1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum plus deprecated
110 syntax of previous versions of the FFI for backwards
111 compatibility.</para>
113 <para>New reserved words: <literal>foreign</literal>.</para>
119 <option>-fno-monomorphism-restriction</option>:
120 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
123 <para> Switch off the Haskell 98 monomorphism restriction.
124 Independent of the <option>-fglasgow-exts</option>
131 <option>-fallow-overlapping-instances</option>
132 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
135 <option>-fallow-undecidable-instances</option>
136 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
139 <option>-fallow-incoherent-instances</option>
140 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
143 <option>-fcontext-stack</option>
144 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
147 <para> See <xref linkend="instance-decls"/>. Only relevant
148 if you also use <option>-fglasgow-exts</option>.</para>
154 <option>-finline-phase</option>
155 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
158 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
159 you also use <option>-fglasgow-exts</option>.</para>
165 <option>-farrows</option>
166 <indexterm><primary><option>-farrows</option></primary></indexterm>
169 <para>See <xref linkend="arrow-notation"/>. Independent of
170 <option>-fglasgow-exts</option>.</para>
172 <para>New reserved words/symbols: <literal>rec</literal>,
173 <literal>proc</literal>, <literal>-<</literal>,
174 <literal>>-</literal>, <literal>-<<</literal>,
175 <literal>>>-</literal>.</para>
177 <para>Other syntax stolen: <literal>(|</literal>,
178 <literal>|)</literal>.</para>
184 <option>-fgenerics</option>
185 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
188 <para>See <xref linkend="generic-classes"/>. Independent of
189 <option>-fglasgow-exts</option>.</para>
194 <term><option>-fno-implicit-prelude</option></term>
196 <para><indexterm><primary>-fno-implicit-prelude
197 option</primary></indexterm> GHC normally imports
198 <filename>Prelude.hi</filename> files for you. If you'd
199 rather it didn't, then give it a
200 <option>-fno-implicit-prelude</option> option. The idea is
201 that you can then import a Prelude of your own. (But don't
202 call it <literal>Prelude</literal>; the Haskell module
203 namespace is flat, and you must not conflict with any
204 Prelude module.)</para>
206 <para>Even though you have not imported the Prelude, most of
207 the built-in syntax still refers to the built-in Haskell
208 Prelude types and values, as specified by the Haskell
209 Report. For example, the type <literal>[Int]</literal>
210 still means <literal>Prelude.[] Int</literal>; tuples
211 continue to refer to the standard Prelude tuples; the
212 translation for list comprehensions continues to use
213 <literal>Prelude.map</literal> etc.</para>
215 <para>However, <option>-fno-implicit-prelude</option> does
216 change the handling of certain built-in syntax: see <xref
217 linkend="rebindable-syntax"/>.</para>
222 <term><option>-fimplicit-params</option></term>
224 <para>Enables implicit parameters (see <xref
225 linkend="implicit-parameters"/>). Currently also implied by
226 <option>-fglasgow-exts</option>.</para>
229 <literal>?<replaceable>varid</replaceable></literal>,
230 <literal>%<replaceable>varid</replaceable></literal>.</para>
235 <term><option>-fscoped-type-variables</option></term>
237 <para>Enables lexically-scoped type variables (see <xref
238 linkend="scoped-type-variables"/>). Implied by
239 <option>-fglasgow-exts</option>.</para>
244 <term><option>-fth</option></term>
246 <para>Enables Template Haskell (see <xref
247 linkend="template-haskell"/>). Currently also implied by
248 <option>-fglasgow-exts</option>.</para>
250 <para>Syntax stolen: <literal>[|</literal>,
251 <literal>[e|</literal>, <literal>[p|</literal>,
252 <literal>[d|</literal>, <literal>[t|</literal>,
253 <literal>$(</literal>,
254 <literal>$<replaceable>varid</replaceable></literal>.</para>
261 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
262 <!-- included from primitives.sgml -->
263 <!-- &primitives; -->
264 <sect1 id="primitives">
265 <title>Unboxed types and primitive operations</title>
267 <para>GHC is built on a raft of primitive data types and operations.
268 While you really can use this stuff to write fast code,
269 we generally find it a lot less painful, and more satisfying in the
270 long run, to use higher-level language features and libraries. With
271 any luck, the code you write will be optimised to the efficient
272 unboxed version in any case. And if it isn't, we'd like to know
275 <para>We do not currently have good, up-to-date documentation about the
276 primitives, perhaps because they are mainly intended for internal use.
277 There used to be a long section about them here in the User Guide, but it
278 became out of date, and wrong information is worse than none.</para>
280 <para>The Real Truth about what primitive types there are, and what operations
281 work over those types, is held in the file
282 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
283 This file is used directly to generate GHC's primitive-operation definitions, so
284 it is always correct! It is also intended for processing into text.</para>
287 the result of such processing is part of the description of the
289 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
290 Core language</ulink>.
291 So that document is a good place to look for a type-set version.
292 We would be very happy if someone wanted to volunteer to produce an SGML
293 back end to the program that processes <filename>primops.txt</filename> so that
294 we could include the results here in the User Guide.</para>
296 <para>What follows here is a brief summary of some main points.</para>
298 <sect2 id="glasgow-unboxed">
303 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
306 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
307 that values of that type are represented by a pointer to a heap
308 object. The representation of a Haskell <literal>Int</literal>, for
309 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
310 type, however, is represented by the value itself, no pointers or heap
311 allocation are involved.
315 Unboxed types correspond to the “raw machine” types you
316 would use in C: <literal>Int#</literal> (long int),
317 <literal>Double#</literal> (double), <literal>Addr#</literal>
318 (void *), etc. The <emphasis>primitive operations</emphasis>
319 (PrimOps) on these types are what you might expect; e.g.,
320 <literal>(+#)</literal> is addition on
321 <literal>Int#</literal>s, and is the machine-addition that we all
322 know and love—usually one instruction.
326 Primitive (unboxed) types cannot be defined in Haskell, and are
327 therefore built into the language and compiler. Primitive types are
328 always unlifted; that is, a value of a primitive type cannot be
329 bottom. We use the convention that primitive types, values, and
330 operations have a <literal>#</literal> suffix.
334 Primitive values are often represented by a simple bit-pattern, such
335 as <literal>Int#</literal>, <literal>Float#</literal>,
336 <literal>Double#</literal>. But this is not necessarily the case:
337 a primitive value might be represented by a pointer to a
338 heap-allocated object. Examples include
339 <literal>Array#</literal>, the type of primitive arrays. A
340 primitive array is heap-allocated because it is too big a value to fit
341 in a register, and would be too expensive to copy around; in a sense,
342 it is accidental that it is represented by a pointer. If a pointer
343 represents a primitive value, then it really does point to that value:
344 no unevaluated thunks, no indirections…nothing can be at the
345 other end of the pointer than the primitive value.
346 A numerically-intensive program using unboxed types can
347 go a <emphasis>lot</emphasis> faster than its “standard”
348 counterpart—we saw a threefold speedup on one example.
352 There are some restrictions on the use of primitive types:
354 <listitem><para>The main restriction
355 is that you can't pass a primitive value to a polymorphic
356 function or store one in a polymorphic data type. This rules out
357 things like <literal>[Int#]</literal> (i.e. lists of primitive
358 integers). The reason for this restriction is that polymorphic
359 arguments and constructor fields are assumed to be pointers: if an
360 unboxed integer is stored in one of these, the garbage collector would
361 attempt to follow it, leading to unpredictable space leaks. Or a
362 <function>seq</function> operation on the polymorphic component may
363 attempt to dereference the pointer, with disastrous results. Even
364 worse, the unboxed value might be larger than a pointer
365 (<literal>Double#</literal> for instance).
368 <listitem><para> You cannot bind a variable with an unboxed type
369 in a <emphasis>top-level</emphasis> binding.
371 <listitem><para> You cannot bind a variable with an unboxed type
372 in a <emphasis>recursive</emphasis> binding.
374 <listitem><para> You may bind unboxed variables in a (non-recursive,
375 non-top-level) pattern binding, but any such variable causes the entire
377 to become strict. For example:
379 data Foo = Foo Int Int#
381 f x = let (Foo a b, w) = ..rhs.. in ..body..
383 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
385 is strict, and the program behaves as if you had written
387 data Foo = Foo Int Int#
389 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
398 <sect2 id="unboxed-tuples">
399 <title>Unboxed Tuples
403 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
404 they're available by default with <option>-fglasgow-exts</option>. An
405 unboxed tuple looks like this:
417 where <literal>e_1..e_n</literal> are expressions of any
418 type (primitive or non-primitive). The type of an unboxed tuple looks
423 Unboxed tuples are used for functions that need to return multiple
424 values, but they avoid the heap allocation normally associated with
425 using fully-fledged tuples. When an unboxed tuple is returned, the
426 components are put directly into registers or on the stack; the
427 unboxed tuple itself does not have a composite representation. Many
428 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
430 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
431 tuples to avoid unnecessary allocation during sequences of operations.
435 There are some pretty stringent restrictions on the use of unboxed tuples:
440 Values of unboxed tuple types are subject to the same restrictions as
441 other unboxed types; i.e. they may not be stored in polymorphic data
442 structures or passed to polymorphic functions.
449 No variable can have an unboxed tuple type, nor may a constructor or function
450 argument have an unboxed tuple type. The following are all illegal:
454 data Foo = Foo (# Int, Int #)
456 f :: (# Int, Int #) -> (# Int, Int #)
459 g :: (# Int, Int #) -> Int
462 h x = let y = (# x,x #) in ...
469 The typical use of unboxed tuples is simply to return multiple values,
470 binding those multiple results with a <literal>case</literal> expression, thus:
472 f x y = (# x+1, y-1 #)
473 g x = case f x x of { (# a, b #) -> a + b }
475 You can have an unboxed tuple in a pattern binding, thus
477 f x = let (# p,q #) = h x in ..body..
479 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
480 the resulting binding is lazy like any other Haskell pattern binding. The
481 above example desugars like this:
483 f x = let t = case h x o f{ (# p,q #) -> (p,q)
488 Indeed, the bindings can even be recursive.
495 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
497 <sect1 id="syntax-extns">
498 <title>Syntactic extensions</title>
500 <!-- ====================== HIERARCHICAL MODULES ======================= -->
502 <sect2 id="hierarchical-modules">
503 <title>Hierarchical Modules</title>
505 <para>GHC supports a small extension to the syntax of module
506 names: a module name is allowed to contain a dot
507 <literal>‘.’</literal>. This is also known as the
508 “hierarchical module namespace” extension, because
509 it extends the normally flat Haskell module namespace into a
510 more flexible hierarchy of modules.</para>
512 <para>This extension has very little impact on the language
513 itself; modules names are <emphasis>always</emphasis> fully
514 qualified, so you can just think of the fully qualified module
515 name as <quote>the module name</quote>. In particular, this
516 means that the full module name must be given after the
517 <literal>module</literal> keyword at the beginning of the
518 module; for example, the module <literal>A.B.C</literal> must
521 <programlisting>module A.B.C</programlisting>
524 <para>It is a common strategy to use the <literal>as</literal>
525 keyword to save some typing when using qualified names with
526 hierarchical modules. For example:</para>
529 import qualified Control.Monad.ST.Strict as ST
532 <para>For details on how GHC searches for source and interface
533 files in the presence of hierarchical modules, see <xref
534 linkend="search-path"/>.</para>
536 <para>GHC comes with a large collection of libraries arranged
537 hierarchically; see the accompanying library documentation.
538 There is an ongoing project to create and maintain a stable set
539 of <quote>core</quote> libraries used by several Haskell
540 compilers, and the libraries that GHC comes with represent the
541 current status of that project. For more details, see <ulink
542 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
543 Libraries</ulink>.</para>
547 <!-- ====================== PATTERN GUARDS ======================= -->
549 <sect2 id="pattern-guards">
550 <title>Pattern guards</title>
553 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
554 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
558 Suppose we have an abstract data type of finite maps, with a
562 lookup :: FiniteMap -> Int -> Maybe Int
565 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
566 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
570 clunky env var1 var2 | ok1 && ok2 = val1 + val2
571 | otherwise = var1 + var2
582 The auxiliary functions are
586 maybeToBool :: Maybe a -> Bool
587 maybeToBool (Just x) = True
588 maybeToBool Nothing = False
590 expectJust :: Maybe a -> a
591 expectJust (Just x) = x
592 expectJust Nothing = error "Unexpected Nothing"
596 What is <function>clunky</function> doing? The guard <literal>ok1 &&
597 ok2</literal> checks that both lookups succeed, using
598 <function>maybeToBool</function> to convert the <function>Maybe</function>
599 types to booleans. The (lazily evaluated) <function>expectJust</function>
600 calls extract the values from the results of the lookups, and binds the
601 returned values to <varname>val1</varname> and <varname>val2</varname>
602 respectively. If either lookup fails, then clunky takes the
603 <literal>otherwise</literal> case and returns the sum of its arguments.
607 This is certainly legal Haskell, but it is a tremendously verbose and
608 un-obvious way to achieve the desired effect. Arguably, a more direct way
609 to write clunky would be to use case expressions:
613 clunky env var1 var1 = case lookup env var1 of
615 Just val1 -> case lookup env var2 of
617 Just val2 -> val1 + val2
623 This is a bit shorter, but hardly better. Of course, we can rewrite any set
624 of pattern-matching, guarded equations as case expressions; that is
625 precisely what the compiler does when compiling equations! The reason that
626 Haskell provides guarded equations is because they allow us to write down
627 the cases we want to consider, one at a time, independently of each other.
628 This structure is hidden in the case version. Two of the right-hand sides
629 are really the same (<function>fail</function>), and the whole expression
630 tends to become more and more indented.
634 Here is how I would write clunky:
639 | Just val1 <- lookup env var1
640 , Just val2 <- lookup env var2
642 ...other equations for clunky...
646 The semantics should be clear enough. The qualifiers are matched in order.
647 For a <literal><-</literal> qualifier, which I call a pattern guard, the
648 right hand side is evaluated and matched against the pattern on the left.
649 If the match fails then the whole guard fails and the next equation is
650 tried. If it succeeds, then the appropriate binding takes place, and the
651 next qualifier is matched, in the augmented environment. Unlike list
652 comprehensions, however, the type of the expression to the right of the
653 <literal><-</literal> is the same as the type of the pattern to its
654 left. The bindings introduced by pattern guards scope over all the
655 remaining guard qualifiers, and over the right hand side of the equation.
659 Just as with list comprehensions, boolean expressions can be freely mixed
660 with among the pattern guards. For example:
671 Haskell's current guards therefore emerge as a special case, in which the
672 qualifier list has just one element, a boolean expression.
676 <!-- ===================== Recursive do-notation =================== -->
678 <sect2 id="mdo-notation">
679 <title>The recursive do-notation
682 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
683 "A recursive do for Haskell",
684 Levent Erkok, John Launchbury",
685 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
688 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
689 that is, the variables bound in a do-expression are visible only in the textually following
690 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
691 group. It turns out that several applications can benefit from recursive bindings in
692 the do-notation, and this extension provides the necessary syntactic support.
695 Here is a simple (yet contrived) example:
698 import Control.Monad.Fix
700 justOnes = mdo xs <- Just (1:xs)
704 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
708 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
711 class Monad m => MonadFix m where
712 mfix :: (a -> m a) -> m a
715 The function <literal>mfix</literal>
716 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
717 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
718 For details, see the above mentioned reference.
721 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
722 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
723 for Haskell's internal state monad (strict and lazy, respectively).
726 There are three important points in using the recursive-do notation:
729 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
730 than <literal>do</literal>).
734 You should <literal>import Control.Monad.Fix</literal>.
735 (Note: Strictly speaking, this import is required only when you need to refer to the name
736 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
737 are encouraged to always import this module when using the mdo-notation.)
741 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
747 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
748 contains up to date information on recursive monadic bindings.
752 Historical note: The old implementation of the mdo-notation (and most
753 of the existing documents) used the name
754 <literal>MonadRec</literal> for the class and the corresponding library.
755 This name is not supported by GHC.
761 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
763 <sect2 id="parallel-list-comprehensions">
764 <title>Parallel List Comprehensions</title>
765 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
767 <indexterm><primary>parallel list comprehensions</primary>
770 <para>Parallel list comprehensions are a natural extension to list
771 comprehensions. List comprehensions can be thought of as a nice
772 syntax for writing maps and filters. Parallel comprehensions
773 extend this to include the zipWith family.</para>
775 <para>A parallel list comprehension has multiple independent
776 branches of qualifier lists, each separated by a `|' symbol. For
777 example, the following zips together two lists:</para>
780 [ (x, y) | x <- xs | y <- ys ]
783 <para>The behavior of parallel list comprehensions follows that of
784 zip, in that the resulting list will have the same length as the
785 shortest branch.</para>
787 <para>We can define parallel list comprehensions by translation to
788 regular comprehensions. Here's the basic idea:</para>
790 <para>Given a parallel comprehension of the form: </para>
793 [ e | p1 <- e11, p2 <- e12, ...
794 | q1 <- e21, q2 <- e22, ...
799 <para>This will be translated to: </para>
802 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
803 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
808 <para>where `zipN' is the appropriate zip for the given number of
813 <sect2 id="rebindable-syntax">
814 <title>Rebindable syntax</title>
817 <para>GHC allows most kinds of built-in syntax to be rebound by
818 the user, to facilitate replacing the <literal>Prelude</literal>
819 with a home-grown version, for example.</para>
821 <para>You may want to define your own numeric class
822 hierarchy. It completely defeats that purpose if the
823 literal "1" means "<literal>Prelude.fromInteger
824 1</literal>", which is what the Haskell Report specifies.
825 So the <option>-fno-implicit-prelude</option> flag causes
826 the following pieces of built-in syntax to refer to
827 <emphasis>whatever is in scope</emphasis>, not the Prelude
832 <para>An integer literal <literal>368</literal> means
833 "<literal>fromInteger (368::Integer)</literal>", rather than
834 "<literal>Prelude.fromInteger (368::Integer)</literal>".
837 <listitem><para>Fractional literals are handed in just the same way,
838 except that the translation is
839 <literal>fromRational (3.68::Rational)</literal>.
842 <listitem><para>The equality test in an overloaded numeric pattern
843 uses whatever <literal>(==)</literal> is in scope.
846 <listitem><para>The subtraction operation, and the
847 greater-than-or-equal test, in <literal>n+k</literal> patterns
848 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
852 <para>Negation (e.g. "<literal>- (f x)</literal>")
853 means "<literal>negate (f x)</literal>", both in numeric
854 patterns, and expressions.
858 <para>"Do" notation is translated using whatever
859 functions <literal>(>>=)</literal>,
860 <literal>(>>)</literal>, and <literal>fail</literal>,
861 are in scope (not the Prelude
862 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
863 comprehensions, are unaffected. </para></listitem>
867 notation (see <xref linkend="arrow-notation"/>)
868 uses whatever <literal>arr</literal>,
869 <literal>(>>>)</literal>, <literal>first</literal>,
870 <literal>app</literal>, <literal>(|||)</literal> and
871 <literal>loop</literal> functions are in scope. But unlike the
872 other constructs, the types of these functions must match the
873 Prelude types very closely. Details are in flux; if you want
877 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
878 even if that is a little unexpected. For emample, the
879 static semantics of the literal <literal>368</literal>
880 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
881 <literal>fromInteger</literal> to have any of the types:
883 fromInteger :: Integer -> Integer
884 fromInteger :: forall a. Foo a => Integer -> a
885 fromInteger :: Num a => a -> Integer
886 fromInteger :: Integer -> Bool -> Bool
890 <para>Be warned: this is an experimental facility, with
891 fewer checks than usual. Use <literal>-dcore-lint</literal>
892 to typecheck the desugared program. If Core Lint is happy
893 you should be all right.</para>
899 <!-- TYPE SYSTEM EXTENSIONS -->
900 <sect1 id="type-extensions">
901 <title>Type system extensions</title>
905 <title>Data types and type synonyms</title>
907 <sect3 id="nullary-types">
908 <title>Data types with no constructors</title>
910 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
911 a data type with no constructors. For example:</para>
915 data T a -- T :: * -> *
918 <para>Syntactically, the declaration lacks the "= constrs" part. The
919 type can be parameterised over types of any kind, but if the kind is
920 not <literal>*</literal> then an explicit kind annotation must be used
921 (see <xref linkend="sec-kinding"/>).</para>
923 <para>Such data types have only one value, namely bottom.
924 Nevertheless, they can be useful when defining "phantom types".</para>
927 <sect3 id="infix-tycons">
928 <title>Infix type constructors, classes, and type variables</title>
931 GHC allows type constructors, classes, and type variables to be operators, and
932 to be written infix, very much like expressions. More specifically:
935 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
936 The lexical syntax is the same as that for data constructors.
939 Data type and type-synonym declarations can be written infix, parenthesised
940 if you want further arguments. E.g.
942 data a :*: b = Foo a b
943 type a :+: b = Either a b
944 class a :=: b where ...
946 data (a :**: b) x = Baz a b x
947 type (a :++: b) y = Either (a,b) y
951 Types, and class constraints, can be written infix. For example
954 f :: (a :=: b) => a -> b
958 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
959 The lexical syntax is the same as that for variable operators, excluding "(.)",
960 "(!)", and "(*)". In a binding position, the operator must be
961 parenthesised. For example:
963 type T (+) = Int + Int
968 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
974 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
975 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
978 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
979 one cannot distinguish between the two in a fixity declaration; a fixity declaration
980 sets the fixity for a data constructor and the corresponding type constructor. For example:
984 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
985 and similarly for <literal>:*:</literal>.
986 <literal>Int `a` Bool</literal>.
989 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
996 <sect3 id="type-synonyms">
997 <title>Liberalised type synonyms</title>
1000 Type synonyms are like macros at the type level, and
1001 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1002 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1004 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1005 in a type synonym, thus:
1007 type Discard a = forall b. Show b => a -> b -> (a, String)
1012 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1019 You can write an unboxed tuple in a type synonym:
1021 type Pr = (# Int, Int #)
1029 You can apply a type synonym to a forall type:
1031 type Foo a = a -> a -> Bool
1033 f :: Foo (forall b. b->b)
1035 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1037 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1042 You can apply a type synonym to a partially applied type synonym:
1044 type Generic i o = forall x. i x -> o x
1047 foo :: Generic Id []
1049 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1051 foo :: forall x. x -> [x]
1059 GHC currently does kind checking before expanding synonyms (though even that
1063 After expanding type synonyms, GHC does validity checking on types, looking for
1064 the following mal-formedness which isn't detected simply by kind checking:
1067 Type constructor applied to a type involving for-alls.
1070 Unboxed tuple on left of an arrow.
1073 Partially-applied type synonym.
1077 this will be rejected:
1079 type Pr = (# Int, Int #)
1084 because GHC does not allow unboxed tuples on the left of a function arrow.
1089 <sect3 id="existential-quantification">
1090 <title>Existentially quantified data constructors
1094 The idea of using existential quantification in data type declarations
1095 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1096 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1097 London, 1991). It was later formalised by Laufer and Odersky
1098 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1099 TOPLAS, 16(5), pp1411-1430, 1994).
1100 It's been in Lennart
1101 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1102 proved very useful. Here's the idea. Consider the declaration:
1108 data Foo = forall a. MkFoo a (a -> Bool)
1115 The data type <literal>Foo</literal> has two constructors with types:
1121 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1128 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1129 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1130 For example, the following expression is fine:
1136 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1142 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1143 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1144 isUpper</function> packages a character with a compatible function. These
1145 two things are each of type <literal>Foo</literal> and can be put in a list.
1149 What can we do with a value of type <literal>Foo</literal>?. In particular,
1150 what happens when we pattern-match on <function>MkFoo</function>?
1156 f (MkFoo val fn) = ???
1162 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1163 are compatible, the only (useful) thing we can do with them is to
1164 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1171 f (MkFoo val fn) = fn val
1177 What this allows us to do is to package heterogenous values
1178 together with a bunch of functions that manipulate them, and then treat
1179 that collection of packages in a uniform manner. You can express
1180 quite a bit of object-oriented-like programming this way.
1183 <sect4 id="existential">
1184 <title>Why existential?
1188 What has this to do with <emphasis>existential</emphasis> quantification?
1189 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1195 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1201 But Haskell programmers can safely think of the ordinary
1202 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1203 adding a new existential quantification construct.
1209 <title>Type classes</title>
1212 An easy extension is to allow
1213 arbitrary contexts before the constructor. For example:
1219 data Baz = forall a. Eq a => Baz1 a a
1220 | forall b. Show b => Baz2 b (b -> b)
1226 The two constructors have the types you'd expect:
1232 Baz1 :: forall a. Eq a => a -> a -> Baz
1233 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1239 But when pattern matching on <function>Baz1</function> the matched values can be compared
1240 for equality, and when pattern matching on <function>Baz2</function> the first matched
1241 value can be converted to a string (as well as applying the function to it).
1242 So this program is legal:
1249 f (Baz1 p q) | p == q = "Yes"
1251 f (Baz2 v fn) = show (fn v)
1257 Operationally, in a dictionary-passing implementation, the
1258 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1259 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1260 extract it on pattern matching.
1264 Notice the way that the syntax fits smoothly with that used for
1265 universal quantification earlier.
1271 <title>Record Constructors</title>
1274 GHC allows existentials to be used with records syntax as well. For example:
1277 data Counter a = forall self. NewCounter
1279 , _inc :: self -> self
1280 , _display :: self -> IO ()
1284 Here <literal>tag</literal> is a public field, with a well-typed selector
1285 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1286 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1287 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1288 compile-time error. In other words, <emphasis>GHC defines a record selector function
1289 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1290 (This example used an underscore in the fields for which record selectors
1291 will not be defined, but that is only programming style; GHC ignores them.)
1295 To make use of these hidden fields, we need to create some helper functions:
1298 inc :: Counter a -> Counter a
1299 inc (NewCounter x i d t) = NewCounter
1300 { _this = i x, _inc = i, _display = d, tag = t }
1302 display :: Counter a -> IO ()
1303 display NewCounter{ _this = x, _display = d } = d x
1306 Now we can define counters with different underlying implementations:
1309 counterA :: Counter String
1310 counterA = NewCounter
1311 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1313 counterB :: Counter String
1314 counterB = NewCounter
1315 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1318 display (inc counterA) -- prints "1"
1319 display (inc (inc counterB)) -- prints "##"
1322 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1323 <literal>forall</literal> may be omitted. For example, we can express
1324 the same <literal>Counter a</literal> using GADT:
1327 data Counter a where
1328 NewCounter { _this :: self
1329 , _inc :: self -> self
1330 , _display :: self -> IO ()
1336 At the moment, record update syntax is only supported for Haskell 98 data types,
1337 so the following function does <emphasis>not</emphasis> work:
1340 -- This is invalid; use explicit NewCounter instead for now
1341 setTag :: Counter a -> a -> Counter a
1342 setTag obj t = obj{ tag = t }
1351 <title>Restrictions</title>
1354 There are several restrictions on the ways in which existentially-quantified
1355 constructors can be use.
1364 When pattern matching, each pattern match introduces a new,
1365 distinct, type for each existential type variable. These types cannot
1366 be unified with any other type, nor can they escape from the scope of
1367 the pattern match. For example, these fragments are incorrect:
1375 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1376 is the result of <function>f1</function>. One way to see why this is wrong is to
1377 ask what type <function>f1</function> has:
1381 f1 :: Foo -> a -- Weird!
1385 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1390 f1 :: forall a. Foo -> a -- Wrong!
1394 The original program is just plain wrong. Here's another sort of error
1398 f2 (Baz1 a b) (Baz1 p q) = a==q
1402 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1403 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1404 from the two <function>Baz1</function> constructors.
1412 You can't pattern-match on an existentially quantified
1413 constructor in a <literal>let</literal> or <literal>where</literal> group of
1414 bindings. So this is illegal:
1418 f3 x = a==b where { Baz1 a b = x }
1421 Instead, use a <literal>case</literal> expression:
1424 f3 x = case x of Baz1 a b -> a==b
1427 In general, you can only pattern-match
1428 on an existentially-quantified constructor in a <literal>case</literal> expression or
1429 in the patterns of a function definition.
1431 The reason for this restriction is really an implementation one.
1432 Type-checking binding groups is already a nightmare without
1433 existentials complicating the picture. Also an existential pattern
1434 binding at the top level of a module doesn't make sense, because it's
1435 not clear how to prevent the existentially-quantified type "escaping".
1436 So for now, there's a simple-to-state restriction. We'll see how
1444 You can't use existential quantification for <literal>newtype</literal>
1445 declarations. So this is illegal:
1449 newtype T = forall a. Ord a => MkT a
1453 Reason: a value of type <literal>T</literal> must be represented as a
1454 pair of a dictionary for <literal>Ord t</literal> and a value of type
1455 <literal>t</literal>. That contradicts the idea that
1456 <literal>newtype</literal> should have no concrete representation.
1457 You can get just the same efficiency and effect by using
1458 <literal>data</literal> instead of <literal>newtype</literal>. If
1459 there is no overloading involved, then there is more of a case for
1460 allowing an existentially-quantified <literal>newtype</literal>,
1461 because the <literal>data</literal> version does carry an
1462 implementation cost, but single-field existentially quantified
1463 constructors aren't much use. So the simple restriction (no
1464 existential stuff on <literal>newtype</literal>) stands, unless there
1465 are convincing reasons to change it.
1473 You can't use <literal>deriving</literal> to define instances of a
1474 data type with existentially quantified data constructors.
1476 Reason: in most cases it would not make sense. For example:#
1479 data T = forall a. MkT [a] deriving( Eq )
1482 To derive <literal>Eq</literal> in the standard way we would need to have equality
1483 between the single component of two <function>MkT</function> constructors:
1487 (MkT a) == (MkT b) = ???
1490 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1491 It's just about possible to imagine examples in which the derived instance
1492 would make sense, but it seems altogether simpler simply to prohibit such
1493 declarations. Define your own instances!
1508 <sect2 id="multi-param-type-classes">
1509 <title>Class declarations</title>
1512 This section, and the next one, documents GHC's type-class extensions.
1513 There's lots of background in the paper <ulink
1514 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1515 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1516 Jones, Erik Meijer).
1519 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1523 <title>Multi-parameter type classes</title>
1525 Multi-parameter type classes are permitted. For example:
1529 class Collection c a where
1530 union :: c a -> c a -> c a
1538 <title>The superclasses of a class declaration</title>
1541 There are no restrictions on the context in a class declaration
1542 (which introduces superclasses), except that the class hierarchy must
1543 be acyclic. So these class declarations are OK:
1547 class Functor (m k) => FiniteMap m k where
1550 class (Monad m, Monad (t m)) => Transform t m where
1551 lift :: m a -> (t m) a
1557 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1558 of "acyclic" involves only the superclass relationships. For example,
1564 op :: D b => a -> b -> b
1567 class C a => D a where { ... }
1571 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1572 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1573 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1580 <sect3 id="class-method-types">
1581 <title>Class method types</title>
1584 Haskell 98 prohibits class method types to mention constraints on the
1585 class type variable, thus:
1588 fromList :: [a] -> s a
1589 elem :: Eq a => a -> s a -> Bool
1591 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1592 contains the constraint <literal>Eq a</literal>, constrains only the
1593 class type variable (in this case <literal>a</literal>).
1594 GHC lifts this restriction.
1601 <sect2 id="functional-dependencies">
1602 <title>Functional dependencies
1605 <para> Functional dependencies are implemented as described by Mark Jones
1606 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1607 In Proceedings of the 9th European Symposium on Programming,
1608 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1612 Functional dependencies are introduced by a vertical bar in the syntax of a
1613 class declaration; e.g.
1615 class (Monad m) => MonadState s m | m -> s where ...
1617 class Foo a b c | a b -> c where ...
1619 There should be more documentation, but there isn't (yet). Yell if you need it.
1622 <sect3><title>Rules for functional dependencies </title>
1624 In a class declaration, all of the class type variables must be reachable (in the sense
1625 mentioned in <xref linkend="type-restrictions"/>)
1626 from the free variables of each method type.
1630 class Coll s a where
1632 insert :: s -> a -> s
1635 is not OK, because the type of <literal>empty</literal> doesn't mention
1636 <literal>a</literal>. Functional dependencies can make the type variable
1639 class Coll s a | s -> a where
1641 insert :: s -> a -> s
1644 Alternatively <literal>Coll</literal> might be rewritten
1647 class Coll s a where
1649 insert :: s a -> a -> s a
1653 which makes the connection between the type of a collection of
1654 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1655 Occasionally this really doesn't work, in which case you can split the
1663 class CollE s => Coll s a where
1664 insert :: s -> a -> s
1671 <title>Background on functional dependencies</title>
1673 <para>The following description of the motivation and use of functional dependencies is taken
1674 from the Hugs user manual, reproduced here (with minor changes) by kind
1675 permission of Mark Jones.
1678 Consider the following class, intended as part of a
1679 library for collection types:
1681 class Collects e ce where
1683 insert :: e -> ce -> ce
1684 member :: e -> ce -> Bool
1686 The type variable e used here represents the element type, while ce is the type
1687 of the container itself. Within this framework, we might want to define
1688 instances of this class for lists or characteristic functions (both of which
1689 can be used to represent collections of any equality type), bit sets (which can
1690 be used to represent collections of characters), or hash tables (which can be
1691 used to represent any collection whose elements have a hash function). Omitting
1692 standard implementation details, this would lead to the following declarations:
1694 instance Eq e => Collects e [e] where ...
1695 instance Eq e => Collects e (e -> Bool) where ...
1696 instance Collects Char BitSet where ...
1697 instance (Hashable e, Collects a ce)
1698 => Collects e (Array Int ce) where ...
1700 All this looks quite promising; we have a class and a range of interesting
1701 implementations. Unfortunately, there are some serious problems with the class
1702 declaration. First, the empty function has an ambiguous type:
1704 empty :: Collects e ce => ce
1706 By "ambiguous" we mean that there is a type variable e that appears on the left
1707 of the <literal>=></literal> symbol, but not on the right. The problem with
1708 this is that, according to the theoretical foundations of Haskell overloading,
1709 we cannot guarantee a well-defined semantics for any term with an ambiguous
1713 We can sidestep this specific problem by removing the empty member from the
1714 class declaration. However, although the remaining members, insert and member,
1715 do not have ambiguous types, we still run into problems when we try to use
1716 them. For example, consider the following two functions:
1718 f x y = insert x . insert y
1721 for which GHC infers the following types:
1723 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1724 g :: (Collects Bool c, Collects Char c) => c -> c
1726 Notice that the type for f allows the two parameters x and y to be assigned
1727 different types, even though it attempts to insert each of the two values, one
1728 after the other, into the same collection. If we're trying to model collections
1729 that contain only one type of value, then this is clearly an inaccurate
1730 type. Worse still, the definition for g is accepted, without causing a type
1731 error. As a result, the error in this code will not be flagged at the point
1732 where it appears. Instead, it will show up only when we try to use g, which
1733 might even be in a different module.
1736 <sect4><title>An attempt to use constructor classes</title>
1739 Faced with the problems described above, some Haskell programmers might be
1740 tempted to use something like the following version of the class declaration:
1742 class Collects e c where
1744 insert :: e -> c e -> c e
1745 member :: e -> c e -> Bool
1747 The key difference here is that we abstract over the type constructor c that is
1748 used to form the collection type c e, and not over that collection type itself,
1749 represented by ce in the original class declaration. This avoids the immediate
1750 problems that we mentioned above: empty has type <literal>Collects e c => c
1751 e</literal>, which is not ambiguous.
1754 The function f from the previous section has a more accurate type:
1756 f :: (Collects e c) => e -> e -> c e -> c e
1758 The function g from the previous section is now rejected with a type error as
1759 we would hope because the type of f does not allow the two arguments to have
1761 This, then, is an example of a multiple parameter class that does actually work
1762 quite well in practice, without ambiguity problems.
1763 There is, however, a catch. This version of the Collects class is nowhere near
1764 as general as the original class seemed to be: only one of the four instances
1765 for <literal>Collects</literal>
1766 given above can be used with this version of Collects because only one of
1767 them---the instance for lists---has a collection type that can be written in
1768 the form c e, for some type constructor c, and element type e.
1772 <sect4><title>Adding functional dependencies</title>
1775 To get a more useful version of the Collects class, Hugs provides a mechanism
1776 that allows programmers to specify dependencies between the parameters of a
1777 multiple parameter class (For readers with an interest in theoretical
1778 foundations and previous work: The use of dependency information can be seen
1779 both as a generalization of the proposal for `parametric type classes' that was
1780 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1781 later framework for "improvement" of qualified types. The
1782 underlying ideas are also discussed in a more theoretical and abstract setting
1783 in a manuscript [implparam], where they are identified as one point in a
1784 general design space for systems of implicit parameterization.).
1786 To start with an abstract example, consider a declaration such as:
1788 class C a b where ...
1790 which tells us simply that C can be thought of as a binary relation on types
1791 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1792 included in the definition of classes to add information about dependencies
1793 between parameters, as in the following examples:
1795 class D a b | a -> b where ...
1796 class E a b | a -> b, b -> a where ...
1798 The notation <literal>a -> b</literal> used here between the | and where
1799 symbols --- not to be
1800 confused with a function type --- indicates that the a parameter uniquely
1801 determines the b parameter, and might be read as "a determines b." Thus D is
1802 not just a relation, but actually a (partial) function. Similarly, from the two
1803 dependencies that are included in the definition of E, we can see that E
1804 represents a (partial) one-one mapping between types.
1807 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1808 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1809 m>=0, meaning that the y parameters are uniquely determined by the x
1810 parameters. Spaces can be used as separators if more than one variable appears
1811 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1812 annotated with multiple dependencies using commas as separators, as in the
1813 definition of E above. Some dependencies that we can write in this notation are
1814 redundant, and will be rejected because they don't serve any useful
1815 purpose, and may instead indicate an error in the program. Examples of
1816 dependencies like this include <literal>a -> a </literal>,
1817 <literal>a -> a a </literal>,
1818 <literal>a -> </literal>, etc. There can also be
1819 some redundancy if multiple dependencies are given, as in
1820 <literal>a->b</literal>,
1821 <literal>b->c </literal>, <literal>a->c </literal>, and
1822 in which some subset implies the remaining dependencies. Examples like this are
1823 not treated as errors. Note that dependencies appear only in class
1824 declarations, and not in any other part of the language. In particular, the
1825 syntax for instance declarations, class constraints, and types is completely
1829 By including dependencies in a class declaration, we provide a mechanism for
1830 the programmer to specify each multiple parameter class more precisely. The
1831 compiler, on the other hand, is responsible for ensuring that the set of
1832 instances that are in scope at any given point in the program is consistent
1833 with any declared dependencies. For example, the following pair of instance
1834 declarations cannot appear together in the same scope because they violate the
1835 dependency for D, even though either one on its own would be acceptable:
1837 instance D Bool Int where ...
1838 instance D Bool Char where ...
1840 Note also that the following declaration is not allowed, even by itself:
1842 instance D [a] b where ...
1844 The problem here is that this instance would allow one particular choice of [a]
1845 to be associated with more than one choice for b, which contradicts the
1846 dependency specified in the definition of D. More generally, this means that,
1847 in any instance of the form:
1849 instance D t s where ...
1851 for some particular types t and s, the only variables that can appear in s are
1852 the ones that appear in t, and hence, if the type t is known, then s will be
1853 uniquely determined.
1856 The benefit of including dependency information is that it allows us to define
1857 more general multiple parameter classes, without ambiguity problems, and with
1858 the benefit of more accurate types. To illustrate this, we return to the
1859 collection class example, and annotate the original definition of <literal>Collects</literal>
1860 with a simple dependency:
1862 class Collects e ce | ce -> e where
1864 insert :: e -> ce -> ce
1865 member :: e -> ce -> Bool
1867 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1868 determined by the type of the collection ce. Note that both parameters of
1869 Collects are of kind *; there are no constructor classes here. Note too that
1870 all of the instances of Collects that we gave earlier can be used
1871 together with this new definition.
1874 What about the ambiguity problems that we encountered with the original
1875 definition? The empty function still has type Collects e ce => ce, but it is no
1876 longer necessary to regard that as an ambiguous type: Although the variable e
1877 does not appear on the right of the => symbol, the dependency for class
1878 Collects tells us that it is uniquely determined by ce, which does appear on
1879 the right of the => symbol. Hence the context in which empty is used can still
1880 give enough information to determine types for both ce and e, without
1881 ambiguity. More generally, we need only regard a type as ambiguous if it
1882 contains a variable on the left of the => that is not uniquely determined
1883 (either directly or indirectly) by the variables on the right.
1886 Dependencies also help to produce more accurate types for user defined
1887 functions, and hence to provide earlier detection of errors, and less cluttered
1888 types for programmers to work with. Recall the previous definition for a
1891 f x y = insert x y = insert x . insert y
1893 for which we originally obtained a type:
1895 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1897 Given the dependency information that we have for Collects, however, we can
1898 deduce that a and b must be equal because they both appear as the second
1899 parameter in a Collects constraint with the same first parameter c. Hence we
1900 can infer a shorter and more accurate type for f:
1902 f :: (Collects a c) => a -> a -> c -> c
1904 In a similar way, the earlier definition of g will now be flagged as a type error.
1907 Although we have given only a few examples here, it should be clear that the
1908 addition of dependency information can help to make multiple parameter classes
1909 more useful in practice, avoiding ambiguity problems, and allowing more general
1910 sets of instance declarations.
1916 <sect2 id="instance-decls">
1917 <title>Instance declarations</title>
1919 <sect3 id="instance-rules">
1920 <title>Relaxed rules for instance declarations</title>
1922 <para>An instance declaration has the form
1924 instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
1926 The part before the "<literal>=></literal>" is the
1927 <emphasis>context</emphasis>, while the part after the
1928 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1932 In Haskell 98 the head of an instance declaration
1933 must be of the form <literal>C (T a1 ... an)</literal>, where
1934 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1935 and the <literal>a1 ... an</literal> are distinct type variables.
1936 Furthermore, the assertions in the context of the instance declaration
1937 must be of the form <literal>C a</literal> where <literal>a</literal>
1938 is a type variable that occurs in the head.
1941 The <option>-fglasgow-exts</option> flag loosens these restrictions
1942 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1943 the context and head of the instance declaration can each consist of arbitrary
1944 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1948 For each assertion in the context:
1950 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1951 <listitem><para>The assertion has fewer constructors and variables (taken together
1952 and counting repetitions) than the head</para></listitem>
1956 <listitem><para>The coverage condition. For each functional dependency,
1957 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
1958 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
1959 every type variable in
1960 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
1961 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
1962 substitution mapping each type variable in the class declaration to the
1963 corresponding type in the instance declaration.
1966 These restrictions ensure that context reduction terminates: each reduction
1967 step makes the problem smaller by at least one
1968 constructor. For example, the following would make the type checker
1969 loop if it wasn't excluded:
1971 instance C a => C a where ...
1973 For example, these are OK:
1975 instance C Int [a] -- Multiple parameters
1976 instance Eq (S [a]) -- Structured type in head
1978 -- Repeated type variable in head
1979 instance C4 a a => C4 [a] [a]
1980 instance Stateful (ST s) (MutVar s)
1982 -- Head can consist of type variables only
1984 instance (Eq a, Show b) => C2 a b
1986 -- Non-type variables in context
1987 instance Show (s a) => Show (Sized s a)
1988 instance C2 Int a => C3 Bool [a]
1989 instance C2 Int a => C3 [a] b
1993 -- Context assertion no smaller than head
1994 instance C a => C a where ...
1995 -- (C b b) has more more occurrences of b than the head
1996 instance C b b => Foo [b] where ...
2001 The same restrictions apply to instances generated by
2002 <literal>deriving</literal> clauses. Thus the following is accepted:
2004 data MinHeap h a = H a (h a)
2007 because the derived instance
2009 instance (Show a, Show (h a)) => Show (MinHeap h a)
2011 conforms to the above rules.
2015 A useful idiom permitted by the above rules is as follows.
2016 If one allows overlapping instance declarations then it's quite
2017 convenient to have a "default instance" declaration that applies if
2018 something more specific does not:
2026 <sect3 id="undecidable-instances">
2027 <title>Undecidable instances</title>
2030 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2031 For example, sometimes you might want to use the following to get the
2032 effect of a "class synonym":
2034 class (C1 a, C2 a, C3 a) => C a where { }
2036 instance (C1 a, C2 a, C3 a) => C a where { }
2038 This allows you to write shorter signatures:
2044 f :: (C1 a, C2 a, C3 a) => ...
2046 The restrictions on functional dependencies (<xref
2047 linkend="functional-dependencies"/>) are particularly troublesome.
2048 It is tempting to introduce type variables in the context that do not appear in
2049 the head, something that is excluded by the normal rules. For example:
2051 class HasConverter a b | a -> b where
2054 data Foo a = MkFoo a
2056 instance (HasConverter a b,Show b) => Show (Foo a) where
2057 show (MkFoo value) = show (convert value)
2059 This is dangerous territory, however. Here, for example, is a program that would make the
2064 instance F [a] [[a]]
2065 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2067 Similarly, it can be tempting to lift the coverage condition:
2069 class Mul a b c | a b -> c where
2070 (.*.) :: a -> b -> c
2072 instance Mul Int Int Int where (.*.) = (*)
2073 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2074 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2076 The third instance declaration does not obey the coverage condition;
2077 and indeed the (somewhat strange) definition:
2079 f = \ b x y -> if b then x .*. [y] else y
2081 makes instance inference go into a loop, because it requires the constraint
2082 <literal>(Mul a [b] b)</literal>.
2085 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2086 the experimental flag <option>-fallow-undecidable-instances</option>
2087 <indexterm><primary>-fallow-undecidable-instances
2088 option</primary></indexterm>, you can use arbitrary
2089 types in both an instance context and instance head. Termination is ensured by having a
2090 fixed-depth recursion stack. If you exceed the stack depth you get a
2091 sort of backtrace, and the opportunity to increase the stack depth
2092 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
2098 <sect3 id="instance-overlap">
2099 <title>Overlapping instances</title>
2101 In general, <emphasis>GHC requires that that it be unambiguous which instance
2103 should be used to resolve a type-class constraint</emphasis>. This behaviour
2104 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2105 <indexterm><primary>-fallow-overlapping-instances
2106 </primary></indexterm>
2107 and <option>-fallow-incoherent-instances</option>
2108 <indexterm><primary>-fallow-incoherent-instances
2109 </primary></indexterm>, as this section discusses.</para>
2111 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2112 it tries to match every instance declaration against the
2114 by instantiating the head of the instance declaration. For example, consider
2117 instance context1 => C Int a where ... -- (A)
2118 instance context2 => C a Bool where ... -- (B)
2119 instance context3 => C Int [a] where ... -- (C)
2120 instance context4 => C Int [Int] where ... -- (D)
2122 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2123 but (C) and (D) do not. When matching, GHC takes
2124 no account of the context of the instance declaration
2125 (<literal>context1</literal> etc).
2126 GHC's default behaviour is that <emphasis>exactly one instance must match the
2127 constraint it is trying to resolve</emphasis>.
2128 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2129 including both declarations (A) and (B), say); an error is only reported if a
2130 particular constraint matches more than one.
2134 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2135 more than one instance to match, provided there is a most specific one. For
2136 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2137 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2138 most-specific match, the program is rejected.
2141 However, GHC is conservative about committing to an overlapping instance. For example:
2146 Suppose that from the RHS of <literal>f</literal> we get the constraint
2147 <literal>C Int [b]</literal>. But
2148 GHC does not commit to instance (C), because in a particular
2149 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2150 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2151 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2152 GHC will instead pick (C), without complaining about
2153 the problem of subsequent instantiations.
2156 The willingness to be overlapped or incoherent is a property of
2157 the <emphasis>instance declaration</emphasis> itself, controlled by the
2158 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2159 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2160 being defined. Neither flag is required in a module that imports and uses the
2161 instance declaration. Specifically, during the lookup process:
2164 An instance declaration is ignored during the lookup process if (a) a more specific
2165 match is found, and (b) the instance declaration was compiled with
2166 <option>-fallow-overlapping-instances</option>. The flag setting for the
2167 more-specific instance does not matter.
2170 Suppose an instance declaration does not matche the constraint being looked up, but
2171 does unify with it, so that it might match when the constraint is further
2172 instantiated. Usually GHC will regard this as a reason for not committing to
2173 some other constraint. But if the instance declaration was compiled with
2174 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2175 check for that declaration.
2178 All this makes it possible for a library author to design a library that relies on
2179 overlapping instances without the library client having to know.
2181 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2182 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2187 <title>Type synonyms in the instance head</title>
2190 <emphasis>Unlike Haskell 98, instance heads may use type
2191 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2192 As always, using a type synonym is just shorthand for
2193 writing the RHS of the type synonym definition. For example:
2197 type Point = (Int,Int)
2198 instance C Point where ...
2199 instance C [Point] where ...
2203 is legal. However, if you added
2207 instance C (Int,Int) where ...
2211 as well, then the compiler will complain about the overlapping
2212 (actually, identical) instance declarations. As always, type synonyms
2213 must be fully applied. You cannot, for example, write:
2218 instance Monad P where ...
2222 This design decision is independent of all the others, and easily
2223 reversed, but it makes sense to me.
2231 <sect2 id="type-restrictions">
2232 <title>Type signatures</title>
2234 <sect3><title>The context of a type signature</title>
2236 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2237 the form <emphasis>(class type-variable)</emphasis> or
2238 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2239 these type signatures are perfectly OK
2242 g :: Ord (T a ()) => ...
2246 GHC imposes the following restrictions on the constraints in a type signature.
2250 forall tv1..tvn (c1, ...,cn) => type
2253 (Here, we write the "foralls" explicitly, although the Haskell source
2254 language omits them; in Haskell 98, all the free type variables of an
2255 explicit source-language type signature are universally quantified,
2256 except for the class type variables in a class declaration. However,
2257 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2266 <emphasis>Each universally quantified type variable
2267 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2269 A type variable <literal>a</literal> is "reachable" if it it appears
2270 in the same constraint as either a type variable free in in
2271 <literal>type</literal>, or another reachable type variable.
2272 A value with a type that does not obey
2273 this reachability restriction cannot be used without introducing
2274 ambiguity; that is why the type is rejected.
2275 Here, for example, is an illegal type:
2279 forall a. Eq a => Int
2283 When a value with this type was used, the constraint <literal>Eq tv</literal>
2284 would be introduced where <literal>tv</literal> is a fresh type variable, and
2285 (in the dictionary-translation implementation) the value would be
2286 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2287 can never know which instance of <literal>Eq</literal> to use because we never
2288 get any more information about <literal>tv</literal>.
2292 that the reachability condition is weaker than saying that <literal>a</literal> is
2293 functionally dependent on a type variable free in
2294 <literal>type</literal> (see <xref
2295 linkend="functional-dependencies"/>). The reason for this is there
2296 might be a "hidden" dependency, in a superclass perhaps. So
2297 "reachable" is a conservative approximation to "functionally dependent".
2298 For example, consider:
2300 class C a b | a -> b where ...
2301 class C a b => D a b where ...
2302 f :: forall a b. D a b => a -> a
2304 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2305 but that is not immediately apparent from <literal>f</literal>'s type.
2311 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2312 universally quantified type variables <literal>tvi</literal></emphasis>.
2314 For example, this type is OK because <literal>C a b</literal> mentions the
2315 universally quantified type variable <literal>b</literal>:
2319 forall a. C a b => burble
2323 The next type is illegal because the constraint <literal>Eq b</literal> does not
2324 mention <literal>a</literal>:
2328 forall a. Eq b => burble
2332 The reason for this restriction is milder than the other one. The
2333 excluded types are never useful or necessary (because the offending
2334 context doesn't need to be witnessed at this point; it can be floated
2335 out). Furthermore, floating them out increases sharing. Lastly,
2336 excluding them is a conservative choice; it leaves a patch of
2337 territory free in case we need it later.
2348 <title>For-all hoisting</title>
2350 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2351 end of an arrow, thus:
2353 type Discard a = forall b. a -> b -> a
2355 g :: Int -> Discard Int
2358 Simply expanding the type synonym would give
2360 g :: Int -> (forall b. Int -> b -> Int)
2362 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2364 g :: forall b. Int -> Int -> b -> Int
2366 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2367 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2368 performs the transformation:</emphasis>
2370 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2372 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2374 (In fact, GHC tries to retain as much synonym information as possible for use in
2375 error messages, but that is a usability issue.) This rule applies, of course, whether
2376 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2377 valid way to write <literal>g</literal>'s type signature:
2379 g :: Int -> Int -> forall b. b -> Int
2383 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2386 type Foo a = (?x::Int) => Bool -> a
2391 g :: (?x::Int) => Bool -> Bool -> Int
2399 <sect2 id="implicit-parameters">
2400 <title>Implicit parameters</title>
2402 <para> Implicit parameters are implemented as described in
2403 "Implicit parameters: dynamic scoping with static types",
2404 J Lewis, MB Shields, E Meijer, J Launchbury,
2405 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2409 <para>(Most of the following, stil rather incomplete, documentation is
2410 due to Jeff Lewis.)</para>
2412 <para>Implicit parameter support is enabled with the option
2413 <option>-fimplicit-params</option>.</para>
2416 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2417 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2418 context. In Haskell, all variables are statically bound. Dynamic
2419 binding of variables is a notion that goes back to Lisp, but was later
2420 discarded in more modern incarnations, such as Scheme. Dynamic binding
2421 can be very confusing in an untyped language, and unfortunately, typed
2422 languages, in particular Hindley-Milner typed languages like Haskell,
2423 only support static scoping of variables.
2426 However, by a simple extension to the type class system of Haskell, we
2427 can support dynamic binding. Basically, we express the use of a
2428 dynamically bound variable as a constraint on the type. These
2429 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2430 function uses a dynamically-bound variable <literal>?x</literal>
2431 of type <literal>t'</literal>". For
2432 example, the following expresses the type of a sort function,
2433 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2435 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2437 The dynamic binding constraints are just a new form of predicate in the type class system.
2440 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2441 where <literal>x</literal> is
2442 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2443 Use of this construct also introduces a new
2444 dynamic-binding constraint in the type of the expression.
2445 For example, the following definition
2446 shows how we can define an implicitly parameterized sort function in
2447 terms of an explicitly parameterized <literal>sortBy</literal> function:
2449 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2451 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2457 <title>Implicit-parameter type constraints</title>
2459 Dynamic binding constraints behave just like other type class
2460 constraints in that they are automatically propagated. Thus, when a
2461 function is used, its implicit parameters are inherited by the
2462 function that called it. For example, our <literal>sort</literal> function might be used
2463 to pick out the least value in a list:
2465 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2466 least xs = fst (sort xs)
2468 Without lifting a finger, the <literal>?cmp</literal> parameter is
2469 propagated to become a parameter of <literal>least</literal> as well. With explicit
2470 parameters, the default is that parameters must always be explicit
2471 propagated. With implicit parameters, the default is to always
2475 An implicit-parameter type constraint differs from other type class constraints in the
2476 following way: All uses of a particular implicit parameter must have
2477 the same type. This means that the type of <literal>(?x, ?x)</literal>
2478 is <literal>(?x::a) => (a,a)</literal>, and not
2479 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2483 <para> You can't have an implicit parameter in the context of a class or instance
2484 declaration. For example, both these declarations are illegal:
2486 class (?x::Int) => C a where ...
2487 instance (?x::a) => Foo [a] where ...
2489 Reason: exactly which implicit parameter you pick up depends on exactly where
2490 you invoke a function. But the ``invocation'' of instance declarations is done
2491 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2492 Easiest thing is to outlaw the offending types.</para>
2494 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2496 f :: (?x :: [a]) => Int -> Int
2499 g :: (Read a, Show a) => String -> String
2502 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2503 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2504 quite unambiguous, and fixes the type <literal>a</literal>.
2509 <title>Implicit-parameter bindings</title>
2512 An implicit parameter is <emphasis>bound</emphasis> using the standard
2513 <literal>let</literal> or <literal>where</literal> binding forms.
2514 For example, we define the <literal>min</literal> function by binding
2515 <literal>cmp</literal>.
2518 min = let ?cmp = (<=) in least
2522 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2523 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2524 (including in a list comprehension, or do-notation, or pattern guards),
2525 or a <literal>where</literal> clause.
2526 Note the following points:
2529 An implicit-parameter binding group must be a
2530 collection of simple bindings to implicit-style variables (no
2531 function-style bindings, and no type signatures); these bindings are
2532 neither polymorphic or recursive.
2535 You may not mix implicit-parameter bindings with ordinary bindings in a
2536 single <literal>let</literal>
2537 expression; use two nested <literal>let</literal>s instead.
2538 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2542 You may put multiple implicit-parameter bindings in a
2543 single binding group; but they are <emphasis>not</emphasis> treated
2544 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2545 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2546 parameter. The bindings are not nested, and may be re-ordered without changing
2547 the meaning of the program.
2548 For example, consider:
2550 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2552 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2553 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2555 f :: (?x::Int) => Int -> Int
2563 <sect3><title>Implicit parameters and polymorphic recursion</title>
2566 Consider these two definitions:
2569 len1 xs = let ?acc = 0 in len_acc1 xs
2572 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2577 len2 xs = let ?acc = 0 in len_acc2 xs
2579 len_acc2 :: (?acc :: Int) => [a] -> Int
2581 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2583 The only difference between the two groups is that in the second group
2584 <literal>len_acc</literal> is given a type signature.
2585 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2586 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2587 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2588 has a type signature, the recursive call is made to the
2589 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2590 as an implicit parameter. So we get the following results in GHCi:
2597 Adding a type signature dramatically changes the result! This is a rather
2598 counter-intuitive phenomenon, worth watching out for.
2602 <sect3><title>Implicit parameters and monomorphism</title>
2604 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2605 Haskell Report) to implicit parameters. For example, consider:
2613 Since the binding for <literal>y</literal> falls under the Monomorphism
2614 Restriction it is not generalised, so the type of <literal>y</literal> is
2615 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2616 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2617 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2618 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2619 <literal>y</literal> in the body of the <literal>let</literal> will see the
2620 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2621 <literal>14</literal>.
2626 <sect2 id="linear-implicit-parameters">
2627 <title>Linear implicit parameters</title>
2629 Linear implicit parameters are an idea developed by Koen Claessen,
2630 Mark Shields, and Simon PJ. They address the long-standing
2631 problem that monads seem over-kill for certain sorts of problem, notably:
2634 <listitem> <para> distributing a supply of unique names </para> </listitem>
2635 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2636 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2640 Linear implicit parameters are just like ordinary implicit parameters,
2641 except that they are "linear" -- that is, they cannot be copied, and
2642 must be explicitly "split" instead. Linear implicit parameters are
2643 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2644 (The '/' in the '%' suggests the split!)
2649 import GHC.Exts( Splittable )
2651 data NameSupply = ...
2653 splitNS :: NameSupply -> (NameSupply, NameSupply)
2654 newName :: NameSupply -> Name
2656 instance Splittable NameSupply where
2660 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2661 f env (Lam x e) = Lam x' (f env e)
2664 env' = extend env x x'
2665 ...more equations for f...
2667 Notice that the implicit parameter %ns is consumed
2669 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2670 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2674 So the translation done by the type checker makes
2675 the parameter explicit:
2677 f :: NameSupply -> Env -> Expr -> Expr
2678 f ns env (Lam x e) = Lam x' (f ns1 env e)
2680 (ns1,ns2) = splitNS ns
2682 env = extend env x x'
2684 Notice the call to 'split' introduced by the type checker.
2685 How did it know to use 'splitNS'? Because what it really did
2686 was to introduce a call to the overloaded function 'split',
2687 defined by the class <literal>Splittable</literal>:
2689 class Splittable a where
2692 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2693 split for name supplies. But we can simply write
2699 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2701 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2702 <literal>GHC.Exts</literal>.
2707 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2708 are entirely distinct implicit parameters: you
2709 can use them together and they won't intefere with each other. </para>
2712 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2714 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2715 in the context of a class or instance declaration. </para></listitem>
2719 <sect3><title>Warnings</title>
2722 The monomorphism restriction is even more important than usual.
2723 Consider the example above:
2725 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2726 f env (Lam x e) = Lam x' (f env e)
2729 env' = extend env x x'
2731 If we replaced the two occurrences of x' by (newName %ns), which is
2732 usually a harmless thing to do, we get:
2734 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2735 f env (Lam x e) = Lam (newName %ns) (f env e)
2737 env' = extend env x (newName %ns)
2739 But now the name supply is consumed in <emphasis>three</emphasis> places
2740 (the two calls to newName,and the recursive call to f), so
2741 the result is utterly different. Urk! We don't even have
2745 Well, this is an experimental change. With implicit
2746 parameters we have already lost beta reduction anyway, and
2747 (as John Launchbury puts it) we can't sensibly reason about
2748 Haskell programs without knowing their typing.
2753 <sect3><title>Recursive functions</title>
2754 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2757 foo :: %x::T => Int -> [Int]
2759 foo n = %x : foo (n-1)
2761 where T is some type in class Splittable.</para>
2763 Do you get a list of all the same T's or all different T's
2764 (assuming that split gives two distinct T's back)?
2766 If you supply the type signature, taking advantage of polymorphic
2767 recursion, you get what you'd probably expect. Here's the
2768 translated term, where the implicit param is made explicit:
2771 foo x n = let (x1,x2) = split x
2772 in x1 : foo x2 (n-1)
2774 But if you don't supply a type signature, GHC uses the Hindley
2775 Milner trick of using a single monomorphic instance of the function
2776 for the recursive calls. That is what makes Hindley Milner type inference
2777 work. So the translation becomes
2781 foom n = x : foom (n-1)
2785 Result: 'x' is not split, and you get a list of identical T's. So the
2786 semantics of the program depends on whether or not foo has a type signature.
2789 You may say that this is a good reason to dislike linear implicit parameters
2790 and you'd be right. That is why they are an experimental feature.
2796 <sect2 id="sec-kinding">
2797 <title>Explicitly-kinded quantification</title>
2800 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2801 to give the kind explicitly as (machine-checked) documentation,
2802 just as it is nice to give a type signature for a function. On some occasions,
2803 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2804 John Hughes had to define the data type:
2806 data Set cxt a = Set [a]
2807 | Unused (cxt a -> ())
2809 The only use for the <literal>Unused</literal> constructor was to force the correct
2810 kind for the type variable <literal>cxt</literal>.
2813 GHC now instead allows you to specify the kind of a type variable directly, wherever
2814 a type variable is explicitly bound. Namely:
2816 <listitem><para><literal>data</literal> declarations:
2818 data Set (cxt :: * -> *) a = Set [a]
2819 </screen></para></listitem>
2820 <listitem><para><literal>type</literal> declarations:
2822 type T (f :: * -> *) = f Int
2823 </screen></para></listitem>
2824 <listitem><para><literal>class</literal> declarations:
2826 class (Eq a) => C (f :: * -> *) a where ...
2827 </screen></para></listitem>
2828 <listitem><para><literal>forall</literal>'s in type signatures:
2830 f :: forall (cxt :: * -> *). Set cxt Int
2831 </screen></para></listitem>
2836 The parentheses are required. Some of the spaces are required too, to
2837 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2838 will get a parse error, because "<literal>::*->*</literal>" is a
2839 single lexeme in Haskell.
2843 As part of the same extension, you can put kind annotations in types
2846 f :: (Int :: *) -> Int
2847 g :: forall a. a -> (a :: *)
2851 atype ::= '(' ctype '::' kind ')
2853 The parentheses are required.
2858 <sect2 id="universal-quantification">
2859 <title>Arbitrary-rank polymorphism
2863 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2864 allows us to say exactly what this means. For example:
2872 g :: forall b. (b -> b)
2874 The two are treated identically.
2878 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2879 explicit universal quantification in
2881 For example, all the following types are legal:
2883 f1 :: forall a b. a -> b -> a
2884 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2886 f2 :: (forall a. a->a) -> Int -> Int
2887 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2889 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2891 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2892 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2893 The <literal>forall</literal> makes explicit the universal quantification that
2894 is implicitly added by Haskell.
2897 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2898 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2899 shows, the polymorphic type on the left of the function arrow can be overloaded.
2902 The function <literal>f3</literal> has a rank-3 type;
2903 it has rank-2 types on the left of a function arrow.
2906 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2907 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2908 that restriction has now been lifted.)
2909 In particular, a forall-type (also called a "type scheme"),
2910 including an operational type class context, is legal:
2912 <listitem> <para> On the left of a function arrow </para> </listitem>
2913 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2914 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2915 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2916 field type signatures.</para> </listitem>
2917 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2918 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2920 There is one place you cannot put a <literal>forall</literal>:
2921 you cannot instantiate a type variable with a forall-type. So you cannot
2922 make a forall-type the argument of a type constructor. So these types are illegal:
2924 x1 :: [forall a. a->a]
2925 x2 :: (forall a. a->a, Int)
2926 x3 :: Maybe (forall a. a->a)
2928 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2929 a type variable any more!
2938 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2939 the types of the constructor arguments. Here are several examples:
2945 data T a = T1 (forall b. b -> b -> b) a
2947 data MonadT m = MkMonad { return :: forall a. a -> m a,
2948 bind :: forall a b. m a -> (a -> m b) -> m b
2951 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2957 The constructors have rank-2 types:
2963 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2964 MkMonad :: forall m. (forall a. a -> m a)
2965 -> (forall a b. m a -> (a -> m b) -> m b)
2967 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2973 Notice that you don't need to use a <literal>forall</literal> if there's an
2974 explicit context. For example in the first argument of the
2975 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2976 prefixed to the argument type. The implicit <literal>forall</literal>
2977 quantifies all type variables that are not already in scope, and are
2978 mentioned in the type quantified over.
2982 As for type signatures, implicit quantification happens for non-overloaded
2983 types too. So if you write this:
2986 data T a = MkT (Either a b) (b -> b)
2989 it's just as if you had written this:
2992 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2995 That is, since the type variable <literal>b</literal> isn't in scope, it's
2996 implicitly universally quantified. (Arguably, it would be better
2997 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2998 where that is what is wanted. Feedback welcomed.)
3002 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3003 the constructor to suitable values, just as usual. For example,
3014 a3 = MkSwizzle reverse
3017 a4 = let r x = Just x
3024 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3025 mkTs f x y = [T1 f x, T1 f y]
3031 The type of the argument can, as usual, be more general than the type
3032 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3033 does not need the <literal>Ord</literal> constraint.)
3037 When you use pattern matching, the bound variables may now have
3038 polymorphic types. For example:
3044 f :: T a -> a -> (a, Char)
3045 f (T1 w k) x = (w k x, w 'c' 'd')
3047 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3048 g (MkSwizzle s) xs f = s (map f (s xs))
3050 h :: MonadT m -> [m a] -> m [a]
3051 h m [] = return m []
3052 h m (x:xs) = bind m x $ \y ->
3053 bind m (h m xs) $ \ys ->
3060 In the function <function>h</function> we use the record selectors <literal>return</literal>
3061 and <literal>bind</literal> to extract the polymorphic bind and return functions
3062 from the <literal>MonadT</literal> data structure, rather than using pattern
3068 <title>Type inference</title>
3071 In general, type inference for arbitrary-rank types is undecidable.
3072 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3073 to get a decidable algorithm by requiring some help from the programmer.
3074 We do not yet have a formal specification of "some help" but the rule is this:
3077 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3078 provides an explicit polymorphic type for x, or GHC's type inference will assume
3079 that x's type has no foralls in it</emphasis>.
3082 What does it mean to "provide" an explicit type for x? You can do that by
3083 giving a type signature for x directly, using a pattern type signature
3084 (<xref linkend="scoped-type-variables"/>), thus:
3086 \ f :: (forall a. a->a) -> (f True, f 'c')
3088 Alternatively, you can give a type signature to the enclosing
3089 context, which GHC can "push down" to find the type for the variable:
3091 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3093 Here the type signature on the expression can be pushed inwards
3094 to give a type signature for f. Similarly, and more commonly,
3095 one can give a type signature for the function itself:
3097 h :: (forall a. a->a) -> (Bool,Char)
3098 h f = (f True, f 'c')
3100 You don't need to give a type signature if the lambda bound variable
3101 is a constructor argument. Here is an example we saw earlier:
3103 f :: T a -> a -> (a, Char)
3104 f (T1 w k) x = (w k x, w 'c' 'd')
3106 Here we do not need to give a type signature to <literal>w</literal>, because
3107 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3114 <sect3 id="implicit-quant">
3115 <title>Implicit quantification</title>
3118 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3119 user-written types, if and only if there is no explicit <literal>forall</literal>,
3120 GHC finds all the type variables mentioned in the type that are not already
3121 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3125 f :: forall a. a -> a
3132 h :: forall b. a -> b -> b
3138 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3141 f :: (a -> a) -> Int
3143 f :: forall a. (a -> a) -> Int
3145 f :: (forall a. a -> a) -> Int
3148 g :: (Ord a => a -> a) -> Int
3149 -- MEANS the illegal type
3150 g :: forall a. (Ord a => a -> a) -> Int
3152 g :: (forall a. Ord a => a -> a) -> Int
3154 The latter produces an illegal type, which you might think is silly,
3155 but at least the rule is simple. If you want the latter type, you
3156 can write your for-alls explicitly. Indeed, doing so is strongly advised
3165 <sect2 id="scoped-type-variables">
3166 <title>Scoped type variables
3170 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3172 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3173 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3174 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
3178 f (xs::[a]) = ys ++ ys
3183 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
3184 This brings the type variable <literal>a</literal> into scope; it scopes over
3185 all the patterns and right hand sides for this equation for <function>f</function>.
3186 In particular, it is in scope at the type signature for <varname>y</varname>.
3190 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
3191 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
3192 implicitly universally quantified. (If there are no type variables in
3193 scope, all type variables mentioned in the signature are universally
3194 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
3195 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
3196 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
3197 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3198 it becomes possible to do so.
3202 Scoped type variables are implemented in both GHC and Hugs. Where the
3203 implementations differ from the specification below, those differences
3208 So much for the basic idea. Here are the details.
3212 <title>What a scoped type variable means</title>
3214 A lexically-scoped type variable is simply
3215 the name for a type. The restriction it expresses is that all occurrences
3216 of the same name mean the same type. For example:
3218 f :: [Int] -> Int -> Int
3219 f (xs::[a]) (y::a) = (head xs + y) :: a
3221 The pattern type signatures on the left hand side of
3222 <literal>f</literal> express the fact that <literal>xs</literal>
3223 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
3224 must have this same type. The type signature on the expression <literal>(head xs)</literal>
3225 specifies that this expression must have the same type <literal>a</literal>.
3226 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
3227 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
3228 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
3229 rules, which specified that a pattern-bound type variable should be universally quantified.)
3230 For example, all of these are legal:</para>
3233 t (x::a) (y::a) = x+y*2
3235 f (x::a) (y::b) = [x,y] -- a unifies with b
3237 g (x::a) = x + 1::Int -- a unifies with Int
3239 h x = let k (y::a) = [x,y] -- a is free in the
3240 in k x -- environment
3242 k (x::a) True = ... -- a unifies with Int
3243 k (x::Int) False = ...
3246 w (x::a) = x -- a unifies with [b]
3252 <title>Scope and implicit quantification</title>
3260 All the type variables mentioned in a pattern,
3261 that are not already in scope,
3262 are brought into scope by the pattern. We describe this set as
3263 the <emphasis>type variables bound by the pattern</emphasis>.
3266 f (x::a) = let g (y::(a,b)) = fst y
3270 The pattern <literal>(x::a)</literal> brings the type variable
3271 <literal>a</literal> into scope, as well as the term
3272 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
3273 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
3274 and brings into scope the type variable <literal>b</literal>.
3280 The type variable(s) bound by the pattern have the same scope
3281 as the term variable(s) bound by the pattern. For example:
3284 f (x::a) = <...rhs of f...>
3285 (p::b, q::b) = (1,2)
3286 in <...body of let...>
3288 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3289 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3290 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3291 just like <literal>p</literal> and <literal>q</literal> do.
3292 Indeed, the newly bound type variables also scope over any ordinary, separate
3293 type signatures in the <literal>let</literal> group.
3300 The type variables bound by the pattern may be
3301 mentioned in ordinary type signatures or pattern
3302 type signatures anywhere within their scope.
3309 In ordinary type signatures, any type variable mentioned in the
3310 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3318 Ordinary type signatures do not bring any new type variables
3319 into scope (except in the type signature itself!). So this is illegal:
3326 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3327 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3328 and that is an incorrect typing.
3335 The pattern type signature is a monotype:
3340 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3344 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3345 not to type schemes.
3349 There is no implicit universal quantification on pattern type signatures (in contrast to
3350 ordinary type signatures).
3360 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3361 scope over the methods defined in the <literal>where</literal> part. For example:
3375 (Not implemented in Hugs yet, Dec 98).
3385 <sect3 id="decl-type-sigs">
3386 <title>Declaration type signatures</title>
3387 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3388 quantification (using <literal>forall</literal>) brings into scope the
3389 explicitly-quantified
3390 type variables, in the definition of the named function(s). For example:
3392 f :: forall a. [a] -> [a]
3393 f (x:xs) = xs ++ [ x :: a ]
3395 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3396 the definition of "<literal>f</literal>".
3398 <para>This only happens if the quantification in <literal>f</literal>'s type
3399 signature is explicit. For example:
3402 g (x:xs) = xs ++ [ x :: a ]
3404 This program will be rejected, because "<literal>a</literal>" does not scope
3405 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3406 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3407 quantification rules.
3411 <sect3 id="pattern-type-sigs">
3412 <title>Where a pattern type signature can occur</title>
3415 A pattern type signature can occur in any pattern. For example:
3420 A pattern type signature can be on an arbitrary sub-pattern, not
3425 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3434 Pattern type signatures, including the result part, can be used
3435 in lambda abstractions:
3438 (\ (x::a, y) :: a -> x)
3445 Pattern type signatures, including the result part, can be used
3446 in <literal>case</literal> expressions:
3449 case e of { ((x::a, y) :: (a,b)) -> x }
3452 Note that the <literal>-></literal> symbol in a case alternative
3453 leads to difficulties when parsing a type signature in the pattern: in
3454 the absence of the extra parentheses in the example above, the parser
3455 would try to interpret the <literal>-></literal> as a function
3456 arrow and give a parse error later.
3464 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3465 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3466 token or a parenthesised type of some sort). To see why,
3467 consider how one would parse this:
3481 Pattern type signatures can bind existential type variables.
3486 data T = forall a. MkT [a]
3489 f (MkT [t::a]) = MkT t3
3502 Pattern type signatures
3503 can be used in pattern bindings:
3506 f x = let (y, z::a) = x in ...
3507 f1 x = let (y, z::Int) = x in ...
3508 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3509 f3 :: (b->b) = \x -> x
3512 In all such cases, the binding is not generalised over the pattern-bound
3513 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3514 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3515 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3516 In contrast, the binding
3521 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3522 in <literal>f4</literal>'s scope.
3528 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3529 type signatures. The two can be used independently or together.</para>
3533 <sect3 id="result-type-sigs">
3534 <title>Result type signatures</title>
3537 The result type of a function can be given a signature, thus:
3541 f (x::a) :: [a] = [x,x,x]
3545 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3546 result type. Sometimes this is the only way of naming the type variable
3551 f :: Int -> [a] -> [a]
3552 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3553 in \xs -> map g (reverse xs `zip` xs)
3558 The type variables bound in a result type signature scope over the right hand side
3559 of the definition. However, consider this corner-case:
3561 rev1 :: [a] -> [a] = \xs -> reverse xs
3563 foo ys = rev (ys::[a])
3565 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3566 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3567 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3568 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3569 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3572 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3573 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3577 rev1 :: [a] -> [a] = \xs -> reverse xs
3582 Result type signatures are not yet implemented in Hugs.
3589 <sect2 id="deriving-typeable">
3590 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3593 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3594 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3595 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3596 classes <literal>Eq</literal>, <literal>Ord</literal>,
3597 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3600 GHC extends this list with two more classes that may be automatically derived
3601 (provided the <option>-fglasgow-exts</option> flag is specified):
3602 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3603 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3604 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3606 <para>An instance of <literal>Typeable</literal> can only be derived if the
3607 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3608 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3610 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3611 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3613 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3614 are used, and only <literal>Typeable1</literal> up to
3615 <literal>Typeable7</literal> are provided in the library.)
3616 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3617 class, whose kind suits that of the data type constructor, and
3618 then writing the data type instance by hand.
3622 <sect2 id="newtype-deriving">
3623 <title>Generalised derived instances for newtypes</title>
3626 When you define an abstract type using <literal>newtype</literal>, you may want
3627 the new type to inherit some instances from its representation. In
3628 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3629 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3630 other classes you have to write an explicit instance declaration. For
3631 example, if you define
3634 newtype Dollars = Dollars Int
3637 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3638 explicitly define an instance of <literal>Num</literal>:
3641 instance Num Dollars where
3642 Dollars a + Dollars b = Dollars (a+b)
3645 All the instance does is apply and remove the <literal>newtype</literal>
3646 constructor. It is particularly galling that, since the constructor
3647 doesn't appear at run-time, this instance declaration defines a
3648 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3649 dictionary, only slower!
3653 <sect3> <title> Generalising the deriving clause </title>
3655 GHC now permits such instances to be derived instead, so one can write
3657 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3660 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3661 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3662 derives an instance declaration of the form
3665 instance Num Int => Num Dollars
3668 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3672 We can also derive instances of constructor classes in a similar
3673 way. For example, suppose we have implemented state and failure monad
3674 transformers, such that
3677 instance Monad m => Monad (State s m)
3678 instance Monad m => Monad (Failure m)
3680 In Haskell 98, we can define a parsing monad by
3682 type Parser tok m a = State [tok] (Failure m) a
3685 which is automatically a monad thanks to the instance declarations
3686 above. With the extension, we can make the parser type abstract,
3687 without needing to write an instance of class <literal>Monad</literal>, via
3690 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3693 In this case the derived instance declaration is of the form
3695 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3698 Notice that, since <literal>Monad</literal> is a constructor class, the
3699 instance is a <emphasis>partial application</emphasis> of the new type, not the
3700 entire left hand side. We can imagine that the type declaration is
3701 ``eta-converted'' to generate the context of the instance
3706 We can even derive instances of multi-parameter classes, provided the
3707 newtype is the last class parameter. In this case, a ``partial
3708 application'' of the class appears in the <literal>deriving</literal>
3709 clause. For example, given the class
3712 class StateMonad s m | m -> s where ...
3713 instance Monad m => StateMonad s (State s m) where ...
3715 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3717 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3718 deriving (Monad, StateMonad [tok])
3721 The derived instance is obtained by completing the application of the
3722 class to the new type:
3725 instance StateMonad [tok] (State [tok] (Failure m)) =>
3726 StateMonad [tok] (Parser tok m)
3731 As a result of this extension, all derived instances in newtype
3732 declarations are treated uniformly (and implemented just by reusing
3733 the dictionary for the representation type), <emphasis>except</emphasis>
3734 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3735 the newtype and its representation.
3739 <sect3> <title> A more precise specification </title>
3741 Derived instance declarations are constructed as follows. Consider the
3742 declaration (after expansion of any type synonyms)
3745 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3751 The type <literal>t</literal> is an arbitrary type
3754 The <literal>vk+1...vn</literal> are type variables which do not occur in
3755 <literal>t</literal>, and
3758 The <literal>ci</literal> are partial applications of
3759 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3760 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3763 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3764 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3765 should not "look through" the type or its constructor. You can still
3766 derive these classes for a newtype, but it happens in the usual way, not
3767 via this new mechanism.
3770 Then, for each <literal>ci</literal>, the derived instance
3773 instance ci (t vk+1...v) => ci (T v1...vp)
3775 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3776 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3780 As an example which does <emphasis>not</emphasis> work, consider
3782 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3784 Here we cannot derive the instance
3786 instance Monad (State s m) => Monad (NonMonad m)
3789 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3790 and so cannot be "eta-converted" away. It is a good thing that this
3791 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3792 not, in fact, a monad --- for the same reason. Try defining
3793 <literal>>>=</literal> with the correct type: you won't be able to.
3797 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3798 important, since we can only derive instances for the last one. If the
3799 <literal>StateMonad</literal> class above were instead defined as
3802 class StateMonad m s | m -> s where ...
3805 then we would not have been able to derive an instance for the
3806 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3807 classes usually have one "main" parameter for which deriving new
3808 instances is most interesting.
3810 <para>Lastly, all of this applies only for classes other than
3811 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3812 and <literal>Data</literal>, for which the built-in derivation applies (section
3813 4.3.3. of the Haskell Report).
3814 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3815 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3816 the standard method is used or the one described here.)
3822 <sect2 id="typing-binds">
3823 <title>Generalised typing of mutually recursive bindings</title>
3826 The Haskell Report specifies that a group of bindings (at top level, or in a
3827 <literal>let</literal> or <literal>where</literal>) should be sorted into
3828 strongly-connected components, and then type-checked in dependency order
3829 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3830 Report, Section 4.5.1</ulink>).
3831 As each group is type-checked, any binders of the group that
3833 an explicit type signature are put in the type environment with the specified
3835 and all others are monomorphic until the group is generalised
3836 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3839 <para>Following a suggestion of Mark Jones, in his paper
3840 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3842 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3844 <emphasis>the dependency analysis ignores references to variables that have an explicit
3845 type signature</emphasis>.
3846 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3847 typecheck. For example, consider:
3849 f :: Eq a => a -> Bool
3850 f x = (x == x) || g True || g "Yes"
3852 g y = (y <= y) || f True
3854 This is rejected by Haskell 98, but under Jones's scheme the definition for
3855 <literal>g</literal> is typechecked first, separately from that for
3856 <literal>f</literal>,
3857 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3858 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3859 type is generalised, to get
3861 g :: Ord a => a -> Bool
3863 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3864 <literal>g</literal> in the type environment.
3868 The same refined dependency analysis also allows the type signatures of
3869 mutually-recursive functions to have different contexts, something that is illegal in
3870 Haskell 98 (Section 4.5.2, last sentence). With
3871 <option>-fglasgow-exts</option>
3872 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3873 type signatures; in practice this means that only variables bound by the same
3874 pattern binding must have the same context. For example, this is fine:
3876 f :: Eq a => a -> Bool
3877 f x = (x == x) || g True
3879 g :: Ord a => a -> Bool
3880 g y = (y <= y) || f True
3886 <!-- ==================== End of type system extensions ================= -->
3888 <!-- ====================== Generalised algebraic data types ======================= -->
3891 <title>Generalised Algebraic Data Types</title>
3893 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3894 to give the type signatures of constructors explicitly. For example:
3897 Lit :: Int -> Term Int
3898 Succ :: Term Int -> Term Int
3899 IsZero :: Term Int -> Term Bool
3900 If :: Term Bool -> Term a -> Term a -> Term a
3901 Pair :: Term a -> Term b -> Term (a,b)
3903 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3904 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3905 for these <literal>Terms</literal>:
3909 eval (Succ t) = 1 + eval t
3910 eval (IsZero t) = eval t == 0
3911 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3912 eval (Pair e1 e2) = (eval e1, eval e2)
3914 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3916 <para> The extensions to GHC are these:
3919 Data type declarations have a 'where' form, as exemplified above. The type signature of
3920 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3921 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3922 have no scope. Indeed, one can write a kind signature instead:
3924 data Term :: * -> * where ...
3926 or even a mixture of the two:
3928 data Foo a :: (* -> *) -> * where ...
3930 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3933 data Foo a (b :: * -> *) where ...
3938 There are no restrictions on the type of the data constructor, except that the result
3939 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3940 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3944 You can use record syntax on a GADT-style data type declaration:
3948 Lit { val :: Int } :: Term Int
3949 Succ { num :: Term Int } :: Term Int
3950 Pred { num :: Term Int } :: Term Int
3951 IsZero { arg :: Term Int } :: Term Bool
3952 Pair { arg1 :: Term a
3955 If { cnd :: Term Bool
3960 For every constructor that has a field <literal>f</literal>, (a) the type of
3961 field <literal>f</literal> must be the same; and (b) the
3962 result type of the constructor must be the same; both modulo alpha conversion.
3963 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3965 single name. Although their field types are both <literal>Term Int</literal>,
3966 their selector functions actually have different types:
3969 num :: Term Int -> Term Int
3970 arg :: Term Bool -> Term Int
3973 At the moment, record updates are not yet possible with GADT, so support is
3974 limited to record construction, selection and pattern matching:
3977 someTerm :: Term Bool
3978 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3981 eval Lit { val = i } = i
3982 eval Succ { num = t } = eval t + 1
3983 eval Pred { num = t } = eval t - 1
3984 eval IsZero { arg = t } = eval t == 0
3985 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3986 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3992 You can use strictness annotations, in the obvious places
3993 in the constructor type:
3996 Lit :: !Int -> Term Int
3997 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3998 Pair :: Term a -> Term b -> Term (a,b)
4003 You can use a <literal>deriving</literal> clause on a GADT-style data type
4004 declaration, but only if the data type could also have been declared in
4005 Haskell-98 syntax. For example, these two declarations are equivalent
4007 data Maybe1 a where {
4008 Nothing1 :: Maybe a ;
4009 Just1 :: a -> Maybe a
4010 } deriving( Eq, Ord )
4012 data Maybe2 a = Nothing2 | Just2 a
4015 This simply allows you to declare a vanilla Haskell-98 data type using the
4016 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
4020 Pattern matching causes type refinement. For example, in the right hand side of the equation
4025 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
4026 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
4027 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
4029 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
4030 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
4031 occur. However, the refinement is quite general. For example, if we had:
4033 eval :: Term a -> a -> a
4034 eval (Lit i) j = i+j
4036 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
4037 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
4038 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
4044 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
4046 data T a = forall b. MkT b (b->a)
4047 data T' a where { MKT :: b -> (b->a) -> T' a }
4052 <!-- ====================== End of Generalised algebraic data types ======================= -->
4054 <!-- ====================== TEMPLATE HASKELL ======================= -->
4056 <sect1 id="template-haskell">
4057 <title>Template Haskell</title>
4059 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
4060 Template Haskell at <ulink url="http://www.haskell.org/th/">
4061 http://www.haskell.org/th/</ulink>, while
4063 the main technical innovations is discussed in "<ulink
4064 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4065 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4066 The details of the Template Haskell design are still in flux. Make sure you
4067 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
4068 (search for the type ExpQ).
4069 [Temporary: many changes to the original design are described in
4070 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4071 Not all of these changes are in GHC 6.2.]
4074 <para> The first example from that paper is set out below as a worked example to help get you started.
4078 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4079 Tim Sheard is going to expand it.)
4083 <title>Syntax</title>
4085 <para> Template Haskell has the following new syntactic
4086 constructions. You need to use the flag
4087 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4088 </indexterm>to switch these syntactic extensions on
4089 (<option>-fth</option> is currently implied by
4090 <option>-fglasgow-exts</option>, but you are encouraged to
4091 specify it explicitly).</para>
4095 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4096 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4097 There must be no space between the "$" and the identifier or parenthesis. This use
4098 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4099 of "." as an infix operator. If you want the infix operator, put spaces around it.
4101 <para> A splice can occur in place of
4103 <listitem><para> an expression; the spliced expression must
4104 have type <literal>Q Exp</literal></para></listitem>
4105 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4106 <listitem><para> [Planned, but not implemented yet.] a
4107 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4109 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4110 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4116 A expression quotation is written in Oxford brackets, thus:
4118 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4119 the quotation has type <literal>Expr</literal>.</para></listitem>
4120 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4121 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4122 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4123 the quotation has type <literal>Type</literal>.</para></listitem>
4124 </itemizedlist></para></listitem>
4127 Reification is written thus:
4129 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4130 has type <literal>Dec</literal>. </para></listitem>
4131 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4132 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4133 <listitem><para> Still to come: fixities </para></listitem>
4135 </itemizedlist></para>
4142 <sect2> <title> Using Template Haskell </title>
4146 The data types and monadic constructor functions for Template Haskell are in the library
4147 <literal>Language.Haskell.THSyntax</literal>.
4151 You can only run a function at compile time if it is imported from another module. That is,
4152 you can't define a function in a module, and call it from within a splice in the same module.
4153 (It would make sense to do so, but it's hard to implement.)
4157 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4160 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4161 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4162 compiles and runs a program, and then looks at the result. So it's important that
4163 the program it compiles produces results whose representations are identical to
4164 those of the compiler itself.
4168 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4169 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4174 <sect2> <title> A Template Haskell Worked Example </title>
4175 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4176 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4183 -- Import our template "pr"
4184 import Printf ( pr )
4186 -- The splice operator $ takes the Haskell source code
4187 -- generated at compile time by "pr" and splices it into
4188 -- the argument of "putStrLn".
4189 main = putStrLn ( $(pr "Hello") )
4195 -- Skeletal printf from the paper.
4196 -- It needs to be in a separate module to the one where
4197 -- you intend to use it.
4199 -- Import some Template Haskell syntax
4200 import Language.Haskell.TH
4202 -- Describe a format string
4203 data Format = D | S | L String
4205 -- Parse a format string. This is left largely to you
4206 -- as we are here interested in building our first ever
4207 -- Template Haskell program and not in building printf.
4208 parse :: String -> [Format]
4211 -- Generate Haskell source code from a parsed representation
4212 -- of the format string. This code will be spliced into
4213 -- the module which calls "pr", at compile time.
4214 gen :: [Format] -> ExpQ
4215 gen [D] = [| \n -> show n |]
4216 gen [S] = [| \s -> s |]
4217 gen [L s] = stringE s
4219 -- Here we generate the Haskell code for the splice
4220 -- from an input format string.
4221 pr :: String -> ExpQ
4222 pr s = gen (parse s)
4225 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4228 $ ghc --make -fth main.hs -o main.exe
4231 <para>Run "main.exe" and here is your output:</para>
4242 <!-- ===================== Arrow notation =================== -->
4244 <sect1 id="arrow-notation">
4245 <title>Arrow notation
4248 <para>Arrows are a generalization of monads introduced by John Hughes.
4249 For more details, see
4254 “Generalising Monads to Arrows”,
4255 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4256 pp67–111, May 2000.
4262 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4263 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4269 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4270 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4276 and the arrows web page at
4277 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4278 With the <option>-farrows</option> flag, GHC supports the arrow
4279 notation described in the second of these papers.
4280 What follows is a brief introduction to the notation;
4281 it won't make much sense unless you've read Hughes's paper.
4282 This notation is translated to ordinary Haskell,
4283 using combinators from the
4284 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4288 <para>The extension adds a new kind of expression for defining arrows:
4290 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4291 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4293 where <literal>proc</literal> is a new keyword.
4294 The variables of the pattern are bound in the body of the
4295 <literal>proc</literal>-expression,
4296 which is a new sort of thing called a <firstterm>command</firstterm>.
4297 The syntax of commands is as follows:
4299 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4300 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4301 | <replaceable>cmd</replaceable><superscript>0</superscript>
4303 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4304 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4305 infix operators as for expressions, and
4307 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4308 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4309 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4310 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4311 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4312 | <replaceable>fcmd</replaceable>
4314 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4315 | ( <replaceable>cmd</replaceable> )
4316 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4318 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4319 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4320 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4321 | <replaceable>cmd</replaceable>
4323 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4324 except that the bodies are commands instead of expressions.
4328 Commands produce values, but (like monadic computations)
4329 may yield more than one value,
4330 or none, and may do other things as well.
4331 For the most part, familiarity with monadic notation is a good guide to
4333 However the values of expressions, even monadic ones,
4334 are determined by the values of the variables they contain;
4335 this is not necessarily the case for commands.
4339 A simple example of the new notation is the expression
4341 proc x -> f -< x+1
4343 We call this a <firstterm>procedure</firstterm> or
4344 <firstterm>arrow abstraction</firstterm>.
4345 As with a lambda expression, the variable <literal>x</literal>
4346 is a new variable bound within the <literal>proc</literal>-expression.
4347 It refers to the input to the arrow.
4348 In the above example, <literal>-<</literal> is not an identifier but an
4349 new reserved symbol used for building commands from an expression of arrow
4350 type and an expression to be fed as input to that arrow.
4351 (The weird look will make more sense later.)
4352 It may be read as analogue of application for arrows.
4353 The above example is equivalent to the Haskell expression
4355 arr (\ x -> x+1) >>> f
4357 That would make no sense if the expression to the left of
4358 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4359 More generally, the expression to the left of <literal>-<</literal>
4360 may not involve any <firstterm>local variable</firstterm>,
4361 i.e. a variable bound in the current arrow abstraction.
4362 For such a situation there is a variant <literal>-<<</literal>, as in
4364 proc x -> f x -<< x+1
4366 which is equivalent to
4368 arr (\ x -> (f x, x+1)) >>> app
4370 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4372 Such an arrow is equivalent to a monad, so if you're using this form
4373 you may find a monadic formulation more convenient.
4377 <title>do-notation for commands</title>
4380 Another form of command is a form of <literal>do</literal>-notation.
4381 For example, you can write
4390 You can read this much like ordinary <literal>do</literal>-notation,
4391 but with commands in place of monadic expressions.
4392 The first line sends the value of <literal>x+1</literal> as an input to
4393 the arrow <literal>f</literal>, and matches its output against
4394 <literal>y</literal>.
4395 In the next line, the output is discarded.
4396 The arrow <function>returnA</function> is defined in the
4397 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4398 module as <literal>arr id</literal>.
4399 The above example is treated as an abbreviation for
4401 arr (\ x -> (x, x)) >>>
4402 first (arr (\ x -> x+1) >>> f) >>>
4403 arr (\ (y, x) -> (y, (x, y))) >>>
4404 first (arr (\ y -> 2*y) >>> g) >>>
4406 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4407 first (arr (\ (x, z) -> x*z) >>> h) >>>
4408 arr (\ (t, z) -> t+z) >>>
4411 Note that variables not used later in the composition are projected out.
4412 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4414 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4415 module, this reduces to
4417 arr (\ x -> (x+1, x)) >>>
4419 arr (\ (y, x) -> (2*y, (x, y))) >>>
4421 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4423 arr (\ (t, z) -> t+z)
4425 which is what you might have written by hand.
4426 With arrow notation, GHC keeps track of all those tuples of variables for you.
4430 Note that although the above translation suggests that
4431 <literal>let</literal>-bound variables like <literal>z</literal> must be
4432 monomorphic, the actual translation produces Core,
4433 so polymorphic variables are allowed.
4437 It's also possible to have mutually recursive bindings,
4438 using the new <literal>rec</literal> keyword, as in the following example:
4440 counter :: ArrowCircuit a => a Bool Int
4441 counter = proc reset -> do
4442 rec output <- returnA -< if reset then 0 else next
4443 next <- delay 0 -< output+1
4444 returnA -< output
4446 The translation of such forms uses the <function>loop</function> combinator,
4447 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4453 <title>Conditional commands</title>
4456 In the previous example, we used a conditional expression to construct the
4458 Sometimes we want to conditionally execute different commands, as in
4465 which is translated to
4467 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4468 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4470 Since the translation uses <function>|||</function>,
4471 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4475 There are also <literal>case</literal> commands, like
4481 y <- h -< (x1, x2)
4485 The syntax is the same as for <literal>case</literal> expressions,
4486 except that the bodies of the alternatives are commands rather than expressions.
4487 The translation is similar to that of <literal>if</literal> commands.
4493 <title>Defining your own control structures</title>
4496 As we're seen, arrow notation provides constructs,
4497 modelled on those for expressions,
4498 for sequencing, value recursion and conditionals.
4499 But suitable combinators,
4500 which you can define in ordinary Haskell,
4501 may also be used to build new commands out of existing ones.
4502 The basic idea is that a command defines an arrow from environments to values.
4503 These environments assign values to the free local variables of the command.
4504 Thus combinators that produce arrows from arrows
4505 may also be used to build commands from commands.
4506 For example, the <literal>ArrowChoice</literal> class includes a combinator
4508 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4510 so we can use it to build commands:
4512 expr' = proc x -> do
4515 symbol Plus -< ()
4516 y <- term -< ()
4519 symbol Minus -< ()
4520 y <- term -< ()
4523 (The <literal>do</literal> on the first line is needed to prevent the first
4524 <literal><+> ...</literal> from being interpreted as part of the
4525 expression on the previous line.)
4526 This is equivalent to
4528 expr' = (proc x -> returnA -< x)
4529 <+> (proc x -> do
4530 symbol Plus -< ()
4531 y <- term -< ()
4533 <+> (proc x -> do
4534 symbol Minus -< ()
4535 y <- term -< ()
4538 It is essential that this operator be polymorphic in <literal>e</literal>
4539 (representing the environment input to the command
4540 and thence to its subcommands)
4541 and satisfy the corresponding naturality property
4543 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4545 at least for strict <literal>k</literal>.
4546 (This should be automatic if you're not using <function>seq</function>.)
4547 This ensures that environments seen by the subcommands are environments
4548 of the whole command,
4549 and also allows the translation to safely trim these environments.
4550 The operator must also not use any variable defined within the current
4555 We could define our own operator
4557 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4558 untilA body cond = proc x ->
4559 if cond x then returnA -< ()
4562 untilA body cond -< x
4564 and use it in the same way.
4565 Of course this infix syntax only makes sense for binary operators;
4566 there is also a more general syntax involving special brackets:
4570 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4577 <title>Primitive constructs</title>
4580 Some operators will need to pass additional inputs to their subcommands.
4581 For example, in an arrow type supporting exceptions,
4582 the operator that attaches an exception handler will wish to pass the
4583 exception that occurred to the handler.
4584 Such an operator might have a type
4586 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4588 where <literal>Ex</literal> is the type of exceptions handled.
4589 You could then use this with arrow notation by writing a command
4591 body `handleA` \ ex -> handler
4593 so that if an exception is raised in the command <literal>body</literal>,
4594 the variable <literal>ex</literal> is bound to the value of the exception
4595 and the command <literal>handler</literal>,
4596 which typically refers to <literal>ex</literal>, is entered.
4597 Though the syntax here looks like a functional lambda,
4598 we are talking about commands, and something different is going on.
4599 The input to the arrow represented by a command consists of values for
4600 the free local variables in the command, plus a stack of anonymous values.
4601 In all the prior examples, this stack was empty.
4602 In the second argument to <function>handleA</function>,
4603 this stack consists of one value, the value of the exception.
4604 The command form of lambda merely gives this value a name.
4609 the values on the stack are paired to the right of the environment.
4610 So operators like <function>handleA</function> that pass
4611 extra inputs to their subcommands can be designed for use with the notation
4612 by pairing the values with the environment in this way.
4613 More precisely, the type of each argument of the operator (and its result)
4614 should have the form
4616 a (...(e,t1), ... tn) t
4618 where <replaceable>e</replaceable> is a polymorphic variable
4619 (representing the environment)
4620 and <replaceable>ti</replaceable> are the types of the values on the stack,
4621 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4622 The polymorphic variable <replaceable>e</replaceable> must not occur in
4623 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4624 <replaceable>t</replaceable>.
4625 However the arrows involved need not be the same.
4626 Here are some more examples of suitable operators:
4628 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4629 runReader :: ... => a e c -> a' (e,State) c
4630 runState :: ... => a e c -> a' (e,State) (c,State)
4632 We can supply the extra input required by commands built with the last two
4633 by applying them to ordinary expressions, as in
4637 (|runReader (do { ... })|) s
4639 which adds <literal>s</literal> to the stack of inputs to the command
4640 built using <function>runReader</function>.
4644 The command versions of lambda abstraction and application are analogous to
4645 the expression versions.
4646 In particular, the beta and eta rules describe equivalences of commands.
4647 These three features (operators, lambda abstraction and application)
4648 are the core of the notation; everything else can be built using them,
4649 though the results would be somewhat clumsy.
4650 For example, we could simulate <literal>do</literal>-notation by defining
4652 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4653 u `bind` f = returnA &&& u >>> f
4655 bind_ :: Arrow a => a e b -> a e c -> a e c
4656 u `bind_` f = u `bind` (arr fst >>> f)
4658 We could simulate <literal>if</literal> by defining
4660 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4661 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4668 <title>Differences with the paper</title>
4673 <para>Instead of a single form of arrow application (arrow tail) with two
4674 translations, the implementation provides two forms
4675 <quote><literal>-<</literal></quote> (first-order)
4676 and <quote><literal>-<<</literal></quote> (higher-order).
4681 <para>User-defined operators are flagged with banana brackets instead of
4682 a new <literal>form</literal> keyword.
4691 <title>Portability</title>
4694 Although only GHC implements arrow notation directly,
4695 there is also a preprocessor
4697 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4698 that translates arrow notation into Haskell 98
4699 for use with other Haskell systems.
4700 You would still want to check arrow programs with GHC;
4701 tracing type errors in the preprocessor output is not easy.
4702 Modules intended for both GHC and the preprocessor must observe some
4703 additional restrictions:
4708 The module must import
4709 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4715 The preprocessor cannot cope with other Haskell extensions.
4716 These would have to go in separate modules.
4722 Because the preprocessor targets Haskell (rather than Core),
4723 <literal>let</literal>-bound variables are monomorphic.
4734 <!-- ==================== ASSERTIONS ================= -->
4736 <sect1 id="sec-assertions">
4738 <indexterm><primary>Assertions</primary></indexterm>
4742 If you want to make use of assertions in your standard Haskell code, you
4743 could define a function like the following:
4749 assert :: Bool -> a -> a
4750 assert False x = error "assertion failed!"
4757 which works, but gives you back a less than useful error message --
4758 an assertion failed, but which and where?
4762 One way out is to define an extended <function>assert</function> function which also
4763 takes a descriptive string to include in the error message and
4764 perhaps combine this with the use of a pre-processor which inserts
4765 the source location where <function>assert</function> was used.
4769 Ghc offers a helping hand here, doing all of this for you. For every
4770 use of <function>assert</function> in the user's source:
4776 kelvinToC :: Double -> Double
4777 kelvinToC k = assert (k >= 0.0) (k+273.15)
4783 Ghc will rewrite this to also include the source location where the
4790 assert pred val ==> assertError "Main.hs|15" pred val
4796 The rewrite is only performed by the compiler when it spots
4797 applications of <function>Control.Exception.assert</function>, so you
4798 can still define and use your own versions of
4799 <function>assert</function>, should you so wish. If not, import
4800 <literal>Control.Exception</literal> to make use
4801 <function>assert</function> in your code.
4805 GHC ignores assertions when optimisation is turned on with the
4806 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4807 <literal>assert pred e</literal> will be rewritten to
4808 <literal>e</literal>. You can also disable assertions using the
4809 <option>-fignore-asserts</option>
4810 option<indexterm><primary><option>-fignore-asserts</option></primary>
4811 </indexterm>.</para>
4814 Assertion failures can be caught, see the documentation for the
4815 <literal>Control.Exception</literal> library for the details.
4821 <!-- =============================== PRAGMAS =========================== -->
4823 <sect1 id="pragmas">
4824 <title>Pragmas</title>
4826 <indexterm><primary>pragma</primary></indexterm>
4828 <para>GHC supports several pragmas, or instructions to the
4829 compiler placed in the source code. Pragmas don't normally affect
4830 the meaning of the program, but they might affect the efficiency
4831 of the generated code.</para>
4833 <para>Pragmas all take the form
4835 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4837 where <replaceable>word</replaceable> indicates the type of
4838 pragma, and is followed optionally by information specific to that
4839 type of pragma. Case is ignored in
4840 <replaceable>word</replaceable>. The various values for
4841 <replaceable>word</replaceable> that GHC understands are described
4842 in the following sections; any pragma encountered with an
4843 unrecognised <replaceable>word</replaceable> is (silently)
4846 <sect2 id="deprecated-pragma">
4847 <title>DEPRECATED pragma</title>
4848 <indexterm><primary>DEPRECATED</primary>
4851 <para>The DEPRECATED pragma lets you specify that a particular
4852 function, class, or type, is deprecated. There are two
4857 <para>You can deprecate an entire module thus:</para>
4859 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4862 <para>When you compile any module that import
4863 <literal>Wibble</literal>, GHC will print the specified
4868 <para>You can deprecate a function, class, type, or data constructor, with the
4869 following top-level declaration:</para>
4871 {-# DEPRECATED f, C, T "Don't use these" #-}
4873 <para>When you compile any module that imports and uses any
4874 of the specified entities, GHC will print the specified
4876 <para> You can only depecate entities declared at top level in the module
4877 being compiled, and you can only use unqualified names in the list of
4878 entities being deprecated. A capitalised name, such as <literal>T</literal>
4879 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4880 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4881 both are in scope. If both are in scope, there is currently no way to deprecate
4882 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4885 Any use of the deprecated item, or of anything from a deprecated
4886 module, will be flagged with an appropriate message. However,
4887 deprecations are not reported for
4888 (a) uses of a deprecated function within its defining module, and
4889 (b) uses of a deprecated function in an export list.
4890 The latter reduces spurious complaints within a library
4891 in which one module gathers together and re-exports
4892 the exports of several others.
4894 <para>You can suppress the warnings with the flag
4895 <option>-fno-warn-deprecations</option>.</para>
4898 <sect2 id="include-pragma">
4899 <title>INCLUDE pragma</title>
4901 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4902 of C header files that should be <literal>#include</literal>'d into
4903 the C source code generated by the compiler for the current module (if
4904 compiling via C). For example:</para>
4907 {-# INCLUDE "foo.h" #-}
4908 {-# INCLUDE <stdio.h> #-}</programlisting>
4910 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4911 your source file with any <literal>OPTIONS_GHC</literal>
4914 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4915 to the <option>-#include</option> option (<xref
4916 linkend="options-C-compiler" />), because the
4917 <literal>INCLUDE</literal> pragma is understood by other
4918 compilers. Yet another alternative is to add the include file to each
4919 <literal>foreign import</literal> declaration in your code, but we
4920 don't recommend using this approach with GHC.</para>
4923 <sect2 id="inline-noinline-pragma">
4924 <title>INLINE and NOINLINE pragmas</title>
4926 <para>These pragmas control the inlining of function
4929 <sect3 id="inline-pragma">
4930 <title>INLINE pragma</title>
4931 <indexterm><primary>INLINE</primary></indexterm>
4933 <para>GHC (with <option>-O</option>, as always) tries to
4934 inline (or “unfold”) functions/values that are
4935 “small enough,” thus avoiding the call overhead
4936 and possibly exposing other more-wonderful optimisations.
4937 Normally, if GHC decides a function is “too
4938 expensive” to inline, it will not do so, nor will it
4939 export that unfolding for other modules to use.</para>
4941 <para>The sledgehammer you can bring to bear is the
4942 <literal>INLINE</literal><indexterm><primary>INLINE
4943 pragma</primary></indexterm> pragma, used thusly:</para>
4946 key_function :: Int -> String -> (Bool, Double)
4948 #ifdef __GLASGOW_HASKELL__
4949 {-# INLINE key_function #-}
4953 <para>(You don't need to do the C pre-processor carry-on
4954 unless you're going to stick the code through HBC—it
4955 doesn't like <literal>INLINE</literal> pragmas.)</para>
4957 <para>The major effect of an <literal>INLINE</literal> pragma
4958 is to declare a function's “cost” to be very low.
4959 The normal unfolding machinery will then be very keen to
4962 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4963 function can be put anywhere its type signature could be
4966 <para><literal>INLINE</literal> pragmas are a particularly
4968 <literal>then</literal>/<literal>return</literal> (or
4969 <literal>bind</literal>/<literal>unit</literal>) functions in
4970 a monad. For example, in GHC's own
4971 <literal>UniqueSupply</literal> monad code, we have:</para>
4974 #ifdef __GLASGOW_HASKELL__
4975 {-# INLINE thenUs #-}
4976 {-# INLINE returnUs #-}
4980 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4981 linkend="noinline-pragma"/>).</para>
4984 <sect3 id="noinline-pragma">
4985 <title>NOINLINE pragma</title>
4987 <indexterm><primary>NOINLINE</primary></indexterm>
4988 <indexterm><primary>NOTINLINE</primary></indexterm>
4990 <para>The <literal>NOINLINE</literal> pragma does exactly what
4991 you'd expect: it stops the named function from being inlined
4992 by the compiler. You shouldn't ever need to do this, unless
4993 you're very cautious about code size.</para>
4995 <para><literal>NOTINLINE</literal> is a synonym for
4996 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4997 specified by Haskell 98 as the standard way to disable
4998 inlining, so it should be used if you want your code to be
5002 <sect3 id="phase-control">
5003 <title>Phase control</title>
5005 <para> Sometimes you want to control exactly when in GHC's
5006 pipeline the INLINE pragma is switched on. Inlining happens
5007 only during runs of the <emphasis>simplifier</emphasis>. Each
5008 run of the simplifier has a different <emphasis>phase
5009 number</emphasis>; the phase number decreases towards zero.
5010 If you use <option>-dverbose-core2core</option> you'll see the
5011 sequence of phase numbers for successive runs of the
5012 simplifier. In an INLINE pragma you can optionally specify a
5013 phase number, thus:</para>
5017 <para>You can say "inline <literal>f</literal> in Phase 2
5018 and all subsequent phases":
5020 {-# INLINE [2] f #-}
5026 <para>You can say "inline <literal>g</literal> in all
5027 phases up to, but not including, Phase 3":
5029 {-# INLINE [~3] g #-}
5035 <para>If you omit the phase indicator, you mean "inline in
5040 <para>You can use a phase number on a NOINLINE pragma too:</para>
5044 <para>You can say "do not inline <literal>f</literal>
5045 until Phase 2; in Phase 2 and subsequently behave as if
5046 there was no pragma at all":
5048 {-# NOINLINE [2] f #-}
5054 <para>You can say "do not inline <literal>g</literal> in
5055 Phase 3 or any subsequent phase; before that, behave as if
5056 there was no pragma":
5058 {-# NOINLINE [~3] g #-}
5064 <para>If you omit the phase indicator, you mean "never
5065 inline this function".</para>
5069 <para>The same phase-numbering control is available for RULES
5070 (<xref linkend="rewrite-rules"/>).</para>
5074 <sect2 id="language-pragma">
5075 <title>LANGUAGE pragma</title>
5077 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5078 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5080 <para>This allows language extensions to be enabled in a portable way.
5081 It is the intention that all Haskell compilers support the
5082 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5083 all extensions are supported by all compilers, of
5084 course. The <literal>LANGUAGE</literal> pragma should be used instead
5085 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5087 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5089 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5091 <para>Any extension from the <literal>Extension</literal> type defined in
5093 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink> may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5097 <sect2 id="line-pragma">
5098 <title>LINE pragma</title>
5100 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5101 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5102 <para>This pragma is similar to C's <literal>#line</literal>
5103 pragma, and is mainly for use in automatically generated Haskell
5104 code. It lets you specify the line number and filename of the
5105 original code; for example</para>
5107 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5109 <para>if you'd generated the current file from something called
5110 <filename>Foo.vhs</filename> and this line corresponds to line
5111 42 in the original. GHC will adjust its error messages to refer
5112 to the line/file named in the <literal>LINE</literal>
5116 <sect2 id="options-pragma">
5117 <title>OPTIONS_GHC pragma</title>
5118 <indexterm><primary>OPTIONS_GHC</primary>
5120 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5123 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5124 additional options that are given to the compiler when compiling
5125 this source file. See <xref linkend="source-file-options"/> for
5128 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5129 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5133 <title>RULES pragma</title>
5135 <para>The RULES pragma lets you specify rewrite rules. It is
5136 described in <xref linkend="rewrite-rules"/>.</para>
5139 <sect2 id="specialize-pragma">
5140 <title>SPECIALIZE pragma</title>
5142 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5143 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5144 <indexterm><primary>overloading, death to</primary></indexterm>
5146 <para>(UK spelling also accepted.) For key overloaded
5147 functions, you can create extra versions (NB: more code space)
5148 specialised to particular types. Thus, if you have an
5149 overloaded function:</para>
5152 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5155 <para>If it is heavily used on lists with
5156 <literal>Widget</literal> keys, you could specialise it as
5160 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5163 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5164 be put anywhere its type signature could be put.</para>
5166 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5167 (a) a specialised version of the function and (b) a rewrite rule
5168 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5169 un-specialised function into a call to the specialised one.</para>
5171 <para>The type in a SPECIALIZE pragma can be any type that is less
5172 polymorphic than the type of the original function. In concrete terms,
5173 if the original function is <literal>f</literal> then the pragma
5175 {-# SPECIALIZE f :: <type> #-}
5177 is valid if and only if the defintion
5179 f_spec :: <type>
5182 is valid. Here are some examples (where we only give the type signature
5183 for the original function, not its code):
5185 f :: Eq a => a -> b -> b
5186 {-# SPECIALISE f :: Int -> b -> b #-}
5188 g :: (Eq a, Ix b) => a -> b -> b
5189 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5191 h :: Eq a => a -> a -> a
5192 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5194 The last of these examples will generate a
5195 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5196 well. If you use this kind of specialisation, let us know how well it works.
5199 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5200 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5201 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5202 The <literal>INLINE</literal> pragma affects the specialised verison of the
5203 function (only), and applies even if the function is recursive. The motivating
5206 -- A GADT for arrays with type-indexed representation
5208 ArrInt :: !Int -> ByteArray# -> Arr Int
5209 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5211 (!:) :: Arr e -> Int -> e
5212 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5213 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5214 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5215 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5217 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5218 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5219 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5220 the specialised function will be inlined. It has two calls to
5221 <literal>(!:)</literal>,
5222 both at type <literal>Int</literal>. Both these calls fire the first
5223 specialisation, whose body is also inlined. The result is a type-based
5224 unrolling of the indexing function.</para>
5225 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5226 on an ordinarily-recursive function.</para>
5228 <para>Note: In earlier versions of GHC, it was possible to provide your own
5229 specialised function for a given type:
5232 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5235 This feature has been removed, as it is now subsumed by the
5236 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5240 <sect2 id="specialize-instance-pragma">
5241 <title>SPECIALIZE instance pragma
5245 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5246 <indexterm><primary>overloading, death to</primary></indexterm>
5247 Same idea, except for instance declarations. For example:
5250 instance (Eq a) => Eq (Foo a) where {
5251 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5255 The pragma must occur inside the <literal>where</literal> part
5256 of the instance declaration.
5259 Compatible with HBC, by the way, except perhaps in the placement
5265 <sect2 id="unpack-pragma">
5266 <title>UNPACK pragma</title>
5268 <indexterm><primary>UNPACK</primary></indexterm>
5270 <para>The <literal>UNPACK</literal> indicates to the compiler
5271 that it should unpack the contents of a constructor field into
5272 the constructor itself, removing a level of indirection. For
5276 data T = T {-# UNPACK #-} !Float
5277 {-# UNPACK #-} !Float
5280 <para>will create a constructor <literal>T</literal> containing
5281 two unboxed floats. This may not always be an optimisation: if
5282 the <function>T</function> constructor is scrutinised and the
5283 floats passed to a non-strict function for example, they will
5284 have to be reboxed (this is done automatically by the
5287 <para>Unpacking constructor fields should only be used in
5288 conjunction with <option>-O</option>, in order to expose
5289 unfoldings to the compiler so the reboxing can be removed as
5290 often as possible. For example:</para>
5294 f (T f1 f2) = f1 + f2
5297 <para>The compiler will avoid reboxing <function>f1</function>
5298 and <function>f2</function> by inlining <function>+</function>
5299 on floats, but only when <option>-O</option> is on.</para>
5301 <para>Any single-constructor data is eligible for unpacking; for
5305 data T = T {-# UNPACK #-} !(Int,Int)
5308 <para>will store the two <literal>Int</literal>s directly in the
5309 <function>T</function> constructor, by flattening the pair.
5310 Multi-level unpacking is also supported:</para>
5313 data T = T {-# UNPACK #-} !S
5314 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5317 <para>will store two unboxed <literal>Int#</literal>s
5318 directly in the <function>T</function> constructor. The
5319 unpacker can see through newtypes, too.</para>
5321 <para>If a field cannot be unpacked, you will not get a warning,
5322 so it might be an idea to check the generated code with
5323 <option>-ddump-simpl</option>.</para>
5325 <para>See also the <option>-funbox-strict-fields</option> flag,
5326 which essentially has the effect of adding
5327 <literal>{-# UNPACK #-}</literal> to every strict
5328 constructor field.</para>
5333 <!-- ======================= REWRITE RULES ======================== -->
5335 <sect1 id="rewrite-rules">
5336 <title>Rewrite rules
5338 <indexterm><primary>RULES pragma</primary></indexterm>
5339 <indexterm><primary>pragma, RULES</primary></indexterm>
5340 <indexterm><primary>rewrite rules</primary></indexterm></title>
5343 The programmer can specify rewrite rules as part of the source program
5344 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5345 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5346 and (b) the <option>-frules-off</option> flag
5347 (<xref linkend="options-f"/>) is not specified.
5355 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5362 <title>Syntax</title>
5365 From a syntactic point of view:
5371 There may be zero or more rules in a <literal>RULES</literal> pragma.
5378 Each rule has a name, enclosed in double quotes. The name itself has
5379 no significance at all. It is only used when reporting how many times the rule fired.
5385 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5386 immediately after the name of the rule. Thus:
5389 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5392 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5393 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5402 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5403 is set, so you must lay out your rules starting in the same column as the
5404 enclosing definitions.
5411 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5412 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5413 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5414 by spaces, just like in a type <literal>forall</literal>.
5420 A pattern variable may optionally have a type signature.
5421 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5422 For example, here is the <literal>foldr/build</literal> rule:
5425 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5426 foldr k z (build g) = g k z
5429 Since <function>g</function> has a polymorphic type, it must have a type signature.
5436 The left hand side of a rule must consist of a top-level variable applied
5437 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5440 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5441 "wrong2" forall f. f True = True
5444 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5451 A rule does not need to be in the same module as (any of) the
5452 variables it mentions, though of course they need to be in scope.
5458 Rules are automatically exported from a module, just as instance declarations are.
5469 <title>Semantics</title>
5472 From a semantic point of view:
5478 Rules are only applied if you use the <option>-O</option> flag.
5484 Rules are regarded as left-to-right rewrite rules.
5485 When GHC finds an expression that is a substitution instance of the LHS
5486 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5487 By "a substitution instance" we mean that the LHS can be made equal to the
5488 expression by substituting for the pattern variables.
5495 The LHS and RHS of a rule are typechecked, and must have the
5503 GHC makes absolutely no attempt to verify that the LHS and RHS
5504 of a rule have the same meaning. That is undecidable in general, and
5505 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5512 GHC makes no attempt to make sure that the rules are confluent or
5513 terminating. For example:
5516 "loop" forall x,y. f x y = f y x
5519 This rule will cause the compiler to go into an infinite loop.
5526 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5532 GHC currently uses a very simple, syntactic, matching algorithm
5533 for matching a rule LHS with an expression. It seeks a substitution
5534 which makes the LHS and expression syntactically equal modulo alpha
5535 conversion. The pattern (rule), but not the expression, is eta-expanded if
5536 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5537 But not beta conversion (that's called higher-order matching).
5541 Matching is carried out on GHC's intermediate language, which includes
5542 type abstractions and applications. So a rule only matches if the
5543 types match too. See <xref linkend="rule-spec"/> below.
5549 GHC keeps trying to apply the rules as it optimises the program.
5550 For example, consider:
5559 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5560 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5561 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5562 not be substituted, and the rule would not fire.
5569 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5570 that appears on the LHS of a rule</emphasis>, because once you have substituted
5571 for something you can't match against it (given the simple minded
5572 matching). So if you write the rule
5575 "map/map" forall f,g. map f . map g = map (f.g)
5578 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5579 It will only match something written with explicit use of ".".
5580 Well, not quite. It <emphasis>will</emphasis> match the expression
5586 where <function>wibble</function> is defined:
5589 wibble f g = map f . map g
5592 because <function>wibble</function> will be inlined (it's small).
5594 Later on in compilation, GHC starts inlining even things on the
5595 LHS of rules, but still leaves the rules enabled. This inlining
5596 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5603 All rules are implicitly exported from the module, and are therefore
5604 in force in any module that imports the module that defined the rule, directly
5605 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5606 in force when compiling A.) The situation is very similar to that for instance
5618 <title>List fusion</title>
5621 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5622 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5623 intermediate list should be eliminated entirely.
5627 The following are good producers:
5639 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5645 Explicit lists (e.g. <literal>[True, False]</literal>)
5651 The cons constructor (e.g <literal>3:4:[]</literal>)
5657 <function>++</function>
5663 <function>map</function>
5669 <function>take</function>, <function>filter</function>
5675 <function>iterate</function>, <function>repeat</function>
5681 <function>zip</function>, <function>zipWith</function>
5690 The following are good consumers:
5702 <function>array</function> (on its second argument)
5708 <function>length</function>
5714 <function>++</function> (on its first argument)
5720 <function>foldr</function>
5726 <function>map</function>
5732 <function>take</function>, <function>filter</function>
5738 <function>concat</function>
5744 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5750 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5751 will fuse with one but not the other)
5757 <function>partition</function>
5763 <function>head</function>
5769 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5775 <function>sequence_</function>
5781 <function>msum</function>
5787 <function>sortBy</function>
5796 So, for example, the following should generate no intermediate lists:
5799 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5805 This list could readily be extended; if there are Prelude functions that you use
5806 a lot which are not included, please tell us.
5810 If you want to write your own good consumers or producers, look at the
5811 Prelude definitions of the above functions to see how to do so.
5816 <sect2 id="rule-spec">
5817 <title>Specialisation
5821 Rewrite rules can be used to get the same effect as a feature
5822 present in earlier versions of GHC.
5823 For example, suppose that:
5826 genericLookup :: Ord a => Table a b -> a -> b
5827 intLookup :: Table Int b -> Int -> b
5830 where <function>intLookup</function> is an implementation of
5831 <function>genericLookup</function> that works very fast for
5832 keys of type <literal>Int</literal>. You might wish
5833 to tell GHC to use <function>intLookup</function> instead of
5834 <function>genericLookup</function> whenever the latter was called with
5835 type <literal>Table Int b -> Int -> b</literal>.
5836 It used to be possible to write
5839 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5842 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5845 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5848 This slightly odd-looking rule instructs GHC to replace
5849 <function>genericLookup</function> by <function>intLookup</function>
5850 <emphasis>whenever the types match</emphasis>.
5851 What is more, this rule does not need to be in the same
5852 file as <function>genericLookup</function>, unlike the
5853 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5854 have an original definition available to specialise).
5857 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5858 <function>intLookup</function> really behaves as a specialised version
5859 of <function>genericLookup</function>!!!</para>
5861 <para>An example in which using <literal>RULES</literal> for
5862 specialisation will Win Big:
5865 toDouble :: Real a => a -> Double
5866 toDouble = fromRational . toRational
5868 {-# RULES "toDouble/Int" toDouble = i2d #-}
5869 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5872 The <function>i2d</function> function is virtually one machine
5873 instruction; the default conversion—via an intermediate
5874 <literal>Rational</literal>—is obscenely expensive by
5881 <title>Controlling what's going on</title>
5889 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5895 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5896 If you add <option>-dppr-debug</option> you get a more detailed listing.
5902 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5905 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5906 {-# INLINE build #-}
5910 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5911 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5912 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5913 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5920 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5921 see how to write rules that will do fusion and yet give an efficient
5922 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5932 <sect2 id="core-pragma">
5933 <title>CORE pragma</title>
5935 <indexterm><primary>CORE pragma</primary></indexterm>
5936 <indexterm><primary>pragma, CORE</primary></indexterm>
5937 <indexterm><primary>core, annotation</primary></indexterm>
5940 The external core format supports <quote>Note</quote> annotations;
5941 the <literal>CORE</literal> pragma gives a way to specify what these
5942 should be in your Haskell source code. Syntactically, core
5943 annotations are attached to expressions and take a Haskell string
5944 literal as an argument. The following function definition shows an
5948 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5951 Semantically, this is equivalent to:
5959 However, when external for is generated (via
5960 <option>-fext-core</option>), there will be Notes attached to the
5961 expressions <function>show</function> and <varname>x</varname>.
5962 The core function declaration for <function>f</function> is:
5966 f :: %forall a . GHCziShow.ZCTShow a ->
5967 a -> GHCziBase.ZMZN GHCziBase.Char =
5968 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5970 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5972 (tpl1::GHCziBase.Int ->
5974 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5976 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5977 (tpl3::GHCziBase.ZMZN a ->
5978 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5986 Here, we can see that the function <function>show</function> (which
5987 has been expanded out to a case expression over the Show dictionary)
5988 has a <literal>%note</literal> attached to it, as does the
5989 expression <varname>eta</varname> (which used to be called
5990 <varname>x</varname>).
5997 <sect1 id="generic-classes">
5998 <title>Generic classes</title>
6000 <para>(Note: support for generic classes is currently broken in
6004 The ideas behind this extension are described in detail in "Derivable type classes",
6005 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6006 An example will give the idea:
6014 fromBin :: [Int] -> (a, [Int])
6016 toBin {| Unit |} Unit = []
6017 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6018 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6019 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6021 fromBin {| Unit |} bs = (Unit, bs)
6022 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6023 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6024 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6025 (y,bs'') = fromBin bs'
6028 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6029 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6030 which are defined thus in the library module <literal>Generics</literal>:
6034 data a :+: b = Inl a | Inr b
6035 data a :*: b = a :*: b
6038 Now you can make a data type into an instance of Bin like this:
6040 instance (Bin a, Bin b) => Bin (a,b)
6041 instance Bin a => Bin [a]
6043 That is, just leave off the "where" clause. Of course, you can put in the
6044 where clause and over-ride whichever methods you please.
6048 <title> Using generics </title>
6049 <para>To use generics you need to</para>
6052 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6053 <option>-fgenerics</option> (to generate extra per-data-type code),
6054 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6058 <para>Import the module <literal>Generics</literal> from the
6059 <literal>lang</literal> package. This import brings into
6060 scope the data types <literal>Unit</literal>,
6061 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6062 don't need this import if you don't mention these types
6063 explicitly; for example, if you are simply giving instance
6064 declarations.)</para>
6069 <sect2> <title> Changes wrt the paper </title>
6071 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6072 can be written infix (indeed, you can now use
6073 any operator starting in a colon as an infix type constructor). Also note that
6074 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6075 Finally, note that the syntax of the type patterns in the class declaration
6076 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6077 alone would ambiguous when they appear on right hand sides (an extension we
6078 anticipate wanting).
6082 <sect2> <title>Terminology and restrictions</title>
6084 Terminology. A "generic default method" in a class declaration
6085 is one that is defined using type patterns as above.
6086 A "polymorphic default method" is a default method defined as in Haskell 98.
6087 A "generic class declaration" is a class declaration with at least one
6088 generic default method.
6096 Alas, we do not yet implement the stuff about constructor names and
6103 A generic class can have only one parameter; you can't have a generic
6104 multi-parameter class.
6110 A default method must be defined entirely using type patterns, or entirely
6111 without. So this is illegal:
6114 op :: a -> (a, Bool)
6115 op {| Unit |} Unit = (Unit, True)
6118 However it is perfectly OK for some methods of a generic class to have
6119 generic default methods and others to have polymorphic default methods.
6125 The type variable(s) in the type pattern for a generic method declaration
6126 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:
6130 op {| p :*: q |} (x :*: y) = op (x :: p)
6138 The type patterns in a generic default method must take one of the forms:
6144 where "a" and "b" are type variables. Furthermore, all the type patterns for
6145 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6146 must use the same type variables. So this is illegal:
6150 op {| a :+: b |} (Inl x) = True
6151 op {| p :+: q |} (Inr y) = False
6153 The type patterns must be identical, even in equations for different methods of the class.
6154 So this too is illegal:
6158 op1 {| a :*: b |} (x :*: y) = True
6161 op2 {| p :*: q |} (x :*: y) = False
6163 (The reason for this restriction is that we gather all the equations for a particular type consructor
6164 into a single generic instance declaration.)
6170 A generic method declaration must give a case for each of the three type constructors.
6176 The type for a generic method can be built only from:
6178 <listitem> <para> Function arrows </para> </listitem>
6179 <listitem> <para> Type variables </para> </listitem>
6180 <listitem> <para> Tuples </para> </listitem>
6181 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6183 Here are some example type signatures for generic methods:
6186 op2 :: Bool -> (a,Bool)
6187 op3 :: [Int] -> a -> a
6190 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6194 This restriction is an implementation restriction: we just havn't got around to
6195 implementing the necessary bidirectional maps over arbitrary type constructors.
6196 It would be relatively easy to add specific type constructors, such as Maybe and list,
6197 to the ones that are allowed.</para>
6202 In an instance declaration for a generic class, the idea is that the compiler
6203 will fill in the methods for you, based on the generic templates. However it can only
6208 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6213 No constructor of the instance type has unboxed fields.
6217 (Of course, these things can only arise if you are already using GHC extensions.)
6218 However, you can still give an instance declarations for types which break these rules,
6219 provided you give explicit code to override any generic default methods.
6227 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6228 what the compiler does with generic declarations.
6233 <sect2> <title> Another example </title>
6235 Just to finish with, here's another example I rather like:
6239 nCons {| Unit |} _ = 1
6240 nCons {| a :*: b |} _ = 1
6241 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6244 tag {| Unit |} _ = 1
6245 tag {| a :*: b |} _ = 1
6246 tag {| a :+: b |} (Inl x) = tag x
6247 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6256 ;;; Local Variables: ***
6258 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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