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>
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.
1793 <title>Type synonyms in the instance head</title>
1796 <emphasis>Unlike Haskell 98, instance heads may use type
1797 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1798 As always, using a type synonym is just shorthand for
1799 writing the RHS of the type synonym definition. For example:
1803 type Point = (Int,Int)
1804 instance C Point where ...
1805 instance C [Point] where ...
1809 is legal. However, if you added
1813 instance C (Int,Int) where ...
1817 as well, then the compiler will complain about the overlapping
1818 (actually, identical) instance declarations. As always, type synonyms
1819 must be fully applied. You cannot, for example, write:
1824 instance Monad P where ...
1828 This design decision is independent of all the others, and easily
1829 reversed, but it makes sense to me.
1834 <sect3 id="undecidable-instances">
1835 <title>Undecidable instances</title>
1837 <para>An instance declaration must normally obey the following rules:
1839 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1840 an instance declaration <emphasis>must not</emphasis> be a type variable.
1841 For example, these are OK:
1844 instance C Int a where ...
1846 instance D (Int, Int) where ...
1848 instance E [[a]] where ...
1852 instance F a where ...
1854 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1855 For example, this is OK:
1857 instance Stateful (ST s) (MutVar s) where ...
1864 <para>All of the types in the <emphasis>context</emphasis> of
1865 an instance declaration <emphasis>must</emphasis> be type variables.
1868 instance C a b => Eq (a,b) where ...
1872 instance C Int b => Foo b where ...
1878 These restrictions ensure that
1879 context reduction terminates: each reduction step removes one type
1880 constructor. For example, the following would make the type checker
1881 loop if it wasn't excluded:
1883 instance C a => C a where ...
1885 There are two situations in which the rule is a bit of a pain. First,
1886 if one allows overlapping instance declarations then it's quite
1887 convenient to have a "default instance" declaration that applies if
1888 something more specific does not:
1897 Second, sometimes you might want to use the following to get the
1898 effect of a "class synonym":
1902 class (C1 a, C2 a, C3 a) => C a where { }
1904 instance (C1 a, C2 a, C3 a) => C a where { }
1908 This allows you to write shorter signatures:
1920 f :: (C1 a, C2 a, C3 a) => ...
1924 Voluminous correspondence on the Haskell mailing list has convinced me
1925 that it's worth experimenting with more liberal rules. If you use
1926 the experimental flag <option>-fallow-undecidable-instances</option>
1927 <indexterm><primary>-fallow-undecidable-instances
1928 option</primary></indexterm>, you can use arbitrary
1929 types in both an instance context and instance head. Termination is ensured by having a
1930 fixed-depth recursion stack. If you exceed the stack depth you get a
1931 sort of backtrace, and the opportunity to increase the stack depth
1932 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1935 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1936 allowing these idioms interesting idioms.
1943 <sect2 id="implicit-parameters">
1944 <title>Implicit parameters</title>
1946 <para> Implicit parameters are implemented as described in
1947 "Implicit parameters: dynamic scoping with static types",
1948 J Lewis, MB Shields, E Meijer, J Launchbury,
1949 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1953 <para>(Most of the following, stil rather incomplete, documentation is
1954 due to Jeff Lewis.)</para>
1956 <para>Implicit parameter support is enabled with the option
1957 <option>-fimplicit-params</option>.</para>
1960 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1961 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1962 context. In Haskell, all variables are statically bound. Dynamic
1963 binding of variables is a notion that goes back to Lisp, but was later
1964 discarded in more modern incarnations, such as Scheme. Dynamic binding
1965 can be very confusing in an untyped language, and unfortunately, typed
1966 languages, in particular Hindley-Milner typed languages like Haskell,
1967 only support static scoping of variables.
1970 However, by a simple extension to the type class system of Haskell, we
1971 can support dynamic binding. Basically, we express the use of a
1972 dynamically bound variable as a constraint on the type. These
1973 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1974 function uses a dynamically-bound variable <literal>?x</literal>
1975 of type <literal>t'</literal>". For
1976 example, the following expresses the type of a sort function,
1977 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1979 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1981 The dynamic binding constraints are just a new form of predicate in the type class system.
1984 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1985 where <literal>x</literal> is
1986 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1987 Use of this construct also introduces a new
1988 dynamic-binding constraint in the type of the expression.
1989 For example, the following definition
1990 shows how we can define an implicitly parameterized sort function in
1991 terms of an explicitly parameterized <literal>sortBy</literal> function:
1993 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1995 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2001 <title>Implicit-parameter type constraints</title>
2003 Dynamic binding constraints behave just like other type class
2004 constraints in that they are automatically propagated. Thus, when a
2005 function is used, its implicit parameters are inherited by the
2006 function that called it. For example, our <literal>sort</literal> function might be used
2007 to pick out the least value in a list:
2009 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2010 least xs = fst (sort xs)
2012 Without lifting a finger, the <literal>?cmp</literal> parameter is
2013 propagated to become a parameter of <literal>least</literal> as well. With explicit
2014 parameters, the default is that parameters must always be explicit
2015 propagated. With implicit parameters, the default is to always
2019 An implicit-parameter type constraint differs from other type class constraints in the
2020 following way: All uses of a particular implicit parameter must have
2021 the same type. This means that the type of <literal>(?x, ?x)</literal>
2022 is <literal>(?x::a) => (a,a)</literal>, and not
2023 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2027 <para> You can't have an implicit parameter in the context of a class or instance
2028 declaration. For example, both these declarations are illegal:
2030 class (?x::Int) => C a where ...
2031 instance (?x::a) => Foo [a] where ...
2033 Reason: exactly which implicit parameter you pick up depends on exactly where
2034 you invoke a function. But the ``invocation'' of instance declarations is done
2035 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2036 Easiest thing is to outlaw the offending types.</para>
2038 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2040 f :: (?x :: [a]) => Int -> Int
2043 g :: (Read a, Show a) => String -> String
2046 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2047 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2048 quite unambiguous, and fixes the type <literal>a</literal>.
2053 <title>Implicit-parameter bindings</title>
2056 An implicit parameter is <emphasis>bound</emphasis> using the standard
2057 <literal>let</literal> or <literal>where</literal> binding forms.
2058 For example, we define the <literal>min</literal> function by binding
2059 <literal>cmp</literal>.
2062 min = let ?cmp = (<=) in least
2066 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2067 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2068 (including in a list comprehension, or do-notation, or pattern guards),
2069 or a <literal>where</literal> clause.
2070 Note the following points:
2073 An implicit-parameter binding group must be a
2074 collection of simple bindings to implicit-style variables (no
2075 function-style bindings, and no type signatures); these bindings are
2076 neither polymorphic or recursive.
2079 You may not mix implicit-parameter bindings with ordinary bindings in a
2080 single <literal>let</literal>
2081 expression; use two nested <literal>let</literal>s instead.
2082 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2086 You may put multiple implicit-parameter bindings in a
2087 single binding group; but they are <emphasis>not</emphasis> treated
2088 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2089 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2090 parameter. The bindings are not nested, and may be re-ordered without changing
2091 the meaning of the program.
2092 For example, consider:
2094 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2096 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2097 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2099 f :: (?x::Int) => Int -> Int
2108 <sect2 id="linear-implicit-parameters">
2109 <title>Linear implicit parameters</title>
2111 Linear implicit parameters are an idea developed by Koen Claessen,
2112 Mark Shields, and Simon PJ. They address the long-standing
2113 problem that monads seem over-kill for certain sorts of problem, notably:
2116 <listitem> <para> distributing a supply of unique names </para> </listitem>
2117 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2118 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2122 Linear implicit parameters are just like ordinary implicit parameters,
2123 except that they are "linear" -- that is, they cannot be copied, and
2124 must be explicitly "split" instead. Linear implicit parameters are
2125 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2126 (The '/' in the '%' suggests the split!)
2131 import GHC.Exts( Splittable )
2133 data NameSupply = ...
2135 splitNS :: NameSupply -> (NameSupply, NameSupply)
2136 newName :: NameSupply -> Name
2138 instance Splittable NameSupply where
2142 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2143 f env (Lam x e) = Lam x' (f env e)
2146 env' = extend env x x'
2147 ...more equations for f...
2149 Notice that the implicit parameter %ns is consumed
2151 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2152 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2156 So the translation done by the type checker makes
2157 the parameter explicit:
2159 f :: NameSupply -> Env -> Expr -> Expr
2160 f ns env (Lam x e) = Lam x' (f ns1 env e)
2162 (ns1,ns2) = splitNS ns
2164 env = extend env x x'
2166 Notice the call to 'split' introduced by the type checker.
2167 How did it know to use 'splitNS'? Because what it really did
2168 was to introduce a call to the overloaded function 'split',
2169 defined by the class <literal>Splittable</literal>:
2171 class Splittable a where
2174 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2175 split for name supplies. But we can simply write
2181 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2183 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2184 <literal>GHC.Exts</literal>.
2189 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2190 are entirely distinct implicit parameters: you
2191 can use them together and they won't intefere with each other. </para>
2194 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2196 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2197 in the context of a class or instance declaration. </para></listitem>
2201 <sect3><title>Warnings</title>
2204 The monomorphism restriction is even more important than usual.
2205 Consider the example above:
2207 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2208 f env (Lam x e) = Lam x' (f env e)
2211 env' = extend env x x'
2213 If we replaced the two occurrences of x' by (newName %ns), which is
2214 usually a harmless thing to do, we get:
2216 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2217 f env (Lam x e) = Lam (newName %ns) (f env e)
2219 env' = extend env x (newName %ns)
2221 But now the name supply is consumed in <emphasis>three</emphasis> places
2222 (the two calls to newName,and the recursive call to f), so
2223 the result is utterly different. Urk! We don't even have
2227 Well, this is an experimental change. With implicit
2228 parameters we have already lost beta reduction anyway, and
2229 (as John Launchbury puts it) we can't sensibly reason about
2230 Haskell programs without knowing their typing.
2235 <sect3><title>Recursive functions</title>
2236 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2239 foo :: %x::T => Int -> [Int]
2241 foo n = %x : foo (n-1)
2243 where T is some type in class Splittable.</para>
2245 Do you get a list of all the same T's or all different T's
2246 (assuming that split gives two distinct T's back)?
2248 If you supply the type signature, taking advantage of polymorphic
2249 recursion, you get what you'd probably expect. Here's the
2250 translated term, where the implicit param is made explicit:
2253 foo x n = let (x1,x2) = split x
2254 in x1 : foo x2 (n-1)
2256 But if you don't supply a type signature, GHC uses the Hindley
2257 Milner trick of using a single monomorphic instance of the function
2258 for the recursive calls. That is what makes Hindley Milner type inference
2259 work. So the translation becomes
2263 foom n = x : foom (n-1)
2267 Result: 'x' is not split, and you get a list of identical T's. So the
2268 semantics of the program depends on whether or not foo has a type signature.
2271 You may say that this is a good reason to dislike linear implicit parameters
2272 and you'd be right. That is why they are an experimental feature.
2278 <sect2 id="functional-dependencies">
2279 <title>Functional dependencies
2282 <para> Functional dependencies are implemented as described by Mark Jones
2283 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2284 In Proceedings of the 9th European Symposium on Programming,
2285 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2289 Functional dependencies are introduced by a vertical bar in the syntax of a
2290 class declaration; e.g.
2292 class (Monad m) => MonadState s m | m -> s where ...
2294 class Foo a b c | a b -> c where ...
2296 There should be more documentation, but there isn't (yet). Yell if you need it.
2302 <sect2 id="sec-kinding">
2303 <title>Explicitly-kinded quantification</title>
2306 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2307 to give the kind explicitly as (machine-checked) documentation,
2308 just as it is nice to give a type signature for a function. On some occasions,
2309 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2310 John Hughes had to define the data type:
2312 data Set cxt a = Set [a]
2313 | Unused (cxt a -> ())
2315 The only use for the <literal>Unused</literal> constructor was to force the correct
2316 kind for the type variable <literal>cxt</literal>.
2319 GHC now instead allows you to specify the kind of a type variable directly, wherever
2320 a type variable is explicitly bound. Namely:
2322 <listitem><para><literal>data</literal> declarations:
2324 data Set (cxt :: * -> *) a = Set [a]
2325 </screen></para></listitem>
2326 <listitem><para><literal>type</literal> declarations:
2328 type T (f :: * -> *) = f Int
2329 </screen></para></listitem>
2330 <listitem><para><literal>class</literal> declarations:
2332 class (Eq a) => C (f :: * -> *) a where ...
2333 </screen></para></listitem>
2334 <listitem><para><literal>forall</literal>'s in type signatures:
2336 f :: forall (cxt :: * -> *). Set cxt Int
2337 </screen></para></listitem>
2342 The parentheses are required. Some of the spaces are required too, to
2343 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2344 will get a parse error, because "<literal>::*->*</literal>" is a
2345 single lexeme in Haskell.
2349 As part of the same extension, you can put kind annotations in types
2352 f :: (Int :: *) -> Int
2353 g :: forall a. a -> (a :: *)
2357 atype ::= '(' ctype '::' kind ')
2359 The parentheses are required.
2364 <sect2 id="universal-quantification">
2365 <title>Arbitrary-rank polymorphism
2369 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2370 allows us to say exactly what this means. For example:
2378 g :: forall b. (b -> b)
2380 The two are treated identically.
2384 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2385 explicit universal quantification in
2387 For example, all the following types are legal:
2389 f1 :: forall a b. a -> b -> a
2390 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2392 f2 :: (forall a. a->a) -> Int -> Int
2393 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2395 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2397 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2398 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2399 The <literal>forall</literal> makes explicit the universal quantification that
2400 is implicitly added by Haskell.
2403 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2404 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2405 shows, the polymorphic type on the left of the function arrow can be overloaded.
2408 The function <literal>f3</literal> has a rank-3 type;
2409 it has rank-2 types on the left of a function arrow.
2412 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2413 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2414 that restriction has now been lifted.)
2415 In particular, a forall-type (also called a "type scheme"),
2416 including an operational type class context, is legal:
2418 <listitem> <para> On the left of a function arrow </para> </listitem>
2419 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2420 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2421 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2422 field type signatures.</para> </listitem>
2423 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2424 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2426 There is one place you cannot put a <literal>forall</literal>:
2427 you cannot instantiate a type variable with a forall-type. So you cannot
2428 make a forall-type the argument of a type constructor. So these types are illegal:
2430 x1 :: [forall a. a->a]
2431 x2 :: (forall a. a->a, Int)
2432 x3 :: Maybe (forall a. a->a)
2434 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2435 a type variable any more!
2444 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2445 the types of the constructor arguments. Here are several examples:
2451 data T a = T1 (forall b. b -> b -> b) a
2453 data MonadT m = MkMonad { return :: forall a. a -> m a,
2454 bind :: forall a b. m a -> (a -> m b) -> m b
2457 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2463 The constructors have rank-2 types:
2469 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2470 MkMonad :: forall m. (forall a. a -> m a)
2471 -> (forall a b. m a -> (a -> m b) -> m b)
2473 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2479 Notice that you don't need to use a <literal>forall</literal> if there's an
2480 explicit context. For example in the first argument of the
2481 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2482 prefixed to the argument type. The implicit <literal>forall</literal>
2483 quantifies all type variables that are not already in scope, and are
2484 mentioned in the type quantified over.
2488 As for type signatures, implicit quantification happens for non-overloaded
2489 types too. So if you write this:
2492 data T a = MkT (Either a b) (b -> b)
2495 it's just as if you had written this:
2498 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2501 That is, since the type variable <literal>b</literal> isn't in scope, it's
2502 implicitly universally quantified. (Arguably, it would be better
2503 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2504 where that is what is wanted. Feedback welcomed.)
2508 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2509 the constructor to suitable values, just as usual. For example,
2520 a3 = MkSwizzle reverse
2523 a4 = let r x = Just x
2530 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2531 mkTs f x y = [T1 f x, T1 f y]
2537 The type of the argument can, as usual, be more general than the type
2538 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2539 does not need the <literal>Ord</literal> constraint.)
2543 When you use pattern matching, the bound variables may now have
2544 polymorphic types. For example:
2550 f :: T a -> a -> (a, Char)
2551 f (T1 w k) x = (w k x, w 'c' 'd')
2553 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2554 g (MkSwizzle s) xs f = s (map f (s xs))
2556 h :: MonadT m -> [m a] -> m [a]
2557 h m [] = return m []
2558 h m (x:xs) = bind m x $ \y ->
2559 bind m (h m xs) $ \ys ->
2566 In the function <function>h</function> we use the record selectors <literal>return</literal>
2567 and <literal>bind</literal> to extract the polymorphic bind and return functions
2568 from the <literal>MonadT</literal> data structure, rather than using pattern
2574 <title>Type inference</title>
2577 In general, type inference for arbitrary-rank types is undecidable.
2578 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2579 to get a decidable algorithm by requiring some help from the programmer.
2580 We do not yet have a formal specification of "some help" but the rule is this:
2583 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2584 provides an explicit polymorphic type for x, or GHC's type inference will assume
2585 that x's type has no foralls in it</emphasis>.
2588 What does it mean to "provide" an explicit type for x? You can do that by
2589 giving a type signature for x directly, using a pattern type signature
2590 (<xref linkend="scoped-type-variables"/>), thus:
2592 \ f :: (forall a. a->a) -> (f True, f 'c')
2594 Alternatively, you can give a type signature to the enclosing
2595 context, which GHC can "push down" to find the type for the variable:
2597 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2599 Here the type signature on the expression can be pushed inwards
2600 to give a type signature for f. Similarly, and more commonly,
2601 one can give a type signature for the function itself:
2603 h :: (forall a. a->a) -> (Bool,Char)
2604 h f = (f True, f 'c')
2606 You don't need to give a type signature if the lambda bound variable
2607 is a constructor argument. Here is an example we saw earlier:
2609 f :: T a -> a -> (a, Char)
2610 f (T1 w k) x = (w k x, w 'c' 'd')
2612 Here we do not need to give a type signature to <literal>w</literal>, because
2613 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2620 <sect3 id="implicit-quant">
2621 <title>Implicit quantification</title>
2624 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2625 user-written types, if and only if there is no explicit <literal>forall</literal>,
2626 GHC finds all the type variables mentioned in the type that are not already
2627 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2631 f :: forall a. a -> a
2638 h :: forall b. a -> b -> b
2644 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2647 f :: (a -> a) -> Int
2649 f :: forall a. (a -> a) -> Int
2651 f :: (forall a. a -> a) -> Int
2654 g :: (Ord a => a -> a) -> Int
2655 -- MEANS the illegal type
2656 g :: forall a. (Ord a => a -> a) -> Int
2658 g :: (forall a. Ord a => a -> a) -> Int
2660 The latter produces an illegal type, which you might think is silly,
2661 but at least the rule is simple. If you want the latter type, you
2662 can write your for-alls explicitly. Indeed, doing so is strongly advised
2671 <sect2 id="scoped-type-variables">
2672 <title>Scoped type variables
2676 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2678 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2679 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2680 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2684 f (xs::[a]) = ys ++ ys
2689 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2690 This brings the type variable <literal>a</literal> into scope; it scopes over
2691 all the patterns and right hand sides for this equation for <function>f</function>.
2692 In particular, it is in scope at the type signature for <varname>y</varname>.
2696 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2697 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2698 implicitly universally quantified. (If there are no type variables in
2699 scope, all type variables mentioned in the signature are universally
2700 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2701 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2702 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2703 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2704 it becomes possible to do so.
2708 Scoped type variables are implemented in both GHC and Hugs. Where the
2709 implementations differ from the specification below, those differences
2714 So much for the basic idea. Here are the details.
2718 <title>What a scoped type variable means</title>
2720 A lexically-scoped type variable is simply
2721 the name for a type. The restriction it expresses is that all occurrences
2722 of the same name mean the same type. For example:
2724 f :: [Int] -> Int -> Int
2725 f (xs::[a]) (y::a) = (head xs + y) :: a
2727 The pattern type signatures on the left hand side of
2728 <literal>f</literal> express the fact that <literal>xs</literal>
2729 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2730 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2731 specifies that this expression must have the same type <literal>a</literal>.
2732 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2733 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2734 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2735 rules, which specified that a pattern-bound type variable should be universally quantified.)
2736 For example, all of these are legal:</para>
2739 t (x::a) (y::a) = x+y*2
2741 f (x::a) (y::b) = [x,y] -- a unifies with b
2743 g (x::a) = x + 1::Int -- a unifies with Int
2745 h x = let k (y::a) = [x,y] -- a is free in the
2746 in k x -- environment
2748 k (x::a) True = ... -- a unifies with Int
2749 k (x::Int) False = ...
2752 w (x::a) = x -- a unifies with [b]
2758 <title>Scope and implicit quantification</title>
2766 All the type variables mentioned in a pattern,
2767 that are not already in scope,
2768 are brought into scope by the pattern. We describe this set as
2769 the <emphasis>type variables bound by the pattern</emphasis>.
2772 f (x::a) = let g (y::(a,b)) = fst y
2776 The pattern <literal>(x::a)</literal> brings the type variable
2777 <literal>a</literal> into scope, as well as the term
2778 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2779 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2780 and brings into scope the type variable <literal>b</literal>.
2786 The type variable(s) bound by the pattern have the same scope
2787 as the term variable(s) bound by the pattern. For example:
2790 f (x::a) = <...rhs of f...>
2791 (p::b, q::b) = (1,2)
2792 in <...body of let...>
2794 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2795 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2796 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2797 just like <literal>p</literal> and <literal>q</literal> do.
2798 Indeed, the newly bound type variables also scope over any ordinary, separate
2799 type signatures in the <literal>let</literal> group.
2806 The type variables bound by the pattern may be
2807 mentioned in ordinary type signatures or pattern
2808 type signatures anywhere within their scope.
2815 In ordinary type signatures, any type variable mentioned in the
2816 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2824 Ordinary type signatures do not bring any new type variables
2825 into scope (except in the type signature itself!). So this is illegal:
2832 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2833 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2834 and that is an incorrect typing.
2841 The pattern type signature is a monotype:
2846 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2850 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2851 not to type schemes.
2855 There is no implicit universal quantification on pattern type signatures (in contrast to
2856 ordinary type signatures).
2866 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2867 scope over the methods defined in the <literal>where</literal> part. For example:
2881 (Not implemented in Hugs yet, Dec 98).
2891 <sect3 id="decl-type-sigs">
2892 <title>Declaration type signatures</title>
2893 <para>A declaration type signature that has <emphasis>explicit</emphasis>
2894 quantification (using <literal>forall</literal>) brings into scope the
2895 explicitly-quantified
2896 type variables, in the definition of the named function(s). For example:
2898 f :: forall a. [a] -> [a]
2899 f (x:xs) = xs ++ [ x :: a ]
2901 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
2902 the definition of "<literal>f</literal>".
2904 <para>This only happens if the quantification in <literal>f</literal>'s type
2905 signature is explicit. For example:
2908 g (x:xs) = xs ++ [ x :: a ]
2910 This program will be rejected, because "<literal>a</literal>" does not scope
2911 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
2912 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
2913 quantification rules.
2917 <sect3 id="pattern-type-sigs">
2918 <title>Where a pattern type signature can occur</title>
2921 A pattern type signature can occur in any pattern. For example:
2926 A pattern type signature can be on an arbitrary sub-pattern, not
2931 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2940 Pattern type signatures, including the result part, can be used
2941 in lambda abstractions:
2944 (\ (x::a, y) :: a -> x)
2951 Pattern type signatures, including the result part, can be used
2952 in <literal>case</literal> expressions:
2955 case e of { ((x::a, y) :: (a,b)) -> x }
2958 Note that the <literal>-></literal> symbol in a case alternative
2959 leads to difficulties when parsing a type signature in the pattern: in
2960 the absence of the extra parentheses in the example above, the parser
2961 would try to interpret the <literal>-></literal> as a function
2962 arrow and give a parse error later.
2970 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2971 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2972 token or a parenthesised type of some sort). To see why,
2973 consider how one would parse this:
2987 Pattern type signatures can bind existential type variables.
2992 data T = forall a. MkT [a]
2995 f (MkT [t::a]) = MkT t3
3008 Pattern type signatures
3009 can be used in pattern bindings:
3012 f x = let (y, z::a) = x in ...
3013 f1 x = let (y, z::Int) = x in ...
3014 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3015 f3 :: (b->b) = \x -> x
3018 In all such cases, the binding is not generalised over the pattern-bound
3019 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3020 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3021 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3022 In contrast, the binding
3027 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3028 in <literal>f4</literal>'s scope.
3034 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3035 type signatures. The two can be used independently or together.</para>
3039 <sect3 id="result-type-sigs">
3040 <title>Result type signatures</title>
3043 The result type of a function can be given a signature, thus:
3047 f (x::a) :: [a] = [x,x,x]
3051 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3052 result type. Sometimes this is the only way of naming the type variable
3057 f :: Int -> [a] -> [a]
3058 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3059 in \xs -> map g (reverse xs `zip` xs)
3064 The type variables bound in a result type signature scope over the right hand side
3065 of the definition. However, consider this corner-case:
3067 rev1 :: [a] -> [a] = \xs -> reverse xs
3069 foo ys = rev (ys::[a])
3071 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3072 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3073 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3074 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3075 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3078 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3079 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3083 rev1 :: [a] -> [a] = \xs -> reverse xs
3088 Result type signatures are not yet implemented in Hugs.
3095 <sect2 id="deriving-typeable">
3096 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3099 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3100 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3101 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3102 classes <literal>Eq</literal>, <literal>Ord</literal>,
3103 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3106 GHC extends this list with two more classes that may be automatically derived
3107 (provided the <option>-fglasgow-exts</option> flag is specified):
3108 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3109 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3110 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3114 <sect2 id="newtype-deriving">
3115 <title>Generalised derived instances for newtypes</title>
3118 When you define an abstract type using <literal>newtype</literal>, you may want
3119 the new type to inherit some instances from its representation. In
3120 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3121 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3122 other classes you have to write an explicit instance declaration. For
3123 example, if you define
3126 newtype Dollars = Dollars Int
3129 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3130 explicitly define an instance of <literal>Num</literal>:
3133 instance Num Dollars where
3134 Dollars a + Dollars b = Dollars (a+b)
3137 All the instance does is apply and remove the <literal>newtype</literal>
3138 constructor. It is particularly galling that, since the constructor
3139 doesn't appear at run-time, this instance declaration defines a
3140 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3141 dictionary, only slower!
3145 <sect3> <title> Generalising the deriving clause </title>
3147 GHC now permits such instances to be derived instead, so one can write
3149 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3152 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3153 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3154 derives an instance declaration of the form
3157 instance Num Int => Num Dollars
3160 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3164 We can also derive instances of constructor classes in a similar
3165 way. For example, suppose we have implemented state and failure monad
3166 transformers, such that
3169 instance Monad m => Monad (State s m)
3170 instance Monad m => Monad (Failure m)
3172 In Haskell 98, we can define a parsing monad by
3174 type Parser tok m a = State [tok] (Failure m) a
3177 which is automatically a monad thanks to the instance declarations
3178 above. With the extension, we can make the parser type abstract,
3179 without needing to write an instance of class <literal>Monad</literal>, via
3182 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3185 In this case the derived instance declaration is of the form
3187 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3190 Notice that, since <literal>Monad</literal> is a constructor class, the
3191 instance is a <emphasis>partial application</emphasis> of the new type, not the
3192 entire left hand side. We can imagine that the type declaration is
3193 ``eta-converted'' to generate the context of the instance
3198 We can even derive instances of multi-parameter classes, provided the
3199 newtype is the last class parameter. In this case, a ``partial
3200 application'' of the class appears in the <literal>deriving</literal>
3201 clause. For example, given the class
3204 class StateMonad s m | m -> s where ...
3205 instance Monad m => StateMonad s (State s m) where ...
3207 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3209 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3210 deriving (Monad, StateMonad [tok])
3213 The derived instance is obtained by completing the application of the
3214 class to the new type:
3217 instance StateMonad [tok] (State [tok] (Failure m)) =>
3218 StateMonad [tok] (Parser tok m)
3223 As a result of this extension, all derived instances in newtype
3224 declarations are treated uniformly (and implemented just by reusing
3225 the dictionary for the representation type), <emphasis>except</emphasis>
3226 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3227 the newtype and its representation.
3231 <sect3> <title> A more precise specification </title>
3233 Derived instance declarations are constructed as follows. Consider the
3234 declaration (after expansion of any type synonyms)
3237 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3243 <literal>S</literal> is a type constructor,
3246 The <literal>t1...tk</literal> are types,
3249 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3250 the <literal>ti</literal>, and
3253 The <literal>ci</literal> are partial applications of
3254 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3255 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3258 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3259 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3260 should not "look through" the type or its constructor. You can still
3261 derive these classes for a newtype, but it happens in the usual way, not
3262 via this new mechanism.
3265 Then, for each <literal>ci</literal>, the derived instance
3268 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3270 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3271 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3275 As an example which does <emphasis>not</emphasis> work, consider
3277 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3279 Here we cannot derive the instance
3281 instance Monad (State s m) => Monad (NonMonad m)
3284 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3285 and so cannot be "eta-converted" away. It is a good thing that this
3286 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3287 not, in fact, a monad --- for the same reason. Try defining
3288 <literal>>>=</literal> with the correct type: you won't be able to.
3292 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3293 important, since we can only derive instances for the last one. If the
3294 <literal>StateMonad</literal> class above were instead defined as
3297 class StateMonad m s | m -> s where ...
3300 then we would not have been able to derive an instance for the
3301 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3302 classes usually have one "main" parameter for which deriving new
3303 instances is most interesting.
3311 <!-- ==================== End of type system extensions ================= -->
3313 <!-- ====================== Generalised algebraic data types ======================= -->
3316 <title>Generalised Algebraic Data Types</title>
3318 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3319 to give the type signatures of constructors explicitly. For example:
3322 Lit :: Int -> Term Int
3323 Succ :: Term Int -> Term Int
3324 IsZero :: Term Int -> Term Bool
3325 If :: Term Bool -> Term a -> Term a -> Term a
3326 Pair :: Term a -> Term b -> Term (a,b)
3328 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3329 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3330 for these <literal>Terms</literal>:
3334 eval (Succ t) = 1 + eval t
3335 eval (IsZero i) = eval i == 0
3336 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3337 eval (Pair e1 e2) = (eval e2, eval e2)
3339 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3341 <para> The extensions to GHC are these:
3344 Data type declarations have a 'where' form, as exemplified above. The type signature of
3345 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3346 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3347 have no scope. Indeed, one can write a kind signature instead:
3349 data Term :: * -> * where ...
3351 or even a mixture of the two:
3353 data Foo a :: (* -> *) -> * where ...
3355 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3358 data Foo a (b :: * -> *) where ...
3363 There are no restrictions on the type of the data constructor, except that the result
3364 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3365 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3369 You cannot use a <literal>deriving</literal> clause on a GADT-style data type declaration,
3370 nor can you use record syntax. (It's not clear what these constructs would mean. For example,
3371 the record selectors might ill-typed.) However, you can use strictness annotations, in the obvious places
3372 in the constructor type:
3375 Lit :: !Int -> Term Int
3376 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3377 Pair :: Term a -> Term b -> Term (a,b)
3382 Pattern matching causes type refinement. For example, in the right hand side of the equation
3387 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3388 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3389 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3391 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3392 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3393 occur. However, the refinement is quite general. For example, if we had:
3395 eval :: Term a -> a -> a
3396 eval (Lit i) j = i+j
3398 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3399 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3400 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3406 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3408 data T a = forall b. MkT b (b->a)
3409 data T' a where { MKT :: b -> (b->a) -> T a }
3414 <!-- ====================== End of Generalised algebraic data types ======================= -->
3416 <!-- ====================== TEMPLATE HASKELL ======================= -->
3418 <sect1 id="template-haskell">
3419 <title>Template Haskell</title>
3421 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3422 Template Haskell at <ulink url="http://www.haskell.org/th/">
3423 http://www.haskell.org/th/</ulink>, while
3425 the main technical innovations is discussed in "<ulink
3426 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3427 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3428 The details of the Template Haskell design are still in flux. Make sure you
3429 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3430 (search for the type ExpQ).
3431 [Temporary: many changes to the original design are described in
3432 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3433 Not all of these changes are in GHC 6.2.]
3436 <para> The first example from that paper is set out below as a worked example to help get you started.
3440 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3441 Tim Sheard is going to expand it.)
3445 <title>Syntax</title>
3447 <para> Template Haskell has the following new syntactic
3448 constructions. You need to use the flag
3449 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3450 </indexterm>to switch these syntactic extensions on
3451 (<option>-fth</option> is currently implied by
3452 <option>-fglasgow-exts</option>, but you are encouraged to
3453 specify it explicitly).</para>
3457 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3458 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3459 There must be no space between the "$" and the identifier or parenthesis. This use
3460 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3461 of "." as an infix operator. If you want the infix operator, put spaces around it.
3463 <para> A splice can occur in place of
3465 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3466 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3467 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3469 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3470 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3476 A expression quotation is written in Oxford brackets, thus:
3478 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3479 the quotation has type <literal>Expr</literal>.</para></listitem>
3480 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3481 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3482 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3483 the quotation has type <literal>Type</literal>.</para></listitem>
3484 </itemizedlist></para></listitem>
3487 Reification is written thus:
3489 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3490 has type <literal>Dec</literal>. </para></listitem>
3491 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3492 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3493 <listitem><para> Still to come: fixities </para></listitem>
3495 </itemizedlist></para>
3502 <sect2> <title> Using Template Haskell </title>
3506 The data types and monadic constructor functions for Template Haskell are in the library
3507 <literal>Language.Haskell.THSyntax</literal>.
3511 You can only run a function at compile time if it is imported from another module. That is,
3512 you can't define a function in a module, and call it from within a splice in the same module.
3513 (It would make sense to do so, but it's hard to implement.)
3517 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3520 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3521 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3522 compiles and runs a program, and then looks at the result. So it's important that
3523 the program it compiles produces results whose representations are identical to
3524 those of the compiler itself.
3528 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3529 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3534 <sect2> <title> A Template Haskell Worked Example </title>
3535 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3536 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3543 -- Import our template "pr"
3544 import Printf ( pr )
3546 -- The splice operator $ takes the Haskell source code
3547 -- generated at compile time by "pr" and splices it into
3548 -- the argument of "putStrLn".
3549 main = putStrLn ( $(pr "Hello") )
3555 -- Skeletal printf from the paper.
3556 -- It needs to be in a separate module to the one where
3557 -- you intend to use it.
3559 -- Import some Template Haskell syntax
3560 import Language.Haskell.TH
3562 -- Describe a format string
3563 data Format = D | S | L String
3565 -- Parse a format string. This is left largely to you
3566 -- as we are here interested in building our first ever
3567 -- Template Haskell program and not in building printf.
3568 parse :: String -> [Format]
3571 -- Generate Haskell source code from a parsed representation
3572 -- of the format string. This code will be spliced into
3573 -- the module which calls "pr", at compile time.
3574 gen :: [Format] -> ExpQ
3575 gen [D] = [| \n -> show n |]
3576 gen [S] = [| \s -> s |]
3577 gen [L s] = stringE s
3579 -- Here we generate the Haskell code for the splice
3580 -- from an input format string.
3581 pr :: String -> ExpQ
3582 pr s = gen (parse s)
3585 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3588 $ ghc --make -fth main.hs -o main.exe
3591 <para>Run "main.exe" and here is your output:</para>
3602 <!-- ===================== Arrow notation =================== -->
3604 <sect1 id="arrow-notation">
3605 <title>Arrow notation
3608 <para>Arrows are a generalization of monads introduced by John Hughes.
3609 For more details, see
3614 “Generalising Monads to Arrows”,
3615 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3616 pp67–111, May 2000.
3622 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3623 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3629 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3630 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3636 and the arrows web page at
3637 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3638 With the <option>-farrows</option> flag, GHC supports the arrow
3639 notation described in the second of these papers.
3640 What follows is a brief introduction to the notation;
3641 it won't make much sense unless you've read Hughes's paper.
3642 This notation is translated to ordinary Haskell,
3643 using combinators from the
3644 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3648 <para>The extension adds a new kind of expression for defining arrows:
3650 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3651 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3653 where <literal>proc</literal> is a new keyword.
3654 The variables of the pattern are bound in the body of the
3655 <literal>proc</literal>-expression,
3656 which is a new sort of thing called a <firstterm>command</firstterm>.
3657 The syntax of commands is as follows:
3659 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3660 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3661 | <replaceable>cmd</replaceable><superscript>0</superscript>
3663 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3664 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3665 infix operators as for expressions, and
3667 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3668 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3669 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3670 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3671 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3672 | <replaceable>fcmd</replaceable>
3674 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3675 | ( <replaceable>cmd</replaceable> )
3676 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3678 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3679 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3680 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3681 | <replaceable>cmd</replaceable>
3683 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3684 except that the bodies are commands instead of expressions.
3688 Commands produce values, but (like monadic computations)
3689 may yield more than one value,
3690 or none, and may do other things as well.
3691 For the most part, familiarity with monadic notation is a good guide to
3693 However the values of expressions, even monadic ones,
3694 are determined by the values of the variables they contain;
3695 this is not necessarily the case for commands.
3699 A simple example of the new notation is the expression
3701 proc x -> f -< x+1
3703 We call this a <firstterm>procedure</firstterm> or
3704 <firstterm>arrow abstraction</firstterm>.
3705 As with a lambda expression, the variable <literal>x</literal>
3706 is a new variable bound within the <literal>proc</literal>-expression.
3707 It refers to the input to the arrow.
3708 In the above example, <literal>-<</literal> is not an identifier but an
3709 new reserved symbol used for building commands from an expression of arrow
3710 type and an expression to be fed as input to that arrow.
3711 (The weird look will make more sense later.)
3712 It may be read as analogue of application for arrows.
3713 The above example is equivalent to the Haskell expression
3715 arr (\ x -> x+1) >>> f
3717 That would make no sense if the expression to the left of
3718 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3719 More generally, the expression to the left of <literal>-<</literal>
3720 may not involve any <firstterm>local variable</firstterm>,
3721 i.e. a variable bound in the current arrow abstraction.
3722 For such a situation there is a variant <literal>-<<</literal>, as in
3724 proc x -> f x -<< x+1
3726 which is equivalent to
3728 arr (\ x -> (f, x+1)) >>> app
3730 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3732 Such an arrow is equivalent to a monad, so if you're using this form
3733 you may find a monadic formulation more convenient.
3737 <title>do-notation for commands</title>
3740 Another form of command is a form of <literal>do</literal>-notation.
3741 For example, you can write
3750 You can read this much like ordinary <literal>do</literal>-notation,
3751 but with commands in place of monadic expressions.
3752 The first line sends the value of <literal>x+1</literal> as an input to
3753 the arrow <literal>f</literal>, and matches its output against
3754 <literal>y</literal>.
3755 In the next line, the output is discarded.
3756 The arrow <function>returnA</function> is defined in the
3757 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3758 module as <literal>arr id</literal>.
3759 The above example is treated as an abbreviation for
3761 arr (\ x -> (x, x)) >>>
3762 first (arr (\ x -> x+1) >>> f) >>>
3763 arr (\ (y, x) -> (y, (x, y))) >>>
3764 first (arr (\ y -> 2*y) >>> g) >>>
3766 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3767 first (arr (\ (x, z) -> x*z) >>> h) >>>
3768 arr (\ (t, z) -> t+z) >>>
3771 Note that variables not used later in the composition are projected out.
3772 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3774 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3775 module, this reduces to
3777 arr (\ x -> (x+1, x)) >>>
3779 arr (\ (y, x) -> (2*y, (x, y))) >>>
3781 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3783 arr (\ (t, z) -> t+z)
3785 which is what you might have written by hand.
3786 With arrow notation, GHC keeps track of all those tuples of variables for you.
3790 Note that although the above translation suggests that
3791 <literal>let</literal>-bound variables like <literal>z</literal> must be
3792 monomorphic, the actual translation produces Core,
3793 so polymorphic variables are allowed.
3797 It's also possible to have mutually recursive bindings,
3798 using the new <literal>rec</literal> keyword, as in the following example:
3800 counter :: ArrowCircuit a => a Bool Int
3801 counter = proc reset -> do
3802 rec output <- returnA -< if reset then 0 else next
3803 next <- delay 0 -< output+1
3804 returnA -< output
3806 The translation of such forms uses the <function>loop</function> combinator,
3807 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3813 <title>Conditional commands</title>
3816 In the previous example, we used a conditional expression to construct the
3818 Sometimes we want to conditionally execute different commands, as in
3825 which is translated to
3827 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3828 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3830 Since the translation uses <function>|||</function>,
3831 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3835 There are also <literal>case</literal> commands, like
3841 y <- h -< (x1, x2)
3845 The syntax is the same as for <literal>case</literal> expressions,
3846 except that the bodies of the alternatives are commands rather than expressions.
3847 The translation is similar to that of <literal>if</literal> commands.
3853 <title>Defining your own control structures</title>
3856 As we're seen, arrow notation provides constructs,
3857 modelled on those for expressions,
3858 for sequencing, value recursion and conditionals.
3859 But suitable combinators,
3860 which you can define in ordinary Haskell,
3861 may also be used to build new commands out of existing ones.
3862 The basic idea is that a command defines an arrow from environments to values.
3863 These environments assign values to the free local variables of the command.
3864 Thus combinators that produce arrows from arrows
3865 may also be used to build commands from commands.
3866 For example, the <literal>ArrowChoice</literal> class includes a combinator
3868 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3870 so we can use it to build commands:
3872 expr' = proc x -> do
3875 symbol Plus -< ()
3876 y <- term -< ()
3879 symbol Minus -< ()
3880 y <- term -< ()
3883 (The <literal>do</literal> on the first line is needed to prevent the first
3884 <literal><+> ...</literal> from being interpreted as part of the
3885 expression on the previous line.)
3886 This is equivalent to
3888 expr' = (proc x -> returnA -< x)
3889 <+> (proc x -> do
3890 symbol Plus -< ()
3891 y <- term -< ()
3893 <+> (proc x -> do
3894 symbol Minus -< ()
3895 y <- term -< ()
3898 It is essential that this operator be polymorphic in <literal>e</literal>
3899 (representing the environment input to the command
3900 and thence to its subcommands)
3901 and satisfy the corresponding naturality property
3903 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3905 at least for strict <literal>k</literal>.
3906 (This should be automatic if you're not using <function>seq</function>.)
3907 This ensures that environments seen by the subcommands are environments
3908 of the whole command,
3909 and also allows the translation to safely trim these environments.
3910 The operator must also not use any variable defined within the current
3915 We could define our own operator
3917 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3918 untilA body cond = proc x ->
3919 if cond x then returnA -< ()
3922 untilA body cond -< x
3924 and use it in the same way.
3925 Of course this infix syntax only makes sense for binary operators;
3926 there is also a more general syntax involving special brackets:
3930 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3937 <title>Primitive constructs</title>
3940 Some operators will need to pass additional inputs to their subcommands.
3941 For example, in an arrow type supporting exceptions,
3942 the operator that attaches an exception handler will wish to pass the
3943 exception that occurred to the handler.
3944 Such an operator might have a type
3946 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3948 where <literal>Ex</literal> is the type of exceptions handled.
3949 You could then use this with arrow notation by writing a command
3951 body `handleA` \ ex -> handler
3953 so that if an exception is raised in the command <literal>body</literal>,
3954 the variable <literal>ex</literal> is bound to the value of the exception
3955 and the command <literal>handler</literal>,
3956 which typically refers to <literal>ex</literal>, is entered.
3957 Though the syntax here looks like a functional lambda,
3958 we are talking about commands, and something different is going on.
3959 The input to the arrow represented by a command consists of values for
3960 the free local variables in the command, plus a stack of anonymous values.
3961 In all the prior examples, this stack was empty.
3962 In the second argument to <function>handleA</function>,
3963 this stack consists of one value, the value of the exception.
3964 The command form of lambda merely gives this value a name.
3969 the values on the stack are paired to the right of the environment.
3970 So operators like <function>handleA</function> that pass
3971 extra inputs to their subcommands can be designed for use with the notation
3972 by pairing the values with the environment in this way.
3973 More precisely, the type of each argument of the operator (and its result)
3974 should have the form
3976 a (...(e,t1), ... tn) t
3978 where <replaceable>e</replaceable> is a polymorphic variable
3979 (representing the environment)
3980 and <replaceable>ti</replaceable> are the types of the values on the stack,
3981 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3982 The polymorphic variable <replaceable>e</replaceable> must not occur in
3983 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3984 <replaceable>t</replaceable>.
3985 However the arrows involved need not be the same.
3986 Here are some more examples of suitable operators:
3988 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3989 runReader :: ... => a e c -> a' (e,State) c
3990 runState :: ... => a e c -> a' (e,State) (c,State)
3992 We can supply the extra input required by commands built with the last two
3993 by applying them to ordinary expressions, as in
3997 (|runReader (do { ... })|) s
3999 which adds <literal>s</literal> to the stack of inputs to the command
4000 built using <function>runReader</function>.
4004 The command versions of lambda abstraction and application are analogous to
4005 the expression versions.
4006 In particular, the beta and eta rules describe equivalences of commands.
4007 These three features (operators, lambda abstraction and application)
4008 are the core of the notation; everything else can be built using them,
4009 though the results would be somewhat clumsy.
4010 For example, we could simulate <literal>do</literal>-notation by defining
4012 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4013 u `bind` f = returnA &&& u >>> f
4015 bind_ :: Arrow a => a e b -> a e c -> a e c
4016 u `bind_` f = u `bind` (arr fst >>> f)
4018 We could simulate <literal>if</literal> by defining
4020 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4021 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4028 <title>Differences with the paper</title>
4033 <para>Instead of a single form of arrow application (arrow tail) with two
4034 translations, the implementation provides two forms
4035 <quote><literal>-<</literal></quote> (first-order)
4036 and <quote><literal>-<<</literal></quote> (higher-order).
4041 <para>User-defined operators are flagged with banana brackets instead of
4042 a new <literal>form</literal> keyword.
4051 <title>Portability</title>
4054 Although only GHC implements arrow notation directly,
4055 there is also a preprocessor
4057 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4058 that translates arrow notation into Haskell 98
4059 for use with other Haskell systems.
4060 You would still want to check arrow programs with GHC;
4061 tracing type errors in the preprocessor output is not easy.
4062 Modules intended for both GHC and the preprocessor must observe some
4063 additional restrictions:
4068 The module must import
4069 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4075 The preprocessor cannot cope with other Haskell extensions.
4076 These would have to go in separate modules.
4082 Because the preprocessor targets Haskell (rather than Core),
4083 <literal>let</literal>-bound variables are monomorphic.
4094 <!-- ==================== ASSERTIONS ================= -->
4096 <sect1 id="sec-assertions">
4098 <indexterm><primary>Assertions</primary></indexterm>
4102 If you want to make use of assertions in your standard Haskell code, you
4103 could define a function like the following:
4109 assert :: Bool -> a -> a
4110 assert False x = error "assertion failed!"
4117 which works, but gives you back a less than useful error message --
4118 an assertion failed, but which and where?
4122 One way out is to define an extended <function>assert</function> function which also
4123 takes a descriptive string to include in the error message and
4124 perhaps combine this with the use of a pre-processor which inserts
4125 the source location where <function>assert</function> was used.
4129 Ghc offers a helping hand here, doing all of this for you. For every
4130 use of <function>assert</function> in the user's source:
4136 kelvinToC :: Double -> Double
4137 kelvinToC k = assert (k >= 0.0) (k+273.15)
4143 Ghc will rewrite this to also include the source location where the
4150 assert pred val ==> assertError "Main.hs|15" pred val
4156 The rewrite is only performed by the compiler when it spots
4157 applications of <function>Control.Exception.assert</function>, so you
4158 can still define and use your own versions of
4159 <function>assert</function>, should you so wish. If not, import
4160 <literal>Control.Exception</literal> to make use
4161 <function>assert</function> in your code.
4165 To have the compiler ignore uses of assert, use the compiler option
4166 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4167 option</primary></indexterm> That is, expressions of the form
4168 <literal>assert pred e</literal> will be rewritten to
4169 <literal>e</literal>.
4173 Assertion failures can be caught, see the documentation for the
4174 <literal>Control.Exception</literal> library for the details.
4180 <!-- =============================== PRAGMAS =========================== -->
4182 <sect1 id="pragmas">
4183 <title>Pragmas</title>
4185 <indexterm><primary>pragma</primary></indexterm>
4187 <para>GHC supports several pragmas, or instructions to the
4188 compiler placed in the source code. Pragmas don't normally affect
4189 the meaning of the program, but they might affect the efficiency
4190 of the generated code.</para>
4192 <para>Pragmas all take the form
4194 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4196 where <replaceable>word</replaceable> indicates the type of
4197 pragma, and is followed optionally by information specific to that
4198 type of pragma. Case is ignored in
4199 <replaceable>word</replaceable>. The various values for
4200 <replaceable>word</replaceable> that GHC understands are described
4201 in the following sections; any pragma encountered with an
4202 unrecognised <replaceable>word</replaceable> is (silently)
4205 <sect2 id="deprecated-pragma">
4206 <title>DEPRECATED pragma</title>
4207 <indexterm><primary>DEPRECATED</primary>
4210 <para>The DEPRECATED pragma lets you specify that a particular
4211 function, class, or type, is deprecated. There are two
4216 <para>You can deprecate an entire module thus:</para>
4218 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4221 <para>When you compile any module that import
4222 <literal>Wibble</literal>, GHC will print the specified
4227 <para>You can deprecate a function, class, or type, with the
4228 following top-level declaration:</para>
4230 {-# DEPRECATED f, C, T "Don't use these" #-}
4232 <para>When you compile any module that imports and uses any
4233 of the specified entities, GHC will print the specified
4237 Any use of the deprecated item, or of anything from a deprecated
4238 module, will be flagged with an appropriate message. However,
4239 deprecations are not reported for
4240 (a) uses of a deprecated function within its defining module, and
4241 (b) uses of a deprecated function in an export list.
4242 The latter reduces spurious complaints within a library
4243 in which one module gathers together and re-exports
4244 the exports of several others.
4246 <para>You can suppress the warnings with the flag
4247 <option>-fno-warn-deprecations</option>.</para>
4250 <sect2 id="include-pragma">
4251 <title>INCLUDE pragma</title>
4253 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4254 of C header files that should be <literal>#include</literal>'d into
4255 the C source code generated by the compiler for the current module (if
4256 compiling via C). For example:</para>
4259 {-# INCLUDE "foo.h" #-}
4260 {-# INCLUDE <stdio.h> #-}</programlisting>
4262 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4263 your source file with any <literal>OPTIONS_GHC</literal>
4266 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4267 to the <option>-#include</option> option (<xref
4268 linkend="options-C-compiler" />), because the
4269 <literal>INCLUDE</literal> pragma is understood by other
4270 compilers. Yet another alternative is to add the include file to each
4271 <literal>foreign import</literal> declaration in your code, but we
4272 don't recommend using this approach with GHC.</para>
4275 <sect2 id="inline-noinline-pragma">
4276 <title>INLINE and NOINLINE pragmas</title>
4278 <para>These pragmas control the inlining of function
4281 <sect3 id="inline-pragma">
4282 <title>INLINE pragma</title>
4283 <indexterm><primary>INLINE</primary></indexterm>
4285 <para>GHC (with <option>-O</option>, as always) tries to
4286 inline (or “unfold”) functions/values that are
4287 “small enough,” thus avoiding the call overhead
4288 and possibly exposing other more-wonderful optimisations.
4289 Normally, if GHC decides a function is “too
4290 expensive” to inline, it will not do so, nor will it
4291 export that unfolding for other modules to use.</para>
4293 <para>The sledgehammer you can bring to bear is the
4294 <literal>INLINE</literal><indexterm><primary>INLINE
4295 pragma</primary></indexterm> pragma, used thusly:</para>
4298 key_function :: Int -> String -> (Bool, Double)
4300 #ifdef __GLASGOW_HASKELL__
4301 {-# INLINE key_function #-}
4305 <para>(You don't need to do the C pre-processor carry-on
4306 unless you're going to stick the code through HBC—it
4307 doesn't like <literal>INLINE</literal> pragmas.)</para>
4309 <para>The major effect of an <literal>INLINE</literal> pragma
4310 is to declare a function's “cost” to be very low.
4311 The normal unfolding machinery will then be very keen to
4314 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4315 function can be put anywhere its type signature could be
4318 <para><literal>INLINE</literal> pragmas are a particularly
4320 <literal>then</literal>/<literal>return</literal> (or
4321 <literal>bind</literal>/<literal>unit</literal>) functions in
4322 a monad. For example, in GHC's own
4323 <literal>UniqueSupply</literal> monad code, we have:</para>
4326 #ifdef __GLASGOW_HASKELL__
4327 {-# INLINE thenUs #-}
4328 {-# INLINE returnUs #-}
4332 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4333 linkend="noinline-pragma"/>).</para>
4336 <sect3 id="noinline-pragma">
4337 <title>NOINLINE pragma</title>
4339 <indexterm><primary>NOINLINE</primary></indexterm>
4340 <indexterm><primary>NOTINLINE</primary></indexterm>
4342 <para>The <literal>NOINLINE</literal> pragma does exactly what
4343 you'd expect: it stops the named function from being inlined
4344 by the compiler. You shouldn't ever need to do this, unless
4345 you're very cautious about code size.</para>
4347 <para><literal>NOTINLINE</literal> is a synonym for
4348 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4349 specified by Haskell 98 as the standard way to disable
4350 inlining, so it should be used if you want your code to be
4354 <sect3 id="phase-control">
4355 <title>Phase control</title>
4357 <para> Sometimes you want to control exactly when in GHC's
4358 pipeline the INLINE pragma is switched on. Inlining happens
4359 only during runs of the <emphasis>simplifier</emphasis>. Each
4360 run of the simplifier has a different <emphasis>phase
4361 number</emphasis>; the phase number decreases towards zero.
4362 If you use <option>-dverbose-core2core</option> you'll see the
4363 sequence of phase numbers for successive runs of the
4364 simplifier. In an INLINE pragma you can optionally specify a
4365 phase number, thus:</para>
4369 <para>You can say "inline <literal>f</literal> in Phase 2
4370 and all subsequent phases":
4372 {-# INLINE [2] f #-}
4378 <para>You can say "inline <literal>g</literal> in all
4379 phases up to, but not including, Phase 3":
4381 {-# INLINE [~3] g #-}
4387 <para>If you omit the phase indicator, you mean "inline in
4392 <para>You can use a phase number on a NOINLINE pragma too:</para>
4396 <para>You can say "do not inline <literal>f</literal>
4397 until Phase 2; in Phase 2 and subsequently behave as if
4398 there was no pragma at all":
4400 {-# NOINLINE [2] f #-}
4406 <para>You can say "do not inline <literal>g</literal> in
4407 Phase 3 or any subsequent phase; before that, behave as if
4408 there was no pragma":
4410 {-# NOINLINE [~3] g #-}
4416 <para>If you omit the phase indicator, you mean "never
4417 inline this function".</para>
4421 <para>The same phase-numbering control is available for RULES
4422 (<xref linkend="rewrite-rules"/>).</para>
4426 <sect2 id="line-pragma">
4427 <title>LINE pragma</title>
4429 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4430 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4431 <para>This pragma is similar to C's <literal>#line</literal>
4432 pragma, and is mainly for use in automatically generated Haskell
4433 code. It lets you specify the line number and filename of the
4434 original code; for example</para>
4437 {-# LINE 42 "Foo.vhs" #-}
4440 <para>if you'd generated the current file from something called
4441 <filename>Foo.vhs</filename> and this line corresponds to line
4442 42 in the original. GHC will adjust its error messages to refer
4443 to the line/file named in the <literal>LINE</literal>
4447 <sect2 id="options-pragma">
4448 <title>OPTIONS_GHC pragma</title>
4449 <indexterm><primary>OPTIONS_GHC</primary>
4451 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4454 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4455 additional options that are given to the compiler when compiling
4456 this source file. See <xref linkend="source-file-options"/> for
4459 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4460 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4464 <title>RULES pragma</title>
4466 <para>The RULES pragma lets you specify rewrite rules. It is
4467 described in <xref linkend="rewrite-rules"/>.</para>
4470 <sect2 id="specialize-pragma">
4471 <title>SPECIALIZE pragma</title>
4473 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4474 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4475 <indexterm><primary>overloading, death to</primary></indexterm>
4477 <para>(UK spelling also accepted.) For key overloaded
4478 functions, you can create extra versions (NB: more code space)
4479 specialised to particular types. Thus, if you have an
4480 overloaded function:</para>
4483 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4486 <para>If it is heavily used on lists with
4487 <literal>Widget</literal> keys, you could specialise it as
4491 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4494 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4495 be put anywhere its type signature could be put.</para>
4497 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4498 (a) a specialised version of the function and (b) a rewrite rule
4499 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4500 un-specialised function into a call to the specialised one.</para>
4502 <para>In earlier versions of GHC, it was possible to provide your own
4503 specialised function for a given type:
4506 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4509 This feature has been removed, as it is now subsumed by the
4510 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4514 <sect2 id="specialize-instance-pragma">
4515 <title>SPECIALIZE instance pragma
4519 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4520 <indexterm><primary>overloading, death to</primary></indexterm>
4521 Same idea, except for instance declarations. For example:
4524 instance (Eq a) => Eq (Foo a) where {
4525 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4529 The pragma must occur inside the <literal>where</literal> part
4530 of the instance declaration.
4533 Compatible with HBC, by the way, except perhaps in the placement
4539 <sect2 id="unpack-pragma">
4540 <title>UNPACK pragma</title>
4542 <indexterm><primary>UNPACK</primary></indexterm>
4544 <para>The <literal>UNPACK</literal> indicates to the compiler
4545 that it should unpack the contents of a constructor field into
4546 the constructor itself, removing a level of indirection. For
4550 data T = T {-# UNPACK #-} !Float
4551 {-# UNPACK #-} !Float
4554 <para>will create a constructor <literal>T</literal> containing
4555 two unboxed floats. This may not always be an optimisation: if
4556 the <function>T</function> constructor is scrutinised and the
4557 floats passed to a non-strict function for example, they will
4558 have to be reboxed (this is done automatically by the
4561 <para>Unpacking constructor fields should only be used in
4562 conjunction with <option>-O</option>, in order to expose
4563 unfoldings to the compiler so the reboxing can be removed as
4564 often as possible. For example:</para>
4568 f (T f1 f2) = f1 + f2
4571 <para>The compiler will avoid reboxing <function>f1</function>
4572 and <function>f2</function> by inlining <function>+</function>
4573 on floats, but only when <option>-O</option> is on.</para>
4575 <para>Any single-constructor data is eligible for unpacking; for
4579 data T = T {-# UNPACK #-} !(Int,Int)
4582 <para>will store the two <literal>Int</literal>s directly in the
4583 <function>T</function> constructor, by flattening the pair.
4584 Multi-level unpacking is also supported:</para>
4587 data T = T {-# UNPACK #-} !S
4588 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4591 <para>will store two unboxed <literal>Int#</literal>s
4592 directly in the <function>T</function> constructor. The
4593 unpacker can see through newtypes, too.</para>
4595 <para>If a field cannot be unpacked, you will not get a warning,
4596 so it might be an idea to check the generated code with
4597 <option>-ddump-simpl</option>.</para>
4599 <para>See also the <option>-funbox-strict-fields</option> flag,
4600 which essentially has the effect of adding
4601 <literal>{-# UNPACK #-}</literal> to every strict
4602 constructor field.</para>
4607 <!-- ======================= REWRITE RULES ======================== -->
4609 <sect1 id="rewrite-rules">
4610 <title>Rewrite rules
4612 <indexterm><primary>RULES pragma</primary></indexterm>
4613 <indexterm><primary>pragma, RULES</primary></indexterm>
4614 <indexterm><primary>rewrite rules</primary></indexterm></title>
4617 The programmer can specify rewrite rules as part of the source program
4618 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4619 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4620 and (b) the <option>-frules-off</option> flag
4621 (<xref linkend="options-f"/>) is not specified.
4629 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4636 <title>Syntax</title>
4639 From a syntactic point of view:
4645 There may be zero or more rules in a <literal>RULES</literal> pragma.
4652 Each rule has a name, enclosed in double quotes. The name itself has
4653 no significance at all. It is only used when reporting how many times the rule fired.
4659 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4660 immediately after the name of the rule. Thus:
4663 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4666 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4667 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4676 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4677 is set, so you must lay out your rules starting in the same column as the
4678 enclosing definitions.
4685 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4686 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4687 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4688 by spaces, just like in a type <literal>forall</literal>.
4694 A pattern variable may optionally have a type signature.
4695 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4696 For example, here is the <literal>foldr/build</literal> rule:
4699 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4700 foldr k z (build g) = g k z
4703 Since <function>g</function> has a polymorphic type, it must have a type signature.
4710 The left hand side of a rule must consist of a top-level variable applied
4711 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4714 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4715 "wrong2" forall f. f True = True
4718 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4725 A rule does not need to be in the same module as (any of) the
4726 variables it mentions, though of course they need to be in scope.
4732 Rules are automatically exported from a module, just as instance declarations are.
4743 <title>Semantics</title>
4746 From a semantic point of view:
4752 Rules are only applied if you use the <option>-O</option> flag.
4758 Rules are regarded as left-to-right rewrite rules.
4759 When GHC finds an expression that is a substitution instance of the LHS
4760 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4761 By "a substitution instance" we mean that the LHS can be made equal to the
4762 expression by substituting for the pattern variables.
4769 The LHS and RHS of a rule are typechecked, and must have the
4777 GHC makes absolutely no attempt to verify that the LHS and RHS
4778 of a rule have the same meaning. That is undecidable in general, and
4779 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4786 GHC makes no attempt to make sure that the rules are confluent or
4787 terminating. For example:
4790 "loop" forall x,y. f x y = f y x
4793 This rule will cause the compiler to go into an infinite loop.
4800 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4806 GHC currently uses a very simple, syntactic, matching algorithm
4807 for matching a rule LHS with an expression. It seeks a substitution
4808 which makes the LHS and expression syntactically equal modulo alpha
4809 conversion. The pattern (rule), but not the expression, is eta-expanded if
4810 necessary. (Eta-expanding the expression can lead to laziness bugs.)
4811 But not beta conversion (that's called higher-order matching).
4815 Matching is carried out on GHC's intermediate language, which includes
4816 type abstractions and applications. So a rule only matches if the
4817 types match too. See <xref linkend="rule-spec"/> below.
4823 GHC keeps trying to apply the rules as it optimises the program.
4824 For example, consider:
4833 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4834 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4835 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4836 not be substituted, and the rule would not fire.
4843 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4844 that appears on the LHS of a rule</emphasis>, because once you have substituted
4845 for something you can't match against it (given the simple minded
4846 matching). So if you write the rule
4849 "map/map" forall f,g. map f . map g = map (f.g)
4852 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4853 It will only match something written with explicit use of ".".
4854 Well, not quite. It <emphasis>will</emphasis> match the expression
4860 where <function>wibble</function> is defined:
4863 wibble f g = map f . map g
4866 because <function>wibble</function> will be inlined (it's small).
4868 Later on in compilation, GHC starts inlining even things on the
4869 LHS of rules, but still leaves the rules enabled. This inlining
4870 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4877 All rules are implicitly exported from the module, and are therefore
4878 in force in any module that imports the module that defined the rule, directly
4879 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4880 in force when compiling A.) The situation is very similar to that for instance
4892 <title>List fusion</title>
4895 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4896 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4897 intermediate list should be eliminated entirely.
4901 The following are good producers:
4913 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4919 Explicit lists (e.g. <literal>[True, False]</literal>)
4925 The cons constructor (e.g <literal>3:4:[]</literal>)
4931 <function>++</function>
4937 <function>map</function>
4943 <function>filter</function>
4949 <function>iterate</function>, <function>repeat</function>
4955 <function>zip</function>, <function>zipWith</function>
4964 The following are good consumers:
4976 <function>array</function> (on its second argument)
4982 <function>length</function>
4988 <function>++</function> (on its first argument)
4994 <function>foldr</function>
5000 <function>map</function>
5006 <function>filter</function>
5012 <function>concat</function>
5018 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5024 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5025 will fuse with one but not the other)
5031 <function>partition</function>
5037 <function>head</function>
5043 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5049 <function>sequence_</function>
5055 <function>msum</function>
5061 <function>sortBy</function>
5070 So, for example, the following should generate no intermediate lists:
5073 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5079 This list could readily be extended; if there are Prelude functions that you use
5080 a lot which are not included, please tell us.
5084 If you want to write your own good consumers or producers, look at the
5085 Prelude definitions of the above functions to see how to do so.
5090 <sect2 id="rule-spec">
5091 <title>Specialisation
5095 Rewrite rules can be used to get the same effect as a feature
5096 present in earlier versions of GHC.
5097 For example, suppose that:
5100 genericLookup :: Ord a => Table a b -> a -> b
5101 intLookup :: Table Int b -> Int -> b
5104 where <function>intLookup</function> is an implementation of
5105 <function>genericLookup</function> that works very fast for
5106 keys of type <literal>Int</literal>. You might wish
5107 to tell GHC to use <function>intLookup</function> instead of
5108 <function>genericLookup</function> whenever the latter was called with
5109 type <literal>Table Int b -> Int -> b</literal>.
5110 It used to be possible to write
5113 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5116 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5119 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5122 This slightly odd-looking rule instructs GHC to replace
5123 <function>genericLookup</function> by <function>intLookup</function>
5124 <emphasis>whenever the types match</emphasis>.
5125 What is more, this rule does not need to be in the same
5126 file as <function>genericLookup</function>, unlike the
5127 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5128 have an original definition available to specialise).
5131 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5132 <function>intLookup</function> really behaves as a specialised version
5133 of <function>genericLookup</function>!!!</para>
5135 <para>An example in which using <literal>RULES</literal> for
5136 specialisation will Win Big:
5139 toDouble :: Real a => a -> Double
5140 toDouble = fromRational . toRational
5142 {-# RULES "toDouble/Int" toDouble = i2d #-}
5143 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5146 The <function>i2d</function> function is virtually one machine
5147 instruction; the default conversion—via an intermediate
5148 <literal>Rational</literal>—is obscenely expensive by
5155 <title>Controlling what's going on</title>
5163 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5169 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5170 If you add <option>-dppr-debug</option> you get a more detailed listing.
5176 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5179 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5180 {-# INLINE build #-}
5184 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5185 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5186 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5187 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5194 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5195 see how to write rules that will do fusion and yet give an efficient
5196 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5206 <sect2 id="core-pragma">
5207 <title>CORE pragma</title>
5209 <indexterm><primary>CORE pragma</primary></indexterm>
5210 <indexterm><primary>pragma, CORE</primary></indexterm>
5211 <indexterm><primary>core, annotation</primary></indexterm>
5214 The external core format supports <quote>Note</quote> annotations;
5215 the <literal>CORE</literal> pragma gives a way to specify what these
5216 should be in your Haskell source code. Syntactically, core
5217 annotations are attached to expressions and take a Haskell string
5218 literal as an argument. The following function definition shows an
5222 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5225 Semantically, this is equivalent to:
5233 However, when external for is generated (via
5234 <option>-fext-core</option>), there will be Notes attached to the
5235 expressions <function>show</function> and <varname>x</varname>.
5236 The core function declaration for <function>f</function> is:
5240 f :: %forall a . GHCziShow.ZCTShow a ->
5241 a -> GHCziBase.ZMZN GHCziBase.Char =
5242 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5244 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5246 (tpl1::GHCziBase.Int ->
5248 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5250 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5251 (tpl3::GHCziBase.ZMZN a ->
5252 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5260 Here, we can see that the function <function>show</function> (which
5261 has been expanded out to a case expression over the Show dictionary)
5262 has a <literal>%note</literal> attached to it, as does the
5263 expression <varname>eta</varname> (which used to be called
5264 <varname>x</varname>).
5271 <sect1 id="generic-classes">
5272 <title>Generic classes</title>
5274 <para>(Note: support for generic classes is currently broken in
5278 The ideas behind this extension are described in detail in "Derivable type classes",
5279 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5280 An example will give the idea:
5288 fromBin :: [Int] -> (a, [Int])
5290 toBin {| Unit |} Unit = []
5291 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5292 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5293 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5295 fromBin {| Unit |} bs = (Unit, bs)
5296 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5297 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5298 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5299 (y,bs'') = fromBin bs'
5302 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5303 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5304 which are defined thus in the library module <literal>Generics</literal>:
5308 data a :+: b = Inl a | Inr b
5309 data a :*: b = a :*: b
5312 Now you can make a data type into an instance of Bin like this:
5314 instance (Bin a, Bin b) => Bin (a,b)
5315 instance Bin a => Bin [a]
5317 That is, just leave off the "where" clause. Of course, you can put in the
5318 where clause and over-ride whichever methods you please.
5322 <title> Using generics </title>
5323 <para>To use generics you need to</para>
5326 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5327 <option>-fgenerics</option> (to generate extra per-data-type code),
5328 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5332 <para>Import the module <literal>Generics</literal> from the
5333 <literal>lang</literal> package. This import brings into
5334 scope the data types <literal>Unit</literal>,
5335 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5336 don't need this import if you don't mention these types
5337 explicitly; for example, if you are simply giving instance
5338 declarations.)</para>
5343 <sect2> <title> Changes wrt the paper </title>
5345 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5346 can be written infix (indeed, you can now use
5347 any operator starting in a colon as an infix type constructor). Also note that
5348 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5349 Finally, note that the syntax of the type patterns in the class declaration
5350 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5351 alone would ambiguous when they appear on right hand sides (an extension we
5352 anticipate wanting).
5356 <sect2> <title>Terminology and restrictions</title>
5358 Terminology. A "generic default method" in a class declaration
5359 is one that is defined using type patterns as above.
5360 A "polymorphic default method" is a default method defined as in Haskell 98.
5361 A "generic class declaration" is a class declaration with at least one
5362 generic default method.
5370 Alas, we do not yet implement the stuff about constructor names and
5377 A generic class can have only one parameter; you can't have a generic
5378 multi-parameter class.
5384 A default method must be defined entirely using type patterns, or entirely
5385 without. So this is illegal:
5388 op :: a -> (a, Bool)
5389 op {| Unit |} Unit = (Unit, True)
5392 However it is perfectly OK for some methods of a generic class to have
5393 generic default methods and others to have polymorphic default methods.
5399 The type variable(s) in the type pattern for a generic method declaration
5400 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:
5404 op {| p :*: q |} (x :*: y) = op (x :: p)
5412 The type patterns in a generic default method must take one of the forms:
5418 where "a" and "b" are type variables. Furthermore, all the type patterns for
5419 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5420 must use the same type variables. So this is illegal:
5424 op {| a :+: b |} (Inl x) = True
5425 op {| p :+: q |} (Inr y) = False
5427 The type patterns must be identical, even in equations for different methods of the class.
5428 So this too is illegal:
5432 op1 {| a :*: b |} (x :*: y) = True
5435 op2 {| p :*: q |} (x :*: y) = False
5437 (The reason for this restriction is that we gather all the equations for a particular type consructor
5438 into a single generic instance declaration.)
5444 A generic method declaration must give a case for each of the three type constructors.
5450 The type for a generic method can be built only from:
5452 <listitem> <para> Function arrows </para> </listitem>
5453 <listitem> <para> Type variables </para> </listitem>
5454 <listitem> <para> Tuples </para> </listitem>
5455 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5457 Here are some example type signatures for generic methods:
5460 op2 :: Bool -> (a,Bool)
5461 op3 :: [Int] -> a -> a
5464 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5468 This restriction is an implementation restriction: we just havn't got around to
5469 implementing the necessary bidirectional maps over arbitrary type constructors.
5470 It would be relatively easy to add specific type constructors, such as Maybe and list,
5471 to the ones that are allowed.</para>
5476 In an instance declaration for a generic class, the idea is that the compiler
5477 will fill in the methods for you, based on the generic templates. However it can only
5482 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5487 No constructor of the instance type has unboxed fields.
5491 (Of course, these things can only arise if you are already using GHC extensions.)
5492 However, you can still give an instance declarations for types which break these rules,
5493 provided you give explicit code to override any generic default methods.
5501 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5502 what the compiler does with generic declarations.
5507 <sect2> <title> Another example </title>
5509 Just to finish with, here's another example I rather like:
5513 nCons {| Unit |} _ = 1
5514 nCons {| a :*: b |} _ = 1
5515 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5518 tag {| Unit |} _ = 1
5519 tag {| a :*: b |} _ = 1
5520 tag {| a :+: b |} (Inl x) = tag x
5521 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5530 ;;; Local Variables: ***
5532 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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