 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2764 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2765 implicitly universally quantified. (If there are no type variables in
2766 scope, all type variables mentioned in the signature are universally
2767 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2768 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2769 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2770 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2771 it becomes possible to do so.
2775 Scoped type variables are implemented in both GHC and Hugs. Where the
2776 implementations differ from the specification below, those differences
2781 So much for the basic idea. Here are the details.
2785 <title>What a scoped type variable means</title>
2787 A lexically-scoped type variable is simply
2788 the name for a type. The restriction it expresses is that all occurrences
2789 of the same name mean the same type. For example:
2791 f :: [Int] -> Int -> Int
2792 f (xs::[a]) (y::a) = (head xs + y) :: a
2794 The pattern type signatures on the left hand side of
2795 <literal>f</literal> express the fact that <literal>xs</literal>
2796 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2797 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2798 specifies that this expression must have the same type <literal>a</literal>.
2799 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2800 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2801 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2802 rules, which specified that a pattern-bound type variable should be universally quantified.)
2803 For example, all of these are legal:</para>
2806 t (x::a) (y::a) = x+y*2
2808 f (x::a) (y::b) = [x,y] -- a unifies with b
2810 g (x::a) = x + 1::Int -- a unifies with Int
2812 h x = let k (y::a) = [x,y] -- a is free in the
2813 in k x -- environment
2815 k (x::a) True = ... -- a unifies with Int
2816 k (x::Int) False = ...
2819 w (x::a) = x -- a unifies with [b]
2825 <title>Scope and implicit quantification</title>
2833 All the type variables mentioned in a pattern,
2834 that are not already in scope,
2835 are brought into scope by the pattern. We describe this set as
2836 the <emphasis>type variables bound by the pattern</emphasis>.
2839 f (x::a) = let g (y::(a,b)) = fst y
2843 The pattern <literal>(x::a)</literal> brings the type variable
2844 <literal>a</literal> into scope, as well as the term
2845 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2846 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2847 and brings into scope the type variable <literal>b</literal>.
2853 The type variable(s) bound by the pattern have the same scope
2854 as the term variable(s) bound by the pattern. For example:
2857 f (x::a) = <...rhs of f...>
2858 (p::b, q::b) = (1,2)
2859 in <...body of let...>
2861 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2862 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2863 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2864 just like <literal>p</literal> and <literal>q</literal> do.
2865 Indeed, the newly bound type variables also scope over any ordinary, separate
2866 type signatures in the <literal>let</literal> group.
2873 The type variables bound by the pattern may be
2874 mentioned in ordinary type signatures or pattern
2875 type signatures anywhere within their scope.
2882 In ordinary type signatures, any type variable mentioned in the
2883 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2891 Ordinary type signatures do not bring any new type variables
2892 into scope (except in the type signature itself!). So this is illegal:
2899 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2900 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2901 and that is an incorrect typing.
2908 The pattern type signature is a monotype:
2913 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2917 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2918 not to type schemes.
2922 There is no implicit universal quantification on pattern type signatures (in contrast to
2923 ordinary type signatures).
2933 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2934 scope over the methods defined in the <literal>where</literal> part. For example:
2948 (Not implemented in Hugs yet, Dec 98).
2958 <sect3 id="decl-type-sigs">
2959 <title>Declaration type signatures</title>
2960 <para>A declaration type signature that has <emphasis>explicit</emphasis>
2961 quantification (using <literal>forall</literal>) brings into scope the
2962 explicitly-quantified
2963 type variables, in the definition of the named function(s). For example:
2965 f :: forall a. [a] -> [a]
2966 f (x:xs) = xs ++ [ x :: a ]
2968 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
2969 the definition of "<literal>f</literal>".
2971 <para>This only happens if the quantification in <literal>f</literal>'s type
2972 signature is explicit. For example:
2975 g (x:xs) = xs ++ [ x :: a ]
2977 This program will be rejected, because "<literal>a</literal>" does not scope
2978 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
2979 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
2980 quantification rules.
2984 <sect3 id="pattern-type-sigs">
2985 <title>Where a pattern type signature can occur</title>
2988 A pattern type signature can occur in any pattern. For example:
2993 A pattern type signature can be on an arbitrary sub-pattern, not
2998 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3007 Pattern type signatures, including the result part, can be used
3008 in lambda abstractions:
3011 (\ (x::a, y) :: a -> x)
3018 Pattern type signatures, including the result part, can be used
3019 in <literal>case</literal> expressions:
3022 case e of { ((x::a, y) :: (a,b)) -> x }
3025 Note that the <literal>-></literal> symbol in a case alternative
3026 leads to difficulties when parsing a type signature in the pattern: in
3027 the absence of the extra parentheses in the example above, the parser
3028 would try to interpret the <literal>-></literal> as a function
3029 arrow and give a parse error later.
3037 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3038 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3039 token or a parenthesised type of some sort). To see why,
3040 consider how one would parse this:
3054 Pattern type signatures can bind existential type variables.
3059 data T = forall a. MkT [a]
3062 f (MkT [t::a]) = MkT t3
3075 Pattern type signatures
3076 can be used in pattern bindings:
3079 f x = let (y, z::a) = x in ...
3080 f1 x = let (y, z::Int) = x in ...
3081 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3082 f3 :: (b->b) = \x -> x
3085 In all such cases, the binding is not generalised over the pattern-bound
3086 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3087 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3088 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3089 In contrast, the binding
3094 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3095 in <literal>f4</literal>'s scope.
3101 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3102 type signatures. The two can be used independently or together.</para>
3106 <sect3 id="result-type-sigs">
3107 <title>Result type signatures</title>
3110 The result type of a function can be given a signature, thus:
3114 f (x::a) :: [a] = [x,x,x]
3118 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3119 result type. Sometimes this is the only way of naming the type variable
3124 f :: Int -> [a] -> [a]
3125 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3126 in \xs -> map g (reverse xs `zip` xs)
3131 The type variables bound in a result type signature scope over the right hand side
3132 of the definition. However, consider this corner-case:
3134 rev1 :: [a] -> [a] = \xs -> reverse xs
3136 foo ys = rev (ys::[a])
3138 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3139 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3140 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3141 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3142 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3145 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3146 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3150 rev1 :: [a] -> [a] = \xs -> reverse xs
3155 Result type signatures are not yet implemented in Hugs.
3162 <sect2 id="deriving-typeable">
3163 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3166 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3167 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3168 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3169 classes <literal>Eq</literal>, <literal>Ord</literal>,
3170 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3173 GHC extends this list with two more classes that may be automatically derived
3174 (provided the <option>-fglasgow-exts</option> flag is specified):
3175 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3176 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3177 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3181 <sect2 id="newtype-deriving">
3182 <title>Generalised derived instances for newtypes</title>
3185 When you define an abstract type using <literal>newtype</literal>, you may want
3186 the new type to inherit some instances from its representation. In
3187 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3188 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3189 other classes you have to write an explicit instance declaration. For
3190 example, if you define
3193 newtype Dollars = Dollars Int
3196 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3197 explicitly define an instance of <literal>Num</literal>:
3200 instance Num Dollars where
3201 Dollars a + Dollars b = Dollars (a+b)
3204 All the instance does is apply and remove the <literal>newtype</literal>
3205 constructor. It is particularly galling that, since the constructor
3206 doesn't appear at run-time, this instance declaration defines a
3207 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3208 dictionary, only slower!
3212 <sect3> <title> Generalising the deriving clause </title>
3214 GHC now permits such instances to be derived instead, so one can write
3216 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3219 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3220 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3221 derives an instance declaration of the form
3224 instance Num Int => Num Dollars
3227 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3231 We can also derive instances of constructor classes in a similar
3232 way. For example, suppose we have implemented state and failure monad
3233 transformers, such that
3236 instance Monad m => Monad (State s m)
3237 instance Monad m => Monad (Failure m)
3239 In Haskell 98, we can define a parsing monad by
3241 type Parser tok m a = State [tok] (Failure m) a
3244 which is automatically a monad thanks to the instance declarations
3245 above. With the extension, we can make the parser type abstract,
3246 without needing to write an instance of class <literal>Monad</literal>, via
3249 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3252 In this case the derived instance declaration is of the form
3254 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3257 Notice that, since <literal>Monad</literal> is a constructor class, the
3258 instance is a <emphasis>partial application</emphasis> of the new type, not the
3259 entire left hand side. We can imagine that the type declaration is
3260 ``eta-converted'' to generate the context of the instance
3265 We can even derive instances of multi-parameter classes, provided the
3266 newtype is the last class parameter. In this case, a ``partial
3267 application'' of the class appears in the <literal>deriving</literal>
3268 clause. For example, given the class
3271 class StateMonad s m | m -> s where ...
3272 instance Monad m => StateMonad s (State s m) where ...
3274 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3276 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3277 deriving (Monad, StateMonad [tok])
3280 The derived instance is obtained by completing the application of the
3281 class to the new type:
3284 instance StateMonad [tok] (State [tok] (Failure m)) =>
3285 StateMonad [tok] (Parser tok m)
3290 As a result of this extension, all derived instances in newtype
3291 declarations are treated uniformly (and implemented just by reusing
3292 the dictionary for the representation type), <emphasis>except</emphasis>
3293 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3294 the newtype and its representation.
3298 <sect3> <title> A more precise specification </title>
3300 Derived instance declarations are constructed as follows. Consider the
3301 declaration (after expansion of any type synonyms)
3304 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3310 <literal>S</literal> is a type constructor,
3313 The <literal>t1...tk</literal> are types,
3316 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3317 the <literal>ti</literal>, and
3320 The <literal>ci</literal> are partial applications of
3321 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3322 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3325 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3326 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3327 should not "look through" the type or its constructor. You can still
3328 derive these classes for a newtype, but it happens in the usual way, not
3329 via this new mechanism.
3332 Then, for each <literal>ci</literal>, the derived instance
3335 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3337 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3338 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3342 As an example which does <emphasis>not</emphasis> work, consider
3344 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3346 Here we cannot derive the instance
3348 instance Monad (State s m) => Monad (NonMonad m)
3351 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3352 and so cannot be "eta-converted" away. It is a good thing that this
3353 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3354 not, in fact, a monad --- for the same reason. Try defining
3355 <literal>>>=</literal> with the correct type: you won't be able to.
3359 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3360 important, since we can only derive instances for the last one. If the
3361 <literal>StateMonad</literal> class above were instead defined as
3364 class StateMonad m s | m -> s where ...
3367 then we would not have been able to derive an instance for the
3368 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3369 classes usually have one "main" parameter for which deriving new
3370 instances is most interesting.
3372 <para>Lastly, all of this applies only for classes other than
3373 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3374 and <literal>Data</literal>, for which the built-in derivation applies (section
3375 4.3.3. of the Haskell Report).
3376 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3377 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3378 the standard method is used or the one described here.)
3386 <!-- ==================== End of type system extensions ================= -->
3388 <!-- ====================== Generalised algebraic data types ======================= -->
3391 <title>Generalised Algebraic Data Types</title>
3393 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3394 to give the type signatures of constructors explicitly. For example:
3397 Lit :: Int -> Term Int
3398 Succ :: Term Int -> Term Int
3399 IsZero :: Term Int -> Term Bool
3400 If :: Term Bool -> Term a -> Term a -> Term a
3401 Pair :: Term a -> Term b -> Term (a,b)
3403 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3404 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3405 for these <literal>Terms</literal>:
3409 eval (Succ t) = 1 + eval t
3410 eval (IsZero i) = eval i == 0
3411 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3412 eval (Pair e1 e2) = (eval e2, eval e2)
3414 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3416 <para> The extensions to GHC are these:
3419 Data type declarations have a 'where' form, as exemplified above. The type signature of
3420 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3421 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3422 have no scope. Indeed, one can write a kind signature instead:
3424 data Term :: * -> * where ...
3426 or even a mixture of the two:
3428 data Foo a :: (* -> *) -> * where ...
3430 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3433 data Foo a (b :: * -> *) where ...
3438 There are no restrictions on the type of the data constructor, except that the result
3439 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3440 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3444 You cannot use a <literal>deriving</literal> clause on a GADT-style data type declaration,
3445 nor can you use record syntax. (It's not clear what these constructs would mean. For example,
3446 the record selectors might ill-typed.) However, you can use strictness annotations, in the obvious places
3447 in the constructor type:
3450 Lit :: !Int -> Term Int
3451 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3452 Pair :: Term a -> Term b -> Term (a,b)
3457 Pattern matching causes type refinement. For example, in the right hand side of the equation
3462 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3463 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3464 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3466 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3467 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3468 occur. However, the refinement is quite general. For example, if we had:
3470 eval :: Term a -> a -> a
3471 eval (Lit i) j = i+j
3473 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3474 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3475 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3481 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3483 data T a = forall b. MkT b (b->a)
3484 data T' a where { MKT :: b -> (b->a) -> T a }
3489 <!-- ====================== End of Generalised algebraic data types ======================= -->
3491 <!-- ====================== TEMPLATE HASKELL ======================= -->
3493 <sect1 id="template-haskell">
3494 <title>Template Haskell</title>
3496 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3497 Template Haskell at <ulink url="http://www.haskell.org/th/">
3498 http://www.haskell.org/th/</ulink>, while
3500 the main technical innovations is discussed in "<ulink
3501 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3502 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3503 The details of the Template Haskell design are still in flux. Make sure you
3504 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3505 (search for the type ExpQ).
3506 [Temporary: many changes to the original design are described in
3507 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3508 Not all of these changes are in GHC 6.2.]
3511 <para> The first example from that paper is set out below as a worked example to help get you started.
3515 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3516 Tim Sheard is going to expand it.)
3520 <title>Syntax</title>
3522 <para> Template Haskell has the following new syntactic
3523 constructions. You need to use the flag
3524 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3525 </indexterm>to switch these syntactic extensions on
3526 (<option>-fth</option> is currently implied by
3527 <option>-fglasgow-exts</option>, but you are encouraged to
3528 specify it explicitly).</para>
3532 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3533 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3534 There must be no space between the "$" and the identifier or parenthesis. This use
3535 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3536 of "." as an infix operator. If you want the infix operator, put spaces around it.
3538 <para> A splice can occur in place of
3540 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3541 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3542 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3544 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3545 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3551 A expression quotation is written in Oxford brackets, thus:
3553 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3554 the quotation has type <literal>Expr</literal>.</para></listitem>
3555 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3556 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3557 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3558 the quotation has type <literal>Type</literal>.</para></listitem>
3559 </itemizedlist></para></listitem>
3562 Reification is written thus:
3564 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3565 has type <literal>Dec</literal>. </para></listitem>
3566 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3567 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3568 <listitem><para> Still to come: fixities </para></listitem>
3570 </itemizedlist></para>
3577 <sect2> <title> Using Template Haskell </title>
3581 The data types and monadic constructor functions for Template Haskell are in the library
3582 <literal>Language.Haskell.THSyntax</literal>.
3586 You can only run a function at compile time if it is imported from another module. That is,
3587 you can't define a function in a module, and call it from within a splice in the same module.
3588 (It would make sense to do so, but it's hard to implement.)
3592 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3595 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3596 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3597 compiles and runs a program, and then looks at the result. So it's important that
3598 the program it compiles produces results whose representations are identical to
3599 those of the compiler itself.
3603 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3604 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3609 <sect2> <title> A Template Haskell Worked Example </title>
3610 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3611 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3618 -- Import our template "pr"
3619 import Printf ( pr )
3621 -- The splice operator $ takes the Haskell source code
3622 -- generated at compile time by "pr" and splices it into
3623 -- the argument of "putStrLn".
3624 main = putStrLn ( $(pr "Hello") )
3630 -- Skeletal printf from the paper.
3631 -- It needs to be in a separate module to the one where
3632 -- you intend to use it.
3634 -- Import some Template Haskell syntax
3635 import Language.Haskell.TH
3637 -- Describe a format string
3638 data Format = D | S | L String
3640 -- Parse a format string. This is left largely to you
3641 -- as we are here interested in building our first ever
3642 -- Template Haskell program and not in building printf.
3643 parse :: String -> [Format]
3646 -- Generate Haskell source code from a parsed representation
3647 -- of the format string. This code will be spliced into
3648 -- the module which calls "pr", at compile time.
3649 gen :: [Format] -> ExpQ
3650 gen [D] = [| \n -> show n |]
3651 gen [S] = [| \s -> s |]
3652 gen [L s] = stringE s
3654 -- Here we generate the Haskell code for the splice
3655 -- from an input format string.
3656 pr :: String -> ExpQ
3657 pr s = gen (parse s)
3660 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3663 $ ghc --make -fth main.hs -o main.exe
3666 <para>Run "main.exe" and here is your output:</para>
3677 <!-- ===================== Arrow notation =================== -->
3679 <sect1 id="arrow-notation">
3680 <title>Arrow notation
3683 <para>Arrows are a generalization of monads introduced by John Hughes.
3684 For more details, see
3689 “Generalising Monads to Arrows”,
3690 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3691 pp67–111, May 2000.
3697 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3698 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3704 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3705 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3711 and the arrows web page at
3712 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3713 With the <option>-farrows</option> flag, GHC supports the arrow
3714 notation described in the second of these papers.
3715 What follows is a brief introduction to the notation;
3716 it won't make much sense unless you've read Hughes's paper.
3717 This notation is translated to ordinary Haskell,
3718 using combinators from the
3719 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3723 <para>The extension adds a new kind of expression for defining arrows:
3725 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3726 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3728 where <literal>proc</literal> is a new keyword.
3729 The variables of the pattern are bound in the body of the
3730 <literal>proc</literal>-expression,
3731 which is a new sort of thing called a <firstterm>command</firstterm>.
3732 The syntax of commands is as follows:
3734 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3735 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3736 | <replaceable>cmd</replaceable><superscript>0</superscript>
3738 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3739 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3740 infix operators as for expressions, and
3742 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3743 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3744 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3745 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3746 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3747 | <replaceable>fcmd</replaceable>
3749 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3750 | ( <replaceable>cmd</replaceable> )
3751 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3753 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3754 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3755 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3756 | <replaceable>cmd</replaceable>
3758 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3759 except that the bodies are commands instead of expressions.
3763 Commands produce values, but (like monadic computations)
3764 may yield more than one value,
3765 or none, and may do other things as well.
3766 For the most part, familiarity with monadic notation is a good guide to
3768 However the values of expressions, even monadic ones,
3769 are determined by the values of the variables they contain;
3770 this is not necessarily the case for commands.
3774 A simple example of the new notation is the expression
3776 proc x -> f -< x+1
3778 We call this a <firstterm>procedure</firstterm> or
3779 <firstterm>arrow abstraction</firstterm>.
3780 As with a lambda expression, the variable <literal>x</literal>
3781 is a new variable bound within the <literal>proc</literal>-expression.
3782 It refers to the input to the arrow.
3783 In the above example, <literal>-<</literal> is not an identifier but an
3784 new reserved symbol used for building commands from an expression of arrow
3785 type and an expression to be fed as input to that arrow.
3786 (The weird look will make more sense later.)
3787 It may be read as analogue of application for arrows.
3788 The above example is equivalent to the Haskell expression
3790 arr (\ x -> x+1) >>> f
3792 That would make no sense if the expression to the left of
3793 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3794 More generally, the expression to the left of <literal>-<</literal>
3795 may not involve any <firstterm>local variable</firstterm>,
3796 i.e. a variable bound in the current arrow abstraction.
3797 For such a situation there is a variant <literal>-<<</literal>, as in
3799 proc x -> f x -<< x+1
3801 which is equivalent to
3803 arr (\ x -> (f, x+1)) >>> app
3805 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3807 Such an arrow is equivalent to a monad, so if you're using this form
3808 you may find a monadic formulation more convenient.
3812 <title>do-notation for commands</title>
3815 Another form of command is a form of <literal>do</literal>-notation.
3816 For example, you can write
3825 You can read this much like ordinary <literal>do</literal>-notation,
3826 but with commands in place of monadic expressions.
3827 The first line sends the value of <literal>x+1</literal> as an input to
3828 the arrow <literal>f</literal>, and matches its output against
3829 <literal>y</literal>.
3830 In the next line, the output is discarded.
3831 The arrow <function>returnA</function> is defined in the
3832 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3833 module as <literal>arr id</literal>.
3834 The above example is treated as an abbreviation for
3836 arr (\ x -> (x, x)) >>>
3837 first (arr (\ x -> x+1) >>> f) >>>
3838 arr (\ (y, x) -> (y, (x, y))) >>>
3839 first (arr (\ y -> 2*y) >>> g) >>>
3841 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3842 first (arr (\ (x, z) -> x*z) >>> h) >>>
3843 arr (\ (t, z) -> t+z) >>>
3846 Note that variables not used later in the composition are projected out.
3847 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3849 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3850 module, this reduces to
3852 arr (\ x -> (x+1, x)) >>>
3854 arr (\ (y, x) -> (2*y, (x, y))) >>>
3856 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3858 arr (\ (t, z) -> t+z)
3860 which is what you might have written by hand.
3861 With arrow notation, GHC keeps track of all those tuples of variables for you.
3865 Note that although the above translation suggests that
3866 <literal>let</literal>-bound variables like <literal>z</literal> must be
3867 monomorphic, the actual translation produces Core,
3868 so polymorphic variables are allowed.
3872 It's also possible to have mutually recursive bindings,
3873 using the new <literal>rec</literal> keyword, as in the following example:
3875 counter :: ArrowCircuit a => a Bool Int
3876 counter = proc reset -> do
3877 rec output <- returnA -< if reset then 0 else next
3878 next <- delay 0 -< output+1
3879 returnA -< output
3881 The translation of such forms uses the <function>loop</function> combinator,
3882 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3888 <title>Conditional commands</title>
3891 In the previous example, we used a conditional expression to construct the
3893 Sometimes we want to conditionally execute different commands, as in
3900 which is translated to
3902 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3903 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3905 Since the translation uses <function>|||</function>,
3906 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3910 There are also <literal>case</literal> commands, like
3916 y <- h -< (x1, x2)
3920 The syntax is the same as for <literal>case</literal> expressions,
3921 except that the bodies of the alternatives are commands rather than expressions.
3922 The translation is similar to that of <literal>if</literal> commands.
3928 <title>Defining your own control structures</title>
3931 As we're seen, arrow notation provides constructs,
3932 modelled on those for expressions,
3933 for sequencing, value recursion and conditionals.
3934 But suitable combinators,
3935 which you can define in ordinary Haskell,
3936 may also be used to build new commands out of existing ones.
3937 The basic idea is that a command defines an arrow from environments to values.
3938 These environments assign values to the free local variables of the command.
3939 Thus combinators that produce arrows from arrows
3940 may also be used to build commands from commands.
3941 For example, the <literal>ArrowChoice</literal> class includes a combinator
3943 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3945 so we can use it to build commands:
3947 expr' = proc x -> do
3950 symbol Plus -< ()
3951 y <- term -< ()
3954 symbol Minus -< ()
3955 y <- term -< ()
3958 (The <literal>do</literal> on the first line is needed to prevent the first
3959 <literal><+> ...</literal> from being interpreted as part of the
3960 expression on the previous line.)
3961 This is equivalent to
3963 expr' = (proc x -> returnA -< x)
3964 <+> (proc x -> do
3965 symbol Plus -< ()
3966 y <- term -< ()
3968 <+> (proc x -> do
3969 symbol Minus -< ()
3970 y <- term -< ()
3973 It is essential that this operator be polymorphic in <literal>e</literal>
3974 (representing the environment input to the command
3975 and thence to its subcommands)
3976 and satisfy the corresponding naturality property
3978 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3980 at least for strict <literal>k</literal>.
3981 (This should be automatic if you're not using <function>seq</function>.)
3982 This ensures that environments seen by the subcommands are environments
3983 of the whole command,
3984 and also allows the translation to safely trim these environments.
3985 The operator must also not use any variable defined within the current
3990 We could define our own operator
3992 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3993 untilA body cond = proc x ->
3994 if cond x then returnA -< ()
3997 untilA body cond -< x
3999 and use it in the same way.
4000 Of course this infix syntax only makes sense for binary operators;
4001 there is also a more general syntax involving special brackets:
4005 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4012 <title>Primitive constructs</title>
4015 Some operators will need to pass additional inputs to their subcommands.
4016 For example, in an arrow type supporting exceptions,
4017 the operator that attaches an exception handler will wish to pass the
4018 exception that occurred to the handler.
4019 Such an operator might have a type
4021 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4023 where <literal>Ex</literal> is the type of exceptions handled.
4024 You could then use this with arrow notation by writing a command
4026 body `handleA` \ ex -> handler
4028 so that if an exception is raised in the command <literal>body</literal>,
4029 the variable <literal>ex</literal> is bound to the value of the exception
4030 and the command <literal>handler</literal>,
4031 which typically refers to <literal>ex</literal>, is entered.
4032 Though the syntax here looks like a functional lambda,
4033 we are talking about commands, and something different is going on.
4034 The input to the arrow represented by a command consists of values for
4035 the free local variables in the command, plus a stack of anonymous values.
4036 In all the prior examples, this stack was empty.
4037 In the second argument to <function>handleA</function>,
4038 this stack consists of one value, the value of the exception.
4039 The command form of lambda merely gives this value a name.
4044 the values on the stack are paired to the right of the environment.
4045 So operators like <function>handleA</function> that pass
4046 extra inputs to their subcommands can be designed for use with the notation
4047 by pairing the values with the environment in this way.
4048 More precisely, the type of each argument of the operator (and its result)
4049 should have the form
4051 a (...(e,t1), ... tn) t
4053 where <replaceable>e</replaceable> is a polymorphic variable
4054 (representing the environment)
4055 and <replaceable>ti</replaceable> are the types of the values on the stack,
4056 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4057 The polymorphic variable <replaceable>e</replaceable> must not occur in
4058 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4059 <replaceable>t</replaceable>.
4060 However the arrows involved need not be the same.
4061 Here are some more examples of suitable operators:
4063 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4064 runReader :: ... => a e c -> a' (e,State) c
4065 runState :: ... => a e c -> a' (e,State) (c,State)
4067 We can supply the extra input required by commands built with the last two
4068 by applying them to ordinary expressions, as in
4072 (|runReader (do { ... })|) s
4074 which adds <literal>s</literal> to the stack of inputs to the command
4075 built using <function>runReader</function>.
4079 The command versions of lambda abstraction and application are analogous to
4080 the expression versions.
4081 In particular, the beta and eta rules describe equivalences of commands.
4082 These three features (operators, lambda abstraction and application)
4083 are the core of the notation; everything else can be built using them,
4084 though the results would be somewhat clumsy.
4085 For example, we could simulate <literal>do</literal>-notation by defining
4087 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4088 u `bind` f = returnA &&& u >>> f
4090 bind_ :: Arrow a => a e b -> a e c -> a e c
4091 u `bind_` f = u `bind` (arr fst >>> f)
4093 We could simulate <literal>if</literal> by defining
4095 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4096 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4103 <title>Differences with the paper</title>
4108 <para>Instead of a single form of arrow application (arrow tail) with two
4109 translations, the implementation provides two forms
4110 <quote><literal>-<</literal></quote> (first-order)
4111 and <quote><literal>-<<</literal></quote> (higher-order).
4116 <para>User-defined operators are flagged with banana brackets instead of
4117 a new <literal>form</literal> keyword.
4126 <title>Portability</title>
4129 Although only GHC implements arrow notation directly,
4130 there is also a preprocessor
4132 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4133 that translates arrow notation into Haskell 98
4134 for use with other Haskell systems.
4135 You would still want to check arrow programs with GHC;
4136 tracing type errors in the preprocessor output is not easy.
4137 Modules intended for both GHC and the preprocessor must observe some
4138 additional restrictions:
4143 The module must import
4144 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4150 The preprocessor cannot cope with other Haskell extensions.
4151 These would have to go in separate modules.
4157 Because the preprocessor targets Haskell (rather than Core),
4158 <literal>let</literal>-bound variables are monomorphic.
4169 <!-- ==================== ASSERTIONS ================= -->
4171 <sect1 id="sec-assertions">
4173 <indexterm><primary>Assertions</primary></indexterm>
4177 If you want to make use of assertions in your standard Haskell code, you
4178 could define a function like the following:
4184 assert :: Bool -> a -> a
4185 assert False x = error "assertion failed!"
4192 which works, but gives you back a less than useful error message --
4193 an assertion failed, but which and where?
4197 One way out is to define an extended <function>assert</function> function which also
4198 takes a descriptive string to include in the error message and
4199 perhaps combine this with the use of a pre-processor which inserts
4200 the source location where <function>assert</function> was used.
4204 Ghc offers a helping hand here, doing all of this for you. For every
4205 use of <function>assert</function> in the user's source:
4211 kelvinToC :: Double -> Double
4212 kelvinToC k = assert (k >= 0.0) (k+273.15)
4218 Ghc will rewrite this to also include the source location where the
4225 assert pred val ==> assertError "Main.hs|15" pred val
4231 The rewrite is only performed by the compiler when it spots
4232 applications of <function>Control.Exception.assert</function>, so you
4233 can still define and use your own versions of
4234 <function>assert</function>, should you so wish. If not, import
4235 <literal>Control.Exception</literal> to make use
4236 <function>assert</function> in your code.
4240 To have the compiler ignore uses of assert, use the compiler option
4241 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4242 option</primary></indexterm> That is, expressions of the form
4243 <literal>assert pred e</literal> will be rewritten to
4244 <literal>e</literal>.
4248 Assertion failures can be caught, see the documentation for the
4249 <literal>Control.Exception</literal> library for the details.
4255 <!-- =============================== PRAGMAS =========================== -->
4257 <sect1 id="pragmas">
4258 <title>Pragmas</title>
4260 <indexterm><primary>pragma</primary></indexterm>
4262 <para>GHC supports several pragmas, or instructions to the
4263 compiler placed in the source code. Pragmas don't normally affect
4264 the meaning of the program, but they might affect the efficiency
4265 of the generated code.</para>
4267 <para>Pragmas all take the form
4269 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4271 where <replaceable>word</replaceable> indicates the type of
4272 pragma, and is followed optionally by information specific to that
4273 type of pragma. Case is ignored in
4274 <replaceable>word</replaceable>. The various values for
4275 <replaceable>word</replaceable> that GHC understands are described
4276 in the following sections; any pragma encountered with an
4277 unrecognised <replaceable>word</replaceable> is (silently)
4280 <sect2 id="deprecated-pragma">
4281 <title>DEPRECATED pragma</title>
4282 <indexterm><primary>DEPRECATED</primary>
4285 <para>The DEPRECATED pragma lets you specify that a particular
4286 function, class, or type, is deprecated. There are two
4291 <para>You can deprecate an entire module thus:</para>
4293 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4296 <para>When you compile any module that import
4297 <literal>Wibble</literal>, GHC will print the specified
4302 <para>You can deprecate a function, class, or type, with the
4303 following top-level declaration:</para>
4305 {-# DEPRECATED f, C, T "Don't use these" #-}
4307 <para>When you compile any module that imports and uses any
4308 of the specified entities, GHC will print the specified
4312 Any use of the deprecated item, or of anything from a deprecated
4313 module, will be flagged with an appropriate message. However,
4314 deprecations are not reported for
4315 (a) uses of a deprecated function within its defining module, and
4316 (b) uses of a deprecated function in an export list.
4317 The latter reduces spurious complaints within a library
4318 in which one module gathers together and re-exports
4319 the exports of several others.
4321 <para>You can suppress the warnings with the flag
4322 <option>-fno-warn-deprecations</option>.</para>
4325 <sect2 id="include-pragma">
4326 <title>INCLUDE pragma</title>
4328 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4329 of C header files that should be <literal>#include</literal>'d into
4330 the C source code generated by the compiler for the current module (if
4331 compiling via C). For example:</para>
4334 {-# INCLUDE "foo.h" #-}
4335 {-# INCLUDE <stdio.h> #-}</programlisting>
4337 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4338 your source file with any <literal>OPTIONS_GHC</literal>
4341 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4342 to the <option>-#include</option> option (<xref
4343 linkend="options-C-compiler" />), because the
4344 <literal>INCLUDE</literal> pragma is understood by other
4345 compilers. Yet another alternative is to add the include file to each
4346 <literal>foreign import</literal> declaration in your code, but we
4347 don't recommend using this approach with GHC.</para>
4350 <sect2 id="inline-noinline-pragma">
4351 <title>INLINE and NOINLINE pragmas</title>
4353 <para>These pragmas control the inlining of function
4356 <sect3 id="inline-pragma">
4357 <title>INLINE pragma</title>
4358 <indexterm><primary>INLINE</primary></indexterm>
4360 <para>GHC (with <option>-O</option>, as always) tries to
4361 inline (or “unfold”) functions/values that are
4362 “small enough,” thus avoiding the call overhead
4363 and possibly exposing other more-wonderful optimisations.
4364 Normally, if GHC decides a function is “too
4365 expensive” to inline, it will not do so, nor will it
4366 export that unfolding for other modules to use.</para>
4368 <para>The sledgehammer you can bring to bear is the
4369 <literal>INLINE</literal><indexterm><primary>INLINE
4370 pragma</primary></indexterm> pragma, used thusly:</para>
4373 key_function :: Int -> String -> (Bool, Double)
4375 #ifdef __GLASGOW_HASKELL__
4376 {-# INLINE key_function #-}
4380 <para>(You don't need to do the C pre-processor carry-on
4381 unless you're going to stick the code through HBC—it
4382 doesn't like <literal>INLINE</literal> pragmas.)</para>
4384 <para>The major effect of an <literal>INLINE</literal> pragma
4385 is to declare a function's “cost” to be very low.
4386 The normal unfolding machinery will then be very keen to
4389 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4390 function can be put anywhere its type signature could be
4393 <para><literal>INLINE</literal> pragmas are a particularly
4395 <literal>then</literal>/<literal>return</literal> (or
4396 <literal>bind</literal>/<literal>unit</literal>) functions in
4397 a monad. For example, in GHC's own
4398 <literal>UniqueSupply</literal> monad code, we have:</para>
4401 #ifdef __GLASGOW_HASKELL__
4402 {-# INLINE thenUs #-}
4403 {-# INLINE returnUs #-}
4407 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4408 linkend="noinline-pragma"/>).</para>
4411 <sect3 id="noinline-pragma">
4412 <title>NOINLINE pragma</title>
4414 <indexterm><primary>NOINLINE</primary></indexterm>
4415 <indexterm><primary>NOTINLINE</primary></indexterm>
4417 <para>The <literal>NOINLINE</literal> pragma does exactly what
4418 you'd expect: it stops the named function from being inlined
4419 by the compiler. You shouldn't ever need to do this, unless
4420 you're very cautious about code size.</para>
4422 <para><literal>NOTINLINE</literal> is a synonym for
4423 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4424 specified by Haskell 98 as the standard way to disable
4425 inlining, so it should be used if you want your code to be
4429 <sect3 id="phase-control">
4430 <title>Phase control</title>
4432 <para> Sometimes you want to control exactly when in GHC's
4433 pipeline the INLINE pragma is switched on. Inlining happens
4434 only during runs of the <emphasis>simplifier</emphasis>. Each
4435 run of the simplifier has a different <emphasis>phase
4436 number</emphasis>; the phase number decreases towards zero.
4437 If you use <option>-dverbose-core2core</option> you'll see the
4438 sequence of phase numbers for successive runs of the
4439 simplifier. In an INLINE pragma you can optionally specify a
4440 phase number, thus:</para>
4444 <para>You can say "inline <literal>f</literal> in Phase 2
4445 and all subsequent phases":
4447 {-# INLINE [2] f #-}
4453 <para>You can say "inline <literal>g</literal> in all
4454 phases up to, but not including, Phase 3":
4456 {-# INLINE [~3] g #-}
4462 <para>If you omit the phase indicator, you mean "inline in
4467 <para>You can use a phase number on a NOINLINE pragma too:</para>
4471 <para>You can say "do not inline <literal>f</literal>
4472 until Phase 2; in Phase 2 and subsequently behave as if
4473 there was no pragma at all":
4475 {-# NOINLINE [2] f #-}
4481 <para>You can say "do not inline <literal>g</literal> in
4482 Phase 3 or any subsequent phase; before that, behave as if
4483 there was no pragma":
4485 {-# NOINLINE [~3] g #-}
4491 <para>If you omit the phase indicator, you mean "never
4492 inline this function".</para>
4496 <para>The same phase-numbering control is available for RULES
4497 (<xref linkend="rewrite-rules"/>).</para>
4501 <sect2 id="line-pragma">
4502 <title>LINE pragma</title>
4504 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4505 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4506 <para>This pragma is similar to C's <literal>#line</literal>
4507 pragma, and is mainly for use in automatically generated Haskell
4508 code. It lets you specify the line number and filename of the
4509 original code; for example</para>
4512 {-# LINE 42 "Foo.vhs" #-}
4515 <para>if you'd generated the current file from something called
4516 <filename>Foo.vhs</filename> and this line corresponds to line
4517 42 in the original. GHC will adjust its error messages to refer
4518 to the line/file named in the <literal>LINE</literal>
4522 <sect2 id="options-pragma">
4523 <title>OPTIONS_GHC pragma</title>
4524 <indexterm><primary>OPTIONS_GHC</primary>
4526 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4529 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4530 additional options that are given to the compiler when compiling
4531 this source file. See <xref linkend="source-file-options"/> for
4534 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4535 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4539 <title>RULES pragma</title>
4541 <para>The RULES pragma lets you specify rewrite rules. It is
4542 described in <xref linkend="rewrite-rules"/>.</para>
4545 <sect2 id="specialize-pragma">
4546 <title>SPECIALIZE pragma</title>
4548 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4549 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4550 <indexterm><primary>overloading, death to</primary></indexterm>
4552 <para>(UK spelling also accepted.) For key overloaded
4553 functions, you can create extra versions (NB: more code space)
4554 specialised to particular types. Thus, if you have an
4555 overloaded function:</para>
4558 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4561 <para>If it is heavily used on lists with
4562 <literal>Widget</literal> keys, you could specialise it as
4566 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4569 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4570 be put anywhere its type signature could be put.</para>
4572 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4573 (a) a specialised version of the function and (b) a rewrite rule
4574 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4575 un-specialised function into a call to the specialised one.</para>
4577 <para>In earlier versions of GHC, it was possible to provide your own
4578 specialised function for a given type:
4581 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4584 This feature has been removed, as it is now subsumed by the
4585 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4589 <sect2 id="specialize-instance-pragma">
4590 <title>SPECIALIZE instance pragma
4594 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4595 <indexterm><primary>overloading, death to</primary></indexterm>
4596 Same idea, except for instance declarations. For example:
4599 instance (Eq a) => Eq (Foo a) where {
4600 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4604 The pragma must occur inside the <literal>where</literal> part
4605 of the instance declaration.
4608 Compatible with HBC, by the way, except perhaps in the placement
4614 <sect2 id="unpack-pragma">
4615 <title>UNPACK pragma</title>
4617 <indexterm><primary>UNPACK</primary></indexterm>
4619 <para>The <literal>UNPACK</literal> indicates to the compiler
4620 that it should unpack the contents of a constructor field into
4621 the constructor itself, removing a level of indirection. For
4625 data T = T {-# UNPACK #-} !Float
4626 {-# UNPACK #-} !Float
4629 <para>will create a constructor <literal>T</literal> containing
4630 two unboxed floats. This may not always be an optimisation: if
4631 the <function>T</function> constructor is scrutinised and the
4632 floats passed to a non-strict function for example, they will
4633 have to be reboxed (this is done automatically by the
4636 <para>Unpacking constructor fields should only be used in
4637 conjunction with <option>-O</option>, in order to expose
4638 unfoldings to the compiler so the reboxing can be removed as
4639 often as possible. For example:</para>
4643 f (T f1 f2) = f1 + f2
4646 <para>The compiler will avoid reboxing <function>f1</function>
4647 and <function>f2</function> by inlining <function>+</function>
4648 on floats, but only when <option>-O</option> is on.</para>
4650 <para>Any single-constructor data is eligible for unpacking; for
4654 data T = T {-# UNPACK #-} !(Int,Int)
4657 <para>will store the two <literal>Int</literal>s directly in the
4658 <function>T</function> constructor, by flattening the pair.
4659 Multi-level unpacking is also supported:</para>
4662 data T = T {-# UNPACK #-} !S
4663 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4666 <para>will store two unboxed <literal>Int#</literal>s
4667 directly in the <function>T</function> constructor. The
4668 unpacker can see through newtypes, too.</para>
4670 <para>If a field cannot be unpacked, you will not get a warning,
4671 so it might be an idea to check the generated code with
4672 <option>-ddump-simpl</option>.</para>
4674 <para>See also the <option>-funbox-strict-fields</option> flag,
4675 which essentially has the effect of adding
4676 <literal>{-# UNPACK #-}</literal> to every strict
4677 constructor field.</para>
4682 <!-- ======================= REWRITE RULES ======================== -->
4684 <sect1 id="rewrite-rules">
4685 <title>Rewrite rules
4687 <indexterm><primary>RULES pragma</primary></indexterm>
4688 <indexterm><primary>pragma, RULES</primary></indexterm>
4689 <indexterm><primary>rewrite rules</primary></indexterm></title>
4692 The programmer can specify rewrite rules as part of the source program
4693 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4694 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4695 and (b) the <option>-frules-off</option> flag
4696 (<xref linkend="options-f"/>) is not specified.
4704 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4711 <title>Syntax</title>
4714 From a syntactic point of view:
4720 There may be zero or more rules in a <literal>RULES</literal> pragma.
4727 Each rule has a name, enclosed in double quotes. The name itself has
4728 no significance at all. It is only used when reporting how many times the rule fired.
4734 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4735 immediately after the name of the rule. Thus:
4738 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4741 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4742 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4751 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4752 is set, so you must lay out your rules starting in the same column as the
4753 enclosing definitions.
4760 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4761 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4762 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4763 by spaces, just like in a type <literal>forall</literal>.
4769 A pattern variable may optionally have a type signature.
4770 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4771 For example, here is the <literal>foldr/build</literal> rule:
4774 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4775 foldr k z (build g) = g k z
4778 Since <function>g</function> has a polymorphic type, it must have a type signature.
4785 The left hand side of a rule must consist of a top-level variable applied
4786 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4789 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4790 "wrong2" forall f. f True = True
4793 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4800 A rule does not need to be in the same module as (any of) the
4801 variables it mentions, though of course they need to be in scope.
4807 Rules are automatically exported from a module, just as instance declarations are.
4818 <title>Semantics</title>
4821 From a semantic point of view:
4827 Rules are only applied if you use the <option>-O</option> flag.
4833 Rules are regarded as left-to-right rewrite rules.
4834 When GHC finds an expression that is a substitution instance of the LHS
4835 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4836 By "a substitution instance" we mean that the LHS can be made equal to the
4837 expression by substituting for the pattern variables.
4844 The LHS and RHS of a rule are typechecked, and must have the
4852 GHC makes absolutely no attempt to verify that the LHS and RHS
4853 of a rule have the same meaning. That is undecidable in general, and
4854 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4861 GHC makes no attempt to make sure that the rules are confluent or
4862 terminating. For example:
4865 "loop" forall x,y. f x y = f y x
4868 This rule will cause the compiler to go into an infinite loop.
4875 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4881 GHC currently uses a very simple, syntactic, matching algorithm
4882 for matching a rule LHS with an expression. It seeks a substitution
4883 which makes the LHS and expression syntactically equal modulo alpha
4884 conversion. The pattern (rule), but not the expression, is eta-expanded if
4885 necessary. (Eta-expanding the expression can lead to laziness bugs.)
4886 But not beta conversion (that's called higher-order matching).
4890 Matching is carried out on GHC's intermediate language, which includes
4891 type abstractions and applications. So a rule only matches if the
4892 types match too. See <xref linkend="rule-spec"/> below.
4898 GHC keeps trying to apply the rules as it optimises the program.
4899 For example, consider:
4908 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4909 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4910 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4911 not be substituted, and the rule would not fire.
4918 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4919 that appears on the LHS of a rule</emphasis>, because once you have substituted
4920 for something you can't match against it (given the simple minded
4921 matching). So if you write the rule
4924 "map/map" forall f,g. map f . map g = map (f.g)
4927 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4928 It will only match something written with explicit use of ".".
4929 Well, not quite. It <emphasis>will</emphasis> match the expression
4935 where <function>wibble</function> is defined:
4938 wibble f g = map f . map g
4941 because <function>wibble</function> will be inlined (it's small).
4943 Later on in compilation, GHC starts inlining even things on the
4944 LHS of rules, but still leaves the rules enabled. This inlining
4945 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4952 All rules are implicitly exported from the module, and are therefore
4953 in force in any module that imports the module that defined the rule, directly
4954 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4955 in force when compiling A.) The situation is very similar to that for instance
4967 <title>List fusion</title>
4970 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4971 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4972 intermediate list should be eliminated entirely.
4976 The following are good producers:
4988 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4994 Explicit lists (e.g. <literal>[True, False]</literal>)
5000 The cons constructor (e.g <literal>3:4:[]</literal>)
5006 <function>++</function>
5012 <function>map</function>
5018 <function>filter</function>
5024 <function>iterate</function>, <function>repeat</function>
5030 <function>zip</function>, <function>zipWith</function>
5039 The following are good consumers:
5051 <function>array</function> (on its second argument)
5057 <function>length</function>
5063 <function>++</function> (on its first argument)
5069 <function>foldr</function>
5075 <function>map</function>
5081 <function>filter</function>
5087 <function>concat</function>
5093 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5099 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5100 will fuse with one but not the other)
5106 <function>partition</function>
5112 <function>head</function>
5118 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5124 <function>sequence_</function>
5130 <function>msum</function>
5136 <function>sortBy</function>
5145 So, for example, the following should generate no intermediate lists:
5148 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5154 This list could readily be extended; if there are Prelude functions that you use
5155 a lot which are not included, please tell us.
5159 If you want to write your own good consumers or producers, look at the
5160 Prelude definitions of the above functions to see how to do so.
5165 <sect2 id="rule-spec">
5166 <title>Specialisation
5170 Rewrite rules can be used to get the same effect as a feature
5171 present in earlier versions of GHC.
5172 For example, suppose that:
5175 genericLookup :: Ord a => Table a b -> a -> b
5176 intLookup :: Table Int b -> Int -> b
5179 where <function>intLookup</function> is an implementation of
5180 <function>genericLookup</function> that works very fast for
5181 keys of type <literal>Int</literal>. You might wish
5182 to tell GHC to use <function>intLookup</function> instead of
5183 <function>genericLookup</function> whenever the latter was called with
5184 type <literal>Table Int b -> Int -> b</literal>.
5185 It used to be possible to write
5188 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5191 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5194 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5197 This slightly odd-looking rule instructs GHC to replace
5198 <function>genericLookup</function> by <function>intLookup</function>
5199 <emphasis>whenever the types match</emphasis>.
5200 What is more, this rule does not need to be in the same
5201 file as <function>genericLookup</function>, unlike the
5202 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5203 have an original definition available to specialise).
5206 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5207 <function>intLookup</function> really behaves as a specialised version
5208 of <function>genericLookup</function>!!!</para>
5210 <para>An example in which using <literal>RULES</literal> for
5211 specialisation will Win Big:
5214 toDouble :: Real a => a -> Double
5215 toDouble = fromRational . toRational
5217 {-# RULES "toDouble/Int" toDouble = i2d #-}
5218 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5221 The <function>i2d</function> function is virtually one machine
5222 instruction; the default conversion—via an intermediate
5223 <literal>Rational</literal>—is obscenely expensive by
5230 <title>Controlling what's going on</title>
5238 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5244 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5245 If you add <option>-dppr-debug</option> you get a more detailed listing.
5251 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5254 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5255 {-# INLINE build #-}
5259 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5260 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5261 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5262 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5269 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5270 see how to write rules that will do fusion and yet give an efficient
5271 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5281 <sect2 id="core-pragma">
5282 <title>CORE pragma</title>
5284 <indexterm><primary>CORE pragma</primary></indexterm>
5285 <indexterm><primary>pragma, CORE</primary></indexterm>
5286 <indexterm><primary>core, annotation</primary></indexterm>
5289 The external core format supports <quote>Note</quote> annotations;
5290 the <literal>CORE</literal> pragma gives a way to specify what these
5291 should be in your Haskell source code. Syntactically, core
5292 annotations are attached to expressions and take a Haskell string
5293 literal as an argument. The following function definition shows an
5297 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5300 Semantically, this is equivalent to:
5308 However, when external for is generated (via
5309 <option>-fext-core</option>), there will be Notes attached to the
5310 expressions <function>show</function> and <varname>x</varname>.
5311 The core function declaration for <function>f</function> is:
5315 f :: %forall a . GHCziShow.ZCTShow a ->
5316 a -> GHCziBase.ZMZN GHCziBase.Char =
5317 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5319 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5321 (tpl1::GHCziBase.Int ->
5323 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5325 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5326 (tpl3::GHCziBase.ZMZN a ->
5327 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5335 Here, we can see that the function <function>show</function> (which
5336 has been expanded out to a case expression over the Show dictionary)
5337 has a <literal>%note</literal> attached to it, as does the
5338 expression <varname>eta</varname> (which used to be called
5339 <varname>x</varname>).
5346 <sect1 id="generic-classes">
5347 <title>Generic classes</title>
5349 <para>(Note: support for generic classes is currently broken in
5353 The ideas behind this extension are described in detail in "Derivable type classes",
5354 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5355 An example will give the idea:
5363 fromBin :: [Int] -> (a, [Int])
5365 toBin {| Unit |} Unit = []
5366 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5367 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5368 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5370 fromBin {| Unit |} bs = (Unit, bs)
5371 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5372 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5373 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5374 (y,bs'') = fromBin bs'
5377 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5378 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5379 which are defined thus in the library module <literal>Generics</literal>:
5383 data a :+: b = Inl a | Inr b
5384 data a :*: b = a :*: b
5387 Now you can make a data type into an instance of Bin like this:
5389 instance (Bin a, Bin b) => Bin (a,b)
5390 instance Bin a => Bin [a]
5392 That is, just leave off the "where" clause. Of course, you can put in the
5393 where clause and over-ride whichever methods you please.
5397 <title> Using generics </title>
5398 <para>To use generics you need to</para>
5401 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5402 <option>-fgenerics</option> (to generate extra per-data-type code),
5403 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5407 <para>Import the module <literal>Generics</literal> from the
5408 <literal>lang</literal> package. This import brings into
5409 scope the data types <literal>Unit</literal>,
5410 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5411 don't need this import if you don't mention these types
5412 explicitly; for example, if you are simply giving instance
5413 declarations.)</para>
5418 <sect2> <title> Changes wrt the paper </title>
5420 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5421 can be written infix (indeed, you can now use
5422 any operator starting in a colon as an infix type constructor). Also note that
5423 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5424 Finally, note that the syntax of the type patterns in the class declaration
5425 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5426 alone would ambiguous when they appear on right hand sides (an extension we
5427 anticipate wanting).
5431 <sect2> <title>Terminology and restrictions</title>
5433 Terminology. A "generic default method" in a class declaration
5434 is one that is defined using type patterns as above.
5435 A "polymorphic default method" is a default method defined as in Haskell 98.
5436 A "generic class declaration" is a class declaration with at least one
5437 generic default method.
5445 Alas, we do not yet implement the stuff about constructor names and
5452 A generic class can have only one parameter; you can't have a generic
5453 multi-parameter class.
5459 A default method must be defined entirely using type patterns, or entirely
5460 without. So this is illegal:
5463 op :: a -> (a, Bool)
5464 op {| Unit |} Unit = (Unit, True)
5467 However it is perfectly OK for some methods of a generic class to have
5468 generic default methods and others to have polymorphic default methods.
5474 The type variable(s) in the type pattern for a generic method declaration
5475 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:
5479 op {| p :*: q |} (x :*: y) = op (x :: p)
5487 The type patterns in a generic default method must take one of the forms:
5493 where "a" and "b" are type variables. Furthermore, all the type patterns for
5494 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5495 must use the same type variables. So this is illegal:
5499 op {| a :+: b |} (Inl x) = True
5500 op {| p :+: q |} (Inr y) = False
5502 The type patterns must be identical, even in equations for different methods of the class.
5503 So this too is illegal:
5507 op1 {| a :*: b |} (x :*: y) = True
5510 op2 {| p :*: q |} (x :*: y) = False
5512 (The reason for this restriction is that we gather all the equations for a particular type consructor
5513 into a single generic instance declaration.)
5519 A generic method declaration must give a case for each of the three type constructors.
5525 The type for a generic method can be built only from:
5527 <listitem> <para> Function arrows </para> </listitem>
5528 <listitem> <para> Type variables </para> </listitem>
5529 <listitem> <para> Tuples </para> </listitem>
5530 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5532 Here are some example type signatures for generic methods:
5535 op2 :: Bool -> (a,Bool)
5536 op3 :: [Int] -> a -> a
5539 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5543 This restriction is an implementation restriction: we just havn't got around to
5544 implementing the necessary bidirectional maps over arbitrary type constructors.
5545 It would be relatively easy to add specific type constructors, such as Maybe and list,
5546 to the ones that are allowed.</para>
5551 In an instance declaration for a generic class, the idea is that the compiler
5552 will fill in the methods for you, based on the generic templates. However it can only
5557 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5562 No constructor of the instance type has unboxed fields.
5566 (Of course, these things can only arise if you are already using GHC extensions.)
5567 However, you can still give an instance declarations for types which break these rules,
5568 provided you give explicit code to override any generic default methods.
5576 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5577 what the compiler does with generic declarations.
5582 <sect2> <title> Another example </title>
5584 Just to finish with, here's another example I rather like:
5588 nCons {| Unit |} _ = 1
5589 nCons {| a :*: b |} _ = 1
5590 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5593 tag {| Unit |} _ = 1
5594 tag {| a :*: b |} _ = 1
5595 tag {| a :+: b |} (Inl x) = tag x
5596 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5605 ;;; Local Variables: ***
5607 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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