1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum plus deprecated
110 syntax of previous versions of the FFI for backwards
111 compatibility.</para>
113 <para>New reserved words: <literal>foreign</literal>.</para>
119 <option>-fno-monomorphism-restriction</option>:
120 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
123 <para> Switch off the Haskell 98 monomorphism restriction.
124 Independent of the <option>-fglasgow-exts</option>
131 <option>-fno-mono-pat-binds</option>:
132 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
133 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
136 <para> As an experimental change, we are exploring the possibility of
137 making pattern bindings monomorphic; that is, not generalised at all.
138 A pattern binding is a binding whose LHS has no function arguments,
139 and is not a simple variable. For example:
141 f x = x -- Not a pattern binding
142 f = \x -> x -- Not a pattern binding
143 f :: Int -> Int = \x -> x -- Not a pattern binding
145 (g,h) = e -- A pattern binding
146 (f) = e -- A pattern binding
147 [x] = e -- A pattern binding
149 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
150 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
158 <option>-fextended-default-rules</option>:
159 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
162 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
163 Independent of the <option>-fglasgow-exts</option>
170 <option>-fallow-overlapping-instances</option>
171 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
174 <option>-fallow-undecidable-instances</option>
175 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
178 <option>-fallow-incoherent-instances</option>
179 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
182 <option>-fcontext-stack=N</option>
183 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
186 <para> See <xref linkend="instance-decls"/>. Only relevant
187 if you also use <option>-fglasgow-exts</option>.</para>
193 <option>-finline-phase</option>
194 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
197 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
198 you also use <option>-fglasgow-exts</option>.</para>
204 <option>-farrows</option>
205 <indexterm><primary><option>-farrows</option></primary></indexterm>
208 <para>See <xref linkend="arrow-notation"/>. Independent of
209 <option>-fglasgow-exts</option>.</para>
211 <para>New reserved words/symbols: <literal>rec</literal>,
212 <literal>proc</literal>, <literal>-<</literal>,
213 <literal>>-</literal>, <literal>-<<</literal>,
214 <literal>>>-</literal>.</para>
216 <para>Other syntax stolen: <literal>(|</literal>,
217 <literal>|)</literal>.</para>
223 <option>-fgenerics</option>
224 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
227 <para>See <xref linkend="generic-classes"/>. Independent of
228 <option>-fglasgow-exts</option>.</para>
233 <term><option>-fno-implicit-prelude</option></term>
235 <para><indexterm><primary>-fno-implicit-prelude
236 option</primary></indexterm> GHC normally imports
237 <filename>Prelude.hi</filename> files for you. If you'd
238 rather it didn't, then give it a
239 <option>-fno-implicit-prelude</option> option. The idea is
240 that you can then import a Prelude of your own. (But don't
241 call it <literal>Prelude</literal>; the Haskell module
242 namespace is flat, and you must not conflict with any
243 Prelude module.)</para>
245 <para>Even though you have not imported the Prelude, most of
246 the built-in syntax still refers to the built-in Haskell
247 Prelude types and values, as specified by the Haskell
248 Report. For example, the type <literal>[Int]</literal>
249 still means <literal>Prelude.[] Int</literal>; tuples
250 continue to refer to the standard Prelude tuples; the
251 translation for list comprehensions continues to use
252 <literal>Prelude.map</literal> etc.</para>
254 <para>However, <option>-fno-implicit-prelude</option> does
255 change the handling of certain built-in syntax: see <xref
256 linkend="rebindable-syntax"/>.</para>
261 <term><option>-fimplicit-params</option></term>
263 <para>Enables implicit parameters (see <xref
264 linkend="implicit-parameters"/>). Currently also implied by
265 <option>-fglasgow-exts</option>.</para>
268 <literal>?<replaceable>varid</replaceable></literal>,
269 <literal>%<replaceable>varid</replaceable></literal>.</para>
274 <term><option>-fscoped-type-variables</option></term>
276 <para>Enables lexically-scoped type variables (see <xref
277 linkend="scoped-type-variables"/>). Implied by
278 <option>-fglasgow-exts</option>.</para>
283 <term><option>-fth</option></term>
285 <para>Enables Template Haskell (see <xref
286 linkend="template-haskell"/>). This flag must
287 be given explicitly; it is no longer implied by
288 <option>-fglasgow-exts</option>.</para>
290 <para>Syntax stolen: <literal>[|</literal>,
291 <literal>[e|</literal>, <literal>[p|</literal>,
292 <literal>[d|</literal>, <literal>[t|</literal>,
293 <literal>$(</literal>,
294 <literal>$<replaceable>varid</replaceable></literal>.</para>
301 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
302 <!-- included from primitives.sgml -->
303 <!-- &primitives; -->
304 <sect1 id="primitives">
305 <title>Unboxed types and primitive operations</title>
307 <para>GHC is built on a raft of primitive data types and operations.
308 While you really can use this stuff to write fast code,
309 we generally find it a lot less painful, and more satisfying in the
310 long run, to use higher-level language features and libraries. With
311 any luck, the code you write will be optimised to the efficient
312 unboxed version in any case. And if it isn't, we'd like to know
315 <para>We do not currently have good, up-to-date documentation about the
316 primitives, perhaps because they are mainly intended for internal use.
317 There used to be a long section about them here in the User Guide, but it
318 became out of date, and wrong information is worse than none.</para>
320 <para>The Real Truth about what primitive types there are, and what operations
321 work over those types, is held in the file
322 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
323 This file is used directly to generate GHC's primitive-operation definitions, so
324 it is always correct! It is also intended for processing into text.</para>
327 the result of such processing is part of the description of the
329 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
330 Core language</ulink>.
331 So that document is a good place to look for a type-set version.
332 We would be very happy if someone wanted to volunteer to produce an SGML
333 back end to the program that processes <filename>primops.txt</filename> so that
334 we could include the results here in the User Guide.</para>
336 <para>What follows here is a brief summary of some main points.</para>
338 <sect2 id="glasgow-unboxed">
343 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
346 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
347 that values of that type are represented by a pointer to a heap
348 object. The representation of a Haskell <literal>Int</literal>, for
349 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
350 type, however, is represented by the value itself, no pointers or heap
351 allocation are involved.
355 Unboxed types correspond to the “raw machine” types you
356 would use in C: <literal>Int#</literal> (long int),
357 <literal>Double#</literal> (double), <literal>Addr#</literal>
358 (void *), etc. The <emphasis>primitive operations</emphasis>
359 (PrimOps) on these types are what you might expect; e.g.,
360 <literal>(+#)</literal> is addition on
361 <literal>Int#</literal>s, and is the machine-addition that we all
362 know and love—usually one instruction.
366 Primitive (unboxed) types cannot be defined in Haskell, and are
367 therefore built into the language and compiler. Primitive types are
368 always unlifted; that is, a value of a primitive type cannot be
369 bottom. We use the convention that primitive types, values, and
370 operations have a <literal>#</literal> suffix.
374 Primitive values are often represented by a simple bit-pattern, such
375 as <literal>Int#</literal>, <literal>Float#</literal>,
376 <literal>Double#</literal>. But this is not necessarily the case:
377 a primitive value might be represented by a pointer to a
378 heap-allocated object. Examples include
379 <literal>Array#</literal>, the type of primitive arrays. A
380 primitive array is heap-allocated because it is too big a value to fit
381 in a register, and would be too expensive to copy around; in a sense,
382 it is accidental that it is represented by a pointer. If a pointer
383 represents a primitive value, then it really does point to that value:
384 no unevaluated thunks, no indirections…nothing can be at the
385 other end of the pointer than the primitive value.
386 A numerically-intensive program using unboxed types can
387 go a <emphasis>lot</emphasis> faster than its “standard”
388 counterpart—we saw a threefold speedup on one example.
392 There are some restrictions on the use of primitive types:
394 <listitem><para>The main restriction
395 is that you can't pass a primitive value to a polymorphic
396 function or store one in a polymorphic data type. This rules out
397 things like <literal>[Int#]</literal> (i.e. lists of primitive
398 integers). The reason for this restriction is that polymorphic
399 arguments and constructor fields are assumed to be pointers: if an
400 unboxed integer is stored in one of these, the garbage collector would
401 attempt to follow it, leading to unpredictable space leaks. Or a
402 <function>seq</function> operation on the polymorphic component may
403 attempt to dereference the pointer, with disastrous results. Even
404 worse, the unboxed value might be larger than a pointer
405 (<literal>Double#</literal> for instance).
408 <listitem><para> You cannot bind a variable with an unboxed type
409 in a <emphasis>top-level</emphasis> binding.
411 <listitem><para> You cannot bind a variable with an unboxed type
412 in a <emphasis>recursive</emphasis> binding.
414 <listitem><para> You may bind unboxed variables in a (non-recursive,
415 non-top-level) pattern binding, but any such variable causes the entire
417 to become strict. For example:
419 data Foo = Foo Int Int#
421 f x = let (Foo a b, w) = ..rhs.. in ..body..
423 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
425 is strict, and the program behaves as if you had written
427 data Foo = Foo Int Int#
429 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
438 <sect2 id="unboxed-tuples">
439 <title>Unboxed Tuples
443 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
444 they're available by default with <option>-fglasgow-exts</option>. An
445 unboxed tuple looks like this:
457 where <literal>e_1..e_n</literal> are expressions of any
458 type (primitive or non-primitive). The type of an unboxed tuple looks
463 Unboxed tuples are used for functions that need to return multiple
464 values, but they avoid the heap allocation normally associated with
465 using fully-fledged tuples. When an unboxed tuple is returned, the
466 components are put directly into registers or on the stack; the
467 unboxed tuple itself does not have a composite representation. Many
468 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
470 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
471 tuples to avoid unnecessary allocation during sequences of operations.
475 There are some pretty stringent restrictions on the use of unboxed tuples:
480 Values of unboxed tuple types are subject to the same restrictions as
481 other unboxed types; i.e. they may not be stored in polymorphic data
482 structures or passed to polymorphic functions.
489 No variable can have an unboxed tuple type, nor may a constructor or function
490 argument have an unboxed tuple type. The following are all illegal:
494 data Foo = Foo (# Int, Int #)
496 f :: (# Int, Int #) -> (# Int, Int #)
499 g :: (# Int, Int #) -> Int
502 h x = let y = (# x,x #) in ...
509 The typical use of unboxed tuples is simply to return multiple values,
510 binding those multiple results with a <literal>case</literal> expression, thus:
512 f x y = (# x+1, y-1 #)
513 g x = case f x x of { (# a, b #) -> a + b }
515 You can have an unboxed tuple in a pattern binding, thus
517 f x = let (# p,q #) = h x in ..body..
519 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
520 the resulting binding is lazy like any other Haskell pattern binding. The
521 above example desugars like this:
523 f x = let t = case h x o f{ (# p,q #) -> (p,q)
528 Indeed, the bindings can even be recursive.
535 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
537 <sect1 id="syntax-extns">
538 <title>Syntactic extensions</title>
540 <!-- ====================== HIERARCHICAL MODULES ======================= -->
542 <sect2 id="hierarchical-modules">
543 <title>Hierarchical Modules</title>
545 <para>GHC supports a small extension to the syntax of module
546 names: a module name is allowed to contain a dot
547 <literal>‘.’</literal>. This is also known as the
548 “hierarchical module namespace” extension, because
549 it extends the normally flat Haskell module namespace into a
550 more flexible hierarchy of modules.</para>
552 <para>This extension has very little impact on the language
553 itself; modules names are <emphasis>always</emphasis> fully
554 qualified, so you can just think of the fully qualified module
555 name as <quote>the module name</quote>. In particular, this
556 means that the full module name must be given after the
557 <literal>module</literal> keyword at the beginning of the
558 module; for example, the module <literal>A.B.C</literal> must
561 <programlisting>module A.B.C</programlisting>
564 <para>It is a common strategy to use the <literal>as</literal>
565 keyword to save some typing when using qualified names with
566 hierarchical modules. For example:</para>
569 import qualified Control.Monad.ST.Strict as ST
572 <para>For details on how GHC searches for source and interface
573 files in the presence of hierarchical modules, see <xref
574 linkend="search-path"/>.</para>
576 <para>GHC comes with a large collection of libraries arranged
577 hierarchically; see the accompanying library documentation.
578 There is an ongoing project to create and maintain a stable set
579 of <quote>core</quote> libraries used by several Haskell
580 compilers, and the libraries that GHC comes with represent the
581 current status of that project. For more details, see <ulink
582 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
583 Libraries</ulink>.</para>
587 <!-- ====================== PATTERN GUARDS ======================= -->
589 <sect2 id="pattern-guards">
590 <title>Pattern guards</title>
593 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
594 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.)
598 Suppose we have an abstract data type of finite maps, with a
602 lookup :: FiniteMap -> Int -> Maybe Int
605 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
606 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
610 clunky env var1 var2 | ok1 && ok2 = val1 + val2
611 | otherwise = var1 + var2
622 The auxiliary functions are
626 maybeToBool :: Maybe a -> Bool
627 maybeToBool (Just x) = True
628 maybeToBool Nothing = False
630 expectJust :: Maybe a -> a
631 expectJust (Just x) = x
632 expectJust Nothing = error "Unexpected Nothing"
636 What is <function>clunky</function> doing? The guard <literal>ok1 &&
637 ok2</literal> checks that both lookups succeed, using
638 <function>maybeToBool</function> to convert the <function>Maybe</function>
639 types to booleans. The (lazily evaluated) <function>expectJust</function>
640 calls extract the values from the results of the lookups, and binds the
641 returned values to <varname>val1</varname> and <varname>val2</varname>
642 respectively. If either lookup fails, then clunky takes the
643 <literal>otherwise</literal> case and returns the sum of its arguments.
647 This is certainly legal Haskell, but it is a tremendously verbose and
648 un-obvious way to achieve the desired effect. Arguably, a more direct way
649 to write clunky would be to use case expressions:
653 clunky env var1 var1 = case lookup env var1 of
655 Just val1 -> case lookup env var2 of
657 Just val2 -> val1 + val2
663 This is a bit shorter, but hardly better. Of course, we can rewrite any set
664 of pattern-matching, guarded equations as case expressions; that is
665 precisely what the compiler does when compiling equations! The reason that
666 Haskell provides guarded equations is because they allow us to write down
667 the cases we want to consider, one at a time, independently of each other.
668 This structure is hidden in the case version. Two of the right-hand sides
669 are really the same (<function>fail</function>), and the whole expression
670 tends to become more and more indented.
674 Here is how I would write clunky:
679 | Just val1 <- lookup env var1
680 , Just val2 <- lookup env var2
682 ...other equations for clunky...
686 The semantics should be clear enough. The qualifiers are matched in order.
687 For a <literal><-</literal> qualifier, which I call a pattern guard, the
688 right hand side is evaluated and matched against the pattern on the left.
689 If the match fails then the whole guard fails and the next equation is
690 tried. If it succeeds, then the appropriate binding takes place, and the
691 next qualifier is matched, in the augmented environment. Unlike list
692 comprehensions, however, the type of the expression to the right of the
693 <literal><-</literal> is the same as the type of the pattern to its
694 left. The bindings introduced by pattern guards scope over all the
695 remaining guard qualifiers, and over the right hand side of the equation.
699 Just as with list comprehensions, boolean expressions can be freely mixed
700 with among the pattern guards. For example:
711 Haskell's current guards therefore emerge as a special case, in which the
712 qualifier list has just one element, a boolean expression.
716 <!-- ===================== Recursive do-notation =================== -->
718 <sect2 id="mdo-notation">
719 <title>The recursive do-notation
722 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
723 "A recursive do for Haskell",
724 Levent Erkok, John Launchbury",
725 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
728 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
729 that is, the variables bound in a do-expression are visible only in the textually following
730 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
731 group. It turns out that several applications can benefit from recursive bindings in
732 the do-notation, and this extension provides the necessary syntactic support.
735 Here is a simple (yet contrived) example:
738 import Control.Monad.Fix
740 justOnes = mdo xs <- Just (1:xs)
744 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
748 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
751 class Monad m => MonadFix m where
752 mfix :: (a -> m a) -> m a
755 The function <literal>mfix</literal>
756 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
757 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
758 For details, see the above mentioned reference.
761 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
762 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
763 for Haskell's internal state monad (strict and lazy, respectively).
766 There are three important points in using the recursive-do notation:
769 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
770 than <literal>do</literal>).
774 You should <literal>import Control.Monad.Fix</literal>.
775 (Note: Strictly speaking, this import is required only when you need to refer to the name
776 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
777 are encouraged to always import this module when using the mdo-notation.)
781 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
787 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
788 contains up to date information on recursive monadic bindings.
792 Historical note: The old implementation of the mdo-notation (and most
793 of the existing documents) used the name
794 <literal>MonadRec</literal> for the class and the corresponding library.
795 This name is not supported by GHC.
801 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
803 <sect2 id="parallel-list-comprehensions">
804 <title>Parallel List Comprehensions</title>
805 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
807 <indexterm><primary>parallel list comprehensions</primary>
810 <para>Parallel list comprehensions are a natural extension to list
811 comprehensions. List comprehensions can be thought of as a nice
812 syntax for writing maps and filters. Parallel comprehensions
813 extend this to include the zipWith family.</para>
815 <para>A parallel list comprehension has multiple independent
816 branches of qualifier lists, each separated by a `|' symbol. For
817 example, the following zips together two lists:</para>
820 [ (x, y) | x <- xs | y <- ys ]
823 <para>The behavior of parallel list comprehensions follows that of
824 zip, in that the resulting list will have the same length as the
825 shortest branch.</para>
827 <para>We can define parallel list comprehensions by translation to
828 regular comprehensions. Here's the basic idea:</para>
830 <para>Given a parallel comprehension of the form: </para>
833 [ e | p1 <- e11, p2 <- e12, ...
834 | q1 <- e21, q2 <- e22, ...
839 <para>This will be translated to: </para>
842 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
843 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
848 <para>where `zipN' is the appropriate zip for the given number of
853 <sect2 id="rebindable-syntax">
854 <title>Rebindable syntax</title>
857 <para>GHC allows most kinds of built-in syntax to be rebound by
858 the user, to facilitate replacing the <literal>Prelude</literal>
859 with a home-grown version, for example.</para>
861 <para>You may want to define your own numeric class
862 hierarchy. It completely defeats that purpose if the
863 literal "1" means "<literal>Prelude.fromInteger
864 1</literal>", which is what the Haskell Report specifies.
865 So the <option>-fno-implicit-prelude</option> flag causes
866 the following pieces of built-in syntax to refer to
867 <emphasis>whatever is in scope</emphasis>, not the Prelude
872 <para>An integer literal <literal>368</literal> means
873 "<literal>fromInteger (368::Integer)</literal>", rather than
874 "<literal>Prelude.fromInteger (368::Integer)</literal>".
877 <listitem><para>Fractional literals are handed in just the same way,
878 except that the translation is
879 <literal>fromRational (3.68::Rational)</literal>.
882 <listitem><para>The equality test in an overloaded numeric pattern
883 uses whatever <literal>(==)</literal> is in scope.
886 <listitem><para>The subtraction operation, and the
887 greater-than-or-equal test, in <literal>n+k</literal> patterns
888 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
892 <para>Negation (e.g. "<literal>- (f x)</literal>")
893 means "<literal>negate (f x)</literal>", both in numeric
894 patterns, and expressions.
898 <para>"Do" notation is translated using whatever
899 functions <literal>(>>=)</literal>,
900 <literal>(>>)</literal>, and <literal>fail</literal>,
901 are in scope (not the Prelude
902 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
903 comprehensions, are unaffected. </para></listitem>
907 notation (see <xref linkend="arrow-notation"/>)
908 uses whatever <literal>arr</literal>,
909 <literal>(>>>)</literal>, <literal>first</literal>,
910 <literal>app</literal>, <literal>(|||)</literal> and
911 <literal>loop</literal> functions are in scope. But unlike the
912 other constructs, the types of these functions must match the
913 Prelude types very closely. Details are in flux; if you want
917 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
918 even if that is a little unexpected. For emample, the
919 static semantics of the literal <literal>368</literal>
920 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
921 <literal>fromInteger</literal> to have any of the types:
923 fromInteger :: Integer -> Integer
924 fromInteger :: forall a. Foo a => Integer -> a
925 fromInteger :: Num a => a -> Integer
926 fromInteger :: Integer -> Bool -> Bool
930 <para>Be warned: this is an experimental facility, with
931 fewer checks than usual. Use <literal>-dcore-lint</literal>
932 to typecheck the desugared program. If Core Lint is happy
933 you should be all right.</para>
939 <!-- TYPE SYSTEM EXTENSIONS -->
940 <sect1 id="type-extensions">
941 <title>Type system extensions</title>
945 <title>Data types and type synonyms</title>
947 <sect3 id="nullary-types">
948 <title>Data types with no constructors</title>
950 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
951 a data type with no constructors. For example:</para>
955 data T a -- T :: * -> *
958 <para>Syntactically, the declaration lacks the "= constrs" part. The
959 type can be parameterised over types of any kind, but if the kind is
960 not <literal>*</literal> then an explicit kind annotation must be used
961 (see <xref linkend="sec-kinding"/>).</para>
963 <para>Such data types have only one value, namely bottom.
964 Nevertheless, they can be useful when defining "phantom types".</para>
967 <sect3 id="infix-tycons">
968 <title>Infix type constructors, classes, and type variables</title>
971 GHC allows type constructors, classes, and type variables to be operators, and
972 to be written infix, very much like expressions. More specifically:
975 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
976 The lexical syntax is the same as that for data constructors.
979 Data type and type-synonym declarations can be written infix, parenthesised
980 if you want further arguments. E.g.
982 data a :*: b = Foo a b
983 type a :+: b = Either a b
984 class a :=: b where ...
986 data (a :**: b) x = Baz a b x
987 type (a :++: b) y = Either (a,b) y
991 Types, and class constraints, can be written infix. For example
994 f :: (a :=: b) => a -> b
998 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
999 The lexical syntax is the same as that for variable operators, excluding "(.)",
1000 "(!)", and "(*)". In a binding position, the operator must be
1001 parenthesised. For example:
1003 type T (+) = Int + Int
1007 liftA2 :: Arrow (~>)
1008 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1014 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1015 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1018 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1019 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1020 sets the fixity for a data constructor and the corresponding type constructor. For example:
1024 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1025 and similarly for <literal>:*:</literal>.
1026 <literal>Int `a` Bool</literal>.
1029 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1036 <sect3 id="type-synonyms">
1037 <title>Liberalised type synonyms</title>
1040 Type synonyms are like macros at the type level, and
1041 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1042 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1044 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1045 in a type synonym, thus:
1047 type Discard a = forall b. Show b => a -> b -> (a, String)
1052 g :: Discard Int -> (Int,String) -- A rank-2 type
1059 You can write an unboxed tuple in a type synonym:
1061 type Pr = (# Int, Int #)
1069 You can apply a type synonym to a forall type:
1071 type Foo a = a -> a -> Bool
1073 f :: Foo (forall b. b->b)
1075 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1077 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1082 You can apply a type synonym to a partially applied type synonym:
1084 type Generic i o = forall x. i x -> o x
1087 foo :: Generic Id []
1089 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1091 foo :: forall x. x -> [x]
1099 GHC currently does kind checking before expanding synonyms (though even that
1103 After expanding type synonyms, GHC does validity checking on types, looking for
1104 the following mal-formedness which isn't detected simply by kind checking:
1107 Type constructor applied to a type involving for-alls.
1110 Unboxed tuple on left of an arrow.
1113 Partially-applied type synonym.
1117 this will be rejected:
1119 type Pr = (# Int, Int #)
1124 because GHC does not allow unboxed tuples on the left of a function arrow.
1129 <sect3 id="existential-quantification">
1130 <title>Existentially quantified data constructors
1134 The idea of using existential quantification in data type declarations
1135 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1136 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1137 London, 1991). It was later formalised by Laufer and Odersky
1138 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1139 TOPLAS, 16(5), pp1411-1430, 1994).
1140 It's been in Lennart
1141 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1142 proved very useful. Here's the idea. Consider the declaration:
1148 data Foo = forall a. MkFoo a (a -> Bool)
1155 The data type <literal>Foo</literal> has two constructors with types:
1161 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1168 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1169 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1170 For example, the following expression is fine:
1176 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1182 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1183 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1184 isUpper</function> packages a character with a compatible function. These
1185 two things are each of type <literal>Foo</literal> and can be put in a list.
1189 What can we do with a value of type <literal>Foo</literal>?. In particular,
1190 what happens when we pattern-match on <function>MkFoo</function>?
1196 f (MkFoo val fn) = ???
1202 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1203 are compatible, the only (useful) thing we can do with them is to
1204 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1211 f (MkFoo val fn) = fn val
1217 What this allows us to do is to package heterogenous values
1218 together with a bunch of functions that manipulate them, and then treat
1219 that collection of packages in a uniform manner. You can express
1220 quite a bit of object-oriented-like programming this way.
1223 <sect4 id="existential">
1224 <title>Why existential?
1228 What has this to do with <emphasis>existential</emphasis> quantification?
1229 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1235 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1241 But Haskell programmers can safely think of the ordinary
1242 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1243 adding a new existential quantification construct.
1249 <title>Type classes</title>
1252 An easy extension is to allow
1253 arbitrary contexts before the constructor. For example:
1259 data Baz = forall a. Eq a => Baz1 a a
1260 | forall b. Show b => Baz2 b (b -> b)
1266 The two constructors have the types you'd expect:
1272 Baz1 :: forall a. Eq a => a -> a -> Baz
1273 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1279 But when pattern matching on <function>Baz1</function> the matched values can be compared
1280 for equality, and when pattern matching on <function>Baz2</function> the first matched
1281 value can be converted to a string (as well as applying the function to it).
1282 So this program is legal:
1289 f (Baz1 p q) | p == q = "Yes"
1291 f (Baz2 v fn) = show (fn v)
1297 Operationally, in a dictionary-passing implementation, the
1298 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1299 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1300 extract it on pattern matching.
1304 Notice the way that the syntax fits smoothly with that used for
1305 universal quantification earlier.
1311 <title>Record Constructors</title>
1314 GHC allows existentials to be used with records syntax as well. For example:
1317 data Counter a = forall self. NewCounter
1319 , _inc :: self -> self
1320 , _display :: self -> IO ()
1324 Here <literal>tag</literal> is a public field, with a well-typed selector
1325 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1326 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1327 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1328 compile-time error. In other words, <emphasis>GHC defines a record selector function
1329 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1330 (This example used an underscore in the fields for which record selectors
1331 will not be defined, but that is only programming style; GHC ignores them.)
1335 To make use of these hidden fields, we need to create some helper functions:
1338 inc :: Counter a -> Counter a
1339 inc (NewCounter x i d t) = NewCounter
1340 { _this = i x, _inc = i, _display = d, tag = t }
1342 display :: Counter a -> IO ()
1343 display NewCounter{ _this = x, _display = d } = d x
1346 Now we can define counters with different underlying implementations:
1349 counterA :: Counter String
1350 counterA = NewCounter
1351 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1353 counterB :: Counter String
1354 counterB = NewCounter
1355 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1358 display (inc counterA) -- prints "1"
1359 display (inc (inc counterB)) -- prints "##"
1362 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1363 <literal>forall</literal> may be omitted. For example, we can express
1364 the same <literal>Counter a</literal> using GADT:
1367 data Counter a where
1368 NewCounter { _this :: self
1369 , _inc :: self -> self
1370 , _display :: self -> IO ()
1376 At the moment, record update syntax is only supported for Haskell 98 data types,
1377 so the following function does <emphasis>not</emphasis> work:
1380 -- This is invalid; use explicit NewCounter instead for now
1381 setTag :: Counter a -> a -> Counter a
1382 setTag obj t = obj{ tag = t }
1391 <title>Restrictions</title>
1394 There are several restrictions on the ways in which existentially-quantified
1395 constructors can be use.
1404 When pattern matching, each pattern match introduces a new,
1405 distinct, type for each existential type variable. These types cannot
1406 be unified with any other type, nor can they escape from the scope of
1407 the pattern match. For example, these fragments are incorrect:
1415 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1416 is the result of <function>f1</function>. One way to see why this is wrong is to
1417 ask what type <function>f1</function> has:
1421 f1 :: Foo -> a -- Weird!
1425 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1430 f1 :: forall a. Foo -> a -- Wrong!
1434 The original program is just plain wrong. Here's another sort of error
1438 f2 (Baz1 a b) (Baz1 p q) = a==q
1442 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1443 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1444 from the two <function>Baz1</function> constructors.
1452 You can't pattern-match on an existentially quantified
1453 constructor in a <literal>let</literal> or <literal>where</literal> group of
1454 bindings. So this is illegal:
1458 f3 x = a==b where { Baz1 a b = x }
1461 Instead, use a <literal>case</literal> expression:
1464 f3 x = case x of Baz1 a b -> a==b
1467 In general, you can only pattern-match
1468 on an existentially-quantified constructor in a <literal>case</literal> expression or
1469 in the patterns of a function definition.
1471 The reason for this restriction is really an implementation one.
1472 Type-checking binding groups is already a nightmare without
1473 existentials complicating the picture. Also an existential pattern
1474 binding at the top level of a module doesn't make sense, because it's
1475 not clear how to prevent the existentially-quantified type "escaping".
1476 So for now, there's a simple-to-state restriction. We'll see how
1484 You can't use existential quantification for <literal>newtype</literal>
1485 declarations. So this is illegal:
1489 newtype T = forall a. Ord a => MkT a
1493 Reason: a value of type <literal>T</literal> must be represented as a
1494 pair of a dictionary for <literal>Ord t</literal> and a value of type
1495 <literal>t</literal>. That contradicts the idea that
1496 <literal>newtype</literal> should have no concrete representation.
1497 You can get just the same efficiency and effect by using
1498 <literal>data</literal> instead of <literal>newtype</literal>. If
1499 there is no overloading involved, then there is more of a case for
1500 allowing an existentially-quantified <literal>newtype</literal>,
1501 because the <literal>data</literal> version does carry an
1502 implementation cost, but single-field existentially quantified
1503 constructors aren't much use. So the simple restriction (no
1504 existential stuff on <literal>newtype</literal>) stands, unless there
1505 are convincing reasons to change it.
1513 You can't use <literal>deriving</literal> to define instances of a
1514 data type with existentially quantified data constructors.
1516 Reason: in most cases it would not make sense. For example:#
1519 data T = forall a. MkT [a] deriving( Eq )
1522 To derive <literal>Eq</literal> in the standard way we would need to have equality
1523 between the single component of two <function>MkT</function> constructors:
1527 (MkT a) == (MkT b) = ???
1530 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1531 It's just about possible to imagine examples in which the derived instance
1532 would make sense, but it seems altogether simpler simply to prohibit such
1533 declarations. Define your own instances!
1548 <sect2 id="multi-param-type-classes">
1549 <title>Class declarations</title>
1552 This section, and the next one, documents GHC's type-class extensions.
1553 There's lots of background in the paper <ulink
1554 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1555 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1556 Jones, Erik Meijer).
1559 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1563 <title>Multi-parameter type classes</title>
1565 Multi-parameter type classes are permitted. For example:
1569 class Collection c a where
1570 union :: c a -> c a -> c a
1578 <title>The superclasses of a class declaration</title>
1581 There are no restrictions on the context in a class declaration
1582 (which introduces superclasses), except that the class hierarchy must
1583 be acyclic. So these class declarations are OK:
1587 class Functor (m k) => FiniteMap m k where
1590 class (Monad m, Monad (t m)) => Transform t m where
1591 lift :: m a -> (t m) a
1597 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1598 of "acyclic" involves only the superclass relationships. For example,
1604 op :: D b => a -> b -> b
1607 class C a => D a where { ... }
1611 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1612 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1613 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1620 <sect3 id="class-method-types">
1621 <title>Class method types</title>
1624 Haskell 98 prohibits class method types to mention constraints on the
1625 class type variable, thus:
1628 fromList :: [a] -> s a
1629 elem :: Eq a => a -> s a -> Bool
1631 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1632 contains the constraint <literal>Eq a</literal>, constrains only the
1633 class type variable (in this case <literal>a</literal>).
1634 GHC lifts this restriction.
1641 <sect2 id="functional-dependencies">
1642 <title>Functional dependencies
1645 <para> Functional dependencies are implemented as described by Mark Jones
1646 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1647 In Proceedings of the 9th European Symposium on Programming,
1648 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1652 Functional dependencies are introduced by a vertical bar in the syntax of a
1653 class declaration; e.g.
1655 class (Monad m) => MonadState s m | m -> s where ...
1657 class Foo a b c | a b -> c where ...
1659 There should be more documentation, but there isn't (yet). Yell if you need it.
1662 <sect3><title>Rules for functional dependencies </title>
1664 In a class declaration, all of the class type variables must be reachable (in the sense
1665 mentioned in <xref linkend="type-restrictions"/>)
1666 from the free variables of each method type.
1670 class Coll s a where
1672 insert :: s -> a -> s
1675 is not OK, because the type of <literal>empty</literal> doesn't mention
1676 <literal>a</literal>. Functional dependencies can make the type variable
1679 class Coll s a | s -> a where
1681 insert :: s -> a -> s
1684 Alternatively <literal>Coll</literal> might be rewritten
1687 class Coll s a where
1689 insert :: s a -> a -> s a
1693 which makes the connection between the type of a collection of
1694 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1695 Occasionally this really doesn't work, in which case you can split the
1703 class CollE s => Coll s a where
1704 insert :: s -> a -> s
1711 <title>Background on functional dependencies</title>
1713 <para>The following description of the motivation and use of functional dependencies is taken
1714 from the Hugs user manual, reproduced here (with minor changes) by kind
1715 permission of Mark Jones.
1718 Consider the following class, intended as part of a
1719 library for collection types:
1721 class Collects e ce where
1723 insert :: e -> ce -> ce
1724 member :: e -> ce -> Bool
1726 The type variable e used here represents the element type, while ce is the type
1727 of the container itself. Within this framework, we might want to define
1728 instances of this class for lists or characteristic functions (both of which
1729 can be used to represent collections of any equality type), bit sets (which can
1730 be used to represent collections of characters), or hash tables (which can be
1731 used to represent any collection whose elements have a hash function). Omitting
1732 standard implementation details, this would lead to the following declarations:
1734 instance Eq e => Collects e [e] where ...
1735 instance Eq e => Collects e (e -> Bool) where ...
1736 instance Collects Char BitSet where ...
1737 instance (Hashable e, Collects a ce)
1738 => Collects e (Array Int ce) where ...
1740 All this looks quite promising; we have a class and a range of interesting
1741 implementations. Unfortunately, there are some serious problems with the class
1742 declaration. First, the empty function has an ambiguous type:
1744 empty :: Collects e ce => ce
1746 By "ambiguous" we mean that there is a type variable e that appears on the left
1747 of the <literal>=></literal> symbol, but not on the right. The problem with
1748 this is that, according to the theoretical foundations of Haskell overloading,
1749 we cannot guarantee a well-defined semantics for any term with an ambiguous
1753 We can sidestep this specific problem by removing the empty member from the
1754 class declaration. However, although the remaining members, insert and member,
1755 do not have ambiguous types, we still run into problems when we try to use
1756 them. For example, consider the following two functions:
1758 f x y = insert x . insert y
1761 for which GHC infers the following types:
1763 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1764 g :: (Collects Bool c, Collects Char c) => c -> c
1766 Notice that the type for f allows the two parameters x and y to be assigned
1767 different types, even though it attempts to insert each of the two values, one
1768 after the other, into the same collection. If we're trying to model collections
1769 that contain only one type of value, then this is clearly an inaccurate
1770 type. Worse still, the definition for g is accepted, without causing a type
1771 error. As a result, the error in this code will not be flagged at the point
1772 where it appears. Instead, it will show up only when we try to use g, which
1773 might even be in a different module.
1776 <sect4><title>An attempt to use constructor classes</title>
1779 Faced with the problems described above, some Haskell programmers might be
1780 tempted to use something like the following version of the class declaration:
1782 class Collects e c where
1784 insert :: e -> c e -> c e
1785 member :: e -> c e -> Bool
1787 The key difference here is that we abstract over the type constructor c that is
1788 used to form the collection type c e, and not over that collection type itself,
1789 represented by ce in the original class declaration. This avoids the immediate
1790 problems that we mentioned above: empty has type <literal>Collects e c => c
1791 e</literal>, which is not ambiguous.
1794 The function f from the previous section has a more accurate type:
1796 f :: (Collects e c) => e -> e -> c e -> c e
1798 The function g from the previous section is now rejected with a type error as
1799 we would hope because the type of f does not allow the two arguments to have
1801 This, then, is an example of a multiple parameter class that does actually work
1802 quite well in practice, without ambiguity problems.
1803 There is, however, a catch. This version of the Collects class is nowhere near
1804 as general as the original class seemed to be: only one of the four instances
1805 for <literal>Collects</literal>
1806 given above can be used with this version of Collects because only one of
1807 them---the instance for lists---has a collection type that can be written in
1808 the form c e, for some type constructor c, and element type e.
1812 <sect4><title>Adding functional dependencies</title>
1815 To get a more useful version of the Collects class, Hugs provides a mechanism
1816 that allows programmers to specify dependencies between the parameters of a
1817 multiple parameter class (For readers with an interest in theoretical
1818 foundations and previous work: The use of dependency information can be seen
1819 both as a generalization of the proposal for `parametric type classes' that was
1820 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1821 later framework for "improvement" of qualified types. The
1822 underlying ideas are also discussed in a more theoretical and abstract setting
1823 in a manuscript [implparam], where they are identified as one point in a
1824 general design space for systems of implicit parameterization.).
1826 To start with an abstract example, consider a declaration such as:
1828 class C a b where ...
1830 which tells us simply that C can be thought of as a binary relation on types
1831 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1832 included in the definition of classes to add information about dependencies
1833 between parameters, as in the following examples:
1835 class D a b | a -> b where ...
1836 class E a b | a -> b, b -> a where ...
1838 The notation <literal>a -> b</literal> used here between the | and where
1839 symbols --- not to be
1840 confused with a function type --- indicates that the a parameter uniquely
1841 determines the b parameter, and might be read as "a determines b." Thus D is
1842 not just a relation, but actually a (partial) function. Similarly, from the two
1843 dependencies that are included in the definition of E, we can see that E
1844 represents a (partial) one-one mapping between types.
1847 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1848 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1849 m>=0, meaning that the y parameters are uniquely determined by the x
1850 parameters. Spaces can be used as separators if more than one variable appears
1851 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1852 annotated with multiple dependencies using commas as separators, as in the
1853 definition of E above. Some dependencies that we can write in this notation are
1854 redundant, and will be rejected because they don't serve any useful
1855 purpose, and may instead indicate an error in the program. Examples of
1856 dependencies like this include <literal>a -> a </literal>,
1857 <literal>a -> a a </literal>,
1858 <literal>a -> </literal>, etc. There can also be
1859 some redundancy if multiple dependencies are given, as in
1860 <literal>a->b</literal>,
1861 <literal>b->c </literal>, <literal>a->c </literal>, and
1862 in which some subset implies the remaining dependencies. Examples like this are
1863 not treated as errors. Note that dependencies appear only in class
1864 declarations, and not in any other part of the language. In particular, the
1865 syntax for instance declarations, class constraints, and types is completely
1869 By including dependencies in a class declaration, we provide a mechanism for
1870 the programmer to specify each multiple parameter class more precisely. The
1871 compiler, on the other hand, is responsible for ensuring that the set of
1872 instances that are in scope at any given point in the program is consistent
1873 with any declared dependencies. For example, the following pair of instance
1874 declarations cannot appear together in the same scope because they violate the
1875 dependency for D, even though either one on its own would be acceptable:
1877 instance D Bool Int where ...
1878 instance D Bool Char where ...
1880 Note also that the following declaration is not allowed, even by itself:
1882 instance D [a] b where ...
1884 The problem here is that this instance would allow one particular choice of [a]
1885 to be associated with more than one choice for b, which contradicts the
1886 dependency specified in the definition of D. More generally, this means that,
1887 in any instance of the form:
1889 instance D t s where ...
1891 for some particular types t and s, the only variables that can appear in s are
1892 the ones that appear in t, and hence, if the type t is known, then s will be
1893 uniquely determined.
1896 The benefit of including dependency information is that it allows us to define
1897 more general multiple parameter classes, without ambiguity problems, and with
1898 the benefit of more accurate types. To illustrate this, we return to the
1899 collection class example, and annotate the original definition of <literal>Collects</literal>
1900 with a simple dependency:
1902 class Collects e ce | ce -> e where
1904 insert :: e -> ce -> ce
1905 member :: e -> ce -> Bool
1907 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1908 determined by the type of the collection ce. Note that both parameters of
1909 Collects are of kind *; there are no constructor classes here. Note too that
1910 all of the instances of Collects that we gave earlier can be used
1911 together with this new definition.
1914 What about the ambiguity problems that we encountered with the original
1915 definition? The empty function still has type Collects e ce => ce, but it is no
1916 longer necessary to regard that as an ambiguous type: Although the variable e
1917 does not appear on the right of the => symbol, the dependency for class
1918 Collects tells us that it is uniquely determined by ce, which does appear on
1919 the right of the => symbol. Hence the context in which empty is used can still
1920 give enough information to determine types for both ce and e, without
1921 ambiguity. More generally, we need only regard a type as ambiguous if it
1922 contains a variable on the left of the => that is not uniquely determined
1923 (either directly or indirectly) by the variables on the right.
1926 Dependencies also help to produce more accurate types for user defined
1927 functions, and hence to provide earlier detection of errors, and less cluttered
1928 types for programmers to work with. Recall the previous definition for a
1931 f x y = insert x y = insert x . insert y
1933 for which we originally obtained a type:
1935 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1937 Given the dependency information that we have for Collects, however, we can
1938 deduce that a and b must be equal because they both appear as the second
1939 parameter in a Collects constraint with the same first parameter c. Hence we
1940 can infer a shorter and more accurate type for f:
1942 f :: (Collects a c) => a -> a -> c -> c
1944 In a similar way, the earlier definition of g will now be flagged as a type error.
1947 Although we have given only a few examples here, it should be clear that the
1948 addition of dependency information can help to make multiple parameter classes
1949 more useful in practice, avoiding ambiguity problems, and allowing more general
1950 sets of instance declarations.
1956 <sect2 id="instance-decls">
1957 <title>Instance declarations</title>
1959 <sect3 id="instance-rules">
1960 <title>Relaxed rules for instance declarations</title>
1962 <para>An instance declaration has the form
1964 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 ...
1966 The part before the "<literal>=></literal>" is the
1967 <emphasis>context</emphasis>, while the part after the
1968 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1972 In Haskell 98 the head of an instance declaration
1973 must be of the form <literal>C (T a1 ... an)</literal>, where
1974 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1975 and the <literal>a1 ... an</literal> are distinct type variables.
1976 Furthermore, the assertions in the context of the instance declaration
1977 must be of the form <literal>C a</literal> where <literal>a</literal>
1978 is a type variable that occurs in the head.
1981 The <option>-fglasgow-exts</option> flag loosens these restrictions
1982 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1983 the context and head of the instance declaration can each consist of arbitrary
1984 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1988 For each assertion in the context:
1990 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1991 <listitem><para>The assertion has fewer constructors and variables (taken together
1992 and counting repetitions) than the head</para></listitem>
1996 <listitem><para>The coverage condition. For each functional dependency,
1997 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
1998 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
1999 every type variable in
2000 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2001 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2002 substitution mapping each type variable in the class declaration to the
2003 corresponding type in the instance declaration.
2006 These restrictions ensure that context reduction terminates: each reduction
2007 step makes the problem smaller by at least one
2008 constructor. For example, the following would make the type checker
2009 loop if it wasn't excluded:
2011 instance C a => C a where ...
2013 For example, these are OK:
2015 instance C Int [a] -- Multiple parameters
2016 instance Eq (S [a]) -- Structured type in head
2018 -- Repeated type variable in head
2019 instance C4 a a => C4 [a] [a]
2020 instance Stateful (ST s) (MutVar s)
2022 -- Head can consist of type variables only
2024 instance (Eq a, Show b) => C2 a b
2026 -- Non-type variables in context
2027 instance Show (s a) => Show (Sized s a)
2028 instance C2 Int a => C3 Bool [a]
2029 instance C2 Int a => C3 [a] b
2033 -- Context assertion no smaller than head
2034 instance C a => C a where ...
2035 -- (C b b) has more more occurrences of b than the head
2036 instance C b b => Foo [b] where ...
2041 The same restrictions apply to instances generated by
2042 <literal>deriving</literal> clauses. Thus the following is accepted:
2044 data MinHeap h a = H a (h a)
2047 because the derived instance
2049 instance (Show a, Show (h a)) => Show (MinHeap h a)
2051 conforms to the above rules.
2055 A useful idiom permitted by the above rules is as follows.
2056 If one allows overlapping instance declarations then it's quite
2057 convenient to have a "default instance" declaration that applies if
2058 something more specific does not:
2064 <para>You can find lots of background material about the reason for these
2065 restrictions in the paper <ulink
2066 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2067 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2071 <sect3 id="undecidable-instances">
2072 <title>Undecidable instances</title>
2075 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2076 For example, sometimes you might want to use the following to get the
2077 effect of a "class synonym":
2079 class (C1 a, C2 a, C3 a) => C a where { }
2081 instance (C1 a, C2 a, C3 a) => C a where { }
2083 This allows you to write shorter signatures:
2089 f :: (C1 a, C2 a, C3 a) => ...
2091 The restrictions on functional dependencies (<xref
2092 linkend="functional-dependencies"/>) are particularly troublesome.
2093 It is tempting to introduce type variables in the context that do not appear in
2094 the head, something that is excluded by the normal rules. For example:
2096 class HasConverter a b | a -> b where
2099 data Foo a = MkFoo a
2101 instance (HasConverter a b,Show b) => Show (Foo a) where
2102 show (MkFoo value) = show (convert value)
2104 This is dangerous territory, however. Here, for example, is a program that would make the
2109 instance F [a] [[a]]
2110 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2112 Similarly, it can be tempting to lift the coverage condition:
2114 class Mul a b c | a b -> c where
2115 (.*.) :: a -> b -> c
2117 instance Mul Int Int Int where (.*.) = (*)
2118 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2119 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2121 The third instance declaration does not obey the coverage condition;
2122 and indeed the (somewhat strange) definition:
2124 f = \ b x y -> if b then x .*. [y] else y
2126 makes instance inference go into a loop, because it requires the constraint
2127 <literal>(Mul a [b] b)</literal>.
2130 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2131 the experimental flag <option>-fallow-undecidable-instances</option>
2132 <indexterm><primary>-fallow-undecidable-instances
2133 option</primary></indexterm>, you can use arbitrary
2134 types in both an instance context and instance head. Termination is ensured by having a
2135 fixed-depth recursion stack. If you exceed the stack depth you get a
2136 sort of backtrace, and the opportunity to increase the stack depth
2137 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2143 <sect3 id="instance-overlap">
2144 <title>Overlapping instances</title>
2146 In general, <emphasis>GHC requires that that it be unambiguous which instance
2148 should be used to resolve a type-class constraint</emphasis>. This behaviour
2149 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2150 <indexterm><primary>-fallow-overlapping-instances
2151 </primary></indexterm>
2152 and <option>-fallow-incoherent-instances</option>
2153 <indexterm><primary>-fallow-incoherent-instances
2154 </primary></indexterm>, as this section discusses. Both these
2155 flags are dynamic flags, and can be set on a per-module basis, using
2156 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2158 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2159 it tries to match every instance declaration against the
2161 by instantiating the head of the instance declaration. For example, consider
2164 instance context1 => C Int a where ... -- (A)
2165 instance context2 => C a Bool where ... -- (B)
2166 instance context3 => C Int [a] where ... -- (C)
2167 instance context4 => C Int [Int] where ... -- (D)
2169 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2170 but (C) and (D) do not. When matching, GHC takes
2171 no account of the context of the instance declaration
2172 (<literal>context1</literal> etc).
2173 GHC's default behaviour is that <emphasis>exactly one instance must match the
2174 constraint it is trying to resolve</emphasis>.
2175 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2176 including both declarations (A) and (B), say); an error is only reported if a
2177 particular constraint matches more than one.
2181 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2182 more than one instance to match, provided there is a most specific one. For
2183 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2184 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2185 most-specific match, the program is rejected.
2188 However, GHC is conservative about committing to an overlapping instance. For example:
2193 Suppose that from the RHS of <literal>f</literal> we get the constraint
2194 <literal>C Int [b]</literal>. But
2195 GHC does not commit to instance (C), because in a particular
2196 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2197 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2198 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2199 GHC will instead pick (C), without complaining about
2200 the problem of subsequent instantiations.
2203 The willingness to be overlapped or incoherent is a property of
2204 the <emphasis>instance declaration</emphasis> itself, controlled by the
2205 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2206 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2207 being defined. Neither flag is required in a module that imports and uses the
2208 instance declaration. Specifically, during the lookup process:
2211 An instance declaration is ignored during the lookup process if (a) a more specific
2212 match is found, and (b) the instance declaration was compiled with
2213 <option>-fallow-overlapping-instances</option>. The flag setting for the
2214 more-specific instance does not matter.
2217 Suppose an instance declaration does not matche the constraint being looked up, but
2218 does unify with it, so that it might match when the constraint is further
2219 instantiated. Usually GHC will regard this as a reason for not committing to
2220 some other constraint. But if the instance declaration was compiled with
2221 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2222 check for that declaration.
2225 All this makes it possible for a library author to design a library that relies on
2226 overlapping instances without the library client having to know.
2228 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2229 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2234 <title>Type synonyms in the instance head</title>
2237 <emphasis>Unlike Haskell 98, instance heads may use type
2238 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2239 As always, using a type synonym is just shorthand for
2240 writing the RHS of the type synonym definition. For example:
2244 type Point = (Int,Int)
2245 instance C Point where ...
2246 instance C [Point] where ...
2250 is legal. However, if you added
2254 instance C (Int,Int) where ...
2258 as well, then the compiler will complain about the overlapping
2259 (actually, identical) instance declarations. As always, type synonyms
2260 must be fully applied. You cannot, for example, write:
2265 instance Monad P where ...
2269 This design decision is independent of all the others, and easily
2270 reversed, but it makes sense to me.
2278 <sect2 id="type-restrictions">
2279 <title>Type signatures</title>
2281 <sect3><title>The context of a type signature</title>
2283 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2284 the form <emphasis>(class type-variable)</emphasis> or
2285 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2286 these type signatures are perfectly OK
2289 g :: Ord (T a ()) => ...
2293 GHC imposes the following restrictions on the constraints in a type signature.
2297 forall tv1..tvn (c1, ...,cn) => type
2300 (Here, we write the "foralls" explicitly, although the Haskell source
2301 language omits them; in Haskell 98, all the free type variables of an
2302 explicit source-language type signature are universally quantified,
2303 except for the class type variables in a class declaration. However,
2304 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2313 <emphasis>Each universally quantified type variable
2314 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2316 A type variable <literal>a</literal> is "reachable" if it it appears
2317 in the same constraint as either a type variable free in in
2318 <literal>type</literal>, or another reachable type variable.
2319 A value with a type that does not obey
2320 this reachability restriction cannot be used without introducing
2321 ambiguity; that is why the type is rejected.
2322 Here, for example, is an illegal type:
2326 forall a. Eq a => Int
2330 When a value with this type was used, the constraint <literal>Eq tv</literal>
2331 would be introduced where <literal>tv</literal> is a fresh type variable, and
2332 (in the dictionary-translation implementation) the value would be
2333 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2334 can never know which instance of <literal>Eq</literal> to use because we never
2335 get any more information about <literal>tv</literal>.
2339 that the reachability condition is weaker than saying that <literal>a</literal> is
2340 functionally dependent on a type variable free in
2341 <literal>type</literal> (see <xref
2342 linkend="functional-dependencies"/>). The reason for this is there
2343 might be a "hidden" dependency, in a superclass perhaps. So
2344 "reachable" is a conservative approximation to "functionally dependent".
2345 For example, consider:
2347 class C a b | a -> b where ...
2348 class C a b => D a b where ...
2349 f :: forall a b. D a b => a -> a
2351 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2352 but that is not immediately apparent from <literal>f</literal>'s type.
2358 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2359 universally quantified type variables <literal>tvi</literal></emphasis>.
2361 For example, this type is OK because <literal>C a b</literal> mentions the
2362 universally quantified type variable <literal>b</literal>:
2366 forall a. C a b => burble
2370 The next type is illegal because the constraint <literal>Eq b</literal> does not
2371 mention <literal>a</literal>:
2375 forall a. Eq b => burble
2379 The reason for this restriction is milder than the other one. The
2380 excluded types are never useful or necessary (because the offending
2381 context doesn't need to be witnessed at this point; it can be floated
2382 out). Furthermore, floating them out increases sharing. Lastly,
2383 excluding them is a conservative choice; it leaves a patch of
2384 territory free in case we need it later.
2395 <title>For-all hoisting</title>
2397 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2398 end of an arrow, thus:
2400 type Discard a = forall b. a -> b -> a
2402 g :: Int -> Discard Int
2405 Simply expanding the type synonym would give
2407 g :: Int -> (forall b. Int -> b -> Int)
2409 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2411 g :: forall b. Int -> Int -> b -> Int
2413 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2414 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2415 performs the transformation:</emphasis>
2417 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2419 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2421 (In fact, GHC tries to retain as much synonym information as possible for use in
2422 error messages, but that is a usability issue.) This rule applies, of course, whether
2423 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2424 valid way to write <literal>g</literal>'s type signature:
2426 g :: Int -> Int -> forall b. b -> Int
2430 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2433 type Foo a = (?x::Int) => Bool -> a
2438 g :: (?x::Int) => Bool -> Bool -> Int
2446 <sect2 id="implicit-parameters">
2447 <title>Implicit parameters</title>
2449 <para> Implicit parameters are implemented as described in
2450 "Implicit parameters: dynamic scoping with static types",
2451 J Lewis, MB Shields, E Meijer, J Launchbury,
2452 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2456 <para>(Most of the following, stil rather incomplete, documentation is
2457 due to Jeff Lewis.)</para>
2459 <para>Implicit parameter support is enabled with the option
2460 <option>-fimplicit-params</option>.</para>
2463 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2464 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2465 context. In Haskell, all variables are statically bound. Dynamic
2466 binding of variables is a notion that goes back to Lisp, but was later
2467 discarded in more modern incarnations, such as Scheme. Dynamic binding
2468 can be very confusing in an untyped language, and unfortunately, typed
2469 languages, in particular Hindley-Milner typed languages like Haskell,
2470 only support static scoping of variables.
2473 However, by a simple extension to the type class system of Haskell, we
2474 can support dynamic binding. Basically, we express the use of a
2475 dynamically bound variable as a constraint on the type. These
2476 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2477 function uses a dynamically-bound variable <literal>?x</literal>
2478 of type <literal>t'</literal>". For
2479 example, the following expresses the type of a sort function,
2480 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2482 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2484 The dynamic binding constraints are just a new form of predicate in the type class system.
2487 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2488 where <literal>x</literal> is
2489 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2490 Use of this construct also introduces a new
2491 dynamic-binding constraint in the type of the expression.
2492 For example, the following definition
2493 shows how we can define an implicitly parameterized sort function in
2494 terms of an explicitly parameterized <literal>sortBy</literal> function:
2496 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2498 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2504 <title>Implicit-parameter type constraints</title>
2506 Dynamic binding constraints behave just like other type class
2507 constraints in that they are automatically propagated. Thus, when a
2508 function is used, its implicit parameters are inherited by the
2509 function that called it. For example, our <literal>sort</literal> function might be used
2510 to pick out the least value in a list:
2512 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2513 least xs = head (sort xs)
2515 Without lifting a finger, the <literal>?cmp</literal> parameter is
2516 propagated to become a parameter of <literal>least</literal> as well. With explicit
2517 parameters, the default is that parameters must always be explicit
2518 propagated. With implicit parameters, the default is to always
2522 An implicit-parameter type constraint differs from other type class constraints in the
2523 following way: All uses of a particular implicit parameter must have
2524 the same type. This means that the type of <literal>(?x, ?x)</literal>
2525 is <literal>(?x::a) => (a,a)</literal>, and not
2526 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2530 <para> You can't have an implicit parameter in the context of a class or instance
2531 declaration. For example, both these declarations are illegal:
2533 class (?x::Int) => C a where ...
2534 instance (?x::a) => Foo [a] where ...
2536 Reason: exactly which implicit parameter you pick up depends on exactly where
2537 you invoke a function. But the ``invocation'' of instance declarations is done
2538 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2539 Easiest thing is to outlaw the offending types.</para>
2541 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2543 f :: (?x :: [a]) => Int -> Int
2546 g :: (Read a, Show a) => String -> String
2549 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2550 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2551 quite unambiguous, and fixes the type <literal>a</literal>.
2556 <title>Implicit-parameter bindings</title>
2559 An implicit parameter is <emphasis>bound</emphasis> using the standard
2560 <literal>let</literal> or <literal>where</literal> binding forms.
2561 For example, we define the <literal>min</literal> function by binding
2562 <literal>cmp</literal>.
2565 min = let ?cmp = (<=) in least
2569 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2570 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2571 (including in a list comprehension, or do-notation, or pattern guards),
2572 or a <literal>where</literal> clause.
2573 Note the following points:
2576 An implicit-parameter binding group must be a
2577 collection of simple bindings to implicit-style variables (no
2578 function-style bindings, and no type signatures); these bindings are
2579 neither polymorphic or recursive.
2582 You may not mix implicit-parameter bindings with ordinary bindings in a
2583 single <literal>let</literal>
2584 expression; use two nested <literal>let</literal>s instead.
2585 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2589 You may put multiple implicit-parameter bindings in a
2590 single binding group; but they are <emphasis>not</emphasis> treated
2591 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2592 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2593 parameter. The bindings are not nested, and may be re-ordered without changing
2594 the meaning of the program.
2595 For example, consider:
2597 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2599 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2600 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2602 f :: (?x::Int) => Int -> Int
2610 <sect3><title>Implicit parameters and polymorphic recursion</title>
2613 Consider these two definitions:
2616 len1 xs = let ?acc = 0 in len_acc1 xs
2619 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2624 len2 xs = let ?acc = 0 in len_acc2 xs
2626 len_acc2 :: (?acc :: Int) => [a] -> Int
2628 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2630 The only difference between the two groups is that in the second group
2631 <literal>len_acc</literal> is given a type signature.
2632 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2633 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2634 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2635 has a type signature, the recursive call is made to the
2636 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2637 as an implicit parameter. So we get the following results in GHCi:
2644 Adding a type signature dramatically changes the result! This is a rather
2645 counter-intuitive phenomenon, worth watching out for.
2649 <sect3><title>Implicit parameters and monomorphism</title>
2651 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2652 Haskell Report) to implicit parameters. For example, consider:
2660 Since the binding for <literal>y</literal> falls under the Monomorphism
2661 Restriction it is not generalised, so the type of <literal>y</literal> is
2662 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2663 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2664 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2665 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2666 <literal>y</literal> in the body of the <literal>let</literal> will see the
2667 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2668 <literal>14</literal>.
2673 <sect2 id="linear-implicit-parameters">
2674 <title>Linear implicit parameters</title>
2676 Linear implicit parameters are an idea developed by Koen Claessen,
2677 Mark Shields, and Simon PJ. They address the long-standing
2678 problem that monads seem over-kill for certain sorts of problem, notably:
2681 <listitem> <para> distributing a supply of unique names </para> </listitem>
2682 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2683 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2687 Linear implicit parameters are just like ordinary implicit parameters,
2688 except that they are "linear" -- that is, they cannot be copied, and
2689 must be explicitly "split" instead. Linear implicit parameters are
2690 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2691 (The '/' in the '%' suggests the split!)
2696 import GHC.Exts( Splittable )
2698 data NameSupply = ...
2700 splitNS :: NameSupply -> (NameSupply, NameSupply)
2701 newName :: NameSupply -> Name
2703 instance Splittable NameSupply where
2707 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2708 f env (Lam x e) = Lam x' (f env e)
2711 env' = extend env x x'
2712 ...more equations for f...
2714 Notice that the implicit parameter %ns is consumed
2716 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2717 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2721 So the translation done by the type checker makes
2722 the parameter explicit:
2724 f :: NameSupply -> Env -> Expr -> Expr
2725 f ns env (Lam x e) = Lam x' (f ns1 env e)
2727 (ns1,ns2) = splitNS ns
2729 env = extend env x x'
2731 Notice the call to 'split' introduced by the type checker.
2732 How did it know to use 'splitNS'? Because what it really did
2733 was to introduce a call to the overloaded function 'split',
2734 defined by the class <literal>Splittable</literal>:
2736 class Splittable a where
2739 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2740 split for name supplies. But we can simply write
2746 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2748 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2749 <literal>GHC.Exts</literal>.
2754 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2755 are entirely distinct implicit parameters: you
2756 can use them together and they won't intefere with each other. </para>
2759 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2761 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2762 in the context of a class or instance declaration. </para></listitem>
2766 <sect3><title>Warnings</title>
2769 The monomorphism restriction is even more important than usual.
2770 Consider the example above:
2772 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2773 f env (Lam x e) = Lam x' (f env e)
2776 env' = extend env x x'
2778 If we replaced the two occurrences of x' by (newName %ns), which is
2779 usually a harmless thing to do, we get:
2781 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2782 f env (Lam x e) = Lam (newName %ns) (f env e)
2784 env' = extend env x (newName %ns)
2786 But now the name supply is consumed in <emphasis>three</emphasis> places
2787 (the two calls to newName,and the recursive call to f), so
2788 the result is utterly different. Urk! We don't even have
2792 Well, this is an experimental change. With implicit
2793 parameters we have already lost beta reduction anyway, and
2794 (as John Launchbury puts it) we can't sensibly reason about
2795 Haskell programs without knowing their typing.
2800 <sect3><title>Recursive functions</title>
2801 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2804 foo :: %x::T => Int -> [Int]
2806 foo n = %x : foo (n-1)
2808 where T is some type in class Splittable.</para>
2810 Do you get a list of all the same T's or all different T's
2811 (assuming that split gives two distinct T's back)?
2813 If you supply the type signature, taking advantage of polymorphic
2814 recursion, you get what you'd probably expect. Here's the
2815 translated term, where the implicit param is made explicit:
2818 foo x n = let (x1,x2) = split x
2819 in x1 : foo x2 (n-1)
2821 But if you don't supply a type signature, GHC uses the Hindley
2822 Milner trick of using a single monomorphic instance of the function
2823 for the recursive calls. That is what makes Hindley Milner type inference
2824 work. So the translation becomes
2828 foom n = x : foom (n-1)
2832 Result: 'x' is not split, and you get a list of identical T's. So the
2833 semantics of the program depends on whether or not foo has a type signature.
2836 You may say that this is a good reason to dislike linear implicit parameters
2837 and you'd be right. That is why they are an experimental feature.
2843 <sect2 id="sec-kinding">
2844 <title>Explicitly-kinded quantification</title>
2847 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2848 to give the kind explicitly as (machine-checked) documentation,
2849 just as it is nice to give a type signature for a function. On some occasions,
2850 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2851 John Hughes had to define the data type:
2853 data Set cxt a = Set [a]
2854 | Unused (cxt a -> ())
2856 The only use for the <literal>Unused</literal> constructor was to force the correct
2857 kind for the type variable <literal>cxt</literal>.
2860 GHC now instead allows you to specify the kind of a type variable directly, wherever
2861 a type variable is explicitly bound. Namely:
2863 <listitem><para><literal>data</literal> declarations:
2865 data Set (cxt :: * -> *) a = Set [a]
2866 </screen></para></listitem>
2867 <listitem><para><literal>type</literal> declarations:
2869 type T (f :: * -> *) = f Int
2870 </screen></para></listitem>
2871 <listitem><para><literal>class</literal> declarations:
2873 class (Eq a) => C (f :: * -> *) a where ...
2874 </screen></para></listitem>
2875 <listitem><para><literal>forall</literal>'s in type signatures:
2877 f :: forall (cxt :: * -> *). Set cxt Int
2878 </screen></para></listitem>
2883 The parentheses are required. Some of the spaces are required too, to
2884 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2885 will get a parse error, because "<literal>::*->*</literal>" is a
2886 single lexeme in Haskell.
2890 As part of the same extension, you can put kind annotations in types
2893 f :: (Int :: *) -> Int
2894 g :: forall a. a -> (a :: *)
2898 atype ::= '(' ctype '::' kind ')
2900 The parentheses are required.
2905 <sect2 id="universal-quantification">
2906 <title>Arbitrary-rank polymorphism
2910 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2911 allows us to say exactly what this means. For example:
2919 g :: forall b. (b -> b)
2921 The two are treated identically.
2925 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2926 explicit universal quantification in
2928 For example, all the following types are legal:
2930 f1 :: forall a b. a -> b -> a
2931 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2933 f2 :: (forall a. a->a) -> Int -> Int
2934 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2936 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2938 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2939 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2940 The <literal>forall</literal> makes explicit the universal quantification that
2941 is implicitly added by Haskell.
2944 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2945 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2946 shows, the polymorphic type on the left of the function arrow can be overloaded.
2949 The function <literal>f3</literal> has a rank-3 type;
2950 it has rank-2 types on the left of a function arrow.
2953 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2954 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2955 that restriction has now been lifted.)
2956 In particular, a forall-type (also called a "type scheme"),
2957 including an operational type class context, is legal:
2959 <listitem> <para> On the left of a function arrow </para> </listitem>
2960 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2961 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2962 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2963 field type signatures.</para> </listitem>
2964 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2965 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2967 There is one place you cannot put a <literal>forall</literal>:
2968 you cannot instantiate a type variable with a forall-type. So you cannot
2969 make a forall-type the argument of a type constructor. So these types are illegal:
2971 x1 :: [forall a. a->a]
2972 x2 :: (forall a. a->a, Int)
2973 x3 :: Maybe (forall a. a->a)
2975 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2976 a type variable any more!
2985 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2986 the types of the constructor arguments. Here are several examples:
2992 data T a = T1 (forall b. b -> b -> b) a
2994 data MonadT m = MkMonad { return :: forall a. a -> m a,
2995 bind :: forall a b. m a -> (a -> m b) -> m b
2998 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3004 The constructors have rank-2 types:
3010 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3011 MkMonad :: forall m. (forall a. a -> m a)
3012 -> (forall a b. m a -> (a -> m b) -> m b)
3014 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3020 Notice that you don't need to use a <literal>forall</literal> if there's an
3021 explicit context. For example in the first argument of the
3022 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3023 prefixed to the argument type. The implicit <literal>forall</literal>
3024 quantifies all type variables that are not already in scope, and are
3025 mentioned in the type quantified over.
3029 As for type signatures, implicit quantification happens for non-overloaded
3030 types too. So if you write this:
3033 data T a = MkT (Either a b) (b -> b)
3036 it's just as if you had written this:
3039 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3042 That is, since the type variable <literal>b</literal> isn't in scope, it's
3043 implicitly universally quantified. (Arguably, it would be better
3044 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3045 where that is what is wanted. Feedback welcomed.)
3049 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3050 the constructor to suitable values, just as usual. For example,
3061 a3 = MkSwizzle reverse
3064 a4 = let r x = Just x
3071 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3072 mkTs f x y = [T1 f x, T1 f y]
3078 The type of the argument can, as usual, be more general than the type
3079 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3080 does not need the <literal>Ord</literal> constraint.)
3084 When you use pattern matching, the bound variables may now have
3085 polymorphic types. For example:
3091 f :: T a -> a -> (a, Char)
3092 f (T1 w k) x = (w k x, w 'c' 'd')
3094 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3095 g (MkSwizzle s) xs f = s (map f (s xs))
3097 h :: MonadT m -> [m a] -> m [a]
3098 h m [] = return m []
3099 h m (x:xs) = bind m x $ \y ->
3100 bind m (h m xs) $ \ys ->
3107 In the function <function>h</function> we use the record selectors <literal>return</literal>
3108 and <literal>bind</literal> to extract the polymorphic bind and return functions
3109 from the <literal>MonadT</literal> data structure, rather than using pattern
3115 <title>Type inference</title>
3118 In general, type inference for arbitrary-rank types is undecidable.
3119 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3120 to get a decidable algorithm by requiring some help from the programmer.
3121 We do not yet have a formal specification of "some help" but the rule is this:
3124 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3125 provides an explicit polymorphic type for x, or GHC's type inference will assume
3126 that x's type has no foralls in it</emphasis>.
3129 What does it mean to "provide" an explicit type for x? You can do that by
3130 giving a type signature for x directly, using a pattern type signature
3131 (<xref linkend="scoped-type-variables"/>), thus:
3133 \ f :: (forall a. a->a) -> (f True, f 'c')
3135 Alternatively, you can give a type signature to the enclosing
3136 context, which GHC can "push down" to find the type for the variable:
3138 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3140 Here the type signature on the expression can be pushed inwards
3141 to give a type signature for f. Similarly, and more commonly,
3142 one can give a type signature for the function itself:
3144 h :: (forall a. a->a) -> (Bool,Char)
3145 h f = (f True, f 'c')
3147 You don't need to give a type signature if the lambda bound variable
3148 is a constructor argument. Here is an example we saw earlier:
3150 f :: T a -> a -> (a, Char)
3151 f (T1 w k) x = (w k x, w 'c' 'd')
3153 Here we do not need to give a type signature to <literal>w</literal>, because
3154 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3161 <sect3 id="implicit-quant">
3162 <title>Implicit quantification</title>
3165 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3166 user-written types, if and only if there is no explicit <literal>forall</literal>,
3167 GHC finds all the type variables mentioned in the type that are not already
3168 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3172 f :: forall a. a -> a
3179 h :: forall b. a -> b -> b
3185 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3188 f :: (a -> a) -> Int
3190 f :: forall a. (a -> a) -> Int
3192 f :: (forall a. a -> a) -> Int
3195 g :: (Ord a => a -> a) -> Int
3196 -- MEANS the illegal type
3197 g :: forall a. (Ord a => a -> a) -> Int
3199 g :: (forall a. Ord a => a -> a) -> Int
3201 The latter produces an illegal type, which you might think is silly,
3202 but at least the rule is simple. If you want the latter type, you
3203 can write your for-alls explicitly. Indeed, doing so is strongly advised
3212 <sect2 id="scoped-type-variables">
3213 <title>Scoped type variables
3217 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3219 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3220 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3221 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
3225 f (xs::[a]) = ys ++ ys
3230 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
3231 This brings the type variable <literal>a</literal> into scope; it scopes over
3232 all the patterns and right hand sides for this equation for <function>f</function>.
3233 In particular, it is in scope at the type signature for <varname>y</varname>.
3237 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
3238 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
3239 implicitly universally quantified. (If there are no type variables in
3240 scope, all type variables mentioned in the signature are universally
3241 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
3242 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
3243 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
3244 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3245 it becomes possible to do so.
3249 Scoped type variables are implemented in both GHC and Hugs. Where the
3250 implementations differ from the specification below, those differences
3255 So much for the basic idea. Here are the details.
3259 <title>What a scoped type variable means</title>
3261 A lexically-scoped type variable is simply
3262 the name for a type. The restriction it expresses is that all occurrences
3263 of the same name mean the same type. For example:
3265 f :: [Int] -> Int -> Int
3266 f (xs::[a]) (y::a) = (head xs + y) :: a
3268 The pattern type signatures on the left hand side of
3269 <literal>f</literal> express the fact that <literal>xs</literal>
3270 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
3271 must have this same type. The type signature on the expression <literal>(head xs)</literal>
3272 specifies that this expression must have the same type <literal>a</literal>.
3273 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
3274 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
3275 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
3276 rules, which specified that a pattern-bound type variable should be universally quantified.)
3277 For example, all of these are legal:</para>
3280 t (x::a) (y::a) = x+y*2
3282 f (x::a) (y::b) = [x,y] -- a unifies with b
3284 g (x::a) = x + 1::Int -- a unifies with Int
3286 h x = let k (y::a) = [x,y] -- a is free in the
3287 in k x -- environment
3289 k (x::a) True = ... -- a unifies with Int
3290 k (x::Int) False = ...
3293 w (x::a) = x -- a unifies with [b]
3299 <title>Scope and implicit quantification</title>
3307 All the type variables mentioned in a pattern,
3308 that are not already in scope,
3309 are brought into scope by the pattern. We describe this set as
3310 the <emphasis>type variables bound by the pattern</emphasis>.
3313 f (x::a) = let g (y::(a,b)) = fst y
3317 The pattern <literal>(x::a)</literal> brings the type variable
3318 <literal>a</literal> into scope, as well as the term
3319 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
3320 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
3321 and brings into scope the type variable <literal>b</literal>.
3327 The type variable(s) bound by the pattern have the same scope
3328 as the term variable(s) bound by the pattern. For example:
3331 f (x::a) = <...rhs of f...>
3332 (p::b, q::b) = (1,2)
3333 in <...body of let...>
3335 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3336 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3337 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3338 just like <literal>p</literal> and <literal>q</literal> do.
3339 Indeed, the newly bound type variables also scope over any ordinary, separate
3340 type signatures in the <literal>let</literal> group.
3347 The type variables bound by the pattern may be
3348 mentioned in ordinary type signatures or pattern
3349 type signatures anywhere within their scope.
3356 In ordinary type signatures, any type variable mentioned in the
3357 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3365 Ordinary type signatures do not bring any new type variables
3366 into scope (except in the type signature itself!). So this is illegal:
3373 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3374 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3375 and that is an incorrect typing.
3382 The pattern type signature is a monotype:
3387 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3391 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3392 not to type schemes.
3396 There is no implicit universal quantification on pattern type signatures (in contrast to
3397 ordinary type signatures).
3407 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3408 scope over the methods defined in the <literal>where</literal> part. For example:
3422 (Not implemented in Hugs yet, Dec 98).
3432 <sect3 id="decl-type-sigs">
3433 <title>Declaration type signatures</title>
3434 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3435 quantification (using <literal>forall</literal>) brings into scope the
3436 explicitly-quantified
3437 type variables, in the definition of the named function(s). For example:
3439 f :: forall a. [a] -> [a]
3440 f (x:xs) = xs ++ [ x :: a ]
3442 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3443 the definition of "<literal>f</literal>".
3445 <para>This only happens if the quantification in <literal>f</literal>'s type
3446 signature is explicit. For example:
3449 g (x:xs) = xs ++ [ x :: a ]
3451 This program will be rejected, because "<literal>a</literal>" does not scope
3452 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3453 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3454 quantification rules.
3458 <sect3 id="pattern-type-sigs">
3459 <title>Where a pattern type signature can occur</title>
3462 A pattern type signature can occur in any pattern. For example:
3467 A pattern type signature can be on an arbitrary sub-pattern, not
3472 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3481 Pattern type signatures, including the result part, can be used
3482 in lambda abstractions:
3485 (\ (x::a, y) :: a -> x)
3492 Pattern type signatures, including the result part, can be used
3493 in <literal>case</literal> expressions:
3496 case e of { ((x::a, y) :: (a,b)) -> x }
3499 Note that the <literal>-></literal> symbol in a case alternative
3500 leads to difficulties when parsing a type signature in the pattern: in
3501 the absence of the extra parentheses in the example above, the parser
3502 would try to interpret the <literal>-></literal> as a function
3503 arrow and give a parse error later.
3511 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3512 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3513 token or a parenthesised type of some sort). To see why,
3514 consider how one would parse this:
3528 Pattern type signatures can bind existential type variables.
3533 data T = forall a. MkT [a]
3536 f (MkT [t::a]) = MkT t3
3549 Pattern type signatures
3550 can be used in pattern bindings:
3553 f x = let (y, z::a) = x in ...
3554 f1 x = let (y, z::Int) = x in ...
3555 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3556 f3 :: (b->b) = \x -> x
3559 In all such cases, the binding is not generalised over the pattern-bound
3560 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3561 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3562 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3563 In contrast, the binding
3568 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3569 in <literal>f4</literal>'s scope.
3575 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3576 type signatures. The two can be used independently or together.</para>
3580 <sect3 id="result-type-sigs">
3581 <title>Result type signatures</title>
3584 The result type of a function can be given a signature, thus:
3588 f (x::a) :: [a] = [x,x,x]
3592 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3593 result type. Sometimes this is the only way of naming the type variable
3598 f :: Int -> [a] -> [a]
3599 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3600 in \xs -> map g (reverse xs `zip` xs)
3605 The type variables bound in a result type signature scope over the right hand side
3606 of the definition. However, consider this corner-case:
3608 rev1 :: [a] -> [a] = \xs -> reverse xs
3610 foo ys = rev (ys::[a])
3612 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3613 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3614 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3615 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3616 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3619 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3620 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3624 rev1 :: [a] -> [a] = \xs -> reverse xs
3629 Result type signatures are not yet implemented in Hugs.
3636 <sect2 id="deriving-typeable">
3637 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3640 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3641 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3642 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3643 classes <literal>Eq</literal>, <literal>Ord</literal>,
3644 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3647 GHC extends this list with two more classes that may be automatically derived
3648 (provided the <option>-fglasgow-exts</option> flag is specified):
3649 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3650 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3651 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3653 <para>An instance of <literal>Typeable</literal> can only be derived if the
3654 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3655 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3657 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3658 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3660 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3661 are used, and only <literal>Typeable1</literal> up to
3662 <literal>Typeable7</literal> are provided in the library.)
3663 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3664 class, whose kind suits that of the data type constructor, and
3665 then writing the data type instance by hand.
3669 <sect2 id="newtype-deriving">
3670 <title>Generalised derived instances for newtypes</title>
3673 When you define an abstract type using <literal>newtype</literal>, you may want
3674 the new type to inherit some instances from its representation. In
3675 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3676 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3677 other classes you have to write an explicit instance declaration. For
3678 example, if you define
3681 newtype Dollars = Dollars Int
3684 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3685 explicitly define an instance of <literal>Num</literal>:
3688 instance Num Dollars where
3689 Dollars a + Dollars b = Dollars (a+b)
3692 All the instance does is apply and remove the <literal>newtype</literal>
3693 constructor. It is particularly galling that, since the constructor
3694 doesn't appear at run-time, this instance declaration defines a
3695 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3696 dictionary, only slower!
3700 <sect3> <title> Generalising the deriving clause </title>
3702 GHC now permits such instances to be derived instead, so one can write
3704 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3707 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3708 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3709 derives an instance declaration of the form
3712 instance Num Int => Num Dollars
3715 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3719 We can also derive instances of constructor classes in a similar
3720 way. For example, suppose we have implemented state and failure monad
3721 transformers, such that
3724 instance Monad m => Monad (State s m)
3725 instance Monad m => Monad (Failure m)
3727 In Haskell 98, we can define a parsing monad by
3729 type Parser tok m a = State [tok] (Failure m) a
3732 which is automatically a monad thanks to the instance declarations
3733 above. With the extension, we can make the parser type abstract,
3734 without needing to write an instance of class <literal>Monad</literal>, via
3737 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3740 In this case the derived instance declaration is of the form
3742 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3745 Notice that, since <literal>Monad</literal> is a constructor class, the
3746 instance is a <emphasis>partial application</emphasis> of the new type, not the
3747 entire left hand side. We can imagine that the type declaration is
3748 ``eta-converted'' to generate the context of the instance
3753 We can even derive instances of multi-parameter classes, provided the
3754 newtype is the last class parameter. In this case, a ``partial
3755 application'' of the class appears in the <literal>deriving</literal>
3756 clause. For example, given the class
3759 class StateMonad s m | m -> s where ...
3760 instance Monad m => StateMonad s (State s m) where ...
3762 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3764 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3765 deriving (Monad, StateMonad [tok])
3768 The derived instance is obtained by completing the application of the
3769 class to the new type:
3772 instance StateMonad [tok] (State [tok] (Failure m)) =>
3773 StateMonad [tok] (Parser tok m)
3778 As a result of this extension, all derived instances in newtype
3779 declarations are treated uniformly (and implemented just by reusing
3780 the dictionary for the representation type), <emphasis>except</emphasis>
3781 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3782 the newtype and its representation.
3786 <sect3> <title> A more precise specification </title>
3788 Derived instance declarations are constructed as follows. Consider the
3789 declaration (after expansion of any type synonyms)
3792 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3798 The type <literal>t</literal> is an arbitrary type
3801 The <literal>vk+1...vn</literal> are type variables which do not occur in
3802 <literal>t</literal>, and
3805 The <literal>ci</literal> are partial applications of
3806 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3807 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3810 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3811 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3812 should not "look through" the type or its constructor. You can still
3813 derive these classes for a newtype, but it happens in the usual way, not
3814 via this new mechanism.
3817 Then, for each <literal>ci</literal>, the derived instance
3820 instance ci (t vk+1...v) => ci (T v1...vp)
3822 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3823 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3827 As an example which does <emphasis>not</emphasis> work, consider
3829 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3831 Here we cannot derive the instance
3833 instance Monad (State s m) => Monad (NonMonad m)
3836 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3837 and so cannot be "eta-converted" away. It is a good thing that this
3838 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3839 not, in fact, a monad --- for the same reason. Try defining
3840 <literal>>>=</literal> with the correct type: you won't be able to.
3844 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3845 important, since we can only derive instances for the last one. If the
3846 <literal>StateMonad</literal> class above were instead defined as
3849 class StateMonad m s | m -> s where ...
3852 then we would not have been able to derive an instance for the
3853 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3854 classes usually have one "main" parameter for which deriving new
3855 instances is most interesting.
3857 <para>Lastly, all of this applies only for classes other than
3858 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3859 and <literal>Data</literal>, for which the built-in derivation applies (section
3860 4.3.3. of the Haskell Report).
3861 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3862 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3863 the standard method is used or the one described here.)
3869 <sect2 id="typing-binds">
3870 <title>Generalised typing of mutually recursive bindings</title>
3873 The Haskell Report specifies that a group of bindings (at top level, or in a
3874 <literal>let</literal> or <literal>where</literal>) should be sorted into
3875 strongly-connected components, and then type-checked in dependency order
3876 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3877 Report, Section 4.5.1</ulink>).
3878 As each group is type-checked, any binders of the group that
3880 an explicit type signature are put in the type environment with the specified
3882 and all others are monomorphic until the group is generalised
3883 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3886 <para>Following a suggestion of Mark Jones, in his paper
3887 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3889 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3891 <emphasis>the dependency analysis ignores references to variables that have an explicit
3892 type signature</emphasis>.
3893 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3894 typecheck. For example, consider:
3896 f :: Eq a => a -> Bool
3897 f x = (x == x) || g True || g "Yes"
3899 g y = (y <= y) || f True
3901 This is rejected by Haskell 98, but under Jones's scheme the definition for
3902 <literal>g</literal> is typechecked first, separately from that for
3903 <literal>f</literal>,
3904 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3905 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3906 type is generalised, to get
3908 g :: Ord a => a -> Bool
3910 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3911 <literal>g</literal> in the type environment.
3915 The same refined dependency analysis also allows the type signatures of
3916 mutually-recursive functions to have different contexts, something that is illegal in
3917 Haskell 98 (Section 4.5.2, last sentence). With
3918 <option>-fglasgow-exts</option>
3919 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3920 type signatures; in practice this means that only variables bound by the same
3921 pattern binding must have the same context. For example, this is fine:
3923 f :: Eq a => a -> Bool
3924 f x = (x == x) || g True
3926 g :: Ord a => a -> Bool
3927 g y = (y <= y) || f True
3933 <!-- ==================== End of type system extensions ================= -->
3935 <!-- ====================== Generalised algebraic data types ======================= -->
3938 <title>Generalised Algebraic Data Types</title>
3940 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3941 to give the type signatures of constructors explicitly. For example:
3944 Lit :: Int -> Term Int
3945 Succ :: Term Int -> Term Int
3946 IsZero :: Term Int -> Term Bool
3947 If :: Term Bool -> Term a -> Term a -> Term a
3948 Pair :: Term a -> Term b -> Term (a,b)
3950 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3951 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3952 for these <literal>Terms</literal>:
3956 eval (Succ t) = 1 + eval t
3957 eval (IsZero t) = eval t == 0
3958 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3959 eval (Pair e1 e2) = (eval e1, eval e2)
3961 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3963 <para> The extensions to GHC are these:
3966 Data type declarations have a 'where' form, as exemplified above. The type signature of
3967 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3968 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3969 have no scope. Indeed, one can write a kind signature instead:
3971 data Term :: * -> * where ...
3973 or even a mixture of the two:
3975 data Foo a :: (* -> *) -> * where ...
3977 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3980 data Foo a (b :: * -> *) where ...
3985 There are no restrictions on the type of the data constructor, except that the result
3986 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3987 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3991 You can use record syntax on a GADT-style data type declaration:
3995 Lit { val :: Int } :: Term Int
3996 Succ { num :: Term Int } :: Term Int
3997 Pred { num :: Term Int } :: Term Int
3998 IsZero { arg :: Term Int } :: Term Bool
3999 Pair { arg1 :: Term a
4002 If { cnd :: Term Bool
4007 For every constructor that has a field <literal>f</literal>, (a) the type of
4008 field <literal>f</literal> must be the same; and (b) the
4009 result type of the constructor must be the same; both modulo alpha conversion.
4010 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
4012 single name. Although their field types are both <literal>Term Int</literal>,
4013 their selector functions actually have different types:
4016 num :: Term Int -> Term Int
4017 arg :: Term Bool -> Term Int
4020 At the moment, record updates are not yet possible with GADT, so support is
4021 limited to record construction, selection and pattern matching:
4024 someTerm :: Term Bool
4025 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
4028 eval Lit { val = i } = i
4029 eval Succ { num = t } = eval t + 1
4030 eval Pred { num = t } = eval t - 1
4031 eval IsZero { arg = t } = eval t == 0
4032 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
4033 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
4039 You can use strictness annotations, in the obvious places
4040 in the constructor type:
4043 Lit :: !Int -> Term Int
4044 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
4045 Pair :: Term a -> Term b -> Term (a,b)
4050 You can use a <literal>deriving</literal> clause on a GADT-style data type
4051 declaration, but only if the data type could also have been declared in
4052 Haskell-98 syntax. For example, these two declarations are equivalent
4054 data Maybe1 a where {
4055 Nothing1 :: Maybe a ;
4056 Just1 :: a -> Maybe a
4057 } deriving( Eq, Ord )
4059 data Maybe2 a = Nothing2 | Just2 a
4062 This simply allows you to declare a vanilla Haskell-98 data type using the
4063 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
4067 Pattern matching causes type refinement. For example, in the right hand side of the equation
4072 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
4073 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
4074 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
4076 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
4077 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
4078 occur. However, the refinement is quite general. For example, if we had:
4080 eval :: Term a -> a -> a
4081 eval (Lit i) j = i+j
4083 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
4084 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
4085 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
4091 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
4093 data T a = forall b. MkT b (b->a)
4094 data T' a where { MKT :: b -> (b->a) -> T' a }
4099 <!-- ====================== End of Generalised algebraic data types ======================= -->
4101 <!-- ====================== TEMPLATE HASKELL ======================= -->
4103 <sect1 id="template-haskell">
4104 <title>Template Haskell</title>
4106 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
4107 Template Haskell at <ulink url="http://www.haskell.org/th/">
4108 http://www.haskell.org/th/</ulink>, while
4110 the main technical innovations is discussed in "<ulink
4111 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4112 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4113 The details of the Template Haskell design are still in flux. Make sure you
4114 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
4115 (search for the type ExpQ).
4116 [Temporary: many changes to the original design are described in
4117 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4118 Not all of these changes are in GHC 6.2.]
4121 <para> The first example from that paper is set out below as a worked example to help get you started.
4125 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4126 Tim Sheard is going to expand it.)
4130 <title>Syntax</title>
4132 <para> Template Haskell has the following new syntactic
4133 constructions. You need to use the flag
4134 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4135 </indexterm>to switch these syntactic extensions on
4136 (<option>-fth</option> is no longer implied by
4137 <option>-fglasgow-exts</option>).</para>
4141 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4142 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4143 There must be no space between the "$" and the identifier or parenthesis. This use
4144 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4145 of "." as an infix operator. If you want the infix operator, put spaces around it.
4147 <para> A splice can occur in place of
4149 <listitem><para> an expression; the spliced expression must
4150 have type <literal>Q Exp</literal></para></listitem>
4151 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4152 <listitem><para> [Planned, but not implemented yet.] a
4153 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4155 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4156 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4162 A expression quotation is written in Oxford brackets, thus:
4164 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4165 the quotation has type <literal>Expr</literal>.</para></listitem>
4166 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4167 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4168 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4169 the quotation has type <literal>Type</literal>.</para></listitem>
4170 </itemizedlist></para></listitem>
4173 Reification is written thus:
4175 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4176 has type <literal>Dec</literal>. </para></listitem>
4177 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4178 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4179 <listitem><para> Still to come: fixities </para></listitem>
4181 </itemizedlist></para>
4188 <sect2> <title> Using Template Haskell </title>
4192 The data types and monadic constructor functions for Template Haskell are in the library
4193 <literal>Language.Haskell.THSyntax</literal>.
4197 You can only run a function at compile time if it is imported from another module. That is,
4198 you can't define a function in a module, and call it from within a splice in the same module.
4199 (It would make sense to do so, but it's hard to implement.)
4203 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4206 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4207 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4208 compiles and runs a program, and then looks at the result. So it's important that
4209 the program it compiles produces results whose representations are identical to
4210 those of the compiler itself.
4214 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4215 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4220 <sect2> <title> A Template Haskell Worked Example </title>
4221 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4222 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4229 -- Import our template "pr"
4230 import Printf ( pr )
4232 -- The splice operator $ takes the Haskell source code
4233 -- generated at compile time by "pr" and splices it into
4234 -- the argument of "putStrLn".
4235 main = putStrLn ( $(pr "Hello") )
4241 -- Skeletal printf from the paper.
4242 -- It needs to be in a separate module to the one where
4243 -- you intend to use it.
4245 -- Import some Template Haskell syntax
4246 import Language.Haskell.TH
4248 -- Describe a format string
4249 data Format = D | S | L String
4251 -- Parse a format string. This is left largely to you
4252 -- as we are here interested in building our first ever
4253 -- Template Haskell program and not in building printf.
4254 parse :: String -> [Format]
4257 -- Generate Haskell source code from a parsed representation
4258 -- of the format string. This code will be spliced into
4259 -- the module which calls "pr", at compile time.
4260 gen :: [Format] -> ExpQ
4261 gen [D] = [| \n -> show n |]
4262 gen [S] = [| \s -> s |]
4263 gen [L s] = stringE s
4265 -- Here we generate the Haskell code for the splice
4266 -- from an input format string.
4267 pr :: String -> ExpQ
4268 pr s = gen (parse s)
4271 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4274 $ ghc --make -fth main.hs -o main.exe
4277 <para>Run "main.exe" and here is your output:</para>
4287 <title>Using Template Haskell with Profiling</title>
4288 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4290 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4291 interpreter to run the splice expressions. The bytecode interpreter
4292 runs the compiled expression on top of the same runtime on which GHC
4293 itself is running; this means that the compiled code referred to by
4294 the interpreted expression must be compatible with this runtime, and
4295 in particular this means that object code that is compiled for
4296 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4297 expression, because profiled object code is only compatible with the
4298 profiling version of the runtime.</para>
4300 <para>This causes difficulties if you have a multi-module program
4301 containing Template Haskell code and you need to compile it for
4302 profiling, because GHC cannot load the profiled object code and use it
4303 when executing the splices. Fortunately GHC provides a workaround.
4304 The basic idea is to compile the program twice:</para>
4308 <para>Compile the program or library first the normal way, without
4309 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4312 <para>Then compile it again with <option>-prof</option>, and
4313 additionally use <option>-osuf
4314 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4315 to name the object files differentliy (you can choose any suffix
4316 that isn't the normal object suffix here). GHC will automatically
4317 load the object files built in the first step when executing splice
4318 expressions. If you omit the <option>-osuf</option> flag when
4319 building with <option>-prof</option> and Template Haskell is used,
4320 GHC will emit an error message. </para>
4327 <!-- ===================== Arrow notation =================== -->
4329 <sect1 id="arrow-notation">
4330 <title>Arrow notation
4333 <para>Arrows are a generalization of monads introduced by John Hughes.
4334 For more details, see
4339 “Generalising Monads to Arrows”,
4340 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4341 pp67–111, May 2000.
4347 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4348 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4354 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4355 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4361 and the arrows web page at
4362 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4363 With the <option>-farrows</option> flag, GHC supports the arrow
4364 notation described in the second of these papers.
4365 What follows is a brief introduction to the notation;
4366 it won't make much sense unless you've read Hughes's paper.
4367 This notation is translated to ordinary Haskell,
4368 using combinators from the
4369 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4373 <para>The extension adds a new kind of expression for defining arrows:
4375 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4376 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4378 where <literal>proc</literal> is a new keyword.
4379 The variables of the pattern are bound in the body of the
4380 <literal>proc</literal>-expression,
4381 which is a new sort of thing called a <firstterm>command</firstterm>.
4382 The syntax of commands is as follows:
4384 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4385 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4386 | <replaceable>cmd</replaceable><superscript>0</superscript>
4388 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4389 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4390 infix operators as for expressions, and
4392 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4393 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4394 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4395 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4396 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4397 | <replaceable>fcmd</replaceable>
4399 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4400 | ( <replaceable>cmd</replaceable> )
4401 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4403 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4404 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4405 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4406 | <replaceable>cmd</replaceable>
4408 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4409 except that the bodies are commands instead of expressions.
4413 Commands produce values, but (like monadic computations)
4414 may yield more than one value,
4415 or none, and may do other things as well.
4416 For the most part, familiarity with monadic notation is a good guide to
4418 However the values of expressions, even monadic ones,
4419 are determined by the values of the variables they contain;
4420 this is not necessarily the case for commands.
4424 A simple example of the new notation is the expression
4426 proc x -> f -< x+1
4428 We call this a <firstterm>procedure</firstterm> or
4429 <firstterm>arrow abstraction</firstterm>.
4430 As with a lambda expression, the variable <literal>x</literal>
4431 is a new variable bound within the <literal>proc</literal>-expression.
4432 It refers to the input to the arrow.
4433 In the above example, <literal>-<</literal> is not an identifier but an
4434 new reserved symbol used for building commands from an expression of arrow
4435 type and an expression to be fed as input to that arrow.
4436 (The weird look will make more sense later.)
4437 It may be read as analogue of application for arrows.
4438 The above example is equivalent to the Haskell expression
4440 arr (\ x -> x+1) >>> f
4442 That would make no sense if the expression to the left of
4443 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4444 More generally, the expression to the left of <literal>-<</literal>
4445 may not involve any <firstterm>local variable</firstterm>,
4446 i.e. a variable bound in the current arrow abstraction.
4447 For such a situation there is a variant <literal>-<<</literal>, as in
4449 proc x -> f x -<< x+1
4451 which is equivalent to
4453 arr (\ x -> (f x, x+1)) >>> app
4455 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4457 Such an arrow is equivalent to a monad, so if you're using this form
4458 you may find a monadic formulation more convenient.
4462 <title>do-notation for commands</title>
4465 Another form of command is a form of <literal>do</literal>-notation.
4466 For example, you can write
4475 You can read this much like ordinary <literal>do</literal>-notation,
4476 but with commands in place of monadic expressions.
4477 The first line sends the value of <literal>x+1</literal> as an input to
4478 the arrow <literal>f</literal>, and matches its output against
4479 <literal>y</literal>.
4480 In the next line, the output is discarded.
4481 The arrow <function>returnA</function> is defined in the
4482 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4483 module as <literal>arr id</literal>.
4484 The above example is treated as an abbreviation for
4486 arr (\ x -> (x, x)) >>>
4487 first (arr (\ x -> x+1) >>> f) >>>
4488 arr (\ (y, x) -> (y, (x, y))) >>>
4489 first (arr (\ y -> 2*y) >>> g) >>>
4491 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4492 first (arr (\ (x, z) -> x*z) >>> h) >>>
4493 arr (\ (t, z) -> t+z) >>>
4496 Note that variables not used later in the composition are projected out.
4497 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4499 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4500 module, this reduces to
4502 arr (\ x -> (x+1, x)) >>>
4504 arr (\ (y, x) -> (2*y, (x, y))) >>>
4506 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4508 arr (\ (t, z) -> t+z)
4510 which is what you might have written by hand.
4511 With arrow notation, GHC keeps track of all those tuples of variables for you.
4515 Note that although the above translation suggests that
4516 <literal>let</literal>-bound variables like <literal>z</literal> must be
4517 monomorphic, the actual translation produces Core,
4518 so polymorphic variables are allowed.
4522 It's also possible to have mutually recursive bindings,
4523 using the new <literal>rec</literal> keyword, as in the following example:
4525 counter :: ArrowCircuit a => a Bool Int
4526 counter = proc reset -> do
4527 rec output <- returnA -< if reset then 0 else next
4528 next <- delay 0 -< output+1
4529 returnA -< output
4531 The translation of such forms uses the <function>loop</function> combinator,
4532 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4538 <title>Conditional commands</title>
4541 In the previous example, we used a conditional expression to construct the
4543 Sometimes we want to conditionally execute different commands, as in
4550 which is translated to
4552 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4553 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4555 Since the translation uses <function>|||</function>,
4556 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4560 There are also <literal>case</literal> commands, like
4566 y <- h -< (x1, x2)
4570 The syntax is the same as for <literal>case</literal> expressions,
4571 except that the bodies of the alternatives are commands rather than expressions.
4572 The translation is similar to that of <literal>if</literal> commands.
4578 <title>Defining your own control structures</title>
4581 As we're seen, arrow notation provides constructs,
4582 modelled on those for expressions,
4583 for sequencing, value recursion and conditionals.
4584 But suitable combinators,
4585 which you can define in ordinary Haskell,
4586 may also be used to build new commands out of existing ones.
4587 The basic idea is that a command defines an arrow from environments to values.
4588 These environments assign values to the free local variables of the command.
4589 Thus combinators that produce arrows from arrows
4590 may also be used to build commands from commands.
4591 For example, the <literal>ArrowChoice</literal> class includes a combinator
4593 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4595 so we can use it to build commands:
4597 expr' = proc x -> do
4600 symbol Plus -< ()
4601 y <- term -< ()
4604 symbol Minus -< ()
4605 y <- term -< ()
4608 (The <literal>do</literal> on the first line is needed to prevent the first
4609 <literal><+> ...</literal> from being interpreted as part of the
4610 expression on the previous line.)
4611 This is equivalent to
4613 expr' = (proc x -> returnA -< x)
4614 <+> (proc x -> do
4615 symbol Plus -< ()
4616 y <- term -< ()
4618 <+> (proc x -> do
4619 symbol Minus -< ()
4620 y <- term -< ()
4623 It is essential that this operator be polymorphic in <literal>e</literal>
4624 (representing the environment input to the command
4625 and thence to its subcommands)
4626 and satisfy the corresponding naturality property
4628 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4630 at least for strict <literal>k</literal>.
4631 (This should be automatic if you're not using <function>seq</function>.)
4632 This ensures that environments seen by the subcommands are environments
4633 of the whole command,
4634 and also allows the translation to safely trim these environments.
4635 The operator must also not use any variable defined within the current
4640 We could define our own operator
4642 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4643 untilA body cond = proc x ->
4644 if cond x then returnA -< ()
4647 untilA body cond -< x
4649 and use it in the same way.
4650 Of course this infix syntax only makes sense for binary operators;
4651 there is also a more general syntax involving special brackets:
4655 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4662 <title>Primitive constructs</title>
4665 Some operators will need to pass additional inputs to their subcommands.
4666 For example, in an arrow type supporting exceptions,
4667 the operator that attaches an exception handler will wish to pass the
4668 exception that occurred to the handler.
4669 Such an operator might have a type
4671 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4673 where <literal>Ex</literal> is the type of exceptions handled.
4674 You could then use this with arrow notation by writing a command
4676 body `handleA` \ ex -> handler
4678 so that if an exception is raised in the command <literal>body</literal>,
4679 the variable <literal>ex</literal> is bound to the value of the exception
4680 and the command <literal>handler</literal>,
4681 which typically refers to <literal>ex</literal>, is entered.
4682 Though the syntax here looks like a functional lambda,
4683 we are talking about commands, and something different is going on.
4684 The input to the arrow represented by a command consists of values for
4685 the free local variables in the command, plus a stack of anonymous values.
4686 In all the prior examples, this stack was empty.
4687 In the second argument to <function>handleA</function>,
4688 this stack consists of one value, the value of the exception.
4689 The command form of lambda merely gives this value a name.
4694 the values on the stack are paired to the right of the environment.
4695 So operators like <function>handleA</function> that pass
4696 extra inputs to their subcommands can be designed for use with the notation
4697 by pairing the values with the environment in this way.
4698 More precisely, the type of each argument of the operator (and its result)
4699 should have the form
4701 a (...(e,t1), ... tn) t
4703 where <replaceable>e</replaceable> is a polymorphic variable
4704 (representing the environment)
4705 and <replaceable>ti</replaceable> are the types of the values on the stack,
4706 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4707 The polymorphic variable <replaceable>e</replaceable> must not occur in
4708 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4709 <replaceable>t</replaceable>.
4710 However the arrows involved need not be the same.
4711 Here are some more examples of suitable operators:
4713 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4714 runReader :: ... => a e c -> a' (e,State) c
4715 runState :: ... => a e c -> a' (e,State) (c,State)
4717 We can supply the extra input required by commands built with the last two
4718 by applying them to ordinary expressions, as in
4722 (|runReader (do { ... })|) s
4724 which adds <literal>s</literal> to the stack of inputs to the command
4725 built using <function>runReader</function>.
4729 The command versions of lambda abstraction and application are analogous to
4730 the expression versions.
4731 In particular, the beta and eta rules describe equivalences of commands.
4732 These three features (operators, lambda abstraction and application)
4733 are the core of the notation; everything else can be built using them,
4734 though the results would be somewhat clumsy.
4735 For example, we could simulate <literal>do</literal>-notation by defining
4737 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4738 u `bind` f = returnA &&& u >>> f
4740 bind_ :: Arrow a => a e b -> a e c -> a e c
4741 u `bind_` f = u `bind` (arr fst >>> f)
4743 We could simulate <literal>if</literal> by defining
4745 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4746 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4753 <title>Differences with the paper</title>
4758 <para>Instead of a single form of arrow application (arrow tail) with two
4759 translations, the implementation provides two forms
4760 <quote><literal>-<</literal></quote> (first-order)
4761 and <quote><literal>-<<</literal></quote> (higher-order).
4766 <para>User-defined operators are flagged with banana brackets instead of
4767 a new <literal>form</literal> keyword.
4776 <title>Portability</title>
4779 Although only GHC implements arrow notation directly,
4780 there is also a preprocessor
4782 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4783 that translates arrow notation into Haskell 98
4784 for use with other Haskell systems.
4785 You would still want to check arrow programs with GHC;
4786 tracing type errors in the preprocessor output is not easy.
4787 Modules intended for both GHC and the preprocessor must observe some
4788 additional restrictions:
4793 The module must import
4794 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4800 The preprocessor cannot cope with other Haskell extensions.
4801 These would have to go in separate modules.
4807 Because the preprocessor targets Haskell (rather than Core),
4808 <literal>let</literal>-bound variables are monomorphic.
4819 <!-- ==================== ASSERTIONS ================= -->
4821 <sect1 id="sec-assertions">
4823 <indexterm><primary>Assertions</primary></indexterm>
4827 If you want to make use of assertions in your standard Haskell code, you
4828 could define a function like the following:
4834 assert :: Bool -> a -> a
4835 assert False x = error "assertion failed!"
4842 which works, but gives you back a less than useful error message --
4843 an assertion failed, but which and where?
4847 One way out is to define an extended <function>assert</function> function which also
4848 takes a descriptive string to include in the error message and
4849 perhaps combine this with the use of a pre-processor which inserts
4850 the source location where <function>assert</function> was used.
4854 Ghc offers a helping hand here, doing all of this for you. For every
4855 use of <function>assert</function> in the user's source:
4861 kelvinToC :: Double -> Double
4862 kelvinToC k = assert (k >= 0.0) (k+273.15)
4868 Ghc will rewrite this to also include the source location where the
4875 assert pred val ==> assertError "Main.hs|15" pred val
4881 The rewrite is only performed by the compiler when it spots
4882 applications of <function>Control.Exception.assert</function>, so you
4883 can still define and use your own versions of
4884 <function>assert</function>, should you so wish. If not, import
4885 <literal>Control.Exception</literal> to make use
4886 <function>assert</function> in your code.
4890 GHC ignores assertions when optimisation is turned on with the
4891 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4892 <literal>assert pred e</literal> will be rewritten to
4893 <literal>e</literal>. You can also disable assertions using the
4894 <option>-fignore-asserts</option>
4895 option<indexterm><primary><option>-fignore-asserts</option></primary>
4896 </indexterm>.</para>
4899 Assertion failures can be caught, see the documentation for the
4900 <literal>Control.Exception</literal> library for the details.
4906 <!-- =============================== PRAGMAS =========================== -->
4908 <sect1 id="pragmas">
4909 <title>Pragmas</title>
4911 <indexterm><primary>pragma</primary></indexterm>
4913 <para>GHC supports several pragmas, or instructions to the
4914 compiler placed in the source code. Pragmas don't normally affect
4915 the meaning of the program, but they might affect the efficiency
4916 of the generated code.</para>
4918 <para>Pragmas all take the form
4920 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4922 where <replaceable>word</replaceable> indicates the type of
4923 pragma, and is followed optionally by information specific to that
4924 type of pragma. Case is ignored in
4925 <replaceable>word</replaceable>. The various values for
4926 <replaceable>word</replaceable> that GHC understands are described
4927 in the following sections; any pragma encountered with an
4928 unrecognised <replaceable>word</replaceable> is (silently)
4931 <sect2 id="deprecated-pragma">
4932 <title>DEPRECATED pragma</title>
4933 <indexterm><primary>DEPRECATED</primary>
4936 <para>The DEPRECATED pragma lets you specify that a particular
4937 function, class, or type, is deprecated. There are two
4942 <para>You can deprecate an entire module thus:</para>
4944 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4947 <para>When you compile any module that import
4948 <literal>Wibble</literal>, GHC will print the specified
4953 <para>You can deprecate a function, class, type, or data constructor, with the
4954 following top-level declaration:</para>
4956 {-# DEPRECATED f, C, T "Don't use these" #-}
4958 <para>When you compile any module that imports and uses any
4959 of the specified entities, GHC will print the specified
4961 <para> You can only depecate entities declared at top level in the module
4962 being compiled, and you can only use unqualified names in the list of
4963 entities being deprecated. A capitalised name, such as <literal>T</literal>
4964 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4965 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4966 both are in scope. If both are in scope, there is currently no way to deprecate
4967 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4970 Any use of the deprecated item, or of anything from a deprecated
4971 module, will be flagged with an appropriate message. However,
4972 deprecations are not reported for
4973 (a) uses of a deprecated function within its defining module, and
4974 (b) uses of a deprecated function in an export list.
4975 The latter reduces spurious complaints within a library
4976 in which one module gathers together and re-exports
4977 the exports of several others.
4979 <para>You can suppress the warnings with the flag
4980 <option>-fno-warn-deprecations</option>.</para>
4983 <sect2 id="include-pragma">
4984 <title>INCLUDE pragma</title>
4986 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4987 of C header files that should be <literal>#include</literal>'d into
4988 the C source code generated by the compiler for the current module (if
4989 compiling via C). For example:</para>
4992 {-# INCLUDE "foo.h" #-}
4993 {-# INCLUDE <stdio.h> #-}</programlisting>
4995 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4996 your source file with any <literal>OPTIONS_GHC</literal>
4999 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5000 to the <option>-#include</option> option (<xref
5001 linkend="options-C-compiler" />), because the
5002 <literal>INCLUDE</literal> pragma is understood by other
5003 compilers. Yet another alternative is to add the include file to each
5004 <literal>foreign import</literal> declaration in your code, but we
5005 don't recommend using this approach with GHC.</para>
5008 <sect2 id="inline-noinline-pragma">
5009 <title>INLINE and NOINLINE pragmas</title>
5011 <para>These pragmas control the inlining of function
5014 <sect3 id="inline-pragma">
5015 <title>INLINE pragma</title>
5016 <indexterm><primary>INLINE</primary></indexterm>
5018 <para>GHC (with <option>-O</option>, as always) tries to
5019 inline (or “unfold”) functions/values that are
5020 “small enough,” thus avoiding the call overhead
5021 and possibly exposing other more-wonderful optimisations.
5022 Normally, if GHC decides a function is “too
5023 expensive” to inline, it will not do so, nor will it
5024 export that unfolding for other modules to use.</para>
5026 <para>The sledgehammer you can bring to bear is the
5027 <literal>INLINE</literal><indexterm><primary>INLINE
5028 pragma</primary></indexterm> pragma, used thusly:</para>
5031 key_function :: Int -> String -> (Bool, Double)
5033 #ifdef __GLASGOW_HASKELL__
5034 {-# INLINE key_function #-}
5038 <para>(You don't need to do the C pre-processor carry-on
5039 unless you're going to stick the code through HBC—it
5040 doesn't like <literal>INLINE</literal> pragmas.)</para>
5042 <para>The major effect of an <literal>INLINE</literal> pragma
5043 is to declare a function's “cost” to be very low.
5044 The normal unfolding machinery will then be very keen to
5047 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5048 function can be put anywhere its type signature could be
5051 <para><literal>INLINE</literal> pragmas are a particularly
5053 <literal>then</literal>/<literal>return</literal> (or
5054 <literal>bind</literal>/<literal>unit</literal>) functions in
5055 a monad. For example, in GHC's own
5056 <literal>UniqueSupply</literal> monad code, we have:</para>
5059 #ifdef __GLASGOW_HASKELL__
5060 {-# INLINE thenUs #-}
5061 {-# INLINE returnUs #-}
5065 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5066 linkend="noinline-pragma"/>).</para>
5069 <sect3 id="noinline-pragma">
5070 <title>NOINLINE pragma</title>
5072 <indexterm><primary>NOINLINE</primary></indexterm>
5073 <indexterm><primary>NOTINLINE</primary></indexterm>
5075 <para>The <literal>NOINLINE</literal> pragma does exactly what
5076 you'd expect: it stops the named function from being inlined
5077 by the compiler. You shouldn't ever need to do this, unless
5078 you're very cautious about code size.</para>
5080 <para><literal>NOTINLINE</literal> is a synonym for
5081 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5082 specified by Haskell 98 as the standard way to disable
5083 inlining, so it should be used if you want your code to be
5087 <sect3 id="phase-control">
5088 <title>Phase control</title>
5090 <para> Sometimes you want to control exactly when in GHC's
5091 pipeline the INLINE pragma is switched on. Inlining happens
5092 only during runs of the <emphasis>simplifier</emphasis>. Each
5093 run of the simplifier has a different <emphasis>phase
5094 number</emphasis>; the phase number decreases towards zero.
5095 If you use <option>-dverbose-core2core</option> you'll see the
5096 sequence of phase numbers for successive runs of the
5097 simplifier. In an INLINE pragma you can optionally specify a
5101 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5102 <literal>f</literal>
5103 until phase <literal>k</literal>, but from phase
5104 <literal>k</literal> onwards be very keen to inline it.
5107 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5108 <literal>f</literal>
5109 until phase <literal>k</literal>, but from phase
5110 <literal>k</literal> onwards do not inline it.
5113 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5114 <literal>f</literal>
5115 until phase <literal>k</literal>, but from phase
5116 <literal>k</literal> onwards be willing to inline it (as if
5117 there was no pragma).
5120 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5121 <literal>f</literal>
5122 until phase <literal>k</literal>, but from phase
5123 <literal>k</literal> onwards do not inline it.
5126 The same information is summarised here:
5128 -- Before phase 2 Phase 2 and later
5129 {-# INLINE [2] f #-} -- No Yes
5130 {-# INLINE [~2] f #-} -- Yes No
5131 {-# NOINLINE [2] f #-} -- No Maybe
5132 {-# NOINLINE [~2] f #-} -- Maybe No
5134 {-# INLINE f #-} -- Yes Yes
5135 {-# NOINLINE f #-} -- No No
5137 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5138 function body is small, or it is applied to interesting-looking arguments etc).
5139 Another way to understand the semantics is this:
5141 <listitem><para>For both INLINE and NOINLINE, the phase number says
5142 when inlining is allowed at all.</para></listitem>
5143 <listitem><para>The INLINE pragma has the additional effect of making the
5144 function body look small, so that when inlining is allowed it is very likely to
5149 <para>The same phase-numbering control is available for RULES
5150 (<xref linkend="rewrite-rules"/>).</para>
5154 <sect2 id="language-pragma">
5155 <title>LANGUAGE pragma</title>
5157 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5158 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5160 <para>This allows language extensions to be enabled in a portable way.
5161 It is the intention that all Haskell compilers support the
5162 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5163 all extensions are supported by all compilers, of
5164 course. The <literal>LANGUAGE</literal> pragma should be used instead
5165 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5167 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5169 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5171 <para>Any extension from the <literal>Extension</literal> type defined in
5173 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>
5177 <sect2 id="line-pragma">
5178 <title>LINE pragma</title>
5180 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5181 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5182 <para>This pragma is similar to C's <literal>#line</literal>
5183 pragma, and is mainly for use in automatically generated Haskell
5184 code. It lets you specify the line number and filename of the
5185 original code; for example</para>
5187 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5189 <para>if you'd generated the current file from something called
5190 <filename>Foo.vhs</filename> and this line corresponds to line
5191 42 in the original. GHC will adjust its error messages to refer
5192 to the line/file named in the <literal>LINE</literal>
5196 <sect2 id="options-pragma">
5197 <title>OPTIONS_GHC pragma</title>
5198 <indexterm><primary>OPTIONS_GHC</primary>
5200 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5203 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5204 additional options that are given to the compiler when compiling
5205 this source file. See <xref linkend="source-file-options"/> for
5208 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5209 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5213 <title>RULES pragma</title>
5215 <para>The RULES pragma lets you specify rewrite rules. It is
5216 described in <xref linkend="rewrite-rules"/>.</para>
5219 <sect2 id="specialize-pragma">
5220 <title>SPECIALIZE pragma</title>
5222 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5223 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5224 <indexterm><primary>overloading, death to</primary></indexterm>
5226 <para>(UK spelling also accepted.) For key overloaded
5227 functions, you can create extra versions (NB: more code space)
5228 specialised to particular types. Thus, if you have an
5229 overloaded function:</para>
5232 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5235 <para>If it is heavily used on lists with
5236 <literal>Widget</literal> keys, you could specialise it as
5240 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5243 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5244 be put anywhere its type signature could be put.</para>
5246 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5247 (a) a specialised version of the function and (b) a rewrite rule
5248 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5249 un-specialised function into a call to the specialised one.</para>
5251 <para>The type in a SPECIALIZE pragma can be any type that is less
5252 polymorphic than the type of the original function. In concrete terms,
5253 if the original function is <literal>f</literal> then the pragma
5255 {-# SPECIALIZE f :: <type> #-}
5257 is valid if and only if the defintion
5259 f_spec :: <type>
5262 is valid. Here are some examples (where we only give the type signature
5263 for the original function, not its code):
5265 f :: Eq a => a -> b -> b
5266 {-# SPECIALISE f :: Int -> b -> b #-}
5268 g :: (Eq a, Ix b) => a -> b -> b
5269 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5271 h :: Eq a => a -> a -> a
5272 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5274 The last of these examples will generate a
5275 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5276 well. If you use this kind of specialisation, let us know how well it works.
5279 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5280 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5281 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5282 The <literal>INLINE</literal> pragma affects the specialised verison of the
5283 function (only), and applies even if the function is recursive. The motivating
5286 -- A GADT for arrays with type-indexed representation
5288 ArrInt :: !Int -> ByteArray# -> Arr Int
5289 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5291 (!:) :: Arr e -> Int -> e
5292 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5293 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5294 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5295 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5297 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5298 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5299 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5300 the specialised function will be inlined. It has two calls to
5301 <literal>(!:)</literal>,
5302 both at type <literal>Int</literal>. Both these calls fire the first
5303 specialisation, whose body is also inlined. The result is a type-based
5304 unrolling of the indexing function.</para>
5305 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5306 on an ordinarily-recursive function.</para>
5308 <para>Note: In earlier versions of GHC, it was possible to provide your own
5309 specialised function for a given type:
5312 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5315 This feature has been removed, as it is now subsumed by the
5316 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5320 <sect2 id="specialize-instance-pragma">
5321 <title>SPECIALIZE instance pragma
5325 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5326 <indexterm><primary>overloading, death to</primary></indexterm>
5327 Same idea, except for instance declarations. For example:
5330 instance (Eq a) => Eq (Foo a) where {
5331 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5335 The pragma must occur inside the <literal>where</literal> part
5336 of the instance declaration.
5339 Compatible with HBC, by the way, except perhaps in the placement
5345 <sect2 id="unpack-pragma">
5346 <title>UNPACK pragma</title>
5348 <indexterm><primary>UNPACK</primary></indexterm>
5350 <para>The <literal>UNPACK</literal> indicates to the compiler
5351 that it should unpack the contents of a constructor field into
5352 the constructor itself, removing a level of indirection. For
5356 data T = T {-# UNPACK #-} !Float
5357 {-# UNPACK #-} !Float
5360 <para>will create a constructor <literal>T</literal> containing
5361 two unboxed floats. This may not always be an optimisation: if
5362 the <function>T</function> constructor is scrutinised and the
5363 floats passed to a non-strict function for example, they will
5364 have to be reboxed (this is done automatically by the
5367 <para>Unpacking constructor fields should only be used in
5368 conjunction with <option>-O</option>, in order to expose
5369 unfoldings to the compiler so the reboxing can be removed as
5370 often as possible. For example:</para>
5374 f (T f1 f2) = f1 + f2
5377 <para>The compiler will avoid reboxing <function>f1</function>
5378 and <function>f2</function> by inlining <function>+</function>
5379 on floats, but only when <option>-O</option> is on.</para>
5381 <para>Any single-constructor data is eligible for unpacking; for
5385 data T = T {-# UNPACK #-} !(Int,Int)
5388 <para>will store the two <literal>Int</literal>s directly in the
5389 <function>T</function> constructor, by flattening the pair.
5390 Multi-level unpacking is also supported:</para>
5393 data T = T {-# UNPACK #-} !S
5394 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5397 <para>will store two unboxed <literal>Int#</literal>s
5398 directly in the <function>T</function> constructor. The
5399 unpacker can see through newtypes, too.</para>
5401 <para>If a field cannot be unpacked, you will not get a warning,
5402 so it might be an idea to check the generated code with
5403 <option>-ddump-simpl</option>.</para>
5405 <para>See also the <option>-funbox-strict-fields</option> flag,
5406 which essentially has the effect of adding
5407 <literal>{-# UNPACK #-}</literal> to every strict
5408 constructor field.</para>
5413 <!-- ======================= REWRITE RULES ======================== -->
5415 <sect1 id="rewrite-rules">
5416 <title>Rewrite rules
5418 <indexterm><primary>RULES pragma</primary></indexterm>
5419 <indexterm><primary>pragma, RULES</primary></indexterm>
5420 <indexterm><primary>rewrite rules</primary></indexterm></title>
5423 The programmer can specify rewrite rules as part of the source program
5424 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5425 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5426 and (b) the <option>-frules-off</option> flag
5427 (<xref linkend="options-f"/>) is not specified, and (c) the
5428 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5437 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5444 <title>Syntax</title>
5447 From a syntactic point of view:
5453 There may be zero or more rules in a <literal>RULES</literal> pragma.
5460 Each rule has a name, enclosed in double quotes. The name itself has
5461 no significance at all. It is only used when reporting how many times the rule fired.
5467 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5468 immediately after the name of the rule. Thus:
5471 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5474 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5475 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5484 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5485 is set, so you must lay out your rules starting in the same column as the
5486 enclosing definitions.
5493 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5494 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5495 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5496 by spaces, just like in a type <literal>forall</literal>.
5502 A pattern variable may optionally have a type signature.
5503 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5504 For example, here is the <literal>foldr/build</literal> rule:
5507 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5508 foldr k z (build g) = g k z
5511 Since <function>g</function> has a polymorphic type, it must have a type signature.
5518 The left hand side of a rule must consist of a top-level variable applied
5519 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5522 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5523 "wrong2" forall f. f True = True
5526 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5533 A rule does not need to be in the same module as (any of) the
5534 variables it mentions, though of course they need to be in scope.
5540 Rules are automatically exported from a module, just as instance declarations are.
5551 <title>Semantics</title>
5554 From a semantic point of view:
5560 Rules are only applied if you use the <option>-O</option> flag.
5566 Rules are regarded as left-to-right rewrite rules.
5567 When GHC finds an expression that is a substitution instance of the LHS
5568 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5569 By "a substitution instance" we mean that the LHS can be made equal to the
5570 expression by substituting for the pattern variables.
5577 The LHS and RHS of a rule are typechecked, and must have the
5585 GHC makes absolutely no attempt to verify that the LHS and RHS
5586 of a rule have the same meaning. That is undecidable in general, and
5587 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5594 GHC makes no attempt to make sure that the rules are confluent or
5595 terminating. For example:
5598 "loop" forall x,y. f x y = f y x
5601 This rule will cause the compiler to go into an infinite loop.
5608 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5614 GHC currently uses a very simple, syntactic, matching algorithm
5615 for matching a rule LHS with an expression. It seeks a substitution
5616 which makes the LHS and expression syntactically equal modulo alpha
5617 conversion. The pattern (rule), but not the expression, is eta-expanded if
5618 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5619 But not beta conversion (that's called higher-order matching).
5623 Matching is carried out on GHC's intermediate language, which includes
5624 type abstractions and applications. So a rule only matches if the
5625 types match too. See <xref linkend="rule-spec"/> below.
5631 GHC keeps trying to apply the rules as it optimises the program.
5632 For example, consider:
5641 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5642 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5643 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5644 not be substituted, and the rule would not fire.
5651 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5652 that appears on the LHS of a rule</emphasis>, because once you have substituted
5653 for something you can't match against it (given the simple minded
5654 matching). So if you write the rule
5657 "map/map" forall f,g. map f . map g = map (f.g)
5660 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5661 It will only match something written with explicit use of ".".
5662 Well, not quite. It <emphasis>will</emphasis> match the expression
5668 where <function>wibble</function> is defined:
5671 wibble f g = map f . map g
5674 because <function>wibble</function> will be inlined (it's small).
5676 Later on in compilation, GHC starts inlining even things on the
5677 LHS of rules, but still leaves the rules enabled. This inlining
5678 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5685 All rules are implicitly exported from the module, and are therefore
5686 in force in any module that imports the module that defined the rule, directly
5687 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5688 in force when compiling A.) The situation is very similar to that for instance
5700 <title>List fusion</title>
5703 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5704 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5705 intermediate list should be eliminated entirely.
5709 The following are good producers:
5721 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5727 Explicit lists (e.g. <literal>[True, False]</literal>)
5733 The cons constructor (e.g <literal>3:4:[]</literal>)
5739 <function>++</function>
5745 <function>map</function>
5751 <function>take</function>, <function>filter</function>
5757 <function>iterate</function>, <function>repeat</function>
5763 <function>zip</function>, <function>zipWith</function>
5772 The following are good consumers:
5784 <function>array</function> (on its second argument)
5790 <function>length</function>
5796 <function>++</function> (on its first argument)
5802 <function>foldr</function>
5808 <function>map</function>
5814 <function>take</function>, <function>filter</function>
5820 <function>concat</function>
5826 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5832 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5833 will fuse with one but not the other)
5839 <function>partition</function>
5845 <function>head</function>
5851 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5857 <function>sequence_</function>
5863 <function>msum</function>
5869 <function>sortBy</function>
5878 So, for example, the following should generate no intermediate lists:
5881 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5887 This list could readily be extended; if there are Prelude functions that you use
5888 a lot which are not included, please tell us.
5892 If you want to write your own good consumers or producers, look at the
5893 Prelude definitions of the above functions to see how to do so.
5898 <sect2 id="rule-spec">
5899 <title>Specialisation
5903 Rewrite rules can be used to get the same effect as a feature
5904 present in earlier versions of GHC.
5905 For example, suppose that:
5908 genericLookup :: Ord a => Table a b -> a -> b
5909 intLookup :: Table Int b -> Int -> b
5912 where <function>intLookup</function> is an implementation of
5913 <function>genericLookup</function> that works very fast for
5914 keys of type <literal>Int</literal>. You might wish
5915 to tell GHC to use <function>intLookup</function> instead of
5916 <function>genericLookup</function> whenever the latter was called with
5917 type <literal>Table Int b -> Int -> b</literal>.
5918 It used to be possible to write
5921 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5924 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5927 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5930 This slightly odd-looking rule instructs GHC to replace
5931 <function>genericLookup</function> by <function>intLookup</function>
5932 <emphasis>whenever the types match</emphasis>.
5933 What is more, this rule does not need to be in the same
5934 file as <function>genericLookup</function>, unlike the
5935 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5936 have an original definition available to specialise).
5939 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5940 <function>intLookup</function> really behaves as a specialised version
5941 of <function>genericLookup</function>!!!</para>
5943 <para>An example in which using <literal>RULES</literal> for
5944 specialisation will Win Big:
5947 toDouble :: Real a => a -> Double
5948 toDouble = fromRational . toRational
5950 {-# RULES "toDouble/Int" toDouble = i2d #-}
5951 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5954 The <function>i2d</function> function is virtually one machine
5955 instruction; the default conversion—via an intermediate
5956 <literal>Rational</literal>—is obscenely expensive by
5963 <title>Controlling what's going on</title>
5971 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5977 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5978 If you add <option>-dppr-debug</option> you get a more detailed listing.
5984 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5987 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5988 {-# INLINE build #-}
5992 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5993 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5994 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5995 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6002 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6003 see how to write rules that will do fusion and yet give an efficient
6004 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6014 <sect2 id="core-pragma">
6015 <title>CORE pragma</title>
6017 <indexterm><primary>CORE pragma</primary></indexterm>
6018 <indexterm><primary>pragma, CORE</primary></indexterm>
6019 <indexterm><primary>core, annotation</primary></indexterm>
6022 The external core format supports <quote>Note</quote> annotations;
6023 the <literal>CORE</literal> pragma gives a way to specify what these
6024 should be in your Haskell source code. Syntactically, core
6025 annotations are attached to expressions and take a Haskell string
6026 literal as an argument. The following function definition shows an
6030 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6033 Semantically, this is equivalent to:
6041 However, when external for is generated (via
6042 <option>-fext-core</option>), there will be Notes attached to the
6043 expressions <function>show</function> and <varname>x</varname>.
6044 The core function declaration for <function>f</function> is:
6048 f :: %forall a . GHCziShow.ZCTShow a ->
6049 a -> GHCziBase.ZMZN GHCziBase.Char =
6050 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6052 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6054 (tpl1::GHCziBase.Int ->
6056 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6058 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6059 (tpl3::GHCziBase.ZMZN a ->
6060 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6068 Here, we can see that the function <function>show</function> (which
6069 has been expanded out to a case expression over the Show dictionary)
6070 has a <literal>%note</literal> attached to it, as does the
6071 expression <varname>eta</varname> (which used to be called
6072 <varname>x</varname>).
6079 <sect1 id="special-ids">
6080 <title>Special built-in functions</title>
6081 <para>GHC has a few built-in funcions with special behaviour,
6082 described in this section. All are exported by
6083 <literal>GHC.Exts</literal>.</para>
6085 <sect2> <title>The <literal>inline</literal> function </title>
6087 The <literal>inline</literal> function is somewhat experimental.
6091 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6092 is inlined, regardless of its size. More precisely, the call
6093 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6095 This allows the programmer to control inlining from
6096 a particular <emphasis>call site</emphasis>
6097 rather than the <emphasis>definition site</emphasis> of the function
6098 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6101 This inlining occurs regardless of the argument to the call
6102 or the size of <literal>f</literal>'s definition; it is unconditional.
6103 The main caveat is that <literal>f</literal>'s definition must be
6104 visible to the compiler. That is, <literal>f</literal> must be
6105 let-bound in the current scope.
6106 If no inlining takes place, the <literal>inline</literal> function
6107 expands to the identity function in Phase zero; so its use imposes
6110 <para> If the function is defined in another
6111 module, GHC only exposes its inlining in the interface file if the
6112 function is sufficiently small that it <emphasis>might</emphasis> be
6113 inlined by the automatic mechanism. There is currently no way to tell
6114 GHC to expose arbitrarily-large functions in the interface file. (This
6115 shortcoming is something that could be fixed, with some kind of pragma.)
6119 <sect2> <title>The <literal>lazy</literal> function </title>
6121 The <literal>lazy</literal> function restrains strictness analysis a little:
6125 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6126 but <literal>lazy</literal> has a magical property so far as strictness
6127 analysis is concerned: it is lazy in its first argument,
6128 even though its semantics is strict. After strictness analysis has run,
6129 calls to <literal>lazy</literal> are inlined to be the identity function.
6132 This behaviour is occasionally useful when controlling evaluation order.
6133 Notably, <literal>lazy</literal> is used in the library definition of
6134 <literal>Control.Parallel.par</literal>:
6137 par x y = case (par# x) of { _ -> lazy y }
6139 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6140 look strict in <literal>y</literal> which would defeat the whole
6141 purpose of <literal>par</literal>.
6145 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6147 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6148 typechecker entirely. It has type
6150 unsafeCoerce# :: a -> b
6152 That is, it allows you to coerce any type into any other type. If you use this
6153 function, you had better get it right, otherwise segmentation faults await.
6154 It is generally used when you want to write a program that you know is
6155 well-typed, but where Haskell's type system is not expressive enough to prove
6156 that it is well typed.
6162 <sect1 id="generic-classes">
6163 <title>Generic classes</title>
6165 <para>(Note: support for generic classes is currently broken in
6169 The ideas behind this extension are described in detail in "Derivable type classes",
6170 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6171 An example will give the idea:
6179 fromBin :: [Int] -> (a, [Int])
6181 toBin {| Unit |} Unit = []
6182 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6183 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6184 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6186 fromBin {| Unit |} bs = (Unit, bs)
6187 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6188 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6189 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6190 (y,bs'') = fromBin bs'
6193 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6194 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6195 which are defined thus in the library module <literal>Generics</literal>:
6199 data a :+: b = Inl a | Inr b
6200 data a :*: b = a :*: b
6203 Now you can make a data type into an instance of Bin like this:
6205 instance (Bin a, Bin b) => Bin (a,b)
6206 instance Bin a => Bin [a]
6208 That is, just leave off the "where" clause. Of course, you can put in the
6209 where clause and over-ride whichever methods you please.
6213 <title> Using generics </title>
6214 <para>To use generics you need to</para>
6217 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6218 <option>-fgenerics</option> (to generate extra per-data-type code),
6219 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6223 <para>Import the module <literal>Generics</literal> from the
6224 <literal>lang</literal> package. This import brings into
6225 scope the data types <literal>Unit</literal>,
6226 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6227 don't need this import if you don't mention these types
6228 explicitly; for example, if you are simply giving instance
6229 declarations.)</para>
6234 <sect2> <title> Changes wrt the paper </title>
6236 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6237 can be written infix (indeed, you can now use
6238 any operator starting in a colon as an infix type constructor). Also note that
6239 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6240 Finally, note that the syntax of the type patterns in the class declaration
6241 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6242 alone would ambiguous when they appear on right hand sides (an extension we
6243 anticipate wanting).
6247 <sect2> <title>Terminology and restrictions</title>
6249 Terminology. A "generic default method" in a class declaration
6250 is one that is defined using type patterns as above.
6251 A "polymorphic default method" is a default method defined as in Haskell 98.
6252 A "generic class declaration" is a class declaration with at least one
6253 generic default method.
6261 Alas, we do not yet implement the stuff about constructor names and
6268 A generic class can have only one parameter; you can't have a generic
6269 multi-parameter class.
6275 A default method must be defined entirely using type patterns, or entirely
6276 without. So this is illegal:
6279 op :: a -> (a, Bool)
6280 op {| Unit |} Unit = (Unit, True)
6283 However it is perfectly OK for some methods of a generic class to have
6284 generic default methods and others to have polymorphic default methods.
6290 The type variable(s) in the type pattern for a generic method declaration
6291 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:
6295 op {| p :*: q |} (x :*: y) = op (x :: p)
6303 The type patterns in a generic default method must take one of the forms:
6309 where "a" and "b" are type variables. Furthermore, all the type patterns for
6310 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6311 must use the same type variables. So this is illegal:
6315 op {| a :+: b |} (Inl x) = True
6316 op {| p :+: q |} (Inr y) = False
6318 The type patterns must be identical, even in equations for different methods of the class.
6319 So this too is illegal:
6323 op1 {| a :*: b |} (x :*: y) = True
6326 op2 {| p :*: q |} (x :*: y) = False
6328 (The reason for this restriction is that we gather all the equations for a particular type consructor
6329 into a single generic instance declaration.)
6335 A generic method declaration must give a case for each of the three type constructors.
6341 The type for a generic method can be built only from:
6343 <listitem> <para> Function arrows </para> </listitem>
6344 <listitem> <para> Type variables </para> </listitem>
6345 <listitem> <para> Tuples </para> </listitem>
6346 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6348 Here are some example type signatures for generic methods:
6351 op2 :: Bool -> (a,Bool)
6352 op3 :: [Int] -> a -> a
6355 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6359 This restriction is an implementation restriction: we just havn't got around to
6360 implementing the necessary bidirectional maps over arbitrary type constructors.
6361 It would be relatively easy to add specific type constructors, such as Maybe and list,
6362 to the ones that are allowed.</para>
6367 In an instance declaration for a generic class, the idea is that the compiler
6368 will fill in the methods for you, based on the generic templates. However it can only
6373 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6378 No constructor of the instance type has unboxed fields.
6382 (Of course, these things can only arise if you are already using GHC extensions.)
6383 However, you can still give an instance declarations for types which break these rules,
6384 provided you give explicit code to override any generic default methods.
6392 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6393 what the compiler does with generic declarations.
6398 <sect2> <title> Another example </title>
6400 Just to finish with, here's another example I rather like:
6404 nCons {| Unit |} _ = 1
6405 nCons {| a :*: b |} _ = 1
6406 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6409 tag {| Unit |} _ = 1
6410 tag {| a :*: b |} _ = 1
6411 tag {| a :+: b |} (Inl x) = tag x
6412 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6421 ;;; Local Variables: ***
6423 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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