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.</para>
111 <para>New reserved words: <literal>foreign</literal>.</para>
117 <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
120 <para> These two flags control how generalisation is done.
121 See <xref linkend="monomorphism"/>.
128 <option>-fextended-default-rules</option>:
129 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
132 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
133 Independent of the <option>-fglasgow-exts</option>
140 <option>-fallow-overlapping-instances</option>
141 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
144 <option>-fallow-undecidable-instances</option>
145 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
148 <option>-fallow-incoherent-instances</option>
149 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
152 <option>-fcontext-stack=N</option>
153 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
156 <para> See <xref linkend="instance-decls"/>. Only relevant
157 if you also use <option>-fglasgow-exts</option>.</para>
163 <option>-finline-phase</option>
164 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
167 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
168 you also use <option>-fglasgow-exts</option>.</para>
174 <option>-farrows</option>
175 <indexterm><primary><option>-farrows</option></primary></indexterm>
178 <para>See <xref linkend="arrow-notation"/>. Independent of
179 <option>-fglasgow-exts</option>.</para>
181 <para>New reserved words/symbols: <literal>rec</literal>,
182 <literal>proc</literal>, <literal>-<</literal>,
183 <literal>>-</literal>, <literal>-<<</literal>,
184 <literal>>>-</literal>.</para>
186 <para>Other syntax stolen: <literal>(|</literal>,
187 <literal>|)</literal>.</para>
193 <option>-fgenerics</option>
194 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
197 <para>See <xref linkend="generic-classes"/>. Independent of
198 <option>-fglasgow-exts</option>.</para>
203 <term><option>-fno-implicit-prelude</option></term>
205 <para><indexterm><primary>-fno-implicit-prelude
206 option</primary></indexterm> GHC normally imports
207 <filename>Prelude.hi</filename> files for you. If you'd
208 rather it didn't, then give it a
209 <option>-fno-implicit-prelude</option> option. The idea is
210 that you can then import a Prelude of your own. (But don't
211 call it <literal>Prelude</literal>; the Haskell module
212 namespace is flat, and you must not conflict with any
213 Prelude module.)</para>
215 <para>Even though you have not imported the Prelude, most of
216 the built-in syntax still refers to the built-in Haskell
217 Prelude types and values, as specified by the Haskell
218 Report. For example, the type <literal>[Int]</literal>
219 still means <literal>Prelude.[] Int</literal>; tuples
220 continue to refer to the standard Prelude tuples; the
221 translation for list comprehensions continues to use
222 <literal>Prelude.map</literal> etc.</para>
224 <para>However, <option>-fno-implicit-prelude</option> does
225 change the handling of certain built-in syntax: see <xref
226 linkend="rebindable-syntax"/>.</para>
231 <term><option>-fimplicit-params</option></term>
233 <para>Enables implicit parameters (see <xref
234 linkend="implicit-parameters"/>). Currently also implied by
235 <option>-fglasgow-exts</option>.</para>
238 <literal>?<replaceable>varid</replaceable></literal>,
239 <literal>%<replaceable>varid</replaceable></literal>.</para>
244 <term><option>-fscoped-type-variables</option></term>
246 <para>Enables lexically-scoped type variables (see <xref
247 linkend="scoped-type-variables"/>). Implied by
248 <option>-fglasgow-exts</option>.</para>
253 <term><option>-fth</option></term>
255 <para>Enables Template Haskell (see <xref
256 linkend="template-haskell"/>). This flag must
257 be given explicitly; it is no longer implied by
258 <option>-fglasgow-exts</option>.</para>
260 <para>Syntax stolen: <literal>[|</literal>,
261 <literal>[e|</literal>, <literal>[p|</literal>,
262 <literal>[d|</literal>, <literal>[t|</literal>,
263 <literal>$(</literal>,
264 <literal>$<replaceable>varid</replaceable></literal>.</para>
271 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
272 <!-- included from primitives.sgml -->
273 <!-- &primitives; -->
274 <sect1 id="primitives">
275 <title>Unboxed types and primitive operations</title>
277 <para>GHC is built on a raft of primitive data types and operations.
278 While you really can use this stuff to write fast code,
279 we generally find it a lot less painful, and more satisfying in the
280 long run, to use higher-level language features and libraries. With
281 any luck, the code you write will be optimised to the efficient
282 unboxed version in any case. And if it isn't, we'd like to know
285 <para>We do not currently have good, up-to-date documentation about the
286 primitives, perhaps because they are mainly intended for internal use.
287 There used to be a long section about them here in the User Guide, but it
288 became out of date, and wrong information is worse than none.</para>
290 <para>The Real Truth about what primitive types there are, and what operations
291 work over those types, is held in the file
292 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
293 This file is used directly to generate GHC's primitive-operation definitions, so
294 it is always correct! It is also intended for processing into text.</para>
297 the result of such processing is part of the description of the
299 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
300 Core language</ulink>.
301 So that document is a good place to look for a type-set version.
302 We would be very happy if someone wanted to volunteer to produce an SGML
303 back end to the program that processes <filename>primops.txt</filename> so that
304 we could include the results here in the User Guide.</para>
306 <para>What follows here is a brief summary of some main points.</para>
308 <sect2 id="glasgow-unboxed">
313 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
316 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
317 that values of that type are represented by a pointer to a heap
318 object. The representation of a Haskell <literal>Int</literal>, for
319 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
320 type, however, is represented by the value itself, no pointers or heap
321 allocation are involved.
325 Unboxed types correspond to the “raw machine” types you
326 would use in C: <literal>Int#</literal> (long int),
327 <literal>Double#</literal> (double), <literal>Addr#</literal>
328 (void *), etc. The <emphasis>primitive operations</emphasis>
329 (PrimOps) on these types are what you might expect; e.g.,
330 <literal>(+#)</literal> is addition on
331 <literal>Int#</literal>s, and is the machine-addition that we all
332 know and love—usually one instruction.
336 Primitive (unboxed) types cannot be defined in Haskell, and are
337 therefore built into the language and compiler. Primitive types are
338 always unlifted; that is, a value of a primitive type cannot be
339 bottom. We use the convention that primitive types, values, and
340 operations have a <literal>#</literal> suffix.
344 Primitive values are often represented by a simple bit-pattern, such
345 as <literal>Int#</literal>, <literal>Float#</literal>,
346 <literal>Double#</literal>. But this is not necessarily the case:
347 a primitive value might be represented by a pointer to a
348 heap-allocated object. Examples include
349 <literal>Array#</literal>, the type of primitive arrays. A
350 primitive array is heap-allocated because it is too big a value to fit
351 in a register, and would be too expensive to copy around; in a sense,
352 it is accidental that it is represented by a pointer. If a pointer
353 represents a primitive value, then it really does point to that value:
354 no unevaluated thunks, no indirections…nothing can be at the
355 other end of the pointer than the primitive value.
356 A numerically-intensive program using unboxed types can
357 go a <emphasis>lot</emphasis> faster than its “standard”
358 counterpart—we saw a threefold speedup on one example.
362 There are some restrictions on the use of primitive types:
364 <listitem><para>The main restriction
365 is that you can't pass a primitive value to a polymorphic
366 function or store one in a polymorphic data type. This rules out
367 things like <literal>[Int#]</literal> (i.e. lists of primitive
368 integers). The reason for this restriction is that polymorphic
369 arguments and constructor fields are assumed to be pointers: if an
370 unboxed integer is stored in one of these, the garbage collector would
371 attempt to follow it, leading to unpredictable space leaks. Or a
372 <function>seq</function> operation on the polymorphic component may
373 attempt to dereference the pointer, with disastrous results. Even
374 worse, the unboxed value might be larger than a pointer
375 (<literal>Double#</literal> for instance).
378 <listitem><para> You cannot bind a variable with an unboxed type
379 in a <emphasis>top-level</emphasis> binding.
381 <listitem><para> You cannot bind a variable with an unboxed type
382 in a <emphasis>recursive</emphasis> binding.
384 <listitem><para> You may bind unboxed variables in a (non-recursive,
385 non-top-level) pattern binding, but any such variable causes the entire
387 to become strict. For example:
389 data Foo = Foo Int Int#
391 f x = let (Foo a b, w) = ..rhs.. in ..body..
393 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
395 is strict, and the program behaves as if you had written
397 data Foo = Foo Int Int#
399 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
408 <sect2 id="unboxed-tuples">
409 <title>Unboxed Tuples
413 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
414 they're available by default with <option>-fglasgow-exts</option>. An
415 unboxed tuple looks like this:
427 where <literal>e_1..e_n</literal> are expressions of any
428 type (primitive or non-primitive). The type of an unboxed tuple looks
433 Unboxed tuples are used for functions that need to return multiple
434 values, but they avoid the heap allocation normally associated with
435 using fully-fledged tuples. When an unboxed tuple is returned, the
436 components are put directly into registers or on the stack; the
437 unboxed tuple itself does not have a composite representation. Many
438 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
440 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
441 tuples to avoid unnecessary allocation during sequences of operations.
445 There are some pretty stringent restrictions on the use of unboxed tuples:
450 Values of unboxed tuple types are subject to the same restrictions as
451 other unboxed types; i.e. they may not be stored in polymorphic data
452 structures or passed to polymorphic functions.
459 No variable can have an unboxed tuple type, nor may a constructor or function
460 argument have an unboxed tuple type. The following are all illegal:
464 data Foo = Foo (# Int, Int #)
466 f :: (# Int, Int #) -> (# Int, Int #)
469 g :: (# Int, Int #) -> Int
472 h x = let y = (# x,x #) in ...
479 The typical use of unboxed tuples is simply to return multiple values,
480 binding those multiple results with a <literal>case</literal> expression, thus:
482 f x y = (# x+1, y-1 #)
483 g x = case f x x of { (# a, b #) -> a + b }
485 You can have an unboxed tuple in a pattern binding, thus
487 f x = let (# p,q #) = h x in ..body..
489 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
490 the resulting binding is lazy like any other Haskell pattern binding. The
491 above example desugars like this:
493 f x = let t = case h x o f{ (# p,q #) -> (p,q)
498 Indeed, the bindings can even be recursive.
505 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
507 <sect1 id="syntax-extns">
508 <title>Syntactic extensions</title>
510 <!-- ====================== HIERARCHICAL MODULES ======================= -->
512 <sect2 id="hierarchical-modules">
513 <title>Hierarchical Modules</title>
515 <para>GHC supports a small extension to the syntax of module
516 names: a module name is allowed to contain a dot
517 <literal>‘.’</literal>. This is also known as the
518 “hierarchical module namespace” extension, because
519 it extends the normally flat Haskell module namespace into a
520 more flexible hierarchy of modules.</para>
522 <para>This extension has very little impact on the language
523 itself; modules names are <emphasis>always</emphasis> fully
524 qualified, so you can just think of the fully qualified module
525 name as <quote>the module name</quote>. In particular, this
526 means that the full module name must be given after the
527 <literal>module</literal> keyword at the beginning of the
528 module; for example, the module <literal>A.B.C</literal> must
531 <programlisting>module A.B.C</programlisting>
534 <para>It is a common strategy to use the <literal>as</literal>
535 keyword to save some typing when using qualified names with
536 hierarchical modules. For example:</para>
539 import qualified Control.Monad.ST.Strict as ST
542 <para>For details on how GHC searches for source and interface
543 files in the presence of hierarchical modules, see <xref
544 linkend="search-path"/>.</para>
546 <para>GHC comes with a large collection of libraries arranged
547 hierarchically; see the accompanying library documentation.
548 There is an ongoing project to create and maintain a stable set
549 of <quote>core</quote> libraries used by several Haskell
550 compilers, and the libraries that GHC comes with represent the
551 current status of that project. For more details, see <ulink
552 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
553 Libraries</ulink>.</para>
557 <!-- ====================== PATTERN GUARDS ======================= -->
559 <sect2 id="pattern-guards">
560 <title>Pattern guards</title>
563 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
564 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.)
568 Suppose we have an abstract data type of finite maps, with a
572 lookup :: FiniteMap -> Int -> Maybe Int
575 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
576 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
580 clunky env var1 var2 | ok1 && ok2 = val1 + val2
581 | otherwise = var1 + var2
592 The auxiliary functions are
596 maybeToBool :: Maybe a -> Bool
597 maybeToBool (Just x) = True
598 maybeToBool Nothing = False
600 expectJust :: Maybe a -> a
601 expectJust (Just x) = x
602 expectJust Nothing = error "Unexpected Nothing"
606 What is <function>clunky</function> doing? The guard <literal>ok1 &&
607 ok2</literal> checks that both lookups succeed, using
608 <function>maybeToBool</function> to convert the <function>Maybe</function>
609 types to booleans. The (lazily evaluated) <function>expectJust</function>
610 calls extract the values from the results of the lookups, and binds the
611 returned values to <varname>val1</varname> and <varname>val2</varname>
612 respectively. If either lookup fails, then clunky takes the
613 <literal>otherwise</literal> case and returns the sum of its arguments.
617 This is certainly legal Haskell, but it is a tremendously verbose and
618 un-obvious way to achieve the desired effect. Arguably, a more direct way
619 to write clunky would be to use case expressions:
623 clunky env var1 var1 = case lookup env var1 of
625 Just val1 -> case lookup env var2 of
627 Just val2 -> val1 + val2
633 This is a bit shorter, but hardly better. Of course, we can rewrite any set
634 of pattern-matching, guarded equations as case expressions; that is
635 precisely what the compiler does when compiling equations! The reason that
636 Haskell provides guarded equations is because they allow us to write down
637 the cases we want to consider, one at a time, independently of each other.
638 This structure is hidden in the case version. Two of the right-hand sides
639 are really the same (<function>fail</function>), and the whole expression
640 tends to become more and more indented.
644 Here is how I would write clunky:
649 | Just val1 <- lookup env var1
650 , Just val2 <- lookup env var2
652 ...other equations for clunky...
656 The semantics should be clear enough. The qualifiers are matched in order.
657 For a <literal><-</literal> qualifier, which I call a pattern guard, the
658 right hand side is evaluated and matched against the pattern on the left.
659 If the match fails then the whole guard fails and the next equation is
660 tried. If it succeeds, then the appropriate binding takes place, and the
661 next qualifier is matched, in the augmented environment. Unlike list
662 comprehensions, however, the type of the expression to the right of the
663 <literal><-</literal> is the same as the type of the pattern to its
664 left. The bindings introduced by pattern guards scope over all the
665 remaining guard qualifiers, and over the right hand side of the equation.
669 Just as with list comprehensions, boolean expressions can be freely mixed
670 with among the pattern guards. For example:
681 Haskell's current guards therefore emerge as a special case, in which the
682 qualifier list has just one element, a boolean expression.
686 <!-- ===================== Recursive do-notation =================== -->
688 <sect2 id="mdo-notation">
689 <title>The recursive do-notation
692 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
693 "A recursive do for Haskell",
694 Levent Erkok, John Launchbury",
695 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
698 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
699 that is, the variables bound in a do-expression are visible only in the textually following
700 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
701 group. It turns out that several applications can benefit from recursive bindings in
702 the do-notation, and this extension provides the necessary syntactic support.
705 Here is a simple (yet contrived) example:
708 import Control.Monad.Fix
710 justOnes = mdo xs <- Just (1:xs)
714 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
718 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
721 class Monad m => MonadFix m where
722 mfix :: (a -> m a) -> m a
725 The function <literal>mfix</literal>
726 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
727 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
728 For details, see the above mentioned reference.
731 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
732 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
733 for Haskell's internal state monad (strict and lazy, respectively).
736 There are three important points in using the recursive-do notation:
739 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
740 than <literal>do</literal>).
744 You should <literal>import Control.Monad.Fix</literal>.
745 (Note: Strictly speaking, this import is required only when you need to refer to the name
746 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
747 are encouraged to always import this module when using the mdo-notation.)
751 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
757 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
758 contains up to date information on recursive monadic bindings.
762 Historical note: The old implementation of the mdo-notation (and most
763 of the existing documents) used the name
764 <literal>MonadRec</literal> for the class and the corresponding library.
765 This name is not supported by GHC.
771 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
773 <sect2 id="parallel-list-comprehensions">
774 <title>Parallel List Comprehensions</title>
775 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
777 <indexterm><primary>parallel list comprehensions</primary>
780 <para>Parallel list comprehensions are a natural extension to list
781 comprehensions. List comprehensions can be thought of as a nice
782 syntax for writing maps and filters. Parallel comprehensions
783 extend this to include the zipWith family.</para>
785 <para>A parallel list comprehension has multiple independent
786 branches of qualifier lists, each separated by a `|' symbol. For
787 example, the following zips together two lists:</para>
790 [ (x, y) | x <- xs | y <- ys ]
793 <para>The behavior of parallel list comprehensions follows that of
794 zip, in that the resulting list will have the same length as the
795 shortest branch.</para>
797 <para>We can define parallel list comprehensions by translation to
798 regular comprehensions. Here's the basic idea:</para>
800 <para>Given a parallel comprehension of the form: </para>
803 [ e | p1 <- e11, p2 <- e12, ...
804 | q1 <- e21, q2 <- e22, ...
809 <para>This will be translated to: </para>
812 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
813 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
818 <para>where `zipN' is the appropriate zip for the given number of
823 <sect2 id="rebindable-syntax">
824 <title>Rebindable syntax</title>
827 <para>GHC allows most kinds of built-in syntax to be rebound by
828 the user, to facilitate replacing the <literal>Prelude</literal>
829 with a home-grown version, for example.</para>
831 <para>You may want to define your own numeric class
832 hierarchy. It completely defeats that purpose if the
833 literal "1" means "<literal>Prelude.fromInteger
834 1</literal>", which is what the Haskell Report specifies.
835 So the <option>-fno-implicit-prelude</option> flag causes
836 the following pieces of built-in syntax to refer to
837 <emphasis>whatever is in scope</emphasis>, not the Prelude
842 <para>An integer literal <literal>368</literal> means
843 "<literal>fromInteger (368::Integer)</literal>", rather than
844 "<literal>Prelude.fromInteger (368::Integer)</literal>".
847 <listitem><para>Fractional literals are handed in just the same way,
848 except that the translation is
849 <literal>fromRational (3.68::Rational)</literal>.
852 <listitem><para>The equality test in an overloaded numeric pattern
853 uses whatever <literal>(==)</literal> is in scope.
856 <listitem><para>The subtraction operation, and the
857 greater-than-or-equal test, in <literal>n+k</literal> patterns
858 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
862 <para>Negation (e.g. "<literal>- (f x)</literal>")
863 means "<literal>negate (f x)</literal>", both in numeric
864 patterns, and expressions.
868 <para>"Do" notation is translated using whatever
869 functions <literal>(>>=)</literal>,
870 <literal>(>>)</literal>, and <literal>fail</literal>,
871 are in scope (not the Prelude
872 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
873 comprehensions, are unaffected. </para></listitem>
877 notation (see <xref linkend="arrow-notation"/>)
878 uses whatever <literal>arr</literal>,
879 <literal>(>>>)</literal>, <literal>first</literal>,
880 <literal>app</literal>, <literal>(|||)</literal> and
881 <literal>loop</literal> functions are in scope. But unlike the
882 other constructs, the types of these functions must match the
883 Prelude types very closely. Details are in flux; if you want
887 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
888 even if that is a little unexpected. For emample, the
889 static semantics of the literal <literal>368</literal>
890 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
891 <literal>fromInteger</literal> to have any of the types:
893 fromInteger :: Integer -> Integer
894 fromInteger :: forall a. Foo a => Integer -> a
895 fromInteger :: Num a => a -> Integer
896 fromInteger :: Integer -> Bool -> Bool
900 <para>Be warned: this is an experimental facility, with
901 fewer checks than usual. Use <literal>-dcore-lint</literal>
902 to typecheck the desugared program. If Core Lint is happy
903 you should be all right.</para>
907 <sect2 id="postfix-operators">
908 <title>Postfix operators</title>
911 GHC allows a small extension to the syntax of left operator sections, which
912 allows you to define postfix operators. The extension is this: the left section
916 is equivalent (from the point of view of both type checking and execution) to the expression
920 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
921 The strict Haskell 98 interpretation is that the section is equivalent to
925 That is, the operator must be a function of two arguments. GHC allows it to
926 take only one argument, and that in turn allows you to write the function
929 <para>Since this extension goes beyond Haskell 98, it should really be enabled
930 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
931 change their behaviour, of course.)
933 <para>The extension does not extend to the left-hand side of function
934 definitions; you must define such a function in prefix form.</para>
941 <!-- TYPE SYSTEM EXTENSIONS -->
942 <sect1 id="data-type-extensions">
943 <title>Extensions to data types and type synonyms</title>
945 <sect2 id="nullary-types">
946 <title>Data types with no constructors</title>
948 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
949 a data type with no constructors. For example:</para>
953 data T a -- T :: * -> *
956 <para>Syntactically, the declaration lacks the "= constrs" part. The
957 type can be parameterised over types of any kind, but if the kind is
958 not <literal>*</literal> then an explicit kind annotation must be used
959 (see <xref linkend="sec-kinding"/>).</para>
961 <para>Such data types have only one value, namely bottom.
962 Nevertheless, they can be useful when defining "phantom types".</para>
965 <sect2 id="infix-tycons">
966 <title>Infix type constructors, classes, and type variables</title>
969 GHC allows type constructors, classes, and type variables to be operators, and
970 to be written infix, very much like expressions. More specifically:
973 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
974 The lexical syntax is the same as that for data constructors.
977 Data type and type-synonym declarations can be written infix, parenthesised
978 if you want further arguments. E.g.
980 data a :*: b = Foo a b
981 type a :+: b = Either a b
982 class a :=: b where ...
984 data (a :**: b) x = Baz a b x
985 type (a :++: b) y = Either (a,b) y
989 Types, and class constraints, can be written infix. For example
992 f :: (a :=: b) => a -> b
996 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
997 The lexical syntax is the same as that for variable operators, excluding "(.)",
998 "(!)", and "(*)". In a binding position, the operator must be
999 parenthesised. For example:
1001 type T (+) = Int + Int
1005 liftA2 :: Arrow (~>)
1006 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1012 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1013 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1016 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1017 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1018 sets the fixity for a data constructor and the corresponding type constructor. For example:
1022 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1023 and similarly for <literal>:*:</literal>.
1024 <literal>Int `a` Bool</literal>.
1027 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1034 <sect2 id="type-synonyms">
1035 <title>Liberalised type synonyms</title>
1038 Type synonyms are like macros at the type level, and
1039 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1040 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1042 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1043 in a type synonym, thus:
1045 type Discard a = forall b. Show b => a -> b -> (a, String)
1050 g :: Discard Int -> (Int,String) -- A rank-2 type
1057 You can write an unboxed tuple in a type synonym:
1059 type Pr = (# Int, Int #)
1067 You can apply a type synonym to a forall type:
1069 type Foo a = a -> a -> Bool
1071 f :: Foo (forall b. b->b)
1073 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1075 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1080 You can apply a type synonym to a partially applied type synonym:
1082 type Generic i o = forall x. i x -> o x
1085 foo :: Generic Id []
1087 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1089 foo :: forall x. x -> [x]
1097 GHC currently does kind checking before expanding synonyms (though even that
1101 After expanding type synonyms, GHC does validity checking on types, looking for
1102 the following mal-formedness which isn't detected simply by kind checking:
1105 Type constructor applied to a type involving for-alls.
1108 Unboxed tuple on left of an arrow.
1111 Partially-applied type synonym.
1115 this will be rejected:
1117 type Pr = (# Int, Int #)
1122 because GHC does not allow unboxed tuples on the left of a function arrow.
1127 <sect2 id="existential-quantification">
1128 <title>Existentially quantified data constructors
1132 The idea of using existential quantification in data type declarations
1133 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1134 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1135 London, 1991). It was later formalised by Laufer and Odersky
1136 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1137 TOPLAS, 16(5), pp1411-1430, 1994).
1138 It's been in Lennart
1139 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1140 proved very useful. Here's the idea. Consider the declaration:
1146 data Foo = forall a. MkFoo a (a -> Bool)
1153 The data type <literal>Foo</literal> has two constructors with types:
1159 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1166 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1167 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1168 For example, the following expression is fine:
1174 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1180 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1181 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1182 isUpper</function> packages a character with a compatible function. These
1183 two things are each of type <literal>Foo</literal> and can be put in a list.
1187 What can we do with a value of type <literal>Foo</literal>?. In particular,
1188 what happens when we pattern-match on <function>MkFoo</function>?
1194 f (MkFoo val fn) = ???
1200 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1201 are compatible, the only (useful) thing we can do with them is to
1202 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1209 f (MkFoo val fn) = fn val
1215 What this allows us to do is to package heterogenous values
1216 together with a bunch of functions that manipulate them, and then treat
1217 that collection of packages in a uniform manner. You can express
1218 quite a bit of object-oriented-like programming this way.
1221 <sect4 id="existential">
1222 <title>Why existential?
1226 What has this to do with <emphasis>existential</emphasis> quantification?
1227 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1233 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1239 But Haskell programmers can safely think of the ordinary
1240 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1241 adding a new existential quantification construct.
1247 <title>Type classes</title>
1250 An easy extension is to allow
1251 arbitrary contexts before the constructor. For example:
1257 data Baz = forall a. Eq a => Baz1 a a
1258 | forall b. Show b => Baz2 b (b -> b)
1264 The two constructors have the types you'd expect:
1270 Baz1 :: forall a. Eq a => a -> a -> Baz
1271 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1277 But when pattern matching on <function>Baz1</function> the matched values can be compared
1278 for equality, and when pattern matching on <function>Baz2</function> the first matched
1279 value can be converted to a string (as well as applying the function to it).
1280 So this program is legal:
1287 f (Baz1 p q) | p == q = "Yes"
1289 f (Baz2 v fn) = show (fn v)
1295 Operationally, in a dictionary-passing implementation, the
1296 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1297 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1298 extract it on pattern matching.
1302 Notice the way that the syntax fits smoothly with that used for
1303 universal quantification earlier.
1308 <sect4 id="existential-records">
1309 <title>Record Constructors</title>
1312 GHC allows existentials to be used with records syntax as well. For example:
1315 data Counter a = forall self. NewCounter
1317 , _inc :: self -> self
1318 , _display :: self -> IO ()
1322 Here <literal>tag</literal> is a public field, with a well-typed selector
1323 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1324 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1325 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1326 compile-time error. In other words, <emphasis>GHC defines a record selector function
1327 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1328 (This example used an underscore in the fields for which record selectors
1329 will not be defined, but that is only programming style; GHC ignores them.)
1333 To make use of these hidden fields, we need to create some helper functions:
1336 inc :: Counter a -> Counter a
1337 inc (NewCounter x i d t) = NewCounter
1338 { _this = i x, _inc = i, _display = d, tag = t }
1340 display :: Counter a -> IO ()
1341 display NewCounter{ _this = x, _display = d } = d x
1344 Now we can define counters with different underlying implementations:
1347 counterA :: Counter String
1348 counterA = NewCounter
1349 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1351 counterB :: Counter String
1352 counterB = NewCounter
1353 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1356 display (inc counterA) -- prints "1"
1357 display (inc (inc counterB)) -- prints "##"
1360 At the moment, record update syntax is only supported for Haskell 98 data types,
1361 so the following function does <emphasis>not</emphasis> work:
1364 -- This is invalid; use explicit NewCounter instead for now
1365 setTag :: Counter a -> a -> Counter a
1366 setTag obj t = obj{ tag = t }
1375 <title>Restrictions</title>
1378 There are several restrictions on the ways in which existentially-quantified
1379 constructors can be use.
1388 When pattern matching, each pattern match introduces a new,
1389 distinct, type for each existential type variable. These types cannot
1390 be unified with any other type, nor can they escape from the scope of
1391 the pattern match. For example, these fragments are incorrect:
1399 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1400 is the result of <function>f1</function>. One way to see why this is wrong is to
1401 ask what type <function>f1</function> has:
1405 f1 :: Foo -> a -- Weird!
1409 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1414 f1 :: forall a. Foo -> a -- Wrong!
1418 The original program is just plain wrong. Here's another sort of error
1422 f2 (Baz1 a b) (Baz1 p q) = a==q
1426 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1427 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1428 from the two <function>Baz1</function> constructors.
1436 You can't pattern-match on an existentially quantified
1437 constructor in a <literal>let</literal> or <literal>where</literal> group of
1438 bindings. So this is illegal:
1442 f3 x = a==b where { Baz1 a b = x }
1445 Instead, use a <literal>case</literal> expression:
1448 f3 x = case x of Baz1 a b -> a==b
1451 In general, you can only pattern-match
1452 on an existentially-quantified constructor in a <literal>case</literal> expression or
1453 in the patterns of a function definition.
1455 The reason for this restriction is really an implementation one.
1456 Type-checking binding groups is already a nightmare without
1457 existentials complicating the picture. Also an existential pattern
1458 binding at the top level of a module doesn't make sense, because it's
1459 not clear how to prevent the existentially-quantified type "escaping".
1460 So for now, there's a simple-to-state restriction. We'll see how
1468 You can't use existential quantification for <literal>newtype</literal>
1469 declarations. So this is illegal:
1473 newtype T = forall a. Ord a => MkT a
1477 Reason: a value of type <literal>T</literal> must be represented as a
1478 pair of a dictionary for <literal>Ord t</literal> and a value of type
1479 <literal>t</literal>. That contradicts the idea that
1480 <literal>newtype</literal> should have no concrete representation.
1481 You can get just the same efficiency and effect by using
1482 <literal>data</literal> instead of <literal>newtype</literal>. If
1483 there is no overloading involved, then there is more of a case for
1484 allowing an existentially-quantified <literal>newtype</literal>,
1485 because the <literal>data</literal> version does carry an
1486 implementation cost, but single-field existentially quantified
1487 constructors aren't much use. So the simple restriction (no
1488 existential stuff on <literal>newtype</literal>) stands, unless there
1489 are convincing reasons to change it.
1497 You can't use <literal>deriving</literal> to define instances of a
1498 data type with existentially quantified data constructors.
1500 Reason: in most cases it would not make sense. For example:;
1503 data T = forall a. MkT [a] deriving( Eq )
1506 To derive <literal>Eq</literal> in the standard way we would need to have equality
1507 between the single component of two <function>MkT</function> constructors:
1511 (MkT a) == (MkT b) = ???
1514 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1515 It's just about possible to imagine examples in which the derived instance
1516 would make sense, but it seems altogether simpler simply to prohibit such
1517 declarations. Define your own instances!
1528 <!-- ====================== Generalised algebraic data types ======================= -->
1530 <sect2 id="gadt-style">
1531 <title>Declaring data types with explicit constructor signatures</title>
1533 <para>GHC allows you to declare an algebraic data type by
1534 giving the type signatures of constructors explicitly. For example:
1538 Just :: a -> Maybe a
1540 The form is called a "GADT-style declaration"
1541 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1542 can only be declared using this form.</para>
1543 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1544 For example, these two declarations are equivalent:
1546 data Foo = forall a. MkFoo a (a -> Bool)
1547 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1550 <para>Any data type that can be declared in standard Haskell-98 syntax
1551 can also be declared using GADT-style syntax.
1552 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1553 they treat class constraints on the data constructors differently.
1554 Specifically, if the constructor is given a type-class context, that
1555 context is made available by pattern matching. For example:
1558 MkSet :: Eq a => [a] -> Set a
1560 makeSet :: Eq a => [a] -> Set a
1561 makeSet xs = MkSet (nub xs)
1563 insert :: a -> Set a -> Set a
1564 insert a (MkSet as) | a `elem` as = MkSet as
1565 | otherwise = MkSet (a:as)
1567 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1568 gives rise to a <literal>(Eq a)</literal>
1569 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1570 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1571 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1572 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1573 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1574 In the example, the equality dictionary is used to satisfy the equality constraint
1575 generated by the call to <literal>elem</literal>, so that the type of
1576 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1578 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1579 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1580 In Haskell 98 the defintion
1582 data Eq a => Set' a = MkSet' [a]
1584 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1585 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1586 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1587 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1588 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1590 For example, a possible application of GHC's behaviour is to reify dictionaries:
1592 data NumInst a where
1593 MkNumInst :: Num a => NumInst a
1595 intInst :: NumInst Int
1598 plus :: NumInst a -> a -> a -> a
1599 plus MkNumInst p q = p + q
1601 Here, a value of type <literal>NumInst a</literal> is equivalent
1602 to an explicit <literal>(Num a)</literal> dictionary.
1606 The rest of this section gives further details about GADT-style data
1611 The result type of each data constructor must begin with the type constructor being defined.
1612 If the result type of all constructors
1613 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1614 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1615 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1619 The type signature of
1620 each constructor is independent, and is implicitly universally quantified as usual.
1621 Different constructors may have different universally-quantified type variables
1622 and different type-class constraints.
1623 For example, this is fine:
1626 T1 :: Eq b => b -> T b
1627 T2 :: (Show c, Ix c) => c -> [c] -> T c
1632 Unlike a Haskell-98-style
1633 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1634 have no scope. Indeed, one can write a kind signature instead:
1636 data Set :: * -> * where ...
1638 or even a mixture of the two:
1640 data Foo a :: (* -> *) -> * where ...
1642 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1645 data Foo a (b :: * -> *) where ...
1651 You can use strictness annotations, in the obvious places
1652 in the constructor type:
1655 Lit :: !Int -> Term Int
1656 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1657 Pair :: Term a -> Term b -> Term (a,b)
1662 You can use a <literal>deriving</literal> clause on a GADT-style data type
1663 declaration. For example, these two declarations are equivalent
1665 data Maybe1 a where {
1666 Nothing1 :: Maybe1 a ;
1667 Just1 :: a -> Maybe1 a
1668 } deriving( Eq, Ord )
1670 data Maybe2 a = Nothing2 | Just2 a
1676 You can use record syntax on a GADT-style data type declaration:
1680 Adult { name :: String, children :: [Person] } :: Person
1681 Child { name :: String } :: Person
1683 As usual, for every constructor that has a field <literal>f</literal>, the type of
1684 field <literal>f</literal> must be the same (modulo alpha conversion).
1687 At the moment, record updates are not yet possible with GADT-style declarations,
1688 so support is limited to record construction, selection and pattern matching.
1691 aPerson = Adult { name = "Fred", children = [] }
1693 shortName :: Person -> Bool
1694 hasChildren (Adult { children = kids }) = not (null kids)
1695 hasChildren (Child {}) = False
1700 As in the case of existentials declared using the Haskell-98-like record syntax
1701 (<xref linkend="existential-records"/>),
1702 record-selector functions are generated only for those fields that have well-typed
1704 Here is the example of that section, in GADT-style syntax:
1706 data Counter a where
1707 NewCounter { _this :: self
1708 , _inc :: self -> self
1709 , _display :: self -> IO ()
1714 As before, only one selector function is generated here, that for <literal>tag</literal>.
1715 Nevertheless, you can still use all the field names in pattern matching and record construction.
1717 </itemizedlist></para>
1721 <title>Generalised Algebraic Data Types (GADTs)</title>
1723 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1724 by allowing constructors to have richer return types. Here is an example:
1727 Lit :: Int -> Term Int
1728 Succ :: Term Int -> Term Int
1729 IsZero :: Term Int -> Term Bool
1730 If :: Term Bool -> Term a -> Term a -> Term a
1731 Pair :: Term a -> Term b -> Term (a,b)
1733 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1734 case with ordinary data types. This generality allows us to
1735 write a well-typed <literal>eval</literal> function
1736 for these <literal>Terms</literal>:
1740 eval (Succ t) = 1 + eval t
1741 eval (IsZero t) = eval t == 0
1742 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1743 eval (Pair e1 e2) = (eval e1, eval e2)
1745 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1746 For example, in the right hand side of the equation
1751 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1752 A precise specification of the type rules is beyond what this user manual aspires to,
1753 but the design closely follows that described in
1755 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1756 unification-based type inference for GADTs</ulink>,
1758 The general principle is this: <emphasis>type refinement is only carried out
1759 based on user-supplied type annotations</emphasis>.
1760 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1761 and lots of obscure error messages will
1762 occur. However, the refinement is quite general. For example, if we had:
1764 eval :: Term a -> a -> a
1765 eval (Lit i) j = i+j
1767 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1768 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1769 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1772 These and many other examples are given in papers by Hongwei Xi, and
1773 Tim Sheard. There is a longer introduction
1774 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1776 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
1777 may use different notation to that implemented in GHC.
1780 The rest of this section outlines the extensions to GHC that support GADTs.
1783 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1784 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1785 The result type of each constructor must begin with the type constructor being defined,
1786 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1787 For example, in the <literal>Term</literal> data
1788 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1789 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1794 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1795 an ordianary data type.
1799 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1803 Lit { val :: Int } :: Term Int
1804 Succ { num :: Term Int } :: Term Int
1805 Pred { num :: Term Int } :: Term Int
1806 IsZero { arg :: Term Int } :: Term Bool
1807 Pair { arg1 :: Term a
1810 If { cnd :: Term Bool
1815 However, for GADTs there is the following additional constraint:
1816 every constructor that has a field <literal>f</literal> must have
1817 the same result type (modulo alpha conversion)
1818 Hence, in the above example, we cannot merge the <literal>num</literal>
1819 and <literal>arg</literal> fields above into a
1820 single name. Although their field types are both <literal>Term Int</literal>,
1821 their selector functions actually have different types:
1824 num :: Term Int -> Term Int
1825 arg :: Term Bool -> Term Int
1834 <!-- ====================== End of Generalised algebraic data types ======================= -->
1837 <sect2 id="deriving-typeable">
1838 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1841 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1842 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1843 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1844 classes <literal>Eq</literal>, <literal>Ord</literal>,
1845 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1848 GHC extends this list with two more classes that may be automatically derived
1849 (provided the <option>-fglasgow-exts</option> flag is specified):
1850 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1851 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1852 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1854 <para>An instance of <literal>Typeable</literal> can only be derived if the
1855 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1856 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1858 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1859 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1861 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1862 are used, and only <literal>Typeable1</literal> up to
1863 <literal>Typeable7</literal> are provided in the library.)
1864 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1865 class, whose kind suits that of the data type constructor, and
1866 then writing the data type instance by hand.
1870 <sect2 id="newtype-deriving">
1871 <title>Generalised derived instances for newtypes</title>
1874 When you define an abstract type using <literal>newtype</literal>, you may want
1875 the new type to inherit some instances from its representation. In
1876 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1877 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1878 other classes you have to write an explicit instance declaration. For
1879 example, if you define
1882 newtype Dollars = Dollars Int
1885 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1886 explicitly define an instance of <literal>Num</literal>:
1889 instance Num Dollars where
1890 Dollars a + Dollars b = Dollars (a+b)
1893 All the instance does is apply and remove the <literal>newtype</literal>
1894 constructor. It is particularly galling that, since the constructor
1895 doesn't appear at run-time, this instance declaration defines a
1896 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1897 dictionary, only slower!
1901 <sect3> <title> Generalising the deriving clause </title>
1903 GHC now permits such instances to be derived instead, so one can write
1905 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1908 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1909 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1910 derives an instance declaration of the form
1913 instance Num Int => Num Dollars
1916 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1920 We can also derive instances of constructor classes in a similar
1921 way. For example, suppose we have implemented state and failure monad
1922 transformers, such that
1925 instance Monad m => Monad (State s m)
1926 instance Monad m => Monad (Failure m)
1928 In Haskell 98, we can define a parsing monad by
1930 type Parser tok m a = State [tok] (Failure m) a
1933 which is automatically a monad thanks to the instance declarations
1934 above. With the extension, we can make the parser type abstract,
1935 without needing to write an instance of class <literal>Monad</literal>, via
1938 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1941 In this case the derived instance declaration is of the form
1943 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1946 Notice that, since <literal>Monad</literal> is a constructor class, the
1947 instance is a <emphasis>partial application</emphasis> of the new type, not the
1948 entire left hand side. We can imagine that the type declaration is
1949 ``eta-converted'' to generate the context of the instance
1954 We can even derive instances of multi-parameter classes, provided the
1955 newtype is the last class parameter. In this case, a ``partial
1956 application'' of the class appears in the <literal>deriving</literal>
1957 clause. For example, given the class
1960 class StateMonad s m | m -> s where ...
1961 instance Monad m => StateMonad s (State s m) where ...
1963 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1965 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1966 deriving (Monad, StateMonad [tok])
1969 The derived instance is obtained by completing the application of the
1970 class to the new type:
1973 instance StateMonad [tok] (State [tok] (Failure m)) =>
1974 StateMonad [tok] (Parser tok m)
1979 As a result of this extension, all derived instances in newtype
1980 declarations are treated uniformly (and implemented just by reusing
1981 the dictionary for the representation type), <emphasis>except</emphasis>
1982 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
1983 the newtype and its representation.
1987 <sect3> <title> A more precise specification </title>
1989 Derived instance declarations are constructed as follows. Consider the
1990 declaration (after expansion of any type synonyms)
1993 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
1999 The <literal>ci</literal> are partial applications of
2000 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2001 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2004 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2007 The type <literal>t</literal> is an arbitrary type.
2010 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2011 nor in the <literal>ci</literal>, and
2014 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2015 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2016 should not "look through" the type or its constructor. You can still
2017 derive these classes for a newtype, but it happens in the usual way, not
2018 via this new mechanism.
2021 Then, for each <literal>ci</literal>, the derived instance
2024 instance ci t => ci (T v1...vk)
2026 As an example which does <emphasis>not</emphasis> work, consider
2028 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2030 Here we cannot derive the instance
2032 instance Monad (State s m) => Monad (NonMonad m)
2035 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2036 and so cannot be "eta-converted" away. It is a good thing that this
2037 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2038 not, in fact, a monad --- for the same reason. Try defining
2039 <literal>>>=</literal> with the correct type: you won't be able to.
2043 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2044 important, since we can only derive instances for the last one. If the
2045 <literal>StateMonad</literal> class above were instead defined as
2048 class StateMonad m s | m -> s where ...
2051 then we would not have been able to derive an instance for the
2052 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2053 classes usually have one "main" parameter for which deriving new
2054 instances is most interesting.
2056 <para>Lastly, all of this applies only for classes other than
2057 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2058 and <literal>Data</literal>, for which the built-in derivation applies (section
2059 4.3.3. of the Haskell Report).
2060 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2061 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2062 the standard method is used or the one described here.)
2068 <sect2 id="stand-alone-deriving">
2069 <title>Stand-alone deriving declarations</title>
2072 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2074 data Foo a = Bar a | Baz String
2076 derive instance Eq (Foo a)
2078 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2079 you can use it as a variable name elsewhere.</para>
2080 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2081 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2084 newtype Foo a = MkFoo (State Int a)
2086 derive instance MonadState Int Foo
2088 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2089 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2097 <!-- TYPE SYSTEM EXTENSIONS -->
2098 <sect1 id="other-type-extensions">
2099 <title>Other type system extensions</title>
2101 <sect2 id="multi-param-type-classes">
2102 <title>Class declarations</title>
2105 This section, and the next one, documents GHC's type-class extensions.
2106 There's lots of background in the paper <ulink
2107 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2108 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2109 Jones, Erik Meijer).
2112 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2116 <title>Multi-parameter type classes</title>
2118 Multi-parameter type classes are permitted. For example:
2122 class Collection c a where
2123 union :: c a -> c a -> c a
2131 <title>The superclasses of a class declaration</title>
2134 There are no restrictions on the context in a class declaration
2135 (which introduces superclasses), except that the class hierarchy must
2136 be acyclic. So these class declarations are OK:
2140 class Functor (m k) => FiniteMap m k where
2143 class (Monad m, Monad (t m)) => Transform t m where
2144 lift :: m a -> (t m) a
2150 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2151 of "acyclic" involves only the superclass relationships. For example,
2157 op :: D b => a -> b -> b
2160 class C a => D a where { ... }
2164 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2165 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2166 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2173 <sect3 id="class-method-types">
2174 <title>Class method types</title>
2177 Haskell 98 prohibits class method types to mention constraints on the
2178 class type variable, thus:
2181 fromList :: [a] -> s a
2182 elem :: Eq a => a -> s a -> Bool
2184 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2185 contains the constraint <literal>Eq a</literal>, constrains only the
2186 class type variable (in this case <literal>a</literal>).
2187 GHC lifts this restriction.
2194 <sect2 id="functional-dependencies">
2195 <title>Functional dependencies
2198 <para> Functional dependencies are implemented as described by Mark Jones
2199 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2200 In Proceedings of the 9th European Symposium on Programming,
2201 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2205 Functional dependencies are introduced by a vertical bar in the syntax of a
2206 class declaration; e.g.
2208 class (Monad m) => MonadState s m | m -> s where ...
2210 class Foo a b c | a b -> c where ...
2212 There should be more documentation, but there isn't (yet). Yell if you need it.
2215 <sect3><title>Rules for functional dependencies </title>
2217 In a class declaration, all of the class type variables must be reachable (in the sense
2218 mentioned in <xref linkend="type-restrictions"/>)
2219 from the free variables of each method type.
2223 class Coll s a where
2225 insert :: s -> a -> s
2228 is not OK, because the type of <literal>empty</literal> doesn't mention
2229 <literal>a</literal>. Functional dependencies can make the type variable
2232 class Coll s a | s -> a where
2234 insert :: s -> a -> s
2237 Alternatively <literal>Coll</literal> might be rewritten
2240 class Coll s a where
2242 insert :: s a -> a -> s a
2246 which makes the connection between the type of a collection of
2247 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2248 Occasionally this really doesn't work, in which case you can split the
2256 class CollE s => Coll s a where
2257 insert :: s -> a -> s
2264 <title>Background on functional dependencies</title>
2266 <para>The following description of the motivation and use of functional dependencies is taken
2267 from the Hugs user manual, reproduced here (with minor changes) by kind
2268 permission of Mark Jones.
2271 Consider the following class, intended as part of a
2272 library for collection types:
2274 class Collects e ce where
2276 insert :: e -> ce -> ce
2277 member :: e -> ce -> Bool
2279 The type variable e used here represents the element type, while ce is the type
2280 of the container itself. Within this framework, we might want to define
2281 instances of this class for lists or characteristic functions (both of which
2282 can be used to represent collections of any equality type), bit sets (which can
2283 be used to represent collections of characters), or hash tables (which can be
2284 used to represent any collection whose elements have a hash function). Omitting
2285 standard implementation details, this would lead to the following declarations:
2287 instance Eq e => Collects e [e] where ...
2288 instance Eq e => Collects e (e -> Bool) where ...
2289 instance Collects Char BitSet where ...
2290 instance (Hashable e, Collects a ce)
2291 => Collects e (Array Int ce) where ...
2293 All this looks quite promising; we have a class and a range of interesting
2294 implementations. Unfortunately, there are some serious problems with the class
2295 declaration. First, the empty function has an ambiguous type:
2297 empty :: Collects e ce => ce
2299 By "ambiguous" we mean that there is a type variable e that appears on the left
2300 of the <literal>=></literal> symbol, but not on the right. The problem with
2301 this is that, according to the theoretical foundations of Haskell overloading,
2302 we cannot guarantee a well-defined semantics for any term with an ambiguous
2306 We can sidestep this specific problem by removing the empty member from the
2307 class declaration. However, although the remaining members, insert and member,
2308 do not have ambiguous types, we still run into problems when we try to use
2309 them. For example, consider the following two functions:
2311 f x y = insert x . insert y
2314 for which GHC infers the following types:
2316 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2317 g :: (Collects Bool c, Collects Char c) => c -> c
2319 Notice that the type for f allows the two parameters x and y to be assigned
2320 different types, even though it attempts to insert each of the two values, one
2321 after the other, into the same collection. If we're trying to model collections
2322 that contain only one type of value, then this is clearly an inaccurate
2323 type. Worse still, the definition for g is accepted, without causing a type
2324 error. As a result, the error in this code will not be flagged at the point
2325 where it appears. Instead, it will show up only when we try to use g, which
2326 might even be in a different module.
2329 <sect4><title>An attempt to use constructor classes</title>
2332 Faced with the problems described above, some Haskell programmers might be
2333 tempted to use something like the following version of the class declaration:
2335 class Collects e c where
2337 insert :: e -> c e -> c e
2338 member :: e -> c e -> Bool
2340 The key difference here is that we abstract over the type constructor c that is
2341 used to form the collection type c e, and not over that collection type itself,
2342 represented by ce in the original class declaration. This avoids the immediate
2343 problems that we mentioned above: empty has type <literal>Collects e c => c
2344 e</literal>, which is not ambiguous.
2347 The function f from the previous section has a more accurate type:
2349 f :: (Collects e c) => e -> e -> c e -> c e
2351 The function g from the previous section is now rejected with a type error as
2352 we would hope because the type of f does not allow the two arguments to have
2354 This, then, is an example of a multiple parameter class that does actually work
2355 quite well in practice, without ambiguity problems.
2356 There is, however, a catch. This version of the Collects class is nowhere near
2357 as general as the original class seemed to be: only one of the four instances
2358 for <literal>Collects</literal>
2359 given above can be used with this version of Collects because only one of
2360 them---the instance for lists---has a collection type that can be written in
2361 the form c e, for some type constructor c, and element type e.
2365 <sect4><title>Adding functional dependencies</title>
2368 To get a more useful version of the Collects class, Hugs provides a mechanism
2369 that allows programmers to specify dependencies between the parameters of a
2370 multiple parameter class (For readers with an interest in theoretical
2371 foundations and previous work: The use of dependency information can be seen
2372 both as a generalization of the proposal for `parametric type classes' that was
2373 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2374 later framework for "improvement" of qualified types. The
2375 underlying ideas are also discussed in a more theoretical and abstract setting
2376 in a manuscript [implparam], where they are identified as one point in a
2377 general design space for systems of implicit parameterization.).
2379 To start with an abstract example, consider a declaration such as:
2381 class C a b where ...
2383 which tells us simply that C can be thought of as a binary relation on types
2384 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2385 included in the definition of classes to add information about dependencies
2386 between parameters, as in the following examples:
2388 class D a b | a -> b where ...
2389 class E a b | a -> b, b -> a where ...
2391 The notation <literal>a -> b</literal> used here between the | and where
2392 symbols --- not to be
2393 confused with a function type --- indicates that the a parameter uniquely
2394 determines the b parameter, and might be read as "a determines b." Thus D is
2395 not just a relation, but actually a (partial) function. Similarly, from the two
2396 dependencies that are included in the definition of E, we can see that E
2397 represents a (partial) one-one mapping between types.
2400 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2401 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2402 m>=0, meaning that the y parameters are uniquely determined by the x
2403 parameters. Spaces can be used as separators if more than one variable appears
2404 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2405 annotated with multiple dependencies using commas as separators, as in the
2406 definition of E above. Some dependencies that we can write in this notation are
2407 redundant, and will be rejected because they don't serve any useful
2408 purpose, and may instead indicate an error in the program. Examples of
2409 dependencies like this include <literal>a -> a </literal>,
2410 <literal>a -> a a </literal>,
2411 <literal>a -> </literal>, etc. There can also be
2412 some redundancy if multiple dependencies are given, as in
2413 <literal>a->b</literal>,
2414 <literal>b->c </literal>, <literal>a->c </literal>, and
2415 in which some subset implies the remaining dependencies. Examples like this are
2416 not treated as errors. Note that dependencies appear only in class
2417 declarations, and not in any other part of the language. In particular, the
2418 syntax for instance declarations, class constraints, and types is completely
2422 By including dependencies in a class declaration, we provide a mechanism for
2423 the programmer to specify each multiple parameter class more precisely. The
2424 compiler, on the other hand, is responsible for ensuring that the set of
2425 instances that are in scope at any given point in the program is consistent
2426 with any declared dependencies. For example, the following pair of instance
2427 declarations cannot appear together in the same scope because they violate the
2428 dependency for D, even though either one on its own would be acceptable:
2430 instance D Bool Int where ...
2431 instance D Bool Char where ...
2433 Note also that the following declaration is not allowed, even by itself:
2435 instance D [a] b where ...
2437 The problem here is that this instance would allow one particular choice of [a]
2438 to be associated with more than one choice for b, which contradicts the
2439 dependency specified in the definition of D. More generally, this means that,
2440 in any instance of the form:
2442 instance D t s where ...
2444 for some particular types t and s, the only variables that can appear in s are
2445 the ones that appear in t, and hence, if the type t is known, then s will be
2446 uniquely determined.
2449 The benefit of including dependency information is that it allows us to define
2450 more general multiple parameter classes, without ambiguity problems, and with
2451 the benefit of more accurate types. To illustrate this, we return to the
2452 collection class example, and annotate the original definition of <literal>Collects</literal>
2453 with a simple dependency:
2455 class Collects e ce | ce -> e where
2457 insert :: e -> ce -> ce
2458 member :: e -> ce -> Bool
2460 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2461 determined by the type of the collection ce. Note that both parameters of
2462 Collects are of kind *; there are no constructor classes here. Note too that
2463 all of the instances of Collects that we gave earlier can be used
2464 together with this new definition.
2467 What about the ambiguity problems that we encountered with the original
2468 definition? The empty function still has type Collects e ce => ce, but it is no
2469 longer necessary to regard that as an ambiguous type: Although the variable e
2470 does not appear on the right of the => symbol, the dependency for class
2471 Collects tells us that it is uniquely determined by ce, which does appear on
2472 the right of the => symbol. Hence the context in which empty is used can still
2473 give enough information to determine types for both ce and e, without
2474 ambiguity. More generally, we need only regard a type as ambiguous if it
2475 contains a variable on the left of the => that is not uniquely determined
2476 (either directly or indirectly) by the variables on the right.
2479 Dependencies also help to produce more accurate types for user defined
2480 functions, and hence to provide earlier detection of errors, and less cluttered
2481 types for programmers to work with. Recall the previous definition for a
2484 f x y = insert x y = insert x . insert y
2486 for which we originally obtained a type:
2488 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2490 Given the dependency information that we have for Collects, however, we can
2491 deduce that a and b must be equal because they both appear as the second
2492 parameter in a Collects constraint with the same first parameter c. Hence we
2493 can infer a shorter and more accurate type for f:
2495 f :: (Collects a c) => a -> a -> c -> c
2497 In a similar way, the earlier definition of g will now be flagged as a type error.
2500 Although we have given only a few examples here, it should be clear that the
2501 addition of dependency information can help to make multiple parameter classes
2502 more useful in practice, avoiding ambiguity problems, and allowing more general
2503 sets of instance declarations.
2509 <sect2 id="instance-decls">
2510 <title>Instance declarations</title>
2512 <sect3 id="instance-rules">
2513 <title>Relaxed rules for instance declarations</title>
2515 <para>An instance declaration has the form
2517 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 ...
2519 The part before the "<literal>=></literal>" is the
2520 <emphasis>context</emphasis>, while the part after the
2521 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2525 In Haskell 98 the head of an instance declaration
2526 must be of the form <literal>C (T a1 ... an)</literal>, where
2527 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2528 and the <literal>a1 ... an</literal> are distinct type variables.
2529 Furthermore, the assertions in the context of the instance declaration
2530 must be of the form <literal>C a</literal> where <literal>a</literal>
2531 is a type variable that occurs in the head.
2534 The <option>-fglasgow-exts</option> flag loosens these restrictions
2535 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2536 the context and head of the instance declaration can each consist of arbitrary
2537 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2541 For each assertion in the context:
2543 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2544 <listitem><para>The assertion has fewer constructors and variables (taken together
2545 and counting repetitions) than the head</para></listitem>
2549 <listitem><para>The coverage condition. For each functional dependency,
2550 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2551 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2552 every type variable in
2553 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2554 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2555 substitution mapping each type variable in the class declaration to the
2556 corresponding type in the instance declaration.
2559 These restrictions ensure that context reduction terminates: each reduction
2560 step makes the problem smaller by at least one
2561 constructor. For example, the following would make the type checker
2562 loop if it wasn't excluded:
2564 instance C a => C a where ...
2566 For example, these are OK:
2568 instance C Int [a] -- Multiple parameters
2569 instance Eq (S [a]) -- Structured type in head
2571 -- Repeated type variable in head
2572 instance C4 a a => C4 [a] [a]
2573 instance Stateful (ST s) (MutVar s)
2575 -- Head can consist of type variables only
2577 instance (Eq a, Show b) => C2 a b
2579 -- Non-type variables in context
2580 instance Show (s a) => Show (Sized s a)
2581 instance C2 Int a => C3 Bool [a]
2582 instance C2 Int a => C3 [a] b
2586 -- Context assertion no smaller than head
2587 instance C a => C a where ...
2588 -- (C b b) has more more occurrences of b than the head
2589 instance C b b => Foo [b] where ...
2594 The same restrictions apply to instances generated by
2595 <literal>deriving</literal> clauses. Thus the following is accepted:
2597 data MinHeap h a = H a (h a)
2600 because the derived instance
2602 instance (Show a, Show (h a)) => Show (MinHeap h a)
2604 conforms to the above rules.
2608 A useful idiom permitted by the above rules is as follows.
2609 If one allows overlapping instance declarations then it's quite
2610 convenient to have a "default instance" declaration that applies if
2611 something more specific does not:
2617 <para>You can find lots of background material about the reason for these
2618 restrictions in the paper <ulink
2619 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2620 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2624 <sect3 id="undecidable-instances">
2625 <title>Undecidable instances</title>
2628 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2629 For example, sometimes you might want to use the following to get the
2630 effect of a "class synonym":
2632 class (C1 a, C2 a, C3 a) => C a where { }
2634 instance (C1 a, C2 a, C3 a) => C a where { }
2636 This allows you to write shorter signatures:
2642 f :: (C1 a, C2 a, C3 a) => ...
2644 The restrictions on functional dependencies (<xref
2645 linkend="functional-dependencies"/>) are particularly troublesome.
2646 It is tempting to introduce type variables in the context that do not appear in
2647 the head, something that is excluded by the normal rules. For example:
2649 class HasConverter a b | a -> b where
2652 data Foo a = MkFoo a
2654 instance (HasConverter a b,Show b) => Show (Foo a) where
2655 show (MkFoo value) = show (convert value)
2657 This is dangerous territory, however. Here, for example, is a program that would make the
2662 instance F [a] [[a]]
2663 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2665 Similarly, it can be tempting to lift the coverage condition:
2667 class Mul a b c | a b -> c where
2668 (.*.) :: a -> b -> c
2670 instance Mul Int Int Int where (.*.) = (*)
2671 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2672 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2674 The third instance declaration does not obey the coverage condition;
2675 and indeed the (somewhat strange) definition:
2677 f = \ b x y -> if b then x .*. [y] else y
2679 makes instance inference go into a loop, because it requires the constraint
2680 <literal>(Mul a [b] b)</literal>.
2683 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2684 the experimental flag <option>-fallow-undecidable-instances</option>
2685 <indexterm><primary>-fallow-undecidable-instances
2686 option</primary></indexterm>, you can use arbitrary
2687 types in both an instance context and instance head. Termination is ensured by having a
2688 fixed-depth recursion stack. If you exceed the stack depth you get a
2689 sort of backtrace, and the opportunity to increase the stack depth
2690 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2696 <sect3 id="instance-overlap">
2697 <title>Overlapping instances</title>
2699 In general, <emphasis>GHC requires that that it be unambiguous which instance
2701 should be used to resolve a type-class constraint</emphasis>. This behaviour
2702 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2703 <indexterm><primary>-fallow-overlapping-instances
2704 </primary></indexterm>
2705 and <option>-fallow-incoherent-instances</option>
2706 <indexterm><primary>-fallow-incoherent-instances
2707 </primary></indexterm>, as this section discusses. Both these
2708 flags are dynamic flags, and can be set on a per-module basis, using
2709 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2711 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2712 it tries to match every instance declaration against the
2714 by instantiating the head of the instance declaration. For example, consider
2717 instance context1 => C Int a where ... -- (A)
2718 instance context2 => C a Bool where ... -- (B)
2719 instance context3 => C Int [a] where ... -- (C)
2720 instance context4 => C Int [Int] where ... -- (D)
2722 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2723 but (C) and (D) do not. When matching, GHC takes
2724 no account of the context of the instance declaration
2725 (<literal>context1</literal> etc).
2726 GHC's default behaviour is that <emphasis>exactly one instance must match the
2727 constraint it is trying to resolve</emphasis>.
2728 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2729 including both declarations (A) and (B), say); an error is only reported if a
2730 particular constraint matches more than one.
2734 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2735 more than one instance to match, provided there is a most specific one. For
2736 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2737 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2738 most-specific match, the program is rejected.
2741 However, GHC is conservative about committing to an overlapping instance. For example:
2746 Suppose that from the RHS of <literal>f</literal> we get the constraint
2747 <literal>C Int [b]</literal>. But
2748 GHC does not commit to instance (C), because in a particular
2749 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2750 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2751 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2752 GHC will instead pick (C), without complaining about
2753 the problem of subsequent instantiations.
2756 The willingness to be overlapped or incoherent is a property of
2757 the <emphasis>instance declaration</emphasis> itself, controlled by the
2758 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2759 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2760 being defined. Neither flag is required in a module that imports and uses the
2761 instance declaration. Specifically, during the lookup process:
2764 An instance declaration is ignored during the lookup process if (a) a more specific
2765 match is found, and (b) the instance declaration was compiled with
2766 <option>-fallow-overlapping-instances</option>. The flag setting for the
2767 more-specific instance does not matter.
2770 Suppose an instance declaration does not matche the constraint being looked up, but
2771 does unify with it, so that it might match when the constraint is further
2772 instantiated. Usually GHC will regard this as a reason for not committing to
2773 some other constraint. But if the instance declaration was compiled with
2774 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2775 check for that declaration.
2778 These rules make it possible for a library author to design a library that relies on
2779 overlapping instances without the library client having to know.
2782 If an instance declaration is compiled without
2783 <option>-fallow-overlapping-instances</option>,
2784 then that instance can never be overlapped. This could perhaps be
2785 inconvenient. Perhaps the rule should instead say that the
2786 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2787 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2788 at a usage site should be permitted regardless of how the instance declarations
2789 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2790 used at the usage site. (Mind you, the exact usage site can occasionally be
2791 hard to pin down.) We are interested to receive feedback on these points.
2793 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2794 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2799 <title>Type synonyms in the instance head</title>
2802 <emphasis>Unlike Haskell 98, instance heads may use type
2803 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2804 As always, using a type synonym is just shorthand for
2805 writing the RHS of the type synonym definition. For example:
2809 type Point = (Int,Int)
2810 instance C Point where ...
2811 instance C [Point] where ...
2815 is legal. However, if you added
2819 instance C (Int,Int) where ...
2823 as well, then the compiler will complain about the overlapping
2824 (actually, identical) instance declarations. As always, type synonyms
2825 must be fully applied. You cannot, for example, write:
2830 instance Monad P where ...
2834 This design decision is independent of all the others, and easily
2835 reversed, but it makes sense to me.
2843 <sect2 id="type-restrictions">
2844 <title>Type signatures</title>
2846 <sect3><title>The context of a type signature</title>
2848 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2849 the form <emphasis>(class type-variable)</emphasis> or
2850 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2851 these type signatures are perfectly OK
2854 g :: Ord (T a ()) => ...
2858 GHC imposes the following restrictions on the constraints in a type signature.
2862 forall tv1..tvn (c1, ...,cn) => type
2865 (Here, we write the "foralls" explicitly, although the Haskell source
2866 language omits them; in Haskell 98, all the free type variables of an
2867 explicit source-language type signature are universally quantified,
2868 except for the class type variables in a class declaration. However,
2869 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2878 <emphasis>Each universally quantified type variable
2879 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2881 A type variable <literal>a</literal> is "reachable" if it it appears
2882 in the same constraint as either a type variable free in in
2883 <literal>type</literal>, or another reachable type variable.
2884 A value with a type that does not obey
2885 this reachability restriction cannot be used without introducing
2886 ambiguity; that is why the type is rejected.
2887 Here, for example, is an illegal type:
2891 forall a. Eq a => Int
2895 When a value with this type was used, the constraint <literal>Eq tv</literal>
2896 would be introduced where <literal>tv</literal> is a fresh type variable, and
2897 (in the dictionary-translation implementation) the value would be
2898 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2899 can never know which instance of <literal>Eq</literal> to use because we never
2900 get any more information about <literal>tv</literal>.
2904 that the reachability condition is weaker than saying that <literal>a</literal> is
2905 functionally dependent on a type variable free in
2906 <literal>type</literal> (see <xref
2907 linkend="functional-dependencies"/>). The reason for this is there
2908 might be a "hidden" dependency, in a superclass perhaps. So
2909 "reachable" is a conservative approximation to "functionally dependent".
2910 For example, consider:
2912 class C a b | a -> b where ...
2913 class C a b => D a b where ...
2914 f :: forall a b. D a b => a -> a
2916 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2917 but that is not immediately apparent from <literal>f</literal>'s type.
2923 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2924 universally quantified type variables <literal>tvi</literal></emphasis>.
2926 For example, this type is OK because <literal>C a b</literal> mentions the
2927 universally quantified type variable <literal>b</literal>:
2931 forall a. C a b => burble
2935 The next type is illegal because the constraint <literal>Eq b</literal> does not
2936 mention <literal>a</literal>:
2940 forall a. Eq b => burble
2944 The reason for this restriction is milder than the other one. The
2945 excluded types are never useful or necessary (because the offending
2946 context doesn't need to be witnessed at this point; it can be floated
2947 out). Furthermore, floating them out increases sharing. Lastly,
2948 excluding them is a conservative choice; it leaves a patch of
2949 territory free in case we need it later.
2963 <sect2 id="implicit-parameters">
2964 <title>Implicit parameters</title>
2966 <para> Implicit parameters are implemented as described in
2967 "Implicit parameters: dynamic scoping with static types",
2968 J Lewis, MB Shields, E Meijer, J Launchbury,
2969 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2973 <para>(Most of the following, stil rather incomplete, documentation is
2974 due to Jeff Lewis.)</para>
2976 <para>Implicit parameter support is enabled with the option
2977 <option>-fimplicit-params</option>.</para>
2980 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2981 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2982 context. In Haskell, all variables are statically bound. Dynamic
2983 binding of variables is a notion that goes back to Lisp, but was later
2984 discarded in more modern incarnations, such as Scheme. Dynamic binding
2985 can be very confusing in an untyped language, and unfortunately, typed
2986 languages, in particular Hindley-Milner typed languages like Haskell,
2987 only support static scoping of variables.
2990 However, by a simple extension to the type class system of Haskell, we
2991 can support dynamic binding. Basically, we express the use of a
2992 dynamically bound variable as a constraint on the type. These
2993 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2994 function uses a dynamically-bound variable <literal>?x</literal>
2995 of type <literal>t'</literal>". For
2996 example, the following expresses the type of a sort function,
2997 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2999 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3001 The dynamic binding constraints are just a new form of predicate in the type class system.
3004 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3005 where <literal>x</literal> is
3006 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3007 Use of this construct also introduces a new
3008 dynamic-binding constraint in the type of the expression.
3009 For example, the following definition
3010 shows how we can define an implicitly parameterized sort function in
3011 terms of an explicitly parameterized <literal>sortBy</literal> function:
3013 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3015 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3021 <title>Implicit-parameter type constraints</title>
3023 Dynamic binding constraints behave just like other type class
3024 constraints in that they are automatically propagated. Thus, when a
3025 function is used, its implicit parameters are inherited by the
3026 function that called it. For example, our <literal>sort</literal> function might be used
3027 to pick out the least value in a list:
3029 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3030 least xs = head (sort xs)
3032 Without lifting a finger, the <literal>?cmp</literal> parameter is
3033 propagated to become a parameter of <literal>least</literal> as well. With explicit
3034 parameters, the default is that parameters must always be explicit
3035 propagated. With implicit parameters, the default is to always
3039 An implicit-parameter type constraint differs from other type class constraints in the
3040 following way: All uses of a particular implicit parameter must have
3041 the same type. This means that the type of <literal>(?x, ?x)</literal>
3042 is <literal>(?x::a) => (a,a)</literal>, and not
3043 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3047 <para> You can't have an implicit parameter in the context of a class or instance
3048 declaration. For example, both these declarations are illegal:
3050 class (?x::Int) => C a where ...
3051 instance (?x::a) => Foo [a] where ...
3053 Reason: exactly which implicit parameter you pick up depends on exactly where
3054 you invoke a function. But the ``invocation'' of instance declarations is done
3055 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3056 Easiest thing is to outlaw the offending types.</para>
3058 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3060 f :: (?x :: [a]) => Int -> Int
3063 g :: (Read a, Show a) => String -> String
3066 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3067 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3068 quite unambiguous, and fixes the type <literal>a</literal>.
3073 <title>Implicit-parameter bindings</title>
3076 An implicit parameter is <emphasis>bound</emphasis> using the standard
3077 <literal>let</literal> or <literal>where</literal> binding forms.
3078 For example, we define the <literal>min</literal> function by binding
3079 <literal>cmp</literal>.
3082 min = let ?cmp = (<=) in least
3086 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3087 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3088 (including in a list comprehension, or do-notation, or pattern guards),
3089 or a <literal>where</literal> clause.
3090 Note the following points:
3093 An implicit-parameter binding group must be a
3094 collection of simple bindings to implicit-style variables (no
3095 function-style bindings, and no type signatures); these bindings are
3096 neither polymorphic or recursive.
3099 You may not mix implicit-parameter bindings with ordinary bindings in a
3100 single <literal>let</literal>
3101 expression; use two nested <literal>let</literal>s instead.
3102 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3106 You may put multiple implicit-parameter bindings in a
3107 single binding group; but they are <emphasis>not</emphasis> treated
3108 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3109 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3110 parameter. The bindings are not nested, and may be re-ordered without changing
3111 the meaning of the program.
3112 For example, consider:
3114 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3116 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3117 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3119 f :: (?x::Int) => Int -> Int
3127 <sect3><title>Implicit parameters and polymorphic recursion</title>
3130 Consider these two definitions:
3133 len1 xs = let ?acc = 0 in len_acc1 xs
3136 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3141 len2 xs = let ?acc = 0 in len_acc2 xs
3143 len_acc2 :: (?acc :: Int) => [a] -> Int
3145 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3147 The only difference between the two groups is that in the second group
3148 <literal>len_acc</literal> is given a type signature.
3149 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3150 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3151 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3152 has a type signature, the recursive call is made to the
3153 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3154 as an implicit parameter. So we get the following results in GHCi:
3161 Adding a type signature dramatically changes the result! This is a rather
3162 counter-intuitive phenomenon, worth watching out for.
3166 <sect3><title>Implicit parameters and monomorphism</title>
3168 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3169 Haskell Report) to implicit parameters. For example, consider:
3177 Since the binding for <literal>y</literal> falls under the Monomorphism
3178 Restriction it is not generalised, so the type of <literal>y</literal> is
3179 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3180 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3181 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3182 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3183 <literal>y</literal> in the body of the <literal>let</literal> will see the
3184 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3185 <literal>14</literal>.
3190 <!-- ======================= COMMENTED OUT ========================
3192 We intend to remove linear implicit parameters, so I'm at least removing
3193 them from the 6.6 user manual
3195 <sect2 id="linear-implicit-parameters">
3196 <title>Linear implicit parameters</title>
3198 Linear implicit parameters are an idea developed by Koen Claessen,
3199 Mark Shields, and Simon PJ. They address the long-standing
3200 problem that monads seem over-kill for certain sorts of problem, notably:
3203 <listitem> <para> distributing a supply of unique names </para> </listitem>
3204 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3205 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3209 Linear implicit parameters are just like ordinary implicit parameters,
3210 except that they are "linear"; that is, they cannot be copied, and
3211 must be explicitly "split" instead. Linear implicit parameters are
3212 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3213 (The '/' in the '%' suggests the split!)
3218 import GHC.Exts( Splittable )
3220 data NameSupply = ...
3222 splitNS :: NameSupply -> (NameSupply, NameSupply)
3223 newName :: NameSupply -> Name
3225 instance Splittable NameSupply where
3229 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3230 f env (Lam x e) = Lam x' (f env e)
3233 env' = extend env x x'
3234 ...more equations for f...
3236 Notice that the implicit parameter %ns is consumed
3238 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3239 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3243 So the translation done by the type checker makes
3244 the parameter explicit:
3246 f :: NameSupply -> Env -> Expr -> Expr
3247 f ns env (Lam x e) = Lam x' (f ns1 env e)
3249 (ns1,ns2) = splitNS ns
3251 env = extend env x x'
3253 Notice the call to 'split' introduced by the type checker.
3254 How did it know to use 'splitNS'? Because what it really did
3255 was to introduce a call to the overloaded function 'split',
3256 defined by the class <literal>Splittable</literal>:
3258 class Splittable a where
3261 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3262 split for name supplies. But we can simply write
3268 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3270 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3271 <literal>GHC.Exts</literal>.
3276 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3277 are entirely distinct implicit parameters: you
3278 can use them together and they won't intefere with each other. </para>
3281 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3283 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3284 in the context of a class or instance declaration. </para></listitem>
3288 <sect3><title>Warnings</title>
3291 The monomorphism restriction is even more important than usual.
3292 Consider the example above:
3294 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3295 f env (Lam x e) = Lam x' (f env e)
3298 env' = extend env x x'
3300 If we replaced the two occurrences of x' by (newName %ns), which is
3301 usually a harmless thing to do, we get:
3303 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3304 f env (Lam x e) = Lam (newName %ns) (f env e)
3306 env' = extend env x (newName %ns)
3308 But now the name supply is consumed in <emphasis>three</emphasis> places
3309 (the two calls to newName,and the recursive call to f), so
3310 the result is utterly different. Urk! We don't even have
3314 Well, this is an experimental change. With implicit
3315 parameters we have already lost beta reduction anyway, and
3316 (as John Launchbury puts it) we can't sensibly reason about
3317 Haskell programs without knowing their typing.
3322 <sect3><title>Recursive functions</title>
3323 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3326 foo :: %x::T => Int -> [Int]
3328 foo n = %x : foo (n-1)
3330 where T is some type in class Splittable.</para>
3332 Do you get a list of all the same T's or all different T's
3333 (assuming that split gives two distinct T's back)?
3335 If you supply the type signature, taking advantage of polymorphic
3336 recursion, you get what you'd probably expect. Here's the
3337 translated term, where the implicit param is made explicit:
3340 foo x n = let (x1,x2) = split x
3341 in x1 : foo x2 (n-1)
3343 But if you don't supply a type signature, GHC uses the Hindley
3344 Milner trick of using a single monomorphic instance of the function
3345 for the recursive calls. That is what makes Hindley Milner type inference
3346 work. So the translation becomes
3350 foom n = x : foom (n-1)
3354 Result: 'x' is not split, and you get a list of identical T's. So the
3355 semantics of the program depends on whether or not foo has a type signature.
3358 You may say that this is a good reason to dislike linear implicit parameters
3359 and you'd be right. That is why they are an experimental feature.
3365 ================ END OF Linear Implicit Parameters commented out -->
3367 <sect2 id="sec-kinding">
3368 <title>Explicitly-kinded quantification</title>
3371 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3372 to give the kind explicitly as (machine-checked) documentation,
3373 just as it is nice to give a type signature for a function. On some occasions,
3374 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3375 John Hughes had to define the data type:
3377 data Set cxt a = Set [a]
3378 | Unused (cxt a -> ())
3380 The only use for the <literal>Unused</literal> constructor was to force the correct
3381 kind for the type variable <literal>cxt</literal>.
3384 GHC now instead allows you to specify the kind of a type variable directly, wherever
3385 a type variable is explicitly bound. Namely:
3387 <listitem><para><literal>data</literal> declarations:
3389 data Set (cxt :: * -> *) a = Set [a]
3390 </screen></para></listitem>
3391 <listitem><para><literal>type</literal> declarations:
3393 type T (f :: * -> *) = f Int
3394 </screen></para></listitem>
3395 <listitem><para><literal>class</literal> declarations:
3397 class (Eq a) => C (f :: * -> *) a where ...
3398 </screen></para></listitem>
3399 <listitem><para><literal>forall</literal>'s in type signatures:
3401 f :: forall (cxt :: * -> *). Set cxt Int
3402 </screen></para></listitem>
3407 The parentheses are required. Some of the spaces are required too, to
3408 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3409 will get a parse error, because "<literal>::*->*</literal>" is a
3410 single lexeme in Haskell.
3414 As part of the same extension, you can put kind annotations in types
3417 f :: (Int :: *) -> Int
3418 g :: forall a. a -> (a :: *)
3422 atype ::= '(' ctype '::' kind ')
3424 The parentheses are required.
3429 <sect2 id="universal-quantification">
3430 <title>Arbitrary-rank polymorphism
3434 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3435 allows us to say exactly what this means. For example:
3443 g :: forall b. (b -> b)
3445 The two are treated identically.
3449 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3450 explicit universal quantification in
3452 For example, all the following types are legal:
3454 f1 :: forall a b. a -> b -> a
3455 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3457 f2 :: (forall a. a->a) -> Int -> Int
3458 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3460 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3462 f4 :: Int -> (forall a. a -> a)
3464 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3465 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3466 The <literal>forall</literal> makes explicit the universal quantification that
3467 is implicitly added by Haskell.
3470 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3471 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3472 shows, the polymorphic type on the left of the function arrow can be overloaded.
3475 The function <literal>f3</literal> has a rank-3 type;
3476 it has rank-2 types on the left of a function arrow.
3479 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3480 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3481 that restriction has now been lifted.)
3482 In particular, a forall-type (also called a "type scheme"),
3483 including an operational type class context, is legal:
3485 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3486 of a function arrow </para> </listitem>
3487 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
3488 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3489 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3490 field type signatures.</para> </listitem>
3491 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3492 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3494 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3495 a type variable any more!
3504 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3505 the types of the constructor arguments. Here are several examples:
3511 data T a = T1 (forall b. b -> b -> b) a
3513 data MonadT m = MkMonad { return :: forall a. a -> m a,
3514 bind :: forall a b. m a -> (a -> m b) -> m b
3517 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3523 The constructors have rank-2 types:
3529 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3530 MkMonad :: forall m. (forall a. a -> m a)
3531 -> (forall a b. m a -> (a -> m b) -> m b)
3533 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3539 Notice that you don't need to use a <literal>forall</literal> if there's an
3540 explicit context. For example in the first argument of the
3541 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3542 prefixed to the argument type. The implicit <literal>forall</literal>
3543 quantifies all type variables that are not already in scope, and are
3544 mentioned in the type quantified over.
3548 As for type signatures, implicit quantification happens for non-overloaded
3549 types too. So if you write this:
3552 data T a = MkT (Either a b) (b -> b)
3555 it's just as if you had written this:
3558 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3561 That is, since the type variable <literal>b</literal> isn't in scope, it's
3562 implicitly universally quantified. (Arguably, it would be better
3563 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3564 where that is what is wanted. Feedback welcomed.)
3568 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3569 the constructor to suitable values, just as usual. For example,
3580 a3 = MkSwizzle reverse
3583 a4 = let r x = Just x
3590 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3591 mkTs f x y = [T1 f x, T1 f y]
3597 The type of the argument can, as usual, be more general than the type
3598 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3599 does not need the <literal>Ord</literal> constraint.)
3603 When you use pattern matching, the bound variables may now have
3604 polymorphic types. For example:
3610 f :: T a -> a -> (a, Char)
3611 f (T1 w k) x = (w k x, w 'c' 'd')
3613 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3614 g (MkSwizzle s) xs f = s (map f (s xs))
3616 h :: MonadT m -> [m a] -> m [a]
3617 h m [] = return m []
3618 h m (x:xs) = bind m x $ \y ->
3619 bind m (h m xs) $ \ys ->
3626 In the function <function>h</function> we use the record selectors <literal>return</literal>
3627 and <literal>bind</literal> to extract the polymorphic bind and return functions
3628 from the <literal>MonadT</literal> data structure, rather than using pattern
3634 <title>Type inference</title>
3637 In general, type inference for arbitrary-rank types is undecidable.
3638 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3639 to get a decidable algorithm by requiring some help from the programmer.
3640 We do not yet have a formal specification of "some help" but the rule is this:
3643 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3644 provides an explicit polymorphic type for x, or GHC's type inference will assume
3645 that x's type has no foralls in it</emphasis>.
3648 What does it mean to "provide" an explicit type for x? You can do that by
3649 giving a type signature for x directly, using a pattern type signature
3650 (<xref linkend="scoped-type-variables"/>), thus:
3652 \ f :: (forall a. a->a) -> (f True, f 'c')
3654 Alternatively, you can give a type signature to the enclosing
3655 context, which GHC can "push down" to find the type for the variable:
3657 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3659 Here the type signature on the expression can be pushed inwards
3660 to give a type signature for f. Similarly, and more commonly,
3661 one can give a type signature for the function itself:
3663 h :: (forall a. a->a) -> (Bool,Char)
3664 h f = (f True, f 'c')
3666 You don't need to give a type signature if the lambda bound variable
3667 is a constructor argument. Here is an example we saw earlier:
3669 f :: T a -> a -> (a, Char)
3670 f (T1 w k) x = (w k x, w 'c' 'd')
3672 Here we do not need to give a type signature to <literal>w</literal>, because
3673 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3680 <sect3 id="implicit-quant">
3681 <title>Implicit quantification</title>
3684 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3685 user-written types, if and only if there is no explicit <literal>forall</literal>,
3686 GHC finds all the type variables mentioned in the type that are not already
3687 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3691 f :: forall a. a -> a
3698 h :: forall b. a -> b -> b
3704 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3707 f :: (a -> a) -> Int
3709 f :: forall a. (a -> a) -> Int
3711 f :: (forall a. a -> a) -> Int
3714 g :: (Ord a => a -> a) -> Int
3715 -- MEANS the illegal type
3716 g :: forall a. (Ord a => a -> a) -> Int
3718 g :: (forall a. Ord a => a -> a) -> Int
3720 The latter produces an illegal type, which you might think is silly,
3721 but at least the rule is simple. If you want the latter type, you
3722 can write your for-alls explicitly. Indeed, doing so is strongly advised
3729 <sect2 id="impredicative-polymorphism">
3730 <title>Impredicative polymorphism
3732 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3733 that you can call a polymorphic function at a polymorphic type, and
3734 parameterise data structures over polymorphic types. For example:
3736 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3737 f (Just g) = Just (g [3], g "hello")
3740 Notice here that the <literal>Maybe</literal> type is parameterised by the
3741 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3744 <para>The technical details of this extension are described in the paper
3745 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3746 type inference for higher-rank types and impredicativity</ulink>,
3747 which appeared at ICFP 2006.
3751 <sect2 id="scoped-type-variables">
3752 <title>Lexically scoped type variables
3756 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3757 which some type signatures are simply impossible to write. For example:
3759 f :: forall a. [a] -> [a]
3765 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3766 the entire definition of <literal>f</literal>.
3767 In particular, it is in scope at the type signature for <varname>ys</varname>.
3768 In Haskell 98 it is not possible to declare
3769 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3770 it becomes possible to do so.
3772 <para>Lexically-scoped type variables are enabled by
3773 <option>-fglasgow-exts</option>.
3775 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3776 variables work, compared to earlier releases. Read this section
3780 <title>Overview</title>
3782 <para>The design follows the following principles
3784 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3785 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3786 design.)</para></listitem>
3787 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3788 type variables. This means that every programmer-written type signature
3789 (includin one that contains free scoped type variables) denotes a
3790 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3791 checker, and no inference is involved.</para></listitem>
3792 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3793 changing the program.</para></listitem>
3797 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3799 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3800 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3801 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3802 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3806 In Haskell, a programmer-written type signature is implicitly quantifed over
3807 its free type variables (<ulink
3808 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3810 of the Haskel Report).
3811 Lexically scoped type variables affect this implicit quantification rules
3812 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3813 quantified. For example, if type variable <literal>a</literal> is in scope,
3816 (e :: a -> a) means (e :: a -> a)
3817 (e :: b -> b) means (e :: forall b. b->b)
3818 (e :: a -> b) means (e :: forall b. a->b)
3826 <sect3 id="decl-type-sigs">
3827 <title>Declaration type signatures</title>
3828 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3829 quantification (using <literal>forall</literal>) brings into scope the
3830 explicitly-quantified
3831 type variables, in the definition of the named function(s). For example:
3833 f :: forall a. [a] -> [a]
3834 f (x:xs) = xs ++ [ x :: a ]
3836 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3837 the definition of "<literal>f</literal>".
3839 <para>This only happens if the quantification in <literal>f</literal>'s type
3840 signature is explicit. For example:
3843 g (x:xs) = xs ++ [ x :: a ]
3845 This program will be rejected, because "<literal>a</literal>" does not scope
3846 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3847 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3848 quantification rules.
3852 <sect3 id="exp-type-sigs">
3853 <title>Expression type signatures</title>
3855 <para>An expression type signature that has <emphasis>explicit</emphasis>
3856 quantification (using <literal>forall</literal>) brings into scope the
3857 explicitly-quantified
3858 type variables, in the annotated expression. For example:
3860 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3862 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3863 type variable <literal>s</literal> into scope, in the annotated expression
3864 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3869 <sect3 id="pattern-type-sigs">
3870 <title>Pattern type signatures</title>
3872 A type signature may occur in any pattern; this is a <emphasis>pattern type
3873 signature</emphasis>.
3876 -- f and g assume that 'a' is already in scope
3877 f = \(x::Int, y::a) -> x
3879 h ((x,y) :: (Int,Bool)) = (y,x)
3881 In the case where all the type variables in the pattern type sigature are
3882 already in scope (i.e. bound by the enclosing context), matters are simple: the
3883 signature simply constrains the type of the pattern in the obvious way.
3886 There is only one situation in which you can write a pattern type signature that
3887 mentions a type variable that is not already in scope, namely in pattern match
3888 of an existential data constructor. For example:
3890 data T = forall a. MkT [a]
3893 k (MkT [t::a]) = MkT t3
3897 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3898 variable that is not already in scope. Indeed, it cannot already be in scope,
3899 because it is bound by the pattern match. GHC's rule is that in this situation
3900 (and only then), a pattern type signature can mention a type variable that is
3901 not already in scope; the effect is to bring it into scope, standing for the
3902 existentially-bound type variable.
3905 If this seems a little odd, we think so too. But we must have
3906 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3907 could not name existentially-bound type variables in subequent type signatures.
3910 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3911 signature is allowed to mention a lexical variable that is not already in
3913 For example, both <literal>f</literal> and <literal>g</literal> would be
3914 illegal if <literal>a</literal> was not already in scope.
3920 <!-- ==================== Commented out part about result type signatures
3922 <sect3 id="result-type-sigs">
3923 <title>Result type signatures</title>
3926 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3929 {- f assumes that 'a' is already in scope -}
3930 f x y :: [a] = [x,y,x]
3932 g = \ x :: [Int] -> [3,4]
3934 h :: forall a. [a] -> a
3938 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3939 the result of the function. Similarly, the body of the lambda in the RHS of
3940 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3941 alternative in <literal>h</literal> is <literal>a</literal>.
3943 <para> A result type signature never brings new type variables into scope.</para>
3945 There are a couple of syntactic wrinkles. First, notice that all three
3946 examples would parse quite differently with parentheses:
3948 {- f assumes that 'a' is already in scope -}
3949 f x (y :: [a]) = [x,y,x]
3951 g = \ (x :: [Int]) -> [3,4]
3953 h :: forall a. [a] -> a
3957 Now the signature is on the <emphasis>pattern</emphasis>; and
3958 <literal>h</literal> would certainly be ill-typed (since the pattern
3959 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3961 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3962 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3963 token or a parenthesised type of some sort). To see why,
3964 consider how one would parse this:
3973 <sect3 id="cls-inst-scoped-tyvars">
3974 <title>Class and instance declarations</title>
3977 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3978 scope over the methods defined in the <literal>where</literal> part. For example:
3996 <sect2 id="typing-binds">
3997 <title>Generalised typing of mutually recursive bindings</title>
4000 The Haskell Report specifies that a group of bindings (at top level, or in a
4001 <literal>let</literal> or <literal>where</literal>) should be sorted into
4002 strongly-connected components, and then type-checked in dependency order
4003 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4004 Report, Section 4.5.1</ulink>).
4005 As each group is type-checked, any binders of the group that
4007 an explicit type signature are put in the type environment with the specified
4009 and all others are monomorphic until the group is generalised
4010 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4013 <para>Following a suggestion of Mark Jones, in his paper
4014 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4016 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4018 <emphasis>the dependency analysis ignores references to variables that have an explicit
4019 type signature</emphasis>.
4020 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4021 typecheck. For example, consider:
4023 f :: Eq a => a -> Bool
4024 f x = (x == x) || g True || g "Yes"
4026 g y = (y <= y) || f True
4028 This is rejected by Haskell 98, but under Jones's scheme the definition for
4029 <literal>g</literal> is typechecked first, separately from that for
4030 <literal>f</literal>,
4031 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4032 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4033 type is generalised, to get
4035 g :: Ord a => a -> Bool
4037 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4038 <literal>g</literal> in the type environment.
4042 The same refined dependency analysis also allows the type signatures of
4043 mutually-recursive functions to have different contexts, something that is illegal in
4044 Haskell 98 (Section 4.5.2, last sentence). With
4045 <option>-fglasgow-exts</option>
4046 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4047 type signatures; in practice this means that only variables bound by the same
4048 pattern binding must have the same context. For example, this is fine:
4050 f :: Eq a => a -> Bool
4051 f x = (x == x) || g True
4053 g :: Ord a => a -> Bool
4054 g y = (y <= y) || f True
4060 <!-- ==================== End of type system extensions ================= -->
4062 <!-- ====================== TEMPLATE HASKELL ======================= -->
4064 <sect1 id="template-haskell">
4065 <title>Template Haskell</title>
4067 <para>Template Haskell allows you to do compile-time meta-programming in
4070 the main technical innovations is discussed in "<ulink
4071 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4072 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4075 There is a Wiki page about
4076 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4077 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4081 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4082 Haskell library reference material</ulink>
4083 (search for the type ExpQ).
4084 [Temporary: many changes to the original design are described in
4085 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4086 Not all of these changes are in GHC 6.6.]
4089 <para> The first example from that paper is set out below as a worked example to help get you started.
4093 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4094 Tim Sheard is going to expand it.)
4098 <title>Syntax</title>
4100 <para> Template Haskell has the following new syntactic
4101 constructions. You need to use the flag
4102 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4103 </indexterm>to switch these syntactic extensions on
4104 (<option>-fth</option> is no longer implied by
4105 <option>-fglasgow-exts</option>).</para>
4109 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4110 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4111 There must be no space between the "$" and the identifier or parenthesis. This use
4112 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4113 of "." as an infix operator. If you want the infix operator, put spaces around it.
4115 <para> A splice can occur in place of
4117 <listitem><para> an expression; the spliced expression must
4118 have type <literal>Q Exp</literal></para></listitem>
4119 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4120 <listitem><para> [Planned, but not implemented yet.] a
4121 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4123 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4124 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4130 A expression quotation is written in Oxford brackets, thus:
4132 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4133 the quotation has type <literal>Expr</literal>.</para></listitem>
4134 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4135 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4136 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4137 the quotation has type <literal>Type</literal>.</para></listitem>
4138 </itemizedlist></para></listitem>
4141 Reification is written thus:
4143 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4144 has type <literal>Dec</literal>. </para></listitem>
4145 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4146 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4147 <listitem><para> Still to come: fixities </para></listitem>
4149 </itemizedlist></para>
4156 <sect2> <title> Using Template Haskell </title>
4160 The data types and monadic constructor functions for Template Haskell are in the library
4161 <literal>Language.Haskell.THSyntax</literal>.
4165 You can only run a function at compile time if it is imported from another module. That is,
4166 you can't define a function in a module, and call it from within a splice in the same module.
4167 (It would make sense to do so, but it's hard to implement.)
4171 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4174 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4175 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4176 compiles and runs a program, and then looks at the result. So it's important that
4177 the program it compiles produces results whose representations are identical to
4178 those of the compiler itself.
4182 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4183 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4188 <sect2> <title> A Template Haskell Worked Example </title>
4189 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4190 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4197 -- Import our template "pr"
4198 import Printf ( pr )
4200 -- The splice operator $ takes the Haskell source code
4201 -- generated at compile time by "pr" and splices it into
4202 -- the argument of "putStrLn".
4203 main = putStrLn ( $(pr "Hello") )
4209 -- Skeletal printf from the paper.
4210 -- It needs to be in a separate module to the one where
4211 -- you intend to use it.
4213 -- Import some Template Haskell syntax
4214 import Language.Haskell.TH
4216 -- Describe a format string
4217 data Format = D | S | L String
4219 -- Parse a format string. This is left largely to you
4220 -- as we are here interested in building our first ever
4221 -- Template Haskell program and not in building printf.
4222 parse :: String -> [Format]
4225 -- Generate Haskell source code from a parsed representation
4226 -- of the format string. This code will be spliced into
4227 -- the module which calls "pr", at compile time.
4228 gen :: [Format] -> ExpQ
4229 gen [D] = [| \n -> show n |]
4230 gen [S] = [| \s -> s |]
4231 gen [L s] = stringE s
4233 -- Here we generate the Haskell code for the splice
4234 -- from an input format string.
4235 pr :: String -> ExpQ
4236 pr s = gen (parse s)
4239 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4242 $ ghc --make -fth main.hs -o main.exe
4245 <para>Run "main.exe" and here is your output:</para>
4255 <title>Using Template Haskell with Profiling</title>
4256 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4258 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4259 interpreter to run the splice expressions. The bytecode interpreter
4260 runs the compiled expression on top of the same runtime on which GHC
4261 itself is running; this means that the compiled code referred to by
4262 the interpreted expression must be compatible with this runtime, and
4263 in particular this means that object code that is compiled for
4264 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4265 expression, because profiled object code is only compatible with the
4266 profiling version of the runtime.</para>
4268 <para>This causes difficulties if you have a multi-module program
4269 containing Template Haskell code and you need to compile it for
4270 profiling, because GHC cannot load the profiled object code and use it
4271 when executing the splices. Fortunately GHC provides a workaround.
4272 The basic idea is to compile the program twice:</para>
4276 <para>Compile the program or library first the normal way, without
4277 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4280 <para>Then compile it again with <option>-prof</option>, and
4281 additionally use <option>-osuf
4282 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4283 to name the object files differentliy (you can choose any suffix
4284 that isn't the normal object suffix here). GHC will automatically
4285 load the object files built in the first step when executing splice
4286 expressions. If you omit the <option>-osuf</option> flag when
4287 building with <option>-prof</option> and Template Haskell is used,
4288 GHC will emit an error message. </para>
4295 <!-- ===================== Arrow notation =================== -->
4297 <sect1 id="arrow-notation">
4298 <title>Arrow notation
4301 <para>Arrows are a generalization of monads introduced by John Hughes.
4302 For more details, see
4307 “Generalising Monads to Arrows”,
4308 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4309 pp67–111, May 2000.
4315 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4316 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4322 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4323 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4329 and the arrows web page at
4330 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4331 With the <option>-farrows</option> flag, GHC supports the arrow
4332 notation described in the second of these papers.
4333 What follows is a brief introduction to the notation;
4334 it won't make much sense unless you've read Hughes's paper.
4335 This notation is translated to ordinary Haskell,
4336 using combinators from the
4337 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4341 <para>The extension adds a new kind of expression for defining arrows:
4343 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4344 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4346 where <literal>proc</literal> is a new keyword.
4347 The variables of the pattern are bound in the body of the
4348 <literal>proc</literal>-expression,
4349 which is a new sort of thing called a <firstterm>command</firstterm>.
4350 The syntax of commands is as follows:
4352 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4353 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4354 | <replaceable>cmd</replaceable><superscript>0</superscript>
4356 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4357 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4358 infix operators as for expressions, and
4360 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4361 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4362 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4363 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4364 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4365 | <replaceable>fcmd</replaceable>
4367 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4368 | ( <replaceable>cmd</replaceable> )
4369 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4371 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4372 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4373 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4374 | <replaceable>cmd</replaceable>
4376 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4377 except that the bodies are commands instead of expressions.
4381 Commands produce values, but (like monadic computations)
4382 may yield more than one value,
4383 or none, and may do other things as well.
4384 For the most part, familiarity with monadic notation is a good guide to
4386 However the values of expressions, even monadic ones,
4387 are determined by the values of the variables they contain;
4388 this is not necessarily the case for commands.
4392 A simple example of the new notation is the expression
4394 proc x -> f -< x+1
4396 We call this a <firstterm>procedure</firstterm> or
4397 <firstterm>arrow abstraction</firstterm>.
4398 As with a lambda expression, the variable <literal>x</literal>
4399 is a new variable bound within the <literal>proc</literal>-expression.
4400 It refers to the input to the arrow.
4401 In the above example, <literal>-<</literal> is not an identifier but an
4402 new reserved symbol used for building commands from an expression of arrow
4403 type and an expression to be fed as input to that arrow.
4404 (The weird look will make more sense later.)
4405 It may be read as analogue of application for arrows.
4406 The above example is equivalent to the Haskell expression
4408 arr (\ x -> x+1) >>> f
4410 That would make no sense if the expression to the left of
4411 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4412 More generally, the expression to the left of <literal>-<</literal>
4413 may not involve any <firstterm>local variable</firstterm>,
4414 i.e. a variable bound in the current arrow abstraction.
4415 For such a situation there is a variant <literal>-<<</literal>, as in
4417 proc x -> f x -<< x+1
4419 which is equivalent to
4421 arr (\ x -> (f x, x+1)) >>> app
4423 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4425 Such an arrow is equivalent to a monad, so if you're using this form
4426 you may find a monadic formulation more convenient.
4430 <title>do-notation for commands</title>
4433 Another form of command is a form of <literal>do</literal>-notation.
4434 For example, you can write
4443 You can read this much like ordinary <literal>do</literal>-notation,
4444 but with commands in place of monadic expressions.
4445 The first line sends the value of <literal>x+1</literal> as an input to
4446 the arrow <literal>f</literal>, and matches its output against
4447 <literal>y</literal>.
4448 In the next line, the output is discarded.
4449 The arrow <function>returnA</function> is defined in the
4450 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4451 module as <literal>arr id</literal>.
4452 The above example is treated as an abbreviation for
4454 arr (\ x -> (x, x)) >>>
4455 first (arr (\ x -> x+1) >>> f) >>>
4456 arr (\ (y, x) -> (y, (x, y))) >>>
4457 first (arr (\ y -> 2*y) >>> g) >>>
4459 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4460 first (arr (\ (x, z) -> x*z) >>> h) >>>
4461 arr (\ (t, z) -> t+z) >>>
4464 Note that variables not used later in the composition are projected out.
4465 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4467 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4468 module, this reduces to
4470 arr (\ x -> (x+1, x)) >>>
4472 arr (\ (y, x) -> (2*y, (x, y))) >>>
4474 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4476 arr (\ (t, z) -> t+z)
4478 which is what you might have written by hand.
4479 With arrow notation, GHC keeps track of all those tuples of variables for you.
4483 Note that although the above translation suggests that
4484 <literal>let</literal>-bound variables like <literal>z</literal> must be
4485 monomorphic, the actual translation produces Core,
4486 so polymorphic variables are allowed.
4490 It's also possible to have mutually recursive bindings,
4491 using the new <literal>rec</literal> keyword, as in the following example:
4493 counter :: ArrowCircuit a => a Bool Int
4494 counter = proc reset -> do
4495 rec output <- returnA -< if reset then 0 else next
4496 next <- delay 0 -< output+1
4497 returnA -< output
4499 The translation of such forms uses the <function>loop</function> combinator,
4500 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4506 <title>Conditional commands</title>
4509 In the previous example, we used a conditional expression to construct the
4511 Sometimes we want to conditionally execute different commands, as in
4518 which is translated to
4520 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4521 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4523 Since the translation uses <function>|||</function>,
4524 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4528 There are also <literal>case</literal> commands, like
4534 y <- h -< (x1, x2)
4538 The syntax is the same as for <literal>case</literal> expressions,
4539 except that the bodies of the alternatives are commands rather than expressions.
4540 The translation is similar to that of <literal>if</literal> commands.
4546 <title>Defining your own control structures</title>
4549 As we're seen, arrow notation provides constructs,
4550 modelled on those for expressions,
4551 for sequencing, value recursion and conditionals.
4552 But suitable combinators,
4553 which you can define in ordinary Haskell,
4554 may also be used to build new commands out of existing ones.
4555 The basic idea is that a command defines an arrow from environments to values.
4556 These environments assign values to the free local variables of the command.
4557 Thus combinators that produce arrows from arrows
4558 may also be used to build commands from commands.
4559 For example, the <literal>ArrowChoice</literal> class includes a combinator
4561 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4563 so we can use it to build commands:
4565 expr' = proc x -> do
4568 symbol Plus -< ()
4569 y <- term -< ()
4572 symbol Minus -< ()
4573 y <- term -< ()
4576 (The <literal>do</literal> on the first line is needed to prevent the first
4577 <literal><+> ...</literal> from being interpreted as part of the
4578 expression on the previous line.)
4579 This is equivalent to
4581 expr' = (proc x -> returnA -< x)
4582 <+> (proc x -> do
4583 symbol Plus -< ()
4584 y <- term -< ()
4586 <+> (proc x -> do
4587 symbol Minus -< ()
4588 y <- term -< ()
4591 It is essential that this operator be polymorphic in <literal>e</literal>
4592 (representing the environment input to the command
4593 and thence to its subcommands)
4594 and satisfy the corresponding naturality property
4596 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4598 at least for strict <literal>k</literal>.
4599 (This should be automatic if you're not using <function>seq</function>.)
4600 This ensures that environments seen by the subcommands are environments
4601 of the whole command,
4602 and also allows the translation to safely trim these environments.
4603 The operator must also not use any variable defined within the current
4608 We could define our own operator
4610 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4611 untilA body cond = proc x ->
4612 if cond x then returnA -< ()
4615 untilA body cond -< x
4617 and use it in the same way.
4618 Of course this infix syntax only makes sense for binary operators;
4619 there is also a more general syntax involving special brackets:
4623 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4630 <title>Primitive constructs</title>
4633 Some operators will need to pass additional inputs to their subcommands.
4634 For example, in an arrow type supporting exceptions,
4635 the operator that attaches an exception handler will wish to pass the
4636 exception that occurred to the handler.
4637 Such an operator might have a type
4639 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4641 where <literal>Ex</literal> is the type of exceptions handled.
4642 You could then use this with arrow notation by writing a command
4644 body `handleA` \ ex -> handler
4646 so that if an exception is raised in the command <literal>body</literal>,
4647 the variable <literal>ex</literal> is bound to the value of the exception
4648 and the command <literal>handler</literal>,
4649 which typically refers to <literal>ex</literal>, is entered.
4650 Though the syntax here looks like a functional lambda,
4651 we are talking about commands, and something different is going on.
4652 The input to the arrow represented by a command consists of values for
4653 the free local variables in the command, plus a stack of anonymous values.
4654 In all the prior examples, this stack was empty.
4655 In the second argument to <function>handleA</function>,
4656 this stack consists of one value, the value of the exception.
4657 The command form of lambda merely gives this value a name.
4662 the values on the stack are paired to the right of the environment.
4663 So operators like <function>handleA</function> that pass
4664 extra inputs to their subcommands can be designed for use with the notation
4665 by pairing the values with the environment in this way.
4666 More precisely, the type of each argument of the operator (and its result)
4667 should have the form
4669 a (...(e,t1), ... tn) t
4671 where <replaceable>e</replaceable> is a polymorphic variable
4672 (representing the environment)
4673 and <replaceable>ti</replaceable> are the types of the values on the stack,
4674 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4675 The polymorphic variable <replaceable>e</replaceable> must not occur in
4676 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4677 <replaceable>t</replaceable>.
4678 However the arrows involved need not be the same.
4679 Here are some more examples of suitable operators:
4681 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4682 runReader :: ... => a e c -> a' (e,State) c
4683 runState :: ... => a e c -> a' (e,State) (c,State)
4685 We can supply the extra input required by commands built with the last two
4686 by applying them to ordinary expressions, as in
4690 (|runReader (do { ... })|) s
4692 which adds <literal>s</literal> to the stack of inputs to the command
4693 built using <function>runReader</function>.
4697 The command versions of lambda abstraction and application are analogous to
4698 the expression versions.
4699 In particular, the beta and eta rules describe equivalences of commands.
4700 These three features (operators, lambda abstraction and application)
4701 are the core of the notation; everything else can be built using them,
4702 though the results would be somewhat clumsy.
4703 For example, we could simulate <literal>do</literal>-notation by defining
4705 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4706 u `bind` f = returnA &&& u >>> f
4708 bind_ :: Arrow a => a e b -> a e c -> a e c
4709 u `bind_` f = u `bind` (arr fst >>> f)
4711 We could simulate <literal>if</literal> by defining
4713 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4714 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4721 <title>Differences with the paper</title>
4726 <para>Instead of a single form of arrow application (arrow tail) with two
4727 translations, the implementation provides two forms
4728 <quote><literal>-<</literal></quote> (first-order)
4729 and <quote><literal>-<<</literal></quote> (higher-order).
4734 <para>User-defined operators are flagged with banana brackets instead of
4735 a new <literal>form</literal> keyword.
4744 <title>Portability</title>
4747 Although only GHC implements arrow notation directly,
4748 there is also a preprocessor
4750 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4751 that translates arrow notation into Haskell 98
4752 for use with other Haskell systems.
4753 You would still want to check arrow programs with GHC;
4754 tracing type errors in the preprocessor output is not easy.
4755 Modules intended for both GHC and the preprocessor must observe some
4756 additional restrictions:
4761 The module must import
4762 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4768 The preprocessor cannot cope with other Haskell extensions.
4769 These would have to go in separate modules.
4775 Because the preprocessor targets Haskell (rather than Core),
4776 <literal>let</literal>-bound variables are monomorphic.
4787 <!-- ==================== BANG PATTERNS ================= -->
4789 <sect1 id="sec-bang-patterns">
4790 <title>Bang patterns
4791 <indexterm><primary>Bang patterns</primary></indexterm>
4793 <para>GHC supports an extension of pattern matching called <emphasis>bang
4794 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4796 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4797 prime feature description</ulink> contains more discussion and examples
4798 than the material below.
4801 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4804 <sect2 id="sec-bang-patterns-informal">
4805 <title>Informal description of bang patterns
4808 The main idea is to add a single new production to the syntax of patterns:
4812 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4813 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4818 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4819 whereas without the bang it would be lazy.
4820 Bang patterns can be nested of course:
4824 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4825 <literal>y</literal>.
4826 A bang only really has an effect if it precedes a variable or wild-card pattern:
4831 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4832 forces evaluation anyway does nothing.
4834 Bang patterns work in <literal>case</literal> expressions too, of course:
4836 g5 x = let y = f x in body
4837 g6 x = case f x of { y -> body }
4838 g7 x = case f x of { !y -> body }
4840 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4841 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4842 result, and then evaluates <literal>body</literal>.
4844 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4845 definitions too. For example:
4849 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4850 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4851 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4852 in a function argument <literal>![x,y]</literal> means the
4853 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4854 is part of the syntax of <literal>let</literal> bindings.
4859 <sect2 id="sec-bang-patterns-sem">
4860 <title>Syntax and semantics
4864 We add a single new production to the syntax of patterns:
4868 There is one problem with syntactic ambiguity. Consider:
4872 Is this a definition of the infix function "<literal>(!)</literal>",
4873 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4874 ambiguity in favour of the latter. If you want to define
4875 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4880 The semantics of Haskell pattern matching is described in <ulink
4881 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4882 Section 3.17.2</ulink> of the Haskell Report. To this description add
4883 one extra item 10, saying:
4884 <itemizedlist><listitem><para>Matching
4885 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4886 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4887 <listitem><para>otherwise, <literal>pat</literal> is matched against
4888 <literal>v</literal></para></listitem>
4890 </para></listitem></itemizedlist>
4891 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4892 Section 3.17.3</ulink>, add a new case (t):
4894 case v of { !pat -> e; _ -> e' }
4895 = v `seq` case v of { pat -> e; _ -> e' }
4898 That leaves let expressions, whose translation is given in
4899 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4901 of the Haskell Report.
4902 In the translation box, first apply
4903 the following transformation: for each pattern <literal>pi</literal> that is of
4904 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4905 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4906 have a bang at the top, apply the rules in the existing box.
4908 <para>The effect of the let rule is to force complete matching of the pattern
4909 <literal>qi</literal> before evaluation of the body is begun. The bang is
4910 retained in the translated form in case <literal>qi</literal> is a variable,
4918 The let-binding can be recursive. However, it is much more common for
4919 the let-binding to be non-recursive, in which case the following law holds:
4920 <literal>(let !p = rhs in body)</literal>
4922 <literal>(case rhs of !p -> body)</literal>
4925 A pattern with a bang at the outermost level is not allowed at the top level of
4931 <!-- ==================== ASSERTIONS ================= -->
4933 <sect1 id="sec-assertions">
4935 <indexterm><primary>Assertions</primary></indexterm>
4939 If you want to make use of assertions in your standard Haskell code, you
4940 could define a function like the following:
4946 assert :: Bool -> a -> a
4947 assert False x = error "assertion failed!"
4954 which works, but gives you back a less than useful error message --
4955 an assertion failed, but which and where?
4959 One way out is to define an extended <function>assert</function> function which also
4960 takes a descriptive string to include in the error message and
4961 perhaps combine this with the use of a pre-processor which inserts
4962 the source location where <function>assert</function> was used.
4966 Ghc offers a helping hand here, doing all of this for you. For every
4967 use of <function>assert</function> in the user's source:
4973 kelvinToC :: Double -> Double
4974 kelvinToC k = assert (k >= 0.0) (k+273.15)
4980 Ghc will rewrite this to also include the source location where the
4987 assert pred val ==> assertError "Main.hs|15" pred val
4993 The rewrite is only performed by the compiler when it spots
4994 applications of <function>Control.Exception.assert</function>, so you
4995 can still define and use your own versions of
4996 <function>assert</function>, should you so wish. If not, import
4997 <literal>Control.Exception</literal> to make use
4998 <function>assert</function> in your code.
5002 GHC ignores assertions when optimisation is turned on with the
5003 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5004 <literal>assert pred e</literal> will be rewritten to
5005 <literal>e</literal>. You can also disable assertions using the
5006 <option>-fignore-asserts</option>
5007 option<indexterm><primary><option>-fignore-asserts</option></primary>
5008 </indexterm>.</para>
5011 Assertion failures can be caught, see the documentation for the
5012 <literal>Control.Exception</literal> library for the details.
5018 <!-- =============================== PRAGMAS =========================== -->
5020 <sect1 id="pragmas">
5021 <title>Pragmas</title>
5023 <indexterm><primary>pragma</primary></indexterm>
5025 <para>GHC supports several pragmas, or instructions to the
5026 compiler placed in the source code. Pragmas don't normally affect
5027 the meaning of the program, but they might affect the efficiency
5028 of the generated code.</para>
5030 <para>Pragmas all take the form
5032 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5034 where <replaceable>word</replaceable> indicates the type of
5035 pragma, and is followed optionally by information specific to that
5036 type of pragma. Case is ignored in
5037 <replaceable>word</replaceable>. The various values for
5038 <replaceable>word</replaceable> that GHC understands are described
5039 in the following sections; any pragma encountered with an
5040 unrecognised <replaceable>word</replaceable> is (silently)
5043 <sect2 id="deprecated-pragma">
5044 <title>DEPRECATED pragma</title>
5045 <indexterm><primary>DEPRECATED</primary>
5048 <para>The DEPRECATED pragma lets you specify that a particular
5049 function, class, or type, is deprecated. There are two
5054 <para>You can deprecate an entire module thus:</para>
5056 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5059 <para>When you compile any module that import
5060 <literal>Wibble</literal>, GHC will print the specified
5065 <para>You can deprecate a function, class, type, or data constructor, with the
5066 following top-level declaration:</para>
5068 {-# DEPRECATED f, C, T "Don't use these" #-}
5070 <para>When you compile any module that imports and uses any
5071 of the specified entities, GHC will print the specified
5073 <para> You can only depecate entities declared at top level in the module
5074 being compiled, and you can only use unqualified names in the list of
5075 entities being deprecated. A capitalised name, such as <literal>T</literal>
5076 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5077 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5078 both are in scope. If both are in scope, there is currently no way to deprecate
5079 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5082 Any use of the deprecated item, or of anything from a deprecated
5083 module, will be flagged with an appropriate message. However,
5084 deprecations are not reported for
5085 (a) uses of a deprecated function within its defining module, and
5086 (b) uses of a deprecated function in an export list.
5087 The latter reduces spurious complaints within a library
5088 in which one module gathers together and re-exports
5089 the exports of several others.
5091 <para>You can suppress the warnings with the flag
5092 <option>-fno-warn-deprecations</option>.</para>
5095 <sect2 id="include-pragma">
5096 <title>INCLUDE pragma</title>
5098 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5099 of C header files that should be <literal>#include</literal>'d into
5100 the C source code generated by the compiler for the current module (if
5101 compiling via C). For example:</para>
5104 {-# INCLUDE "foo.h" #-}
5105 {-# INCLUDE <stdio.h> #-}</programlisting>
5107 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5108 your source file with any <literal>OPTIONS_GHC</literal>
5111 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5112 to the <option>-#include</option> option (<xref
5113 linkend="options-C-compiler" />), because the
5114 <literal>INCLUDE</literal> pragma is understood by other
5115 compilers. Yet another alternative is to add the include file to each
5116 <literal>foreign import</literal> declaration in your code, but we
5117 don't recommend using this approach with GHC.</para>
5120 <sect2 id="inline-noinline-pragma">
5121 <title>INLINE and NOINLINE pragmas</title>
5123 <para>These pragmas control the inlining of function
5126 <sect3 id="inline-pragma">
5127 <title>INLINE pragma</title>
5128 <indexterm><primary>INLINE</primary></indexterm>
5130 <para>GHC (with <option>-O</option>, as always) tries to
5131 inline (or “unfold”) functions/values that are
5132 “small enough,” thus avoiding the call overhead
5133 and possibly exposing other more-wonderful optimisations.
5134 Normally, if GHC decides a function is “too
5135 expensive” to inline, it will not do so, nor will it
5136 export that unfolding for other modules to use.</para>
5138 <para>The sledgehammer you can bring to bear is the
5139 <literal>INLINE</literal><indexterm><primary>INLINE
5140 pragma</primary></indexterm> pragma, used thusly:</para>
5143 key_function :: Int -> String -> (Bool, Double)
5145 #ifdef __GLASGOW_HASKELL__
5146 {-# INLINE key_function #-}
5150 <para>(You don't need to do the C pre-processor carry-on
5151 unless you're going to stick the code through HBC—it
5152 doesn't like <literal>INLINE</literal> pragmas.)</para>
5154 <para>The major effect of an <literal>INLINE</literal> pragma
5155 is to declare a function's “cost” to be very low.
5156 The normal unfolding machinery will then be very keen to
5159 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5160 function can be put anywhere its type signature could be
5163 <para><literal>INLINE</literal> pragmas are a particularly
5165 <literal>then</literal>/<literal>return</literal> (or
5166 <literal>bind</literal>/<literal>unit</literal>) functions in
5167 a monad. For example, in GHC's own
5168 <literal>UniqueSupply</literal> monad code, we have:</para>
5171 #ifdef __GLASGOW_HASKELL__
5172 {-# INLINE thenUs #-}
5173 {-# INLINE returnUs #-}
5177 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5178 linkend="noinline-pragma"/>).</para>
5181 <sect3 id="noinline-pragma">
5182 <title>NOINLINE pragma</title>
5184 <indexterm><primary>NOINLINE</primary></indexterm>
5185 <indexterm><primary>NOTINLINE</primary></indexterm>
5187 <para>The <literal>NOINLINE</literal> pragma does exactly what
5188 you'd expect: it stops the named function from being inlined
5189 by the compiler. You shouldn't ever need to do this, unless
5190 you're very cautious about code size.</para>
5192 <para><literal>NOTINLINE</literal> is a synonym for
5193 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5194 specified by Haskell 98 as the standard way to disable
5195 inlining, so it should be used if you want your code to be
5199 <sect3 id="phase-control">
5200 <title>Phase control</title>
5202 <para> Sometimes you want to control exactly when in GHC's
5203 pipeline the INLINE pragma is switched on. Inlining happens
5204 only during runs of the <emphasis>simplifier</emphasis>. Each
5205 run of the simplifier has a different <emphasis>phase
5206 number</emphasis>; the phase number decreases towards zero.
5207 If you use <option>-dverbose-core2core</option> you'll see the
5208 sequence of phase numbers for successive runs of the
5209 simplifier. In an INLINE pragma you can optionally specify a
5213 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5214 <literal>f</literal>
5215 until phase <literal>k</literal>, but from phase
5216 <literal>k</literal> onwards be very keen to inline it.
5219 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5220 <literal>f</literal>
5221 until phase <literal>k</literal>, but from phase
5222 <literal>k</literal> onwards do not inline it.
5225 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5226 <literal>f</literal>
5227 until phase <literal>k</literal>, but from phase
5228 <literal>k</literal> onwards be willing to inline it (as if
5229 there was no pragma).
5232 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5233 <literal>f</literal>
5234 until phase <literal>k</literal>, but from phase
5235 <literal>k</literal> onwards do not inline it.
5238 The same information is summarised here:
5240 -- Before phase 2 Phase 2 and later
5241 {-# INLINE [2] f #-} -- No Yes
5242 {-# INLINE [~2] f #-} -- Yes No
5243 {-# NOINLINE [2] f #-} -- No Maybe
5244 {-# NOINLINE [~2] f #-} -- Maybe No
5246 {-# INLINE f #-} -- Yes Yes
5247 {-# NOINLINE f #-} -- No No
5249 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5250 function body is small, or it is applied to interesting-looking arguments etc).
5251 Another way to understand the semantics is this:
5253 <listitem><para>For both INLINE and NOINLINE, the phase number says
5254 when inlining is allowed at all.</para></listitem>
5255 <listitem><para>The INLINE pragma has the additional effect of making the
5256 function body look small, so that when inlining is allowed it is very likely to
5261 <para>The same phase-numbering control is available for RULES
5262 (<xref linkend="rewrite-rules"/>).</para>
5266 <sect2 id="language-pragma">
5267 <title>LANGUAGE pragma</title>
5269 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5270 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5272 <para>This allows language extensions to be enabled in a portable way.
5273 It is the intention that all Haskell compilers support the
5274 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5275 all extensions are supported by all compilers, of
5276 course. The <literal>LANGUAGE</literal> pragma should be used instead
5277 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5279 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5281 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5283 <para>Any extension from the <literal>Extension</literal> type defined in
5285 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>
5289 <sect2 id="line-pragma">
5290 <title>LINE pragma</title>
5292 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5293 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5294 <para>This pragma is similar to C's <literal>#line</literal>
5295 pragma, and is mainly for use in automatically generated Haskell
5296 code. It lets you specify the line number and filename of the
5297 original code; for example</para>
5299 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5301 <para>if you'd generated the current file from something called
5302 <filename>Foo.vhs</filename> and this line corresponds to line
5303 42 in the original. GHC will adjust its error messages to refer
5304 to the line/file named in the <literal>LINE</literal>
5308 <sect2 id="options-pragma">
5309 <title>OPTIONS_GHC pragma</title>
5310 <indexterm><primary>OPTIONS_GHC</primary>
5312 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5315 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5316 additional options that are given to the compiler when compiling
5317 this source file. See <xref linkend="source-file-options"/> for
5320 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5321 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5325 <title>RULES pragma</title>
5327 <para>The RULES pragma lets you specify rewrite rules. It is
5328 described in <xref linkend="rewrite-rules"/>.</para>
5331 <sect2 id="specialize-pragma">
5332 <title>SPECIALIZE pragma</title>
5334 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5335 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5336 <indexterm><primary>overloading, death to</primary></indexterm>
5338 <para>(UK spelling also accepted.) For key overloaded
5339 functions, you can create extra versions (NB: more code space)
5340 specialised to particular types. Thus, if you have an
5341 overloaded function:</para>
5344 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5347 <para>If it is heavily used on lists with
5348 <literal>Widget</literal> keys, you could specialise it as
5352 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5355 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5356 be put anywhere its type signature could be put.</para>
5358 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5359 (a) a specialised version of the function and (b) a rewrite rule
5360 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5361 un-specialised function into a call to the specialised one.</para>
5363 <para>The type in a SPECIALIZE pragma can be any type that is less
5364 polymorphic than the type of the original function. In concrete terms,
5365 if the original function is <literal>f</literal> then the pragma
5367 {-# SPECIALIZE f :: <type> #-}
5369 is valid if and only if the defintion
5371 f_spec :: <type>
5374 is valid. Here are some examples (where we only give the type signature
5375 for the original function, not its code):
5377 f :: Eq a => a -> b -> b
5378 {-# SPECIALISE f :: Int -> b -> b #-}
5380 g :: (Eq a, Ix b) => a -> b -> b
5381 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5383 h :: Eq a => a -> a -> a
5384 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5386 The last of these examples will generate a
5387 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5388 well. If you use this kind of specialisation, let us know how well it works.
5391 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5392 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5393 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5394 The <literal>INLINE</literal> pragma affects the specialised verison of the
5395 function (only), and applies even if the function is recursive. The motivating
5398 -- A GADT for arrays with type-indexed representation
5400 ArrInt :: !Int -> ByteArray# -> Arr Int
5401 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5403 (!:) :: Arr e -> Int -> e
5404 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5405 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5406 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5407 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5409 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5410 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5411 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5412 the specialised function will be inlined. It has two calls to
5413 <literal>(!:)</literal>,
5414 both at type <literal>Int</literal>. Both these calls fire the first
5415 specialisation, whose body is also inlined. The result is a type-based
5416 unrolling of the indexing function.</para>
5417 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5418 on an ordinarily-recursive function.</para>
5420 <para>Note: In earlier versions of GHC, it was possible to provide your own
5421 specialised function for a given type:
5424 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5427 This feature has been removed, as it is now subsumed by the
5428 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5432 <sect2 id="specialize-instance-pragma">
5433 <title>SPECIALIZE instance pragma
5437 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5438 <indexterm><primary>overloading, death to</primary></indexterm>
5439 Same idea, except for instance declarations. For example:
5442 instance (Eq a) => Eq (Foo a) where {
5443 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5447 The pragma must occur inside the <literal>where</literal> part
5448 of the instance declaration.
5451 Compatible with HBC, by the way, except perhaps in the placement
5457 <sect2 id="unpack-pragma">
5458 <title>UNPACK pragma</title>
5460 <indexterm><primary>UNPACK</primary></indexterm>
5462 <para>The <literal>UNPACK</literal> indicates to the compiler
5463 that it should unpack the contents of a constructor field into
5464 the constructor itself, removing a level of indirection. For
5468 data T = T {-# UNPACK #-} !Float
5469 {-# UNPACK #-} !Float
5472 <para>will create a constructor <literal>T</literal> containing
5473 two unboxed floats. This may not always be an optimisation: if
5474 the <function>T</function> constructor is scrutinised and the
5475 floats passed to a non-strict function for example, they will
5476 have to be reboxed (this is done automatically by the
5479 <para>Unpacking constructor fields should only be used in
5480 conjunction with <option>-O</option>, in order to expose
5481 unfoldings to the compiler so the reboxing can be removed as
5482 often as possible. For example:</para>
5486 f (T f1 f2) = f1 + f2
5489 <para>The compiler will avoid reboxing <function>f1</function>
5490 and <function>f2</function> by inlining <function>+</function>
5491 on floats, but only when <option>-O</option> is on.</para>
5493 <para>Any single-constructor data is eligible for unpacking; for
5497 data T = T {-# UNPACK #-} !(Int,Int)
5500 <para>will store the two <literal>Int</literal>s directly in the
5501 <function>T</function> constructor, by flattening the pair.
5502 Multi-level unpacking is also supported:</para>
5505 data T = T {-# UNPACK #-} !S
5506 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5509 <para>will store two unboxed <literal>Int#</literal>s
5510 directly in the <function>T</function> constructor. The
5511 unpacker can see through newtypes, too.</para>
5513 <para>If a field cannot be unpacked, you will not get a warning,
5514 so it might be an idea to check the generated code with
5515 <option>-ddump-simpl</option>.</para>
5517 <para>See also the <option>-funbox-strict-fields</option> flag,
5518 which essentially has the effect of adding
5519 <literal>{-# UNPACK #-}</literal> to every strict
5520 constructor field.</para>
5525 <!-- ======================= REWRITE RULES ======================== -->
5527 <sect1 id="rewrite-rules">
5528 <title>Rewrite rules
5530 <indexterm><primary>RULES pragma</primary></indexterm>
5531 <indexterm><primary>pragma, RULES</primary></indexterm>
5532 <indexterm><primary>rewrite rules</primary></indexterm></title>
5535 The programmer can specify rewrite rules as part of the source program
5536 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5537 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5538 and (b) the <option>-frules-off</option> flag
5539 (<xref linkend="options-f"/>) is not specified, and (c) the
5540 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5549 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5556 <title>Syntax</title>
5559 From a syntactic point of view:
5565 There may be zero or more rules in a <literal>RULES</literal> pragma.
5572 Each rule has a name, enclosed in double quotes. The name itself has
5573 no significance at all. It is only used when reporting how many times the rule fired.
5579 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5580 immediately after the name of the rule. Thus:
5583 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5586 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5587 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5596 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5597 is set, so you must lay out your rules starting in the same column as the
5598 enclosing definitions.
5605 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5606 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5607 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5608 by spaces, just like in a type <literal>forall</literal>.
5614 A pattern variable may optionally have a type signature.
5615 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5616 For example, here is the <literal>foldr/build</literal> rule:
5619 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5620 foldr k z (build g) = g k z
5623 Since <function>g</function> has a polymorphic type, it must have a type signature.
5630 The left hand side of a rule must consist of a top-level variable applied
5631 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5634 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5635 "wrong2" forall f. f True = True
5638 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5645 A rule does not need to be in the same module as (any of) the
5646 variables it mentions, though of course they need to be in scope.
5652 Rules are automatically exported from a module, just as instance declarations are.
5663 <title>Semantics</title>
5666 From a semantic point of view:
5672 Rules are only applied if you use the <option>-O</option> flag.
5678 Rules are regarded as left-to-right rewrite rules.
5679 When GHC finds an expression that is a substitution instance of the LHS
5680 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5681 By "a substitution instance" we mean that the LHS can be made equal to the
5682 expression by substituting for the pattern variables.
5689 The LHS and RHS of a rule are typechecked, and must have the
5697 GHC makes absolutely no attempt to verify that the LHS and RHS
5698 of a rule have the same meaning. That is undecidable in general, and
5699 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5706 GHC makes no attempt to make sure that the rules are confluent or
5707 terminating. For example:
5710 "loop" forall x,y. f x y = f y x
5713 This rule will cause the compiler to go into an infinite loop.
5720 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5726 GHC currently uses a very simple, syntactic, matching algorithm
5727 for matching a rule LHS with an expression. It seeks a substitution
5728 which makes the LHS and expression syntactically equal modulo alpha
5729 conversion. The pattern (rule), but not the expression, is eta-expanded if
5730 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5731 But not beta conversion (that's called higher-order matching).
5735 Matching is carried out on GHC's intermediate language, which includes
5736 type abstractions and applications. So a rule only matches if the
5737 types match too. See <xref linkend="rule-spec"/> below.
5743 GHC keeps trying to apply the rules as it optimises the program.
5744 For example, consider:
5753 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5754 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5755 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5756 not be substituted, and the rule would not fire.
5763 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5764 that appears on the LHS of a rule</emphasis>, because once you have substituted
5765 for something you can't match against it (given the simple minded
5766 matching). So if you write the rule
5769 "map/map" forall f,g. map f . map g = map (f.g)
5772 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5773 It will only match something written with explicit use of ".".
5774 Well, not quite. It <emphasis>will</emphasis> match the expression
5780 where <function>wibble</function> is defined:
5783 wibble f g = map f . map g
5786 because <function>wibble</function> will be inlined (it's small).
5788 Later on in compilation, GHC starts inlining even things on the
5789 LHS of rules, but still leaves the rules enabled. This inlining
5790 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5797 All rules are implicitly exported from the module, and are therefore
5798 in force in any module that imports the module that defined the rule, directly
5799 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5800 in force when compiling A.) The situation is very similar to that for instance
5812 <title>List fusion</title>
5815 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5816 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5817 intermediate list should be eliminated entirely.
5821 The following are good producers:
5833 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5839 Explicit lists (e.g. <literal>[True, False]</literal>)
5845 The cons constructor (e.g <literal>3:4:[]</literal>)
5851 <function>++</function>
5857 <function>map</function>
5863 <function>take</function>, <function>filter</function>
5869 <function>iterate</function>, <function>repeat</function>
5875 <function>zip</function>, <function>zipWith</function>
5884 The following are good consumers:
5896 <function>array</function> (on its second argument)
5902 <function>length</function>
5908 <function>++</function> (on its first argument)
5914 <function>foldr</function>
5920 <function>map</function>
5926 <function>take</function>, <function>filter</function>
5932 <function>concat</function>
5938 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5944 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5945 will fuse with one but not the other)
5951 <function>partition</function>
5957 <function>head</function>
5963 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5969 <function>sequence_</function>
5975 <function>msum</function>
5981 <function>sortBy</function>
5990 So, for example, the following should generate no intermediate lists:
5993 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5999 This list could readily be extended; if there are Prelude functions that you use
6000 a lot which are not included, please tell us.
6004 If you want to write your own good consumers or producers, look at the
6005 Prelude definitions of the above functions to see how to do so.
6010 <sect2 id="rule-spec">
6011 <title>Specialisation
6015 Rewrite rules can be used to get the same effect as a feature
6016 present in earlier versions of GHC.
6017 For example, suppose that:
6020 genericLookup :: Ord a => Table a b -> a -> b
6021 intLookup :: Table Int b -> Int -> b
6024 where <function>intLookup</function> is an implementation of
6025 <function>genericLookup</function> that works very fast for
6026 keys of type <literal>Int</literal>. You might wish
6027 to tell GHC to use <function>intLookup</function> instead of
6028 <function>genericLookup</function> whenever the latter was called with
6029 type <literal>Table Int b -> Int -> b</literal>.
6030 It used to be possible to write
6033 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6036 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6039 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6042 This slightly odd-looking rule instructs GHC to replace
6043 <function>genericLookup</function> by <function>intLookup</function>
6044 <emphasis>whenever the types match</emphasis>.
6045 What is more, this rule does not need to be in the same
6046 file as <function>genericLookup</function>, unlike the
6047 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6048 have an original definition available to specialise).
6051 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6052 <function>intLookup</function> really behaves as a specialised version
6053 of <function>genericLookup</function>!!!</para>
6055 <para>An example in which using <literal>RULES</literal> for
6056 specialisation will Win Big:
6059 toDouble :: Real a => a -> Double
6060 toDouble = fromRational . toRational
6062 {-# RULES "toDouble/Int" toDouble = i2d #-}
6063 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6066 The <function>i2d</function> function is virtually one machine
6067 instruction; the default conversion—via an intermediate
6068 <literal>Rational</literal>—is obscenely expensive by
6075 <title>Controlling what's going on</title>
6083 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6089 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6090 If you add <option>-dppr-debug</option> you get a more detailed listing.
6096 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6099 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6100 {-# INLINE build #-}
6104 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6105 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6106 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6107 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6114 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6115 see how to write rules that will do fusion and yet give an efficient
6116 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6126 <sect2 id="core-pragma">
6127 <title>CORE pragma</title>
6129 <indexterm><primary>CORE pragma</primary></indexterm>
6130 <indexterm><primary>pragma, CORE</primary></indexterm>
6131 <indexterm><primary>core, annotation</primary></indexterm>
6134 The external core format supports <quote>Note</quote> annotations;
6135 the <literal>CORE</literal> pragma gives a way to specify what these
6136 should be in your Haskell source code. Syntactically, core
6137 annotations are attached to expressions and take a Haskell string
6138 literal as an argument. The following function definition shows an
6142 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6145 Semantically, this is equivalent to:
6153 However, when external for is generated (via
6154 <option>-fext-core</option>), there will be Notes attached to the
6155 expressions <function>show</function> and <varname>x</varname>.
6156 The core function declaration for <function>f</function> is:
6160 f :: %forall a . GHCziShow.ZCTShow a ->
6161 a -> GHCziBase.ZMZN GHCziBase.Char =
6162 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6164 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6166 (tpl1::GHCziBase.Int ->
6168 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6170 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6171 (tpl3::GHCziBase.ZMZN a ->
6172 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6180 Here, we can see that the function <function>show</function> (which
6181 has been expanded out to a case expression over the Show dictionary)
6182 has a <literal>%note</literal> attached to it, as does the
6183 expression <varname>eta</varname> (which used to be called
6184 <varname>x</varname>).
6191 <sect1 id="special-ids">
6192 <title>Special built-in functions</title>
6193 <para>GHC has a few built-in funcions with special behaviour,
6194 described in this section. All are exported by
6195 <literal>GHC.Exts</literal>.</para>
6197 <sect2> <title>The <literal>seq</literal> function </title>
6199 The function <literal>seq</literal> is as described in the Haskell98 Report.
6203 It evaluates its first argument to head normal form, and then returns its
6204 second argument as the result. The reason that it is documented here is
6205 that, despite <literal>seq</literal>'s polymorphism, its
6206 second argument can have an unboxed type, or
6207 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6208 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6209 to be instantiated to an unboxed type, which is not usually allowed.
6213 <sect2> <title>The <literal>inline</literal> function </title>
6215 The <literal>inline</literal> function is somewhat experimental.
6219 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6220 is inlined, regardless of its size. More precisely, the call
6221 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6223 This allows the programmer to control inlining from
6224 a particular <emphasis>call site</emphasis>
6225 rather than the <emphasis>definition site</emphasis> of the function
6226 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6229 This inlining occurs regardless of the argument to the call
6230 or the size of <literal>f</literal>'s definition; it is unconditional.
6231 The main caveat is that <literal>f</literal>'s definition must be
6232 visible to the compiler. That is, <literal>f</literal> must be
6233 let-bound in the current scope.
6234 If no inlining takes place, the <literal>inline</literal> function
6235 expands to the identity function in Phase zero; so its use imposes
6238 <para> If the function is defined in another
6239 module, GHC only exposes its inlining in the interface file if the
6240 function is sufficiently small that it <emphasis>might</emphasis> be
6241 inlined by the automatic mechanism. There is currently no way to tell
6242 GHC to expose arbitrarily-large functions in the interface file. (This
6243 shortcoming is something that could be fixed, with some kind of pragma.)
6247 <sect2> <title>The <literal>lazy</literal> function </title>
6249 The <literal>lazy</literal> function restrains strictness analysis a little:
6253 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6254 but <literal>lazy</literal> has a magical property so far as strictness
6255 analysis is concerned: it is lazy in its first argument,
6256 even though its semantics is strict. After strictness analysis has run,
6257 calls to <literal>lazy</literal> are inlined to be the identity function.
6260 This behaviour is occasionally useful when controlling evaluation order.
6261 Notably, <literal>lazy</literal> is used in the library definition of
6262 <literal>Control.Parallel.par</literal>:
6265 par x y = case (par# x) of { _ -> lazy y }
6267 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6268 look strict in <literal>y</literal> which would defeat the whole
6269 purpose of <literal>par</literal>.
6272 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6278 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6280 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6281 typechecker entirely. It has type
6283 unsafeCoerce# :: a -> b
6285 That is, it allows you to coerce any type into any other type. If you use this
6286 function, you had better get it right, otherwise segmentation faults await.
6287 It is generally used when you want to write a program that you know is
6288 well-typed, but where Haskell's type system is not expressive enough to prove
6289 that it is well typed.
6292 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6293 although extremely bad things will happen if you coerce a boxed type
6302 <sect1 id="generic-classes">
6303 <title>Generic classes</title>
6306 The ideas behind this extension are described in detail in "Derivable type classes",
6307 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6308 An example will give the idea:
6316 fromBin :: [Int] -> (a, [Int])
6318 toBin {| Unit |} Unit = []
6319 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6320 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6321 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6323 fromBin {| Unit |} bs = (Unit, bs)
6324 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6325 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6326 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6327 (y,bs'') = fromBin bs'
6330 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6331 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6332 which are defined thus in the library module <literal>Generics</literal>:
6336 data a :+: b = Inl a | Inr b
6337 data a :*: b = a :*: b
6340 Now you can make a data type into an instance of Bin like this:
6342 instance (Bin a, Bin b) => Bin (a,b)
6343 instance Bin a => Bin [a]
6345 That is, just leave off the "where" clause. Of course, you can put in the
6346 where clause and over-ride whichever methods you please.
6350 <title> Using generics </title>
6351 <para>To use generics you need to</para>
6354 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6355 <option>-fgenerics</option> (to generate extra per-data-type code),
6356 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6360 <para>Import the module <literal>Generics</literal> from the
6361 <literal>lang</literal> package. This import brings into
6362 scope the data types <literal>Unit</literal>,
6363 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6364 don't need this import if you don't mention these types
6365 explicitly; for example, if you are simply giving instance
6366 declarations.)</para>
6371 <sect2> <title> Changes wrt the paper </title>
6373 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6374 can be written infix (indeed, you can now use
6375 any operator starting in a colon as an infix type constructor). Also note that
6376 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6377 Finally, note that the syntax of the type patterns in the class declaration
6378 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6379 alone would ambiguous when they appear on right hand sides (an extension we
6380 anticipate wanting).
6384 <sect2> <title>Terminology and restrictions</title>
6386 Terminology. A "generic default method" in a class declaration
6387 is one that is defined using type patterns as above.
6388 A "polymorphic default method" is a default method defined as in Haskell 98.
6389 A "generic class declaration" is a class declaration with at least one
6390 generic default method.
6398 Alas, we do not yet implement the stuff about constructor names and
6405 A generic class can have only one parameter; you can't have a generic
6406 multi-parameter class.
6412 A default method must be defined entirely using type patterns, or entirely
6413 without. So this is illegal:
6416 op :: a -> (a, Bool)
6417 op {| Unit |} Unit = (Unit, True)
6420 However it is perfectly OK for some methods of a generic class to have
6421 generic default methods and others to have polymorphic default methods.
6427 The type variable(s) in the type pattern for a generic method declaration
6428 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:
6432 op {| p :*: q |} (x :*: y) = op (x :: p)
6440 The type patterns in a generic default method must take one of the forms:
6446 where "a" and "b" are type variables. Furthermore, all the type patterns for
6447 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6448 must use the same type variables. So this is illegal:
6452 op {| a :+: b |} (Inl x) = True
6453 op {| p :+: q |} (Inr y) = False
6455 The type patterns must be identical, even in equations for different methods of the class.
6456 So this too is illegal:
6460 op1 {| a :*: b |} (x :*: y) = True
6463 op2 {| p :*: q |} (x :*: y) = False
6465 (The reason for this restriction is that we gather all the equations for a particular type consructor
6466 into a single generic instance declaration.)
6472 A generic method declaration must give a case for each of the three type constructors.
6478 The type for a generic method can be built only from:
6480 <listitem> <para> Function arrows </para> </listitem>
6481 <listitem> <para> Type variables </para> </listitem>
6482 <listitem> <para> Tuples </para> </listitem>
6483 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6485 Here are some example type signatures for generic methods:
6488 op2 :: Bool -> (a,Bool)
6489 op3 :: [Int] -> a -> a
6492 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6496 This restriction is an implementation restriction: we just havn't got around to
6497 implementing the necessary bidirectional maps over arbitrary type constructors.
6498 It would be relatively easy to add specific type constructors, such as Maybe and list,
6499 to the ones that are allowed.</para>
6504 In an instance declaration for a generic class, the idea is that the compiler
6505 will fill in the methods for you, based on the generic templates. However it can only
6510 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6515 No constructor of the instance type has unboxed fields.
6519 (Of course, these things can only arise if you are already using GHC extensions.)
6520 However, you can still give an instance declarations for types which break these rules,
6521 provided you give explicit code to override any generic default methods.
6529 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6530 what the compiler does with generic declarations.
6535 <sect2> <title> Another example </title>
6537 Just to finish with, here's another example I rather like:
6541 nCons {| Unit |} _ = 1
6542 nCons {| a :*: b |} _ = 1
6543 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6546 tag {| Unit |} _ = 1
6547 tag {| a :*: b |} _ = 1
6548 tag {| a :+: b |} (Inl x) = tag x
6549 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6555 <sect1 id="monomorphism">
6556 <title>Control over monomorphism</title>
6558 <para>GHC supports two flags that control the way in which generalisation is
6559 carried out at let and where bindings.
6563 <title>Switching off the dreaded Monomorphism Restriction</title>
6564 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6566 <para>Haskell's monomorphism restriction (see
6567 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6569 of the Haskell Report)
6570 can be completely switched off by
6571 <option>-fno-monomorphism-restriction</option>.
6576 <title>Monomorphic pattern bindings</title>
6577 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6578 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6580 <para> As an experimental change, we are exploring the possibility of
6581 making pattern bindings monomorphic; that is, not generalised at all.
6582 A pattern binding is a binding whose LHS has no function arguments,
6583 and is not a simple variable. For example:
6585 f x = x -- Not a pattern binding
6586 f = \x -> x -- Not a pattern binding
6587 f :: Int -> Int = \x -> x -- Not a pattern binding
6589 (g,h) = e -- A pattern binding
6590 (f) = e -- A pattern binding
6591 [x] = e -- A pattern binding
6593 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6594 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6603 ;;; Local Variables: ***
6605 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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