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>,<option>-fno-monomorphism-restriction</option>:
122 <para> These two flags control how generalisation is done.
123 See <xref linkend="monomorphism"/>.
130 <option>-fextended-default-rules</option>:
131 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
134 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
135 Independent of the <option>-fglasgow-exts</option>
142 <option>-fallow-overlapping-instances</option>
143 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
146 <option>-fallow-undecidable-instances</option>
147 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
150 <option>-fallow-incoherent-instances</option>
151 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
154 <option>-fcontext-stack=N</option>
155 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
158 <para> See <xref linkend="instance-decls"/>. Only relevant
159 if you also use <option>-fglasgow-exts</option>.</para>
165 <option>-finline-phase</option>
166 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
169 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
170 you also use <option>-fglasgow-exts</option>.</para>
176 <option>-farrows</option>
177 <indexterm><primary><option>-farrows</option></primary></indexterm>
180 <para>See <xref linkend="arrow-notation"/>. Independent of
181 <option>-fglasgow-exts</option>.</para>
183 <para>New reserved words/symbols: <literal>rec</literal>,
184 <literal>proc</literal>, <literal>-<</literal>,
185 <literal>>-</literal>, <literal>-<<</literal>,
186 <literal>>>-</literal>.</para>
188 <para>Other syntax stolen: <literal>(|</literal>,
189 <literal>|)</literal>.</para>
195 <option>-fgenerics</option>
196 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
199 <para>See <xref linkend="generic-classes"/>. Independent of
200 <option>-fglasgow-exts</option>.</para>
205 <term><option>-fno-implicit-prelude</option></term>
207 <para><indexterm><primary>-fno-implicit-prelude
208 option</primary></indexterm> GHC normally imports
209 <filename>Prelude.hi</filename> files for you. If you'd
210 rather it didn't, then give it a
211 <option>-fno-implicit-prelude</option> option. The idea is
212 that you can then import a Prelude of your own. (But don't
213 call it <literal>Prelude</literal>; the Haskell module
214 namespace is flat, and you must not conflict with any
215 Prelude module.)</para>
217 <para>Even though you have not imported the Prelude, most of
218 the built-in syntax still refers to the built-in Haskell
219 Prelude types and values, as specified by the Haskell
220 Report. For example, the type <literal>[Int]</literal>
221 still means <literal>Prelude.[] Int</literal>; tuples
222 continue to refer to the standard Prelude tuples; the
223 translation for list comprehensions continues to use
224 <literal>Prelude.map</literal> etc.</para>
226 <para>However, <option>-fno-implicit-prelude</option> does
227 change the handling of certain built-in syntax: see <xref
228 linkend="rebindable-syntax"/>.</para>
233 <term><option>-fimplicit-params</option></term>
235 <para>Enables implicit parameters (see <xref
236 linkend="implicit-parameters"/>). Currently also implied by
237 <option>-fglasgow-exts</option>.</para>
240 <literal>?<replaceable>varid</replaceable></literal>,
241 <literal>%<replaceable>varid</replaceable></literal>.</para>
246 <term><option>-fscoped-type-variables</option></term>
248 <para>Enables lexically-scoped type variables (see <xref
249 linkend="scoped-type-variables"/>). Implied by
250 <option>-fglasgow-exts</option>.</para>
255 <term><option>-fth</option></term>
257 <para>Enables Template Haskell (see <xref
258 linkend="template-haskell"/>). This flag must
259 be given explicitly; it is no longer implied by
260 <option>-fglasgow-exts</option>.</para>
262 <para>Syntax stolen: <literal>[|</literal>,
263 <literal>[e|</literal>, <literal>[p|</literal>,
264 <literal>[d|</literal>, <literal>[t|</literal>,
265 <literal>$(</literal>,
266 <literal>$<replaceable>varid</replaceable></literal>.</para>
273 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
274 <!-- included from primitives.sgml -->
275 <!-- &primitives; -->
276 <sect1 id="primitives">
277 <title>Unboxed types and primitive operations</title>
279 <para>GHC is built on a raft of primitive data types and operations.
280 While you really can use this stuff to write fast code,
281 we generally find it a lot less painful, and more satisfying in the
282 long run, to use higher-level language features and libraries. With
283 any luck, the code you write will be optimised to the efficient
284 unboxed version in any case. And if it isn't, we'd like to know
287 <para>We do not currently have good, up-to-date documentation about the
288 primitives, perhaps because they are mainly intended for internal use.
289 There used to be a long section about them here in the User Guide, but it
290 became out of date, and wrong information is worse than none.</para>
292 <para>The Real Truth about what primitive types there are, and what operations
293 work over those types, is held in the file
294 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
295 This file is used directly to generate GHC's primitive-operation definitions, so
296 it is always correct! It is also intended for processing into text.</para>
299 the result of such processing is part of the description of the
301 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
302 Core language</ulink>.
303 So that document is a good place to look for a type-set version.
304 We would be very happy if someone wanted to volunteer to produce an SGML
305 back end to the program that processes <filename>primops.txt</filename> so that
306 we could include the results here in the User Guide.</para>
308 <para>What follows here is a brief summary of some main points.</para>
310 <sect2 id="glasgow-unboxed">
315 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
318 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
319 that values of that type are represented by a pointer to a heap
320 object. The representation of a Haskell <literal>Int</literal>, for
321 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
322 type, however, is represented by the value itself, no pointers or heap
323 allocation are involved.
327 Unboxed types correspond to the “raw machine” types you
328 would use in C: <literal>Int#</literal> (long int),
329 <literal>Double#</literal> (double), <literal>Addr#</literal>
330 (void *), etc. The <emphasis>primitive operations</emphasis>
331 (PrimOps) on these types are what you might expect; e.g.,
332 <literal>(+#)</literal> is addition on
333 <literal>Int#</literal>s, and is the machine-addition that we all
334 know and love—usually one instruction.
338 Primitive (unboxed) types cannot be defined in Haskell, and are
339 therefore built into the language and compiler. Primitive types are
340 always unlifted; that is, a value of a primitive type cannot be
341 bottom. We use the convention that primitive types, values, and
342 operations have a <literal>#</literal> suffix.
346 Primitive values are often represented by a simple bit-pattern, such
347 as <literal>Int#</literal>, <literal>Float#</literal>,
348 <literal>Double#</literal>. But this is not necessarily the case:
349 a primitive value might be represented by a pointer to a
350 heap-allocated object. Examples include
351 <literal>Array#</literal>, the type of primitive arrays. A
352 primitive array is heap-allocated because it is too big a value to fit
353 in a register, and would be too expensive to copy around; in a sense,
354 it is accidental that it is represented by a pointer. If a pointer
355 represents a primitive value, then it really does point to that value:
356 no unevaluated thunks, no indirections…nothing can be at the
357 other end of the pointer than the primitive value.
358 A numerically-intensive program using unboxed types can
359 go a <emphasis>lot</emphasis> faster than its “standard”
360 counterpart—we saw a threefold speedup on one example.
364 There are some restrictions on the use of primitive types:
366 <listitem><para>The main restriction
367 is that you can't pass a primitive value to a polymorphic
368 function or store one in a polymorphic data type. This rules out
369 things like <literal>[Int#]</literal> (i.e. lists of primitive
370 integers). The reason for this restriction is that polymorphic
371 arguments and constructor fields are assumed to be pointers: if an
372 unboxed integer is stored in one of these, the garbage collector would
373 attempt to follow it, leading to unpredictable space leaks. Or a
374 <function>seq</function> operation on the polymorphic component may
375 attempt to dereference the pointer, with disastrous results. Even
376 worse, the unboxed value might be larger than a pointer
377 (<literal>Double#</literal> for instance).
380 <listitem><para> You cannot bind a variable with an unboxed type
381 in a <emphasis>top-level</emphasis> binding.
383 <listitem><para> You cannot bind a variable with an unboxed type
384 in a <emphasis>recursive</emphasis> binding.
386 <listitem><para> You may bind unboxed variables in a (non-recursive,
387 non-top-level) pattern binding, but any such variable causes the entire
389 to become strict. For example:
391 data Foo = Foo Int Int#
393 f x = let (Foo a b, w) = ..rhs.. in ..body..
395 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
397 is strict, and the program behaves as if you had written
399 data Foo = Foo Int Int#
401 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
410 <sect2 id="unboxed-tuples">
411 <title>Unboxed Tuples
415 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
416 they're available by default with <option>-fglasgow-exts</option>. An
417 unboxed tuple looks like this:
429 where <literal>e_1..e_n</literal> are expressions of any
430 type (primitive or non-primitive). The type of an unboxed tuple looks
435 Unboxed tuples are used for functions that need to return multiple
436 values, but they avoid the heap allocation normally associated with
437 using fully-fledged tuples. When an unboxed tuple is returned, the
438 components are put directly into registers or on the stack; the
439 unboxed tuple itself does not have a composite representation. Many
440 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
442 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
443 tuples to avoid unnecessary allocation during sequences of operations.
447 There are some pretty stringent restrictions on the use of unboxed tuples:
452 Values of unboxed tuple types are subject to the same restrictions as
453 other unboxed types; i.e. they may not be stored in polymorphic data
454 structures or passed to polymorphic functions.
461 No variable can have an unboxed tuple type, nor may a constructor or function
462 argument have an unboxed tuple type. The following are all illegal:
466 data Foo = Foo (# Int, Int #)
468 f :: (# Int, Int #) -> (# Int, Int #)
471 g :: (# Int, Int #) -> Int
474 h x = let y = (# x,x #) in ...
481 The typical use of unboxed tuples is simply to return multiple values,
482 binding those multiple results with a <literal>case</literal> expression, thus:
484 f x y = (# x+1, y-1 #)
485 g x = case f x x of { (# a, b #) -> a + b }
487 You can have an unboxed tuple in a pattern binding, thus
489 f x = let (# p,q #) = h x in ..body..
491 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
492 the resulting binding is lazy like any other Haskell pattern binding. The
493 above example desugars like this:
495 f x = let t = case h x o f{ (# p,q #) -> (p,q)
500 Indeed, the bindings can even be recursive.
507 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
509 <sect1 id="syntax-extns">
510 <title>Syntactic extensions</title>
512 <!-- ====================== HIERARCHICAL MODULES ======================= -->
514 <sect2 id="hierarchical-modules">
515 <title>Hierarchical Modules</title>
517 <para>GHC supports a small extension to the syntax of module
518 names: a module name is allowed to contain a dot
519 <literal>‘.’</literal>. This is also known as the
520 “hierarchical module namespace” extension, because
521 it extends the normally flat Haskell module namespace into a
522 more flexible hierarchy of modules.</para>
524 <para>This extension has very little impact on the language
525 itself; modules names are <emphasis>always</emphasis> fully
526 qualified, so you can just think of the fully qualified module
527 name as <quote>the module name</quote>. In particular, this
528 means that the full module name must be given after the
529 <literal>module</literal> keyword at the beginning of the
530 module; for example, the module <literal>A.B.C</literal> must
533 <programlisting>module A.B.C</programlisting>
536 <para>It is a common strategy to use the <literal>as</literal>
537 keyword to save some typing when using qualified names with
538 hierarchical modules. For example:</para>
541 import qualified Control.Monad.ST.Strict as ST
544 <para>For details on how GHC searches for source and interface
545 files in the presence of hierarchical modules, see <xref
546 linkend="search-path"/>.</para>
548 <para>GHC comes with a large collection of libraries arranged
549 hierarchically; see the accompanying library documentation.
550 There is an ongoing project to create and maintain a stable set
551 of <quote>core</quote> libraries used by several Haskell
552 compilers, and the libraries that GHC comes with represent the
553 current status of that project. For more details, see <ulink
554 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
555 Libraries</ulink>.</para>
559 <!-- ====================== PATTERN GUARDS ======================= -->
561 <sect2 id="pattern-guards">
562 <title>Pattern guards</title>
565 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
566 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.)
570 Suppose we have an abstract data type of finite maps, with a
574 lookup :: FiniteMap -> Int -> Maybe Int
577 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
578 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
582 clunky env var1 var2 | ok1 && ok2 = val1 + val2
583 | otherwise = var1 + var2
594 The auxiliary functions are
598 maybeToBool :: Maybe a -> Bool
599 maybeToBool (Just x) = True
600 maybeToBool Nothing = False
602 expectJust :: Maybe a -> a
603 expectJust (Just x) = x
604 expectJust Nothing = error "Unexpected Nothing"
608 What is <function>clunky</function> doing? The guard <literal>ok1 &&
609 ok2</literal> checks that both lookups succeed, using
610 <function>maybeToBool</function> to convert the <function>Maybe</function>
611 types to booleans. The (lazily evaluated) <function>expectJust</function>
612 calls extract the values from the results of the lookups, and binds the
613 returned values to <varname>val1</varname> and <varname>val2</varname>
614 respectively. If either lookup fails, then clunky takes the
615 <literal>otherwise</literal> case and returns the sum of its arguments.
619 This is certainly legal Haskell, but it is a tremendously verbose and
620 un-obvious way to achieve the desired effect. Arguably, a more direct way
621 to write clunky would be to use case expressions:
625 clunky env var1 var1 = case lookup env var1 of
627 Just val1 -> case lookup env var2 of
629 Just val2 -> val1 + val2
635 This is a bit shorter, but hardly better. Of course, we can rewrite any set
636 of pattern-matching, guarded equations as case expressions; that is
637 precisely what the compiler does when compiling equations! The reason that
638 Haskell provides guarded equations is because they allow us to write down
639 the cases we want to consider, one at a time, independently of each other.
640 This structure is hidden in the case version. Two of the right-hand sides
641 are really the same (<function>fail</function>), and the whole expression
642 tends to become more and more indented.
646 Here is how I would write clunky:
651 | Just val1 <- lookup env var1
652 , Just val2 <- lookup env var2
654 ...other equations for clunky...
658 The semantics should be clear enough. The qualifiers are matched in order.
659 For a <literal><-</literal> qualifier, which I call a pattern guard, the
660 right hand side is evaluated and matched against the pattern on the left.
661 If the match fails then the whole guard fails and the next equation is
662 tried. If it succeeds, then the appropriate binding takes place, and the
663 next qualifier is matched, in the augmented environment. Unlike list
664 comprehensions, however, the type of the expression to the right of the
665 <literal><-</literal> is the same as the type of the pattern to its
666 left. The bindings introduced by pattern guards scope over all the
667 remaining guard qualifiers, and over the right hand side of the equation.
671 Just as with list comprehensions, boolean expressions can be freely mixed
672 with among the pattern guards. For example:
683 Haskell's current guards therefore emerge as a special case, in which the
684 qualifier list has just one element, a boolean expression.
688 <!-- ===================== Recursive do-notation =================== -->
690 <sect2 id="mdo-notation">
691 <title>The recursive do-notation
694 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
695 "A recursive do for Haskell",
696 Levent Erkok, John Launchbury",
697 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
700 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
701 that is, the variables bound in a do-expression are visible only in the textually following
702 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
703 group. It turns out that several applications can benefit from recursive bindings in
704 the do-notation, and this extension provides the necessary syntactic support.
707 Here is a simple (yet contrived) example:
710 import Control.Monad.Fix
712 justOnes = mdo xs <- Just (1:xs)
716 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
720 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
723 class Monad m => MonadFix m where
724 mfix :: (a -> m a) -> m a
727 The function <literal>mfix</literal>
728 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
729 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
730 For details, see the above mentioned reference.
733 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
734 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
735 for Haskell's internal state monad (strict and lazy, respectively).
738 There are three important points in using the recursive-do notation:
741 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
742 than <literal>do</literal>).
746 You should <literal>import Control.Monad.Fix</literal>.
747 (Note: Strictly speaking, this import is required only when you need to refer to the name
748 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
749 are encouraged to always import this module when using the mdo-notation.)
753 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
759 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
760 contains up to date information on recursive monadic bindings.
764 Historical note: The old implementation of the mdo-notation (and most
765 of the existing documents) used the name
766 <literal>MonadRec</literal> for the class and the corresponding library.
767 This name is not supported by GHC.
773 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
775 <sect2 id="parallel-list-comprehensions">
776 <title>Parallel List Comprehensions</title>
777 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
779 <indexterm><primary>parallel list comprehensions</primary>
782 <para>Parallel list comprehensions are a natural extension to list
783 comprehensions. List comprehensions can be thought of as a nice
784 syntax for writing maps and filters. Parallel comprehensions
785 extend this to include the zipWith family.</para>
787 <para>A parallel list comprehension has multiple independent
788 branches of qualifier lists, each separated by a `|' symbol. For
789 example, the following zips together two lists:</para>
792 [ (x, y) | x <- xs | y <- ys ]
795 <para>The behavior of parallel list comprehensions follows that of
796 zip, in that the resulting list will have the same length as the
797 shortest branch.</para>
799 <para>We can define parallel list comprehensions by translation to
800 regular comprehensions. Here's the basic idea:</para>
802 <para>Given a parallel comprehension of the form: </para>
805 [ e | p1 <- e11, p2 <- e12, ...
806 | q1 <- e21, q2 <- e22, ...
811 <para>This will be translated to: </para>
814 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
815 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
820 <para>where `zipN' is the appropriate zip for the given number of
825 <sect2 id="rebindable-syntax">
826 <title>Rebindable syntax</title>
829 <para>GHC allows most kinds of built-in syntax to be rebound by
830 the user, to facilitate replacing the <literal>Prelude</literal>
831 with a home-grown version, for example.</para>
833 <para>You may want to define your own numeric class
834 hierarchy. It completely defeats that purpose if the
835 literal "1" means "<literal>Prelude.fromInteger
836 1</literal>", which is what the Haskell Report specifies.
837 So the <option>-fno-implicit-prelude</option> flag causes
838 the following pieces of built-in syntax to refer to
839 <emphasis>whatever is in scope</emphasis>, not the Prelude
844 <para>An integer literal <literal>368</literal> means
845 "<literal>fromInteger (368::Integer)</literal>", rather than
846 "<literal>Prelude.fromInteger (368::Integer)</literal>".
849 <listitem><para>Fractional literals are handed in just the same way,
850 except that the translation is
851 <literal>fromRational (3.68::Rational)</literal>.
854 <listitem><para>The equality test in an overloaded numeric pattern
855 uses whatever <literal>(==)</literal> is in scope.
858 <listitem><para>The subtraction operation, and the
859 greater-than-or-equal test, in <literal>n+k</literal> patterns
860 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
864 <para>Negation (e.g. "<literal>- (f x)</literal>")
865 means "<literal>negate (f x)</literal>", both in numeric
866 patterns, and expressions.
870 <para>"Do" notation is translated using whatever
871 functions <literal>(>>=)</literal>,
872 <literal>(>>)</literal>, and <literal>fail</literal>,
873 are in scope (not the Prelude
874 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
875 comprehensions, are unaffected. </para></listitem>
879 notation (see <xref linkend="arrow-notation"/>)
880 uses whatever <literal>arr</literal>,
881 <literal>(>>>)</literal>, <literal>first</literal>,
882 <literal>app</literal>, <literal>(|||)</literal> and
883 <literal>loop</literal> functions are in scope. But unlike the
884 other constructs, the types of these functions must match the
885 Prelude types very closely. Details are in flux; if you want
889 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
890 even if that is a little unexpected. For emample, the
891 static semantics of the literal <literal>368</literal>
892 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
893 <literal>fromInteger</literal> to have any of the types:
895 fromInteger :: Integer -> Integer
896 fromInteger :: forall a. Foo a => Integer -> a
897 fromInteger :: Num a => a -> Integer
898 fromInteger :: Integer -> Bool -> Bool
902 <para>Be warned: this is an experimental facility, with
903 fewer checks than usual. Use <literal>-dcore-lint</literal>
904 to typecheck the desugared program. If Core Lint is happy
905 you should be all right.</para>
911 <!-- TYPE SYSTEM EXTENSIONS -->
912 <sect1 id="type-extensions">
913 <title>Type system extensions</title>
917 <title>Data types and type synonyms</title>
919 <sect3 id="nullary-types">
920 <title>Data types with no constructors</title>
922 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
923 a data type with no constructors. For example:</para>
927 data T a -- T :: * -> *
930 <para>Syntactically, the declaration lacks the "= constrs" part. The
931 type can be parameterised over types of any kind, but if the kind is
932 not <literal>*</literal> then an explicit kind annotation must be used
933 (see <xref linkend="sec-kinding"/>).</para>
935 <para>Such data types have only one value, namely bottom.
936 Nevertheless, they can be useful when defining "phantom types".</para>
939 <sect3 id="infix-tycons">
940 <title>Infix type constructors, classes, and type variables</title>
943 GHC allows type constructors, classes, and type variables to be operators, and
944 to be written infix, very much like expressions. More specifically:
947 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
948 The lexical syntax is the same as that for data constructors.
951 Data type and type-synonym declarations can be written infix, parenthesised
952 if you want further arguments. E.g.
954 data a :*: b = Foo a b
955 type a :+: b = Either a b
956 class a :=: b where ...
958 data (a :**: b) x = Baz a b x
959 type (a :++: b) y = Either (a,b) y
963 Types, and class constraints, can be written infix. For example
966 f :: (a :=: b) => a -> b
970 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
971 The lexical syntax is the same as that for variable operators, excluding "(.)",
972 "(!)", and "(*)". In a binding position, the operator must be
973 parenthesised. For example:
975 type T (+) = Int + Int
980 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
986 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
987 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
990 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
991 one cannot distinguish between the two in a fixity declaration; a fixity declaration
992 sets the fixity for a data constructor and the corresponding type constructor. For example:
996 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
997 and similarly for <literal>:*:</literal>.
998 <literal>Int `a` Bool</literal>.
1001 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1008 <sect3 id="type-synonyms">
1009 <title>Liberalised type synonyms</title>
1012 Type synonyms are like macros at the type level, and
1013 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1014 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1016 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1017 in a type synonym, thus:
1019 type Discard a = forall b. Show b => a -> b -> (a, String)
1024 g :: Discard Int -> (Int,String) -- A rank-2 type
1031 You can write an unboxed tuple in a type synonym:
1033 type Pr = (# Int, Int #)
1041 You can apply a type synonym to a forall type:
1043 type Foo a = a -> a -> Bool
1045 f :: Foo (forall b. b->b)
1047 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1049 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1054 You can apply a type synonym to a partially applied type synonym:
1056 type Generic i o = forall x. i x -> o x
1059 foo :: Generic Id []
1061 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1063 foo :: forall x. x -> [x]
1071 GHC currently does kind checking before expanding synonyms (though even that
1075 After expanding type synonyms, GHC does validity checking on types, looking for
1076 the following mal-formedness which isn't detected simply by kind checking:
1079 Type constructor applied to a type involving for-alls.
1082 Unboxed tuple on left of an arrow.
1085 Partially-applied type synonym.
1089 this will be rejected:
1091 type Pr = (# Int, Int #)
1096 because GHC does not allow unboxed tuples on the left of a function arrow.
1101 <sect3 id="existential-quantification">
1102 <title>Existentially quantified data constructors
1106 The idea of using existential quantification in data type declarations
1107 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1108 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1109 London, 1991). It was later formalised by Laufer and Odersky
1110 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1111 TOPLAS, 16(5), pp1411-1430, 1994).
1112 It's been in Lennart
1113 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1114 proved very useful. Here's the idea. Consider the declaration:
1120 data Foo = forall a. MkFoo a (a -> Bool)
1127 The data type <literal>Foo</literal> has two constructors with types:
1133 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1140 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1141 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1142 For example, the following expression is fine:
1148 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1154 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1155 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1156 isUpper</function> packages a character with a compatible function. These
1157 two things are each of type <literal>Foo</literal> and can be put in a list.
1161 What can we do with a value of type <literal>Foo</literal>?. In particular,
1162 what happens when we pattern-match on <function>MkFoo</function>?
1168 f (MkFoo val fn) = ???
1174 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1175 are compatible, the only (useful) thing we can do with them is to
1176 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1183 f (MkFoo val fn) = fn val
1189 What this allows us to do is to package heterogenous values
1190 together with a bunch of functions that manipulate them, and then treat
1191 that collection of packages in a uniform manner. You can express
1192 quite a bit of object-oriented-like programming this way.
1195 <sect4 id="existential">
1196 <title>Why existential?
1200 What has this to do with <emphasis>existential</emphasis> quantification?
1201 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1207 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1213 But Haskell programmers can safely think of the ordinary
1214 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1215 adding a new existential quantification construct.
1221 <title>Type classes</title>
1224 An easy extension is to allow
1225 arbitrary contexts before the constructor. For example:
1231 data Baz = forall a. Eq a => Baz1 a a
1232 | forall b. Show b => Baz2 b (b -> b)
1238 The two constructors have the types you'd expect:
1244 Baz1 :: forall a. Eq a => a -> a -> Baz
1245 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1251 But when pattern matching on <function>Baz1</function> the matched values can be compared
1252 for equality, and when pattern matching on <function>Baz2</function> the first matched
1253 value can be converted to a string (as well as applying the function to it).
1254 So this program is legal:
1261 f (Baz1 p q) | p == q = "Yes"
1263 f (Baz2 v fn) = show (fn v)
1269 Operationally, in a dictionary-passing implementation, the
1270 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1271 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1272 extract it on pattern matching.
1276 Notice the way that the syntax fits smoothly with that used for
1277 universal quantification earlier.
1283 <title>Record Constructors</title>
1286 GHC allows existentials to be used with records syntax as well. For example:
1289 data Counter a = forall self. NewCounter
1291 , _inc :: self -> self
1292 , _display :: self -> IO ()
1296 Here <literal>tag</literal> is a public field, with a well-typed selector
1297 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1298 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1299 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1300 compile-time error. In other words, <emphasis>GHC defines a record selector function
1301 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1302 (This example used an underscore in the fields for which record selectors
1303 will not be defined, but that is only programming style; GHC ignores them.)
1307 To make use of these hidden fields, we need to create some helper functions:
1310 inc :: Counter a -> Counter a
1311 inc (NewCounter x i d t) = NewCounter
1312 { _this = i x, _inc = i, _display = d, tag = t }
1314 display :: Counter a -> IO ()
1315 display NewCounter{ _this = x, _display = d } = d x
1318 Now we can define counters with different underlying implementations:
1321 counterA :: Counter String
1322 counterA = NewCounter
1323 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1325 counterB :: Counter String
1326 counterB = NewCounter
1327 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1330 display (inc counterA) -- prints "1"
1331 display (inc (inc counterB)) -- prints "##"
1334 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1335 <literal>forall</literal> may be omitted. For example, we can express
1336 the same <literal>Counter a</literal> using GADT:
1339 data Counter a where
1340 NewCounter { _this :: self
1341 , _inc :: self -> self
1342 , _display :: self -> IO ()
1348 At the moment, record update syntax is only supported for Haskell 98 data types,
1349 so the following function does <emphasis>not</emphasis> work:
1352 -- This is invalid; use explicit NewCounter instead for now
1353 setTag :: Counter a -> a -> Counter a
1354 setTag obj t = obj{ tag = t }
1363 <title>Restrictions</title>
1366 There are several restrictions on the ways in which existentially-quantified
1367 constructors can be use.
1376 When pattern matching, each pattern match introduces a new,
1377 distinct, type for each existential type variable. These types cannot
1378 be unified with any other type, nor can they escape from the scope of
1379 the pattern match. For example, these fragments are incorrect:
1387 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1388 is the result of <function>f1</function>. One way to see why this is wrong is to
1389 ask what type <function>f1</function> has:
1393 f1 :: Foo -> a -- Weird!
1397 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1402 f1 :: forall a. Foo -> a -- Wrong!
1406 The original program is just plain wrong. Here's another sort of error
1410 f2 (Baz1 a b) (Baz1 p q) = a==q
1414 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1415 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1416 from the two <function>Baz1</function> constructors.
1424 You can't pattern-match on an existentially quantified
1425 constructor in a <literal>let</literal> or <literal>where</literal> group of
1426 bindings. So this is illegal:
1430 f3 x = a==b where { Baz1 a b = x }
1433 Instead, use a <literal>case</literal> expression:
1436 f3 x = case x of Baz1 a b -> a==b
1439 In general, you can only pattern-match
1440 on an existentially-quantified constructor in a <literal>case</literal> expression or
1441 in the patterns of a function definition.
1443 The reason for this restriction is really an implementation one.
1444 Type-checking binding groups is already a nightmare without
1445 existentials complicating the picture. Also an existential pattern
1446 binding at the top level of a module doesn't make sense, because it's
1447 not clear how to prevent the existentially-quantified type "escaping".
1448 So for now, there's a simple-to-state restriction. We'll see how
1456 You can't use existential quantification for <literal>newtype</literal>
1457 declarations. So this is illegal:
1461 newtype T = forall a. Ord a => MkT a
1465 Reason: a value of type <literal>T</literal> must be represented as a
1466 pair of a dictionary for <literal>Ord t</literal> and a value of type
1467 <literal>t</literal>. That contradicts the idea that
1468 <literal>newtype</literal> should have no concrete representation.
1469 You can get just the same efficiency and effect by using
1470 <literal>data</literal> instead of <literal>newtype</literal>. If
1471 there is no overloading involved, then there is more of a case for
1472 allowing an existentially-quantified <literal>newtype</literal>,
1473 because the <literal>data</literal> version does carry an
1474 implementation cost, but single-field existentially quantified
1475 constructors aren't much use. So the simple restriction (no
1476 existential stuff on <literal>newtype</literal>) stands, unless there
1477 are convincing reasons to change it.
1485 You can't use <literal>deriving</literal> to define instances of a
1486 data type with existentially quantified data constructors.
1488 Reason: in most cases it would not make sense. For example:#
1491 data T = forall a. MkT [a] deriving( Eq )
1494 To derive <literal>Eq</literal> in the standard way we would need to have equality
1495 between the single component of two <function>MkT</function> constructors:
1499 (MkT a) == (MkT b) = ???
1502 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1503 It's just about possible to imagine examples in which the derived instance
1504 would make sense, but it seems altogether simpler simply to prohibit such
1505 declarations. Define your own instances!
1520 <sect2 id="multi-param-type-classes">
1521 <title>Class declarations</title>
1524 This section, and the next one, documents GHC's type-class extensions.
1525 There's lots of background in the paper <ulink
1526 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1527 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1528 Jones, Erik Meijer).
1531 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1535 <title>Multi-parameter type classes</title>
1537 Multi-parameter type classes are permitted. For example:
1541 class Collection c a where
1542 union :: c a -> c a -> c a
1550 <title>The superclasses of a class declaration</title>
1553 There are no restrictions on the context in a class declaration
1554 (which introduces superclasses), except that the class hierarchy must
1555 be acyclic. So these class declarations are OK:
1559 class Functor (m k) => FiniteMap m k where
1562 class (Monad m, Monad (t m)) => Transform t m where
1563 lift :: m a -> (t m) a
1569 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1570 of "acyclic" involves only the superclass relationships. For example,
1576 op :: D b => a -> b -> b
1579 class C a => D a where { ... }
1583 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1584 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1585 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1592 <sect3 id="class-method-types">
1593 <title>Class method types</title>
1596 Haskell 98 prohibits class method types to mention constraints on the
1597 class type variable, thus:
1600 fromList :: [a] -> s a
1601 elem :: Eq a => a -> s a -> Bool
1603 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1604 contains the constraint <literal>Eq a</literal>, constrains only the
1605 class type variable (in this case <literal>a</literal>).
1606 GHC lifts this restriction.
1613 <sect2 id="functional-dependencies">
1614 <title>Functional dependencies
1617 <para> Functional dependencies are implemented as described by Mark Jones
1618 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1619 In Proceedings of the 9th European Symposium on Programming,
1620 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1624 Functional dependencies are introduced by a vertical bar in the syntax of a
1625 class declaration; e.g.
1627 class (Monad m) => MonadState s m | m -> s where ...
1629 class Foo a b c | a b -> c where ...
1631 There should be more documentation, but there isn't (yet). Yell if you need it.
1634 <sect3><title>Rules for functional dependencies </title>
1636 In a class declaration, all of the class type variables must be reachable (in the sense
1637 mentioned in <xref linkend="type-restrictions"/>)
1638 from the free variables of each method type.
1642 class Coll s a where
1644 insert :: s -> a -> s
1647 is not OK, because the type of <literal>empty</literal> doesn't mention
1648 <literal>a</literal>. Functional dependencies can make the type variable
1651 class Coll s a | s -> a where
1653 insert :: s -> a -> s
1656 Alternatively <literal>Coll</literal> might be rewritten
1659 class Coll s a where
1661 insert :: s a -> a -> s a
1665 which makes the connection between the type of a collection of
1666 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1667 Occasionally this really doesn't work, in which case you can split the
1675 class CollE s => Coll s a where
1676 insert :: s -> a -> s
1683 <title>Background on functional dependencies</title>
1685 <para>The following description of the motivation and use of functional dependencies is taken
1686 from the Hugs user manual, reproduced here (with minor changes) by kind
1687 permission of Mark Jones.
1690 Consider the following class, intended as part of a
1691 library for collection types:
1693 class Collects e ce where
1695 insert :: e -> ce -> ce
1696 member :: e -> ce -> Bool
1698 The type variable e used here represents the element type, while ce is the type
1699 of the container itself. Within this framework, we might want to define
1700 instances of this class for lists or characteristic functions (both of which
1701 can be used to represent collections of any equality type), bit sets (which can
1702 be used to represent collections of characters), or hash tables (which can be
1703 used to represent any collection whose elements have a hash function). Omitting
1704 standard implementation details, this would lead to the following declarations:
1706 instance Eq e => Collects e [e] where ...
1707 instance Eq e => Collects e (e -> Bool) where ...
1708 instance Collects Char BitSet where ...
1709 instance (Hashable e, Collects a ce)
1710 => Collects e (Array Int ce) where ...
1712 All this looks quite promising; we have a class and a range of interesting
1713 implementations. Unfortunately, there are some serious problems with the class
1714 declaration. First, the empty function has an ambiguous type:
1716 empty :: Collects e ce => ce
1718 By "ambiguous" we mean that there is a type variable e that appears on the left
1719 of the <literal>=></literal> symbol, but not on the right. The problem with
1720 this is that, according to the theoretical foundations of Haskell overloading,
1721 we cannot guarantee a well-defined semantics for any term with an ambiguous
1725 We can sidestep this specific problem by removing the empty member from the
1726 class declaration. However, although the remaining members, insert and member,
1727 do not have ambiguous types, we still run into problems when we try to use
1728 them. For example, consider the following two functions:
1730 f x y = insert x . insert y
1733 for which GHC infers the following types:
1735 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1736 g :: (Collects Bool c, Collects Char c) => c -> c
1738 Notice that the type for f allows the two parameters x and y to be assigned
1739 different types, even though it attempts to insert each of the two values, one
1740 after the other, into the same collection. If we're trying to model collections
1741 that contain only one type of value, then this is clearly an inaccurate
1742 type. Worse still, the definition for g is accepted, without causing a type
1743 error. As a result, the error in this code will not be flagged at the point
1744 where it appears. Instead, it will show up only when we try to use g, which
1745 might even be in a different module.
1748 <sect4><title>An attempt to use constructor classes</title>
1751 Faced with the problems described above, some Haskell programmers might be
1752 tempted to use something like the following version of the class declaration:
1754 class Collects e c where
1756 insert :: e -> c e -> c e
1757 member :: e -> c e -> Bool
1759 The key difference here is that we abstract over the type constructor c that is
1760 used to form the collection type c e, and not over that collection type itself,
1761 represented by ce in the original class declaration. This avoids the immediate
1762 problems that we mentioned above: empty has type <literal>Collects e c => c
1763 e</literal>, which is not ambiguous.
1766 The function f from the previous section has a more accurate type:
1768 f :: (Collects e c) => e -> e -> c e -> c e
1770 The function g from the previous section is now rejected with a type error as
1771 we would hope because the type of f does not allow the two arguments to have
1773 This, then, is an example of a multiple parameter class that does actually work
1774 quite well in practice, without ambiguity problems.
1775 There is, however, a catch. This version of the Collects class is nowhere near
1776 as general as the original class seemed to be: only one of the four instances
1777 for <literal>Collects</literal>
1778 given above can be used with this version of Collects because only one of
1779 them---the instance for lists---has a collection type that can be written in
1780 the form c e, for some type constructor c, and element type e.
1784 <sect4><title>Adding functional dependencies</title>
1787 To get a more useful version of the Collects class, Hugs provides a mechanism
1788 that allows programmers to specify dependencies between the parameters of a
1789 multiple parameter class (For readers with an interest in theoretical
1790 foundations and previous work: The use of dependency information can be seen
1791 both as a generalization of the proposal for `parametric type classes' that was
1792 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1793 later framework for "improvement" of qualified types. The
1794 underlying ideas are also discussed in a more theoretical and abstract setting
1795 in a manuscript [implparam], where they are identified as one point in a
1796 general design space for systems of implicit parameterization.).
1798 To start with an abstract example, consider a declaration such as:
1800 class C a b where ...
1802 which tells us simply that C can be thought of as a binary relation on types
1803 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1804 included in the definition of classes to add information about dependencies
1805 between parameters, as in the following examples:
1807 class D a b | a -> b where ...
1808 class E a b | a -> b, b -> a where ...
1810 The notation <literal>a -> b</literal> used here between the | and where
1811 symbols --- not to be
1812 confused with a function type --- indicates that the a parameter uniquely
1813 determines the b parameter, and might be read as "a determines b." Thus D is
1814 not just a relation, but actually a (partial) function. Similarly, from the two
1815 dependencies that are included in the definition of E, we can see that E
1816 represents a (partial) one-one mapping between types.
1819 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1820 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1821 m>=0, meaning that the y parameters are uniquely determined by the x
1822 parameters. Spaces can be used as separators if more than one variable appears
1823 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1824 annotated with multiple dependencies using commas as separators, as in the
1825 definition of E above. Some dependencies that we can write in this notation are
1826 redundant, and will be rejected because they don't serve any useful
1827 purpose, and may instead indicate an error in the program. Examples of
1828 dependencies like this include <literal>a -> a </literal>,
1829 <literal>a -> a a </literal>,
1830 <literal>a -> </literal>, etc. There can also be
1831 some redundancy if multiple dependencies are given, as in
1832 <literal>a->b</literal>,
1833 <literal>b->c </literal>, <literal>a->c </literal>, and
1834 in which some subset implies the remaining dependencies. Examples like this are
1835 not treated as errors. Note that dependencies appear only in class
1836 declarations, and not in any other part of the language. In particular, the
1837 syntax for instance declarations, class constraints, and types is completely
1841 By including dependencies in a class declaration, we provide a mechanism for
1842 the programmer to specify each multiple parameter class more precisely. The
1843 compiler, on the other hand, is responsible for ensuring that the set of
1844 instances that are in scope at any given point in the program is consistent
1845 with any declared dependencies. For example, the following pair of instance
1846 declarations cannot appear together in the same scope because they violate the
1847 dependency for D, even though either one on its own would be acceptable:
1849 instance D Bool Int where ...
1850 instance D Bool Char where ...
1852 Note also that the following declaration is not allowed, even by itself:
1854 instance D [a] b where ...
1856 The problem here is that this instance would allow one particular choice of [a]
1857 to be associated with more than one choice for b, which contradicts the
1858 dependency specified in the definition of D. More generally, this means that,
1859 in any instance of the form:
1861 instance D t s where ...
1863 for some particular types t and s, the only variables that can appear in s are
1864 the ones that appear in t, and hence, if the type t is known, then s will be
1865 uniquely determined.
1868 The benefit of including dependency information is that it allows us to define
1869 more general multiple parameter classes, without ambiguity problems, and with
1870 the benefit of more accurate types. To illustrate this, we return to the
1871 collection class example, and annotate the original definition of <literal>Collects</literal>
1872 with a simple dependency:
1874 class Collects e ce | ce -> e where
1876 insert :: e -> ce -> ce
1877 member :: e -> ce -> Bool
1879 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1880 determined by the type of the collection ce. Note that both parameters of
1881 Collects are of kind *; there are no constructor classes here. Note too that
1882 all of the instances of Collects that we gave earlier can be used
1883 together with this new definition.
1886 What about the ambiguity problems that we encountered with the original
1887 definition? The empty function still has type Collects e ce => ce, but it is no
1888 longer necessary to regard that as an ambiguous type: Although the variable e
1889 does not appear on the right of the => symbol, the dependency for class
1890 Collects tells us that it is uniquely determined by ce, which does appear on
1891 the right of the => symbol. Hence the context in which empty is used can still
1892 give enough information to determine types for both ce and e, without
1893 ambiguity. More generally, we need only regard a type as ambiguous if it
1894 contains a variable on the left of the => that is not uniquely determined
1895 (either directly or indirectly) by the variables on the right.
1898 Dependencies also help to produce more accurate types for user defined
1899 functions, and hence to provide earlier detection of errors, and less cluttered
1900 types for programmers to work with. Recall the previous definition for a
1903 f x y = insert x y = insert x . insert y
1905 for which we originally obtained a type:
1907 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1909 Given the dependency information that we have for Collects, however, we can
1910 deduce that a and b must be equal because they both appear as the second
1911 parameter in a Collects constraint with the same first parameter c. Hence we
1912 can infer a shorter and more accurate type for f:
1914 f :: (Collects a c) => a -> a -> c -> c
1916 In a similar way, the earlier definition of g will now be flagged as a type error.
1919 Although we have given only a few examples here, it should be clear that the
1920 addition of dependency information can help to make multiple parameter classes
1921 more useful in practice, avoiding ambiguity problems, and allowing more general
1922 sets of instance declarations.
1928 <sect2 id="instance-decls">
1929 <title>Instance declarations</title>
1931 <sect3 id="instance-rules">
1932 <title>Relaxed rules for instance declarations</title>
1934 <para>An instance declaration has the form
1936 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 ...
1938 The part before the "<literal>=></literal>" is the
1939 <emphasis>context</emphasis>, while the part after the
1940 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1944 In Haskell 98 the head of an instance declaration
1945 must be of the form <literal>C (T a1 ... an)</literal>, where
1946 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1947 and the <literal>a1 ... an</literal> are distinct type variables.
1948 Furthermore, the assertions in the context of the instance declaration
1949 must be of the form <literal>C a</literal> where <literal>a</literal>
1950 is a type variable that occurs in the head.
1953 The <option>-fglasgow-exts</option> flag loosens these restrictions
1954 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1955 the context and head of the instance declaration can each consist of arbitrary
1956 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1960 For each assertion in the context:
1962 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1963 <listitem><para>The assertion has fewer constructors and variables (taken together
1964 and counting repetitions) than the head</para></listitem>
1968 <listitem><para>The coverage condition. For each functional dependency,
1969 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
1970 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
1971 every type variable in
1972 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
1973 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
1974 substitution mapping each type variable in the class declaration to the
1975 corresponding type in the instance declaration.
1978 These restrictions ensure that context reduction terminates: each reduction
1979 step makes the problem smaller by at least one
1980 constructor. For example, the following would make the type checker
1981 loop if it wasn't excluded:
1983 instance C a => C a where ...
1985 For example, these are OK:
1987 instance C Int [a] -- Multiple parameters
1988 instance Eq (S [a]) -- Structured type in head
1990 -- Repeated type variable in head
1991 instance C4 a a => C4 [a] [a]
1992 instance Stateful (ST s) (MutVar s)
1994 -- Head can consist of type variables only
1996 instance (Eq a, Show b) => C2 a b
1998 -- Non-type variables in context
1999 instance Show (s a) => Show (Sized s a)
2000 instance C2 Int a => C3 Bool [a]
2001 instance C2 Int a => C3 [a] b
2005 -- Context assertion no smaller than head
2006 instance C a => C a where ...
2007 -- (C b b) has more more occurrences of b than the head
2008 instance C b b => Foo [b] where ...
2013 The same restrictions apply to instances generated by
2014 <literal>deriving</literal> clauses. Thus the following is accepted:
2016 data MinHeap h a = H a (h a)
2019 because the derived instance
2021 instance (Show a, Show (h a)) => Show (MinHeap h a)
2023 conforms to the above rules.
2027 A useful idiom permitted by the above rules is as follows.
2028 If one allows overlapping instance declarations then it's quite
2029 convenient to have a "default instance" declaration that applies if
2030 something more specific does not:
2036 <para>You can find lots of background material about the reason for these
2037 restrictions in the paper <ulink
2038 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2039 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2043 <sect3 id="undecidable-instances">
2044 <title>Undecidable instances</title>
2047 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2048 For example, sometimes you might want to use the following to get the
2049 effect of a "class synonym":
2051 class (C1 a, C2 a, C3 a) => C a where { }
2053 instance (C1 a, C2 a, C3 a) => C a where { }
2055 This allows you to write shorter signatures:
2061 f :: (C1 a, C2 a, C3 a) => ...
2063 The restrictions on functional dependencies (<xref
2064 linkend="functional-dependencies"/>) are particularly troublesome.
2065 It is tempting to introduce type variables in the context that do not appear in
2066 the head, something that is excluded by the normal rules. For example:
2068 class HasConverter a b | a -> b where
2071 data Foo a = MkFoo a
2073 instance (HasConverter a b,Show b) => Show (Foo a) where
2074 show (MkFoo value) = show (convert value)
2076 This is dangerous territory, however. Here, for example, is a program that would make the
2081 instance F [a] [[a]]
2082 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2084 Similarly, it can be tempting to lift the coverage condition:
2086 class Mul a b c | a b -> c where
2087 (.*.) :: a -> b -> c
2089 instance Mul Int Int Int where (.*.) = (*)
2090 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2091 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2093 The third instance declaration does not obey the coverage condition;
2094 and indeed the (somewhat strange) definition:
2096 f = \ b x y -> if b then x .*. [y] else y
2098 makes instance inference go into a loop, because it requires the constraint
2099 <literal>(Mul a [b] b)</literal>.
2102 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2103 the experimental flag <option>-fallow-undecidable-instances</option>
2104 <indexterm><primary>-fallow-undecidable-instances
2105 option</primary></indexterm>, you can use arbitrary
2106 types in both an instance context and instance head. Termination is ensured by having a
2107 fixed-depth recursion stack. If you exceed the stack depth you get a
2108 sort of backtrace, and the opportunity to increase the stack depth
2109 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2115 <sect3 id="instance-overlap">
2116 <title>Overlapping instances</title>
2118 In general, <emphasis>GHC requires that that it be unambiguous which instance
2120 should be used to resolve a type-class constraint</emphasis>. This behaviour
2121 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2122 <indexterm><primary>-fallow-overlapping-instances
2123 </primary></indexterm>
2124 and <option>-fallow-incoherent-instances</option>
2125 <indexterm><primary>-fallow-incoherent-instances
2126 </primary></indexterm>, as this section discusses. Both these
2127 flags are dynamic flags, and can be set on a per-module basis, using
2128 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2130 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2131 it tries to match every instance declaration against the
2133 by instantiating the head of the instance declaration. For example, consider
2136 instance context1 => C Int a where ... -- (A)
2137 instance context2 => C a Bool where ... -- (B)
2138 instance context3 => C Int [a] where ... -- (C)
2139 instance context4 => C Int [Int] where ... -- (D)
2141 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2142 but (C) and (D) do not. When matching, GHC takes
2143 no account of the context of the instance declaration
2144 (<literal>context1</literal> etc).
2145 GHC's default behaviour is that <emphasis>exactly one instance must match the
2146 constraint it is trying to resolve</emphasis>.
2147 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2148 including both declarations (A) and (B), say); an error is only reported if a
2149 particular constraint matches more than one.
2153 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2154 more than one instance to match, provided there is a most specific one. For
2155 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2156 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2157 most-specific match, the program is rejected.
2160 However, GHC is conservative about committing to an overlapping instance. For example:
2165 Suppose that from the RHS of <literal>f</literal> we get the constraint
2166 <literal>C Int [b]</literal>. But
2167 GHC does not commit to instance (C), because in a particular
2168 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2169 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2170 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2171 GHC will instead pick (C), without complaining about
2172 the problem of subsequent instantiations.
2175 The willingness to be overlapped or incoherent is a property of
2176 the <emphasis>instance declaration</emphasis> itself, controlled by the
2177 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2178 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2179 being defined. Neither flag is required in a module that imports and uses the
2180 instance declaration. Specifically, during the lookup process:
2183 An instance declaration is ignored during the lookup process if (a) a more specific
2184 match is found, and (b) the instance declaration was compiled with
2185 <option>-fallow-overlapping-instances</option>. The flag setting for the
2186 more-specific instance does not matter.
2189 Suppose an instance declaration does not matche the constraint being looked up, but
2190 does unify with it, so that it might match when the constraint is further
2191 instantiated. Usually GHC will regard this as a reason for not committing to
2192 some other constraint. But if the instance declaration was compiled with
2193 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2194 check for that declaration.
2197 These rules make it possible for a library author to design a library that relies on
2198 overlapping instances without the library client having to know.
2201 If an instance declaration is compiled without
2202 <option>-fallow-overlapping-instances</option>,
2203 then that instance can never be overlapped. This could perhaps be
2204 inconvenient. Perhaps the rule should instead say that the
2205 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2206 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2207 at a usage site should be permitted regardless of how the instance declarations
2208 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2209 used at the usage site. (Mind you, the exact usage site can occasionally be
2210 hard to pin down.) We are interested to receive feedback on these points.
2212 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2213 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2218 <title>Type synonyms in the instance head</title>
2221 <emphasis>Unlike Haskell 98, instance heads may use type
2222 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2223 As always, using a type synonym is just shorthand for
2224 writing the RHS of the type synonym definition. For example:
2228 type Point = (Int,Int)
2229 instance C Point where ...
2230 instance C [Point] where ...
2234 is legal. However, if you added
2238 instance C (Int,Int) where ...
2242 as well, then the compiler will complain about the overlapping
2243 (actually, identical) instance declarations. As always, type synonyms
2244 must be fully applied. You cannot, for example, write:
2249 instance Monad P where ...
2253 This design decision is independent of all the others, and easily
2254 reversed, but it makes sense to me.
2262 <sect2 id="type-restrictions">
2263 <title>Type signatures</title>
2265 <sect3><title>The context of a type signature</title>
2267 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2268 the form <emphasis>(class type-variable)</emphasis> or
2269 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2270 these type signatures are perfectly OK
2273 g :: Ord (T a ()) => ...
2277 GHC imposes the following restrictions on the constraints in a type signature.
2281 forall tv1..tvn (c1, ...,cn) => type
2284 (Here, we write the "foralls" explicitly, although the Haskell source
2285 language omits them; in Haskell 98, all the free type variables of an
2286 explicit source-language type signature are universally quantified,
2287 except for the class type variables in a class declaration. However,
2288 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2297 <emphasis>Each universally quantified type variable
2298 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2300 A type variable <literal>a</literal> is "reachable" if it it appears
2301 in the same constraint as either a type variable free in in
2302 <literal>type</literal>, or another reachable type variable.
2303 A value with a type that does not obey
2304 this reachability restriction cannot be used without introducing
2305 ambiguity; that is why the type is rejected.
2306 Here, for example, is an illegal type:
2310 forall a. Eq a => Int
2314 When a value with this type was used, the constraint <literal>Eq tv</literal>
2315 would be introduced where <literal>tv</literal> is a fresh type variable, and
2316 (in the dictionary-translation implementation) the value would be
2317 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2318 can never know which instance of <literal>Eq</literal> to use because we never
2319 get any more information about <literal>tv</literal>.
2323 that the reachability condition is weaker than saying that <literal>a</literal> is
2324 functionally dependent on a type variable free in
2325 <literal>type</literal> (see <xref
2326 linkend="functional-dependencies"/>). The reason for this is there
2327 might be a "hidden" dependency, in a superclass perhaps. So
2328 "reachable" is a conservative approximation to "functionally dependent".
2329 For example, consider:
2331 class C a b | a -> b where ...
2332 class C a b => D a b where ...
2333 f :: forall a b. D a b => a -> a
2335 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2336 but that is not immediately apparent from <literal>f</literal>'s type.
2342 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2343 universally quantified type variables <literal>tvi</literal></emphasis>.
2345 For example, this type is OK because <literal>C a b</literal> mentions the
2346 universally quantified type variable <literal>b</literal>:
2350 forall a. C a b => burble
2354 The next type is illegal because the constraint <literal>Eq b</literal> does not
2355 mention <literal>a</literal>:
2359 forall a. Eq b => burble
2363 The reason for this restriction is milder than the other one. The
2364 excluded types are never useful or necessary (because the offending
2365 context doesn't need to be witnessed at this point; it can be floated
2366 out). Furthermore, floating them out increases sharing. Lastly,
2367 excluding them is a conservative choice; it leaves a patch of
2368 territory free in case we need it later.
2379 <title>For-all hoisting</title>
2381 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2382 end of an arrow, thus:
2384 type Discard a = forall b. a -> b -> a
2386 g :: Int -> Discard Int
2389 Simply expanding the type synonym would give
2391 g :: Int -> (forall b. Int -> b -> Int)
2393 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2395 g :: forall b. Int -> Int -> b -> Int
2397 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2398 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2399 performs the transformation:</emphasis>
2401 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2403 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2405 (In fact, GHC tries to retain as much synonym information as possible for use in
2406 error messages, but that is a usability issue.) This rule applies, of course, whether
2407 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2408 valid way to write <literal>g</literal>'s type signature:
2410 g :: Int -> Int -> forall b. b -> Int
2414 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2417 type Foo a = (?x::Int) => Bool -> a
2422 g :: (?x::Int) => Bool -> Bool -> Int
2430 <sect2 id="implicit-parameters">
2431 <title>Implicit parameters</title>
2433 <para> Implicit parameters are implemented as described in
2434 "Implicit parameters: dynamic scoping with static types",
2435 J Lewis, MB Shields, E Meijer, J Launchbury,
2436 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2440 <para>(Most of the following, stil rather incomplete, documentation is
2441 due to Jeff Lewis.)</para>
2443 <para>Implicit parameter support is enabled with the option
2444 <option>-fimplicit-params</option>.</para>
2447 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2448 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2449 context. In Haskell, all variables are statically bound. Dynamic
2450 binding of variables is a notion that goes back to Lisp, but was later
2451 discarded in more modern incarnations, such as Scheme. Dynamic binding
2452 can be very confusing in an untyped language, and unfortunately, typed
2453 languages, in particular Hindley-Milner typed languages like Haskell,
2454 only support static scoping of variables.
2457 However, by a simple extension to the type class system of Haskell, we
2458 can support dynamic binding. Basically, we express the use of a
2459 dynamically bound variable as a constraint on the type. These
2460 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2461 function uses a dynamically-bound variable <literal>?x</literal>
2462 of type <literal>t'</literal>". For
2463 example, the following expresses the type of a sort function,
2464 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2466 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2468 The dynamic binding constraints are just a new form of predicate in the type class system.
2471 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2472 where <literal>x</literal> is
2473 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2474 Use of this construct also introduces a new
2475 dynamic-binding constraint in the type of the expression.
2476 For example, the following definition
2477 shows how we can define an implicitly parameterized sort function in
2478 terms of an explicitly parameterized <literal>sortBy</literal> function:
2480 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2482 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2488 <title>Implicit-parameter type constraints</title>
2490 Dynamic binding constraints behave just like other type class
2491 constraints in that they are automatically propagated. Thus, when a
2492 function is used, its implicit parameters are inherited by the
2493 function that called it. For example, our <literal>sort</literal> function might be used
2494 to pick out the least value in a list:
2496 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2497 least xs = head (sort xs)
2499 Without lifting a finger, the <literal>?cmp</literal> parameter is
2500 propagated to become a parameter of <literal>least</literal> as well. With explicit
2501 parameters, the default is that parameters must always be explicit
2502 propagated. With implicit parameters, the default is to always
2506 An implicit-parameter type constraint differs from other type class constraints in the
2507 following way: All uses of a particular implicit parameter must have
2508 the same type. This means that the type of <literal>(?x, ?x)</literal>
2509 is <literal>(?x::a) => (a,a)</literal>, and not
2510 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2514 <para> You can't have an implicit parameter in the context of a class or instance
2515 declaration. For example, both these declarations are illegal:
2517 class (?x::Int) => C a where ...
2518 instance (?x::a) => Foo [a] where ...
2520 Reason: exactly which implicit parameter you pick up depends on exactly where
2521 you invoke a function. But the ``invocation'' of instance declarations is done
2522 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2523 Easiest thing is to outlaw the offending types.</para>
2525 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2527 f :: (?x :: [a]) => Int -> Int
2530 g :: (Read a, Show a) => String -> String
2533 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2534 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2535 quite unambiguous, and fixes the type <literal>a</literal>.
2540 <title>Implicit-parameter bindings</title>
2543 An implicit parameter is <emphasis>bound</emphasis> using the standard
2544 <literal>let</literal> or <literal>where</literal> binding forms.
2545 For example, we define the <literal>min</literal> function by binding
2546 <literal>cmp</literal>.
2549 min = let ?cmp = (<=) in least
2553 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2554 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2555 (including in a list comprehension, or do-notation, or pattern guards),
2556 or a <literal>where</literal> clause.
2557 Note the following points:
2560 An implicit-parameter binding group must be a
2561 collection of simple bindings to implicit-style variables (no
2562 function-style bindings, and no type signatures); these bindings are
2563 neither polymorphic or recursive.
2566 You may not mix implicit-parameter bindings with ordinary bindings in a
2567 single <literal>let</literal>
2568 expression; use two nested <literal>let</literal>s instead.
2569 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2573 You may put multiple implicit-parameter bindings in a
2574 single binding group; but they are <emphasis>not</emphasis> treated
2575 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2576 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2577 parameter. The bindings are not nested, and may be re-ordered without changing
2578 the meaning of the program.
2579 For example, consider:
2581 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2583 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2584 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2586 f :: (?x::Int) => Int -> Int
2594 <sect3><title>Implicit parameters and polymorphic recursion</title>
2597 Consider these two definitions:
2600 len1 xs = let ?acc = 0 in len_acc1 xs
2603 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2608 len2 xs = let ?acc = 0 in len_acc2 xs
2610 len_acc2 :: (?acc :: Int) => [a] -> Int
2612 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2614 The only difference between the two groups is that in the second group
2615 <literal>len_acc</literal> is given a type signature.
2616 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2617 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2618 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2619 has a type signature, the recursive call is made to the
2620 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2621 as an implicit parameter. So we get the following results in GHCi:
2628 Adding a type signature dramatically changes the result! This is a rather
2629 counter-intuitive phenomenon, worth watching out for.
2633 <sect3><title>Implicit parameters and monomorphism</title>
2635 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2636 Haskell Report) to implicit parameters. For example, consider:
2644 Since the binding for <literal>y</literal> falls under the Monomorphism
2645 Restriction it is not generalised, so the type of <literal>y</literal> is
2646 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2647 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2648 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2649 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2650 <literal>y</literal> in the body of the <literal>let</literal> will see the
2651 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2652 <literal>14</literal>.
2657 <!-- ======================= COMMENTED OUT ========================
2659 We intend to remove linear implicit parameters, so I'm at least removing
2660 them from the 6.6 user manual
2662 <sect2 id="linear-implicit-parameters">
2663 <title>Linear implicit parameters</title>
2665 Linear implicit parameters are an idea developed by Koen Claessen,
2666 Mark Shields, and Simon PJ. They address the long-standing
2667 problem that monads seem over-kill for certain sorts of problem, notably:
2670 <listitem> <para> distributing a supply of unique names </para> </listitem>
2671 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2672 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2676 Linear implicit parameters are just like ordinary implicit parameters,
2677 except that they are "linear"; that is, they cannot be copied, and
2678 must be explicitly "split" instead. Linear implicit parameters are
2679 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2680 (The '/' in the '%' suggests the split!)
2685 import GHC.Exts( Splittable )
2687 data NameSupply = ...
2689 splitNS :: NameSupply -> (NameSupply, NameSupply)
2690 newName :: NameSupply -> Name
2692 instance Splittable NameSupply where
2696 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2697 f env (Lam x e) = Lam x' (f env e)
2700 env' = extend env x x'
2701 ...more equations for f...
2703 Notice that the implicit parameter %ns is consumed
2705 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2706 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2710 So the translation done by the type checker makes
2711 the parameter explicit:
2713 f :: NameSupply -> Env -> Expr -> Expr
2714 f ns env (Lam x e) = Lam x' (f ns1 env e)
2716 (ns1,ns2) = splitNS ns
2718 env = extend env x x'
2720 Notice the call to 'split' introduced by the type checker.
2721 How did it know to use 'splitNS'? Because what it really did
2722 was to introduce a call to the overloaded function 'split',
2723 defined by the class <literal>Splittable</literal>:
2725 class Splittable a where
2728 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2729 split for name supplies. But we can simply write
2735 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2737 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2738 <literal>GHC.Exts</literal>.
2743 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2744 are entirely distinct implicit parameters: you
2745 can use them together and they won't intefere with each other. </para>
2748 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2750 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2751 in the context of a class or instance declaration. </para></listitem>
2755 <sect3><title>Warnings</title>
2758 The monomorphism restriction is even more important than usual.
2759 Consider the example above:
2761 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2762 f env (Lam x e) = Lam x' (f env e)
2765 env' = extend env x x'
2767 If we replaced the two occurrences of x' by (newName %ns), which is
2768 usually a harmless thing to do, we get:
2770 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2771 f env (Lam x e) = Lam (newName %ns) (f env e)
2773 env' = extend env x (newName %ns)
2775 But now the name supply is consumed in <emphasis>three</emphasis> places
2776 (the two calls to newName,and the recursive call to f), so
2777 the result is utterly different. Urk! We don't even have
2781 Well, this is an experimental change. With implicit
2782 parameters we have already lost beta reduction anyway, and
2783 (as John Launchbury puts it) we can't sensibly reason about
2784 Haskell programs without knowing their typing.
2789 <sect3><title>Recursive functions</title>
2790 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2793 foo :: %x::T => Int -> [Int]
2795 foo n = %x : foo (n-1)
2797 where T is some type in class Splittable.</para>
2799 Do you get a list of all the same T's or all different T's
2800 (assuming that split gives two distinct T's back)?
2802 If you supply the type signature, taking advantage of polymorphic
2803 recursion, you get what you'd probably expect. Here's the
2804 translated term, where the implicit param is made explicit:
2807 foo x n = let (x1,x2) = split x
2808 in x1 : foo x2 (n-1)
2810 But if you don't supply a type signature, GHC uses the Hindley
2811 Milner trick of using a single monomorphic instance of the function
2812 for the recursive calls. That is what makes Hindley Milner type inference
2813 work. So the translation becomes
2817 foom n = x : foom (n-1)
2821 Result: 'x' is not split, and you get a list of identical T's. So the
2822 semantics of the program depends on whether or not foo has a type signature.
2825 You may say that this is a good reason to dislike linear implicit parameters
2826 and you'd be right. That is why they are an experimental feature.
2832 ================ END OF Linear Implicit Parameters commented out -->
2834 <sect2 id="sec-kinding">
2835 <title>Explicitly-kinded quantification</title>
2838 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2839 to give the kind explicitly as (machine-checked) documentation,
2840 just as it is nice to give a type signature for a function. On some occasions,
2841 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2842 John Hughes had to define the data type:
2844 data Set cxt a = Set [a]
2845 | Unused (cxt a -> ())
2847 The only use for the <literal>Unused</literal> constructor was to force the correct
2848 kind for the type variable <literal>cxt</literal>.
2851 GHC now instead allows you to specify the kind of a type variable directly, wherever
2852 a type variable is explicitly bound. Namely:
2854 <listitem><para><literal>data</literal> declarations:
2856 data Set (cxt :: * -> *) a = Set [a]
2857 </screen></para></listitem>
2858 <listitem><para><literal>type</literal> declarations:
2860 type T (f :: * -> *) = f Int
2861 </screen></para></listitem>
2862 <listitem><para><literal>class</literal> declarations:
2864 class (Eq a) => C (f :: * -> *) a where ...
2865 </screen></para></listitem>
2866 <listitem><para><literal>forall</literal>'s in type signatures:
2868 f :: forall (cxt :: * -> *). Set cxt Int
2869 </screen></para></listitem>
2874 The parentheses are required. Some of the spaces are required too, to
2875 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2876 will get a parse error, because "<literal>::*->*</literal>" is a
2877 single lexeme in Haskell.
2881 As part of the same extension, you can put kind annotations in types
2884 f :: (Int :: *) -> Int
2885 g :: forall a. a -> (a :: *)
2889 atype ::= '(' ctype '::' kind ')
2891 The parentheses are required.
2896 <sect2 id="universal-quantification">
2897 <title>Arbitrary-rank polymorphism
2901 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2902 allows us to say exactly what this means. For example:
2910 g :: forall b. (b -> b)
2912 The two are treated identically.
2916 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2917 explicit universal quantification in
2919 For example, all the following types are legal:
2921 f1 :: forall a b. a -> b -> a
2922 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2924 f2 :: (forall a. a->a) -> Int -> Int
2925 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2927 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2929 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2930 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2931 The <literal>forall</literal> makes explicit the universal quantification that
2932 is implicitly added by Haskell.
2935 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2936 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2937 shows, the polymorphic type on the left of the function arrow can be overloaded.
2940 The function <literal>f3</literal> has a rank-3 type;
2941 it has rank-2 types on the left of a function arrow.
2944 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2945 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2946 that restriction has now been lifted.)
2947 In particular, a forall-type (also called a "type scheme"),
2948 including an operational type class context, is legal:
2950 <listitem> <para> On the left of a function arrow </para> </listitem>
2951 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2952 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2953 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2954 field type signatures.</para> </listitem>
2955 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2956 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2958 There is one place you cannot put a <literal>forall</literal>:
2959 you cannot instantiate a type variable with a forall-type. So you cannot
2960 make a forall-type the argument of a type constructor. So these types are illegal:
2962 x1 :: [forall a. a->a]
2963 x2 :: (forall a. a->a, Int)
2964 x3 :: Maybe (forall a. a->a)
2966 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2967 a type variable any more!
2976 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2977 the types of the constructor arguments. Here are several examples:
2983 data T a = T1 (forall b. b -> b -> b) a
2985 data MonadT m = MkMonad { return :: forall a. a -> m a,
2986 bind :: forall a b. m a -> (a -> m b) -> m b
2989 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2995 The constructors have rank-2 types:
3001 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3002 MkMonad :: forall m. (forall a. a -> m a)
3003 -> (forall a b. m a -> (a -> m b) -> m b)
3005 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3011 Notice that you don't need to use a <literal>forall</literal> if there's an
3012 explicit context. For example in the first argument of the
3013 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3014 prefixed to the argument type. The implicit <literal>forall</literal>
3015 quantifies all type variables that are not already in scope, and are
3016 mentioned in the type quantified over.
3020 As for type signatures, implicit quantification happens for non-overloaded
3021 types too. So if you write this:
3024 data T a = MkT (Either a b) (b -> b)
3027 it's just as if you had written this:
3030 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3033 That is, since the type variable <literal>b</literal> isn't in scope, it's
3034 implicitly universally quantified. (Arguably, it would be better
3035 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3036 where that is what is wanted. Feedback welcomed.)
3040 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3041 the constructor to suitable values, just as usual. For example,
3052 a3 = MkSwizzle reverse
3055 a4 = let r x = Just x
3062 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3063 mkTs f x y = [T1 f x, T1 f y]
3069 The type of the argument can, as usual, be more general than the type
3070 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3071 does not need the <literal>Ord</literal> constraint.)
3075 When you use pattern matching, the bound variables may now have
3076 polymorphic types. For example:
3082 f :: T a -> a -> (a, Char)
3083 f (T1 w k) x = (w k x, w 'c' 'd')
3085 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3086 g (MkSwizzle s) xs f = s (map f (s xs))
3088 h :: MonadT m -> [m a] -> m [a]
3089 h m [] = return m []
3090 h m (x:xs) = bind m x $ \y ->
3091 bind m (h m xs) $ \ys ->
3098 In the function <function>h</function> we use the record selectors <literal>return</literal>
3099 and <literal>bind</literal> to extract the polymorphic bind and return functions
3100 from the <literal>MonadT</literal> data structure, rather than using pattern
3106 <title>Type inference</title>
3109 In general, type inference for arbitrary-rank types is undecidable.
3110 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3111 to get a decidable algorithm by requiring some help from the programmer.
3112 We do not yet have a formal specification of "some help" but the rule is this:
3115 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3116 provides an explicit polymorphic type for x, or GHC's type inference will assume
3117 that x's type has no foralls in it</emphasis>.
3120 What does it mean to "provide" an explicit type for x? You can do that by
3121 giving a type signature for x directly, using a pattern type signature
3122 (<xref linkend="scoped-type-variables"/>), thus:
3124 \ f :: (forall a. a->a) -> (f True, f 'c')
3126 Alternatively, you can give a type signature to the enclosing
3127 context, which GHC can "push down" to find the type for the variable:
3129 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3131 Here the type signature on the expression can be pushed inwards
3132 to give a type signature for f. Similarly, and more commonly,
3133 one can give a type signature for the function itself:
3135 h :: (forall a. a->a) -> (Bool,Char)
3136 h f = (f True, f 'c')
3138 You don't need to give a type signature if the lambda bound variable
3139 is a constructor argument. Here is an example we saw earlier:
3141 f :: T a -> a -> (a, Char)
3142 f (T1 w k) x = (w k x, w 'c' 'd')
3144 Here we do not need to give a type signature to <literal>w</literal>, because
3145 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3152 <sect3 id="implicit-quant">
3153 <title>Implicit quantification</title>
3156 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3157 user-written types, if and only if there is no explicit <literal>forall</literal>,
3158 GHC finds all the type variables mentioned in the type that are not already
3159 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3163 f :: forall a. a -> a
3170 h :: forall b. a -> b -> b
3176 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3179 f :: (a -> a) -> Int
3181 f :: forall a. (a -> a) -> Int
3183 f :: (forall a. a -> a) -> Int
3186 g :: (Ord a => a -> a) -> Int
3187 -- MEANS the illegal type
3188 g :: forall a. (Ord a => a -> a) -> Int
3190 g :: (forall a. Ord a => a -> a) -> Int
3192 The latter produces an illegal type, which you might think is silly,
3193 but at least the rule is simple. If you want the latter type, you
3194 can write your for-alls explicitly. Indeed, doing so is strongly advised
3203 <sect2 id="scoped-type-variables">
3204 <title>Scoped type variables
3208 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3210 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3211 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3212 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
3216 f (xs::[a]) = ys ++ ys
3221 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
3222 This brings the type variable <literal>a</literal> into scope; it scopes over
3223 all the patterns and right hand sides for this equation for <function>f</function>.
3224 In particular, it is in scope at the type signature for <varname>y</varname>.
3228 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
3229 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
3230 implicitly universally quantified. (If there are no type variables in
3231 scope, all type variables mentioned in the signature are universally
3232 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
3233 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
3234 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
3235 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3236 it becomes possible to do so.
3240 Scoped type variables are implemented in both GHC and Hugs. Where the
3241 implementations differ from the specification below, those differences
3246 So much for the basic idea. Here are the details.
3250 <title>What a scoped type variable means</title>
3252 A lexically-scoped type variable is simply
3253 the name for a type. The restriction it expresses is that all occurrences
3254 of the same name mean the same type. For example:
3256 f :: [Int] -> Int -> Int
3257 f (xs::[a]) (y::a) = (head xs + y) :: a
3259 The pattern type signatures on the left hand side of
3260 <literal>f</literal> express the fact that <literal>xs</literal>
3261 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
3262 must have this same type. The type signature on the expression <literal>(head xs)</literal>
3263 specifies that this expression must have the same type <literal>a</literal>.
3264 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
3265 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
3266 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
3267 rules, which specified that a pattern-bound type variable should be universally quantified.)
3268 For example, all of these are legal:</para>
3271 t (x::a) (y::a) = x+y*2
3273 f (x::a) (y::b) = [x,y] -- a unifies with b
3275 g (x::a) = x + 1::Int -- a unifies with Int
3277 h x = let k (y::a) = [x,y] -- a is free in the
3278 in k x -- environment
3280 k (x::a) True = ... -- a unifies with Int
3281 k (x::Int) False = ...
3284 w (x::a) = x -- a unifies with [b]
3290 <title>Scope and implicit quantification</title>
3298 All the type variables mentioned in a pattern,
3299 that are not already in scope,
3300 are brought into scope by the pattern. We describe this set as
3301 the <emphasis>type variables bound by the pattern</emphasis>.
3304 f (x::a) = let g (y::(a,b)) = fst y
3308 The pattern <literal>(x::a)</literal> brings the type variable
3309 <literal>a</literal> into scope, as well as the term
3310 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
3311 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
3312 and brings into scope the type variable <literal>b</literal>.
3318 The type variable(s) bound by the pattern have the same scope
3319 as the term variable(s) bound by the pattern. For example:
3322 f (x::a) = <...rhs of f...>
3323 (p::b, q::b) = (1,2)
3324 in <...body of let...>
3326 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3327 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3328 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3329 just like <literal>p</literal> and <literal>q</literal> do.
3330 Indeed, the newly bound type variables also scope over any ordinary, separate
3331 type signatures in the <literal>let</literal> group.
3338 The type variables bound by the pattern may be
3339 mentioned in ordinary type signatures or pattern
3340 type signatures anywhere within their scope.
3347 In ordinary type signatures, any type variable mentioned in the
3348 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3356 Ordinary type signatures do not bring any new type variables
3357 into scope (except in the type signature itself!). So this is illegal:
3364 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3365 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3366 and that is an incorrect typing.
3373 The pattern type signature is a monotype:
3378 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3382 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3383 not to type schemes.
3387 There is no implicit universal quantification on pattern type signatures (in contrast to
3388 ordinary type signatures).
3398 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3399 scope over the methods defined in the <literal>where</literal> part. For example:
3413 (Not implemented in Hugs yet, Dec 98).
3423 <sect3 id="decl-type-sigs">
3424 <title>Declaration type signatures</title>
3425 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3426 quantification (using <literal>forall</literal>) brings into scope the
3427 explicitly-quantified
3428 type variables, in the definition of the named function(s). For example:
3430 f :: forall a. [a] -> [a]
3431 f (x:xs) = xs ++ [ x :: a ]
3433 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3434 the definition of "<literal>f</literal>".
3436 <para>This only happens if the quantification in <literal>f</literal>'s type
3437 signature is explicit. For example:
3440 g (x:xs) = xs ++ [ x :: a ]
3442 This program will be rejected, because "<literal>a</literal>" does not scope
3443 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3444 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3445 quantification rules.
3449 <sect3 id="pattern-type-sigs">
3450 <title>Where a pattern type signature can occur</title>
3453 A pattern type signature can occur in any pattern. For example:
3458 A pattern type signature can be on an arbitrary sub-pattern, not
3463 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3472 Pattern type signatures, including the result part, can be used
3473 in lambda abstractions:
3476 (\ (x::a, y) :: a -> x)
3483 Pattern type signatures, including the result part, can be used
3484 in <literal>case</literal> expressions:
3487 case e of { ((x::a, y) :: (a,b)) -> x }
3490 Note that the <literal>-></literal> symbol in a case alternative
3491 leads to difficulties when parsing a type signature in the pattern: in
3492 the absence of the extra parentheses in the example above, the parser
3493 would try to interpret the <literal>-></literal> as a function
3494 arrow and give a parse error later.
3502 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3503 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3504 token or a parenthesised type of some sort). To see why,
3505 consider how one would parse this:
3519 Pattern type signatures can bind existential type variables.
3524 data T = forall a. MkT [a]
3527 f (MkT [t::a]) = MkT t3
3540 Pattern type signatures
3541 can be used in pattern bindings:
3544 f x = let (y, z::a) = x in ...
3545 f1 x = let (y, z::Int) = x in ...
3546 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3547 f3 :: (b->b) = \x -> x
3550 In all such cases, the binding is not generalised over the pattern-bound
3551 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3552 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3553 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3554 In contrast, the binding
3559 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3560 in <literal>f4</literal>'s scope.
3566 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3567 type signatures. The two can be used independently or together.</para>
3571 <sect3 id="result-type-sigs">
3572 <title>Result type signatures</title>
3575 The result type of a function can be given a signature, thus:
3579 f (x::a) :: [a] = [x,x,x]
3583 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3584 result type. Sometimes this is the only way of naming the type variable
3589 f :: Int -> [a] -> [a]
3590 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3591 in \xs -> map g (reverse xs `zip` xs)
3596 The type variables bound in a result type signature scope over the right hand side
3597 of the definition. However, consider this corner-case:
3599 rev1 :: [a] -> [a] = \xs -> reverse xs
3601 foo ys = rev (ys::[a])
3603 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3604 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3605 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3606 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3607 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3610 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3611 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3615 rev1 :: [a] -> [a] = \xs -> reverse xs
3620 Result type signatures are not yet implemented in Hugs.
3627 <sect2 id="deriving-typeable">
3628 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3631 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3632 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3633 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3634 classes <literal>Eq</literal>, <literal>Ord</literal>,
3635 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3638 GHC extends this list with two more classes that may be automatically derived
3639 (provided the <option>-fglasgow-exts</option> flag is specified):
3640 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3641 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3642 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3644 <para>An instance of <literal>Typeable</literal> can only be derived if the
3645 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3646 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3648 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3649 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3651 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3652 are used, and only <literal>Typeable1</literal> up to
3653 <literal>Typeable7</literal> are provided in the library.)
3654 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3655 class, whose kind suits that of the data type constructor, and
3656 then writing the data type instance by hand.
3660 <sect2 id="newtype-deriving">
3661 <title>Generalised derived instances for newtypes</title>
3664 When you define an abstract type using <literal>newtype</literal>, you may want
3665 the new type to inherit some instances from its representation. In
3666 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3667 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3668 other classes you have to write an explicit instance declaration. For
3669 example, if you define
3672 newtype Dollars = Dollars Int
3675 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3676 explicitly define an instance of <literal>Num</literal>:
3679 instance Num Dollars where
3680 Dollars a + Dollars b = Dollars (a+b)
3683 All the instance does is apply and remove the <literal>newtype</literal>
3684 constructor. It is particularly galling that, since the constructor
3685 doesn't appear at run-time, this instance declaration defines a
3686 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3687 dictionary, only slower!
3691 <sect3> <title> Generalising the deriving clause </title>
3693 GHC now permits such instances to be derived instead, so one can write
3695 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3698 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3699 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3700 derives an instance declaration of the form
3703 instance Num Int => Num Dollars
3706 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3710 We can also derive instances of constructor classes in a similar
3711 way. For example, suppose we have implemented state and failure monad
3712 transformers, such that
3715 instance Monad m => Monad (State s m)
3716 instance Monad m => Monad (Failure m)
3718 In Haskell 98, we can define a parsing monad by
3720 type Parser tok m a = State [tok] (Failure m) a
3723 which is automatically a monad thanks to the instance declarations
3724 above. With the extension, we can make the parser type abstract,
3725 without needing to write an instance of class <literal>Monad</literal>, via
3728 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3731 In this case the derived instance declaration is of the form
3733 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3736 Notice that, since <literal>Monad</literal> is a constructor class, the
3737 instance is a <emphasis>partial application</emphasis> of the new type, not the
3738 entire left hand side. We can imagine that the type declaration is
3739 ``eta-converted'' to generate the context of the instance
3744 We can even derive instances of multi-parameter classes, provided the
3745 newtype is the last class parameter. In this case, a ``partial
3746 application'' of the class appears in the <literal>deriving</literal>
3747 clause. For example, given the class
3750 class StateMonad s m | m -> s where ...
3751 instance Monad m => StateMonad s (State s m) where ...
3753 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3755 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3756 deriving (Monad, StateMonad [tok])
3759 The derived instance is obtained by completing the application of the
3760 class to the new type:
3763 instance StateMonad [tok] (State [tok] (Failure m)) =>
3764 StateMonad [tok] (Parser tok m)
3769 As a result of this extension, all derived instances in newtype
3770 declarations are treated uniformly (and implemented just by reusing
3771 the dictionary for the representation type), <emphasis>except</emphasis>
3772 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3773 the newtype and its representation.
3777 <sect3> <title> A more precise specification </title>
3779 Derived instance declarations are constructed as follows. Consider the
3780 declaration (after expansion of any type synonyms)
3783 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3789 The type <literal>t</literal> is an arbitrary type
3792 The <literal>vk+1...vn</literal> are type variables which do not occur in
3793 <literal>t</literal>, and
3796 The <literal>ci</literal> are partial applications of
3797 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3798 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3801 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3802 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3803 should not "look through" the type or its constructor. You can still
3804 derive these classes for a newtype, but it happens in the usual way, not
3805 via this new mechanism.
3808 Then, for each <literal>ci</literal>, the derived instance
3811 instance ci (t vk+1...v) => ci (T v1...vp)
3813 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3814 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3818 As an example which does <emphasis>not</emphasis> work, consider
3820 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3822 Here we cannot derive the instance
3824 instance Monad (State s m) => Monad (NonMonad m)
3827 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3828 and so cannot be "eta-converted" away. It is a good thing that this
3829 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3830 not, in fact, a monad --- for the same reason. Try defining
3831 <literal>>>=</literal> with the correct type: you won't be able to.
3835 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3836 important, since we can only derive instances for the last one. If the
3837 <literal>StateMonad</literal> class above were instead defined as
3840 class StateMonad m s | m -> s where ...
3843 then we would not have been able to derive an instance for the
3844 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3845 classes usually have one "main" parameter for which deriving new
3846 instances is most interesting.
3848 <para>Lastly, all of this applies only for classes other than
3849 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3850 and <literal>Data</literal>, for which the built-in derivation applies (section
3851 4.3.3. of the Haskell Report).
3852 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3853 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3854 the standard method is used or the one described here.)
3860 <sect2 id="typing-binds">
3861 <title>Generalised typing of mutually recursive bindings</title>
3864 The Haskell Report specifies that a group of bindings (at top level, or in a
3865 <literal>let</literal> or <literal>where</literal>) should be sorted into
3866 strongly-connected components, and then type-checked in dependency order
3867 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3868 Report, Section 4.5.1</ulink>).
3869 As each group is type-checked, any binders of the group that
3871 an explicit type signature are put in the type environment with the specified
3873 and all others are monomorphic until the group is generalised
3874 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3877 <para>Following a suggestion of Mark Jones, in his paper
3878 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3880 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3882 <emphasis>the dependency analysis ignores references to variables that have an explicit
3883 type signature</emphasis>.
3884 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3885 typecheck. For example, consider:
3887 f :: Eq a => a -> Bool
3888 f x = (x == x) || g True || g "Yes"
3890 g y = (y <= y) || f True
3892 This is rejected by Haskell 98, but under Jones's scheme the definition for
3893 <literal>g</literal> is typechecked first, separately from that for
3894 <literal>f</literal>,
3895 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3896 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3897 type is generalised, to get
3899 g :: Ord a => a -> Bool
3901 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3902 <literal>g</literal> in the type environment.
3906 The same refined dependency analysis also allows the type signatures of
3907 mutually-recursive functions to have different contexts, something that is illegal in
3908 Haskell 98 (Section 4.5.2, last sentence). With
3909 <option>-fglasgow-exts</option>
3910 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3911 type signatures; in practice this means that only variables bound by the same
3912 pattern binding must have the same context. For example, this is fine:
3914 f :: Eq a => a -> Bool
3915 f x = (x == x) || g True
3917 g :: Ord a => a -> Bool
3918 g y = (y <= y) || f True
3924 <!-- ==================== End of type system extensions ================= -->
3926 <!-- ====================== Generalised algebraic data types ======================= -->
3929 <title>Generalised Algebraic Data Types</title>
3931 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3932 to give the type signatures of constructors explicitly. For example:
3935 Lit :: Int -> Term Int
3936 Succ :: Term Int -> Term Int
3937 IsZero :: Term Int -> Term Bool
3938 If :: Term Bool -> Term a -> Term a -> Term a
3939 Pair :: Term a -> Term b -> Term (a,b)
3941 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3942 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3943 for these <literal>Terms</literal>:
3947 eval (Succ t) = 1 + eval t
3948 eval (IsZero t) = eval t == 0
3949 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3950 eval (Pair e1 e2) = (eval e1, eval e2)
3952 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3954 <para> The extensions to GHC are these:
3957 Data type declarations have a 'where' form, as exemplified above. The type signature of
3958 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3959 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3960 have no scope. Indeed, one can write a kind signature instead:
3962 data Term :: * -> * where ...
3964 or even a mixture of the two:
3966 data Foo a :: (* -> *) -> * where ...
3968 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3971 data Foo a (b :: * -> *) where ...
3976 There are no restrictions on the type of the data constructor, except that the result
3977 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3978 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3982 You can use record syntax on a GADT-style data type declaration:
3986 Lit { val :: Int } :: Term Int
3987 Succ { num :: Term Int } :: Term Int
3988 Pred { num :: Term Int } :: Term Int
3989 IsZero { arg :: Term Int } :: Term Bool
3990 Pair { arg1 :: Term a
3993 If { cnd :: Term Bool
3998 For every constructor that has a field <literal>f</literal>, (a) the type of
3999 field <literal>f</literal> must be the same; and (b) the
4000 result type of the constructor must be the same; both modulo alpha conversion.
4001 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
4003 single name. Although their field types are both <literal>Term Int</literal>,
4004 their selector functions actually have different types:
4007 num :: Term Int -> Term Int
4008 arg :: Term Bool -> Term Int
4011 At the moment, record updates are not yet possible with GADT, so support is
4012 limited to record construction, selection and pattern matching:
4015 someTerm :: Term Bool
4016 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
4019 eval Lit { val = i } = i
4020 eval Succ { num = t } = eval t + 1
4021 eval Pred { num = t } = eval t - 1
4022 eval IsZero { arg = t } = eval t == 0
4023 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
4024 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
4030 You can use strictness annotations, in the obvious places
4031 in the constructor type:
4034 Lit :: !Int -> Term Int
4035 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
4036 Pair :: Term a -> Term b -> Term (a,b)
4041 You can use a <literal>deriving</literal> clause on a GADT-style data type
4042 declaration, but only if the data type could also have been declared in
4043 Haskell-98 syntax. For example, these two declarations are equivalent
4045 data Maybe1 a where {
4046 Nothing1 :: Maybe a ;
4047 Just1 :: a -> Maybe a
4048 } deriving( Eq, Ord )
4050 data Maybe2 a = Nothing2 | Just2 a
4053 This simply allows you to declare a vanilla Haskell-98 data type using the
4054 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
4058 Pattern matching causes type refinement. For example, in the right hand side of the equation
4063 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
4064 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
4065 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
4067 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
4068 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
4069 occur. However, the refinement is quite general. For example, if we had:
4071 eval :: Term a -> a -> a
4072 eval (Lit i) j = i+j
4074 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
4075 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
4076 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
4082 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
4084 data T a = forall b. MkT b (b->a)
4085 data T' a where { MKT :: b -> (b->a) -> T' a }
4090 <!-- ====================== End of Generalised algebraic data types ======================= -->
4092 <!-- ====================== TEMPLATE HASKELL ======================= -->
4094 <sect1 id="template-haskell">
4095 <title>Template Haskell</title>
4097 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
4098 Template Haskell at <ulink url="http://www.haskell.org/th/">
4099 http://www.haskell.org/th/</ulink>, while
4101 the main technical innovations is discussed in "<ulink
4102 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4103 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4104 The details of the Template Haskell design are still in flux. Make sure you
4105 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
4106 (search for the type ExpQ).
4107 [Temporary: many changes to the original design are described in
4108 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4109 Not all of these changes are in GHC 6.2.]
4112 <para> The first example from that paper is set out below as a worked example to help get you started.
4116 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4117 Tim Sheard is going to expand it.)
4121 <title>Syntax</title>
4123 <para> Template Haskell has the following new syntactic
4124 constructions. You need to use the flag
4125 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4126 </indexterm>to switch these syntactic extensions on
4127 (<option>-fth</option> is no longer implied by
4128 <option>-fglasgow-exts</option>).</para>
4132 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4133 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4134 There must be no space between the "$" and the identifier or parenthesis. This use
4135 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4136 of "." as an infix operator. If you want the infix operator, put spaces around it.
4138 <para> A splice can occur in place of
4140 <listitem><para> an expression; the spliced expression must
4141 have type <literal>Q Exp</literal></para></listitem>
4142 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4143 <listitem><para> [Planned, but not implemented yet.] a
4144 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4146 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4147 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4153 A expression quotation is written in Oxford brackets, thus:
4155 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4156 the quotation has type <literal>Expr</literal>.</para></listitem>
4157 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4158 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4159 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4160 the quotation has type <literal>Type</literal>.</para></listitem>
4161 </itemizedlist></para></listitem>
4164 Reification is written thus:
4166 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4167 has type <literal>Dec</literal>. </para></listitem>
4168 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4169 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4170 <listitem><para> Still to come: fixities </para></listitem>
4172 </itemizedlist></para>
4179 <sect2> <title> Using Template Haskell </title>
4183 The data types and monadic constructor functions for Template Haskell are in the library
4184 <literal>Language.Haskell.THSyntax</literal>.
4188 You can only run a function at compile time if it is imported from another module. That is,
4189 you can't define a function in a module, and call it from within a splice in the same module.
4190 (It would make sense to do so, but it's hard to implement.)
4194 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4197 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4198 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4199 compiles and runs a program, and then looks at the result. So it's important that
4200 the program it compiles produces results whose representations are identical to
4201 those of the compiler itself.
4205 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4206 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4211 <sect2> <title> A Template Haskell Worked Example </title>
4212 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4213 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4220 -- Import our template "pr"
4221 import Printf ( pr )
4223 -- The splice operator $ takes the Haskell source code
4224 -- generated at compile time by "pr" and splices it into
4225 -- the argument of "putStrLn".
4226 main = putStrLn ( $(pr "Hello") )
4232 -- Skeletal printf from the paper.
4233 -- It needs to be in a separate module to the one where
4234 -- you intend to use it.
4236 -- Import some Template Haskell syntax
4237 import Language.Haskell.TH
4239 -- Describe a format string
4240 data Format = D | S | L String
4242 -- Parse a format string. This is left largely to you
4243 -- as we are here interested in building our first ever
4244 -- Template Haskell program and not in building printf.
4245 parse :: String -> [Format]
4248 -- Generate Haskell source code from a parsed representation
4249 -- of the format string. This code will be spliced into
4250 -- the module which calls "pr", at compile time.
4251 gen :: [Format] -> ExpQ
4252 gen [D] = [| \n -> show n |]
4253 gen [S] = [| \s -> s |]
4254 gen [L s] = stringE s
4256 -- Here we generate the Haskell code for the splice
4257 -- from an input format string.
4258 pr :: String -> ExpQ
4259 pr s = gen (parse s)
4262 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4265 $ ghc --make -fth main.hs -o main.exe
4268 <para>Run "main.exe" and here is your output:</para>
4278 <title>Using Template Haskell with Profiling</title>
4279 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4281 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4282 interpreter to run the splice expressions. The bytecode interpreter
4283 runs the compiled expression on top of the same runtime on which GHC
4284 itself is running; this means that the compiled code referred to by
4285 the interpreted expression must be compatible with this runtime, and
4286 in particular this means that object code that is compiled for
4287 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4288 expression, because profiled object code is only compatible with the
4289 profiling version of the runtime.</para>
4291 <para>This causes difficulties if you have a multi-module program
4292 containing Template Haskell code and you need to compile it for
4293 profiling, because GHC cannot load the profiled object code and use it
4294 when executing the splices. Fortunately GHC provides a workaround.
4295 The basic idea is to compile the program twice:</para>
4299 <para>Compile the program or library first the normal way, without
4300 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4303 <para>Then compile it again with <option>-prof</option>, and
4304 additionally use <option>-osuf
4305 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4306 to name the object files differentliy (you can choose any suffix
4307 that isn't the normal object suffix here). GHC will automatically
4308 load the object files built in the first step when executing splice
4309 expressions. If you omit the <option>-osuf</option> flag when
4310 building with <option>-prof</option> and Template Haskell is used,
4311 GHC will emit an error message. </para>
4318 <!-- ===================== Arrow notation =================== -->
4320 <sect1 id="arrow-notation">
4321 <title>Arrow notation
4324 <para>Arrows are a generalization of monads introduced by John Hughes.
4325 For more details, see
4330 “Generalising Monads to Arrows”,
4331 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4332 pp67–111, May 2000.
4338 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4339 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4345 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4346 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4352 and the arrows web page at
4353 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4354 With the <option>-farrows</option> flag, GHC supports the arrow
4355 notation described in the second of these papers.
4356 What follows is a brief introduction to the notation;
4357 it won't make much sense unless you've read Hughes's paper.
4358 This notation is translated to ordinary Haskell,
4359 using combinators from the
4360 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4364 <para>The extension adds a new kind of expression for defining arrows:
4366 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4367 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4369 where <literal>proc</literal> is a new keyword.
4370 The variables of the pattern are bound in the body of the
4371 <literal>proc</literal>-expression,
4372 which is a new sort of thing called a <firstterm>command</firstterm>.
4373 The syntax of commands is as follows:
4375 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4376 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4377 | <replaceable>cmd</replaceable><superscript>0</superscript>
4379 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4380 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4381 infix operators as for expressions, and
4383 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4384 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4385 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4386 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4387 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4388 | <replaceable>fcmd</replaceable>
4390 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4391 | ( <replaceable>cmd</replaceable> )
4392 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4394 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4395 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4396 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4397 | <replaceable>cmd</replaceable>
4399 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4400 except that the bodies are commands instead of expressions.
4404 Commands produce values, but (like monadic computations)
4405 may yield more than one value,
4406 or none, and may do other things as well.
4407 For the most part, familiarity with monadic notation is a good guide to
4409 However the values of expressions, even monadic ones,
4410 are determined by the values of the variables they contain;
4411 this is not necessarily the case for commands.
4415 A simple example of the new notation is the expression
4417 proc x -> f -< x+1
4419 We call this a <firstterm>procedure</firstterm> or
4420 <firstterm>arrow abstraction</firstterm>.
4421 As with a lambda expression, the variable <literal>x</literal>
4422 is a new variable bound within the <literal>proc</literal>-expression.
4423 It refers to the input to the arrow.
4424 In the above example, <literal>-<</literal> is not an identifier but an
4425 new reserved symbol used for building commands from an expression of arrow
4426 type and an expression to be fed as input to that arrow.
4427 (The weird look will make more sense later.)
4428 It may be read as analogue of application for arrows.
4429 The above example is equivalent to the Haskell expression
4431 arr (\ x -> x+1) >>> f
4433 That would make no sense if the expression to the left of
4434 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4435 More generally, the expression to the left of <literal>-<</literal>
4436 may not involve any <firstterm>local variable</firstterm>,
4437 i.e. a variable bound in the current arrow abstraction.
4438 For such a situation there is a variant <literal>-<<</literal>, as in
4440 proc x -> f x -<< x+1
4442 which is equivalent to
4444 arr (\ x -> (f x, x+1)) >>> app
4446 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4448 Such an arrow is equivalent to a monad, so if you're using this form
4449 you may find a monadic formulation more convenient.
4453 <title>do-notation for commands</title>
4456 Another form of command is a form of <literal>do</literal>-notation.
4457 For example, you can write
4466 You can read this much like ordinary <literal>do</literal>-notation,
4467 but with commands in place of monadic expressions.
4468 The first line sends the value of <literal>x+1</literal> as an input to
4469 the arrow <literal>f</literal>, and matches its output against
4470 <literal>y</literal>.
4471 In the next line, the output is discarded.
4472 The arrow <function>returnA</function> is defined in the
4473 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4474 module as <literal>arr id</literal>.
4475 The above example is treated as an abbreviation for
4477 arr (\ x -> (x, x)) >>>
4478 first (arr (\ x -> x+1) >>> f) >>>
4479 arr (\ (y, x) -> (y, (x, y))) >>>
4480 first (arr (\ y -> 2*y) >>> g) >>>
4482 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4483 first (arr (\ (x, z) -> x*z) >>> h) >>>
4484 arr (\ (t, z) -> t+z) >>>
4487 Note that variables not used later in the composition are projected out.
4488 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4490 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4491 module, this reduces to
4493 arr (\ x -> (x+1, x)) >>>
4495 arr (\ (y, x) -> (2*y, (x, y))) >>>
4497 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4499 arr (\ (t, z) -> t+z)
4501 which is what you might have written by hand.
4502 With arrow notation, GHC keeps track of all those tuples of variables for you.
4506 Note that although the above translation suggests that
4507 <literal>let</literal>-bound variables like <literal>z</literal> must be
4508 monomorphic, the actual translation produces Core,
4509 so polymorphic variables are allowed.
4513 It's also possible to have mutually recursive bindings,
4514 using the new <literal>rec</literal> keyword, as in the following example:
4516 counter :: ArrowCircuit a => a Bool Int
4517 counter = proc reset -> do
4518 rec output <- returnA -< if reset then 0 else next
4519 next <- delay 0 -< output+1
4520 returnA -< output
4522 The translation of such forms uses the <function>loop</function> combinator,
4523 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4529 <title>Conditional commands</title>
4532 In the previous example, we used a conditional expression to construct the
4534 Sometimes we want to conditionally execute different commands, as in
4541 which is translated to
4543 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4544 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4546 Since the translation uses <function>|||</function>,
4547 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4551 There are also <literal>case</literal> commands, like
4557 y <- h -< (x1, x2)
4561 The syntax is the same as for <literal>case</literal> expressions,
4562 except that the bodies of the alternatives are commands rather than expressions.
4563 The translation is similar to that of <literal>if</literal> commands.
4569 <title>Defining your own control structures</title>
4572 As we're seen, arrow notation provides constructs,
4573 modelled on those for expressions,
4574 for sequencing, value recursion and conditionals.
4575 But suitable combinators,
4576 which you can define in ordinary Haskell,
4577 may also be used to build new commands out of existing ones.
4578 The basic idea is that a command defines an arrow from environments to values.
4579 These environments assign values to the free local variables of the command.
4580 Thus combinators that produce arrows from arrows
4581 may also be used to build commands from commands.
4582 For example, the <literal>ArrowChoice</literal> class includes a combinator
4584 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4586 so we can use it to build commands:
4588 expr' = proc x -> do
4591 symbol Plus -< ()
4592 y <- term -< ()
4595 symbol Minus -< ()
4596 y <- term -< ()
4599 (The <literal>do</literal> on the first line is needed to prevent the first
4600 <literal><+> ...</literal> from being interpreted as part of the
4601 expression on the previous line.)
4602 This is equivalent to
4604 expr' = (proc x -> returnA -< x)
4605 <+> (proc x -> do
4606 symbol Plus -< ()
4607 y <- term -< ()
4609 <+> (proc x -> do
4610 symbol Minus -< ()
4611 y <- term -< ()
4614 It is essential that this operator be polymorphic in <literal>e</literal>
4615 (representing the environment input to the command
4616 and thence to its subcommands)
4617 and satisfy the corresponding naturality property
4619 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4621 at least for strict <literal>k</literal>.
4622 (This should be automatic if you're not using <function>seq</function>.)
4623 This ensures that environments seen by the subcommands are environments
4624 of the whole command,
4625 and also allows the translation to safely trim these environments.
4626 The operator must also not use any variable defined within the current
4631 We could define our own operator
4633 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4634 untilA body cond = proc x ->
4635 if cond x then returnA -< ()
4638 untilA body cond -< x
4640 and use it in the same way.
4641 Of course this infix syntax only makes sense for binary operators;
4642 there is also a more general syntax involving special brackets:
4646 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4653 <title>Primitive constructs</title>
4656 Some operators will need to pass additional inputs to their subcommands.
4657 For example, in an arrow type supporting exceptions,
4658 the operator that attaches an exception handler will wish to pass the
4659 exception that occurred to the handler.
4660 Such an operator might have a type
4662 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4664 where <literal>Ex</literal> is the type of exceptions handled.
4665 You could then use this with arrow notation by writing a command
4667 body `handleA` \ ex -> handler
4669 so that if an exception is raised in the command <literal>body</literal>,
4670 the variable <literal>ex</literal> is bound to the value of the exception
4671 and the command <literal>handler</literal>,
4672 which typically refers to <literal>ex</literal>, is entered.
4673 Though the syntax here looks like a functional lambda,
4674 we are talking about commands, and something different is going on.
4675 The input to the arrow represented by a command consists of values for
4676 the free local variables in the command, plus a stack of anonymous values.
4677 In all the prior examples, this stack was empty.
4678 In the second argument to <function>handleA</function>,
4679 this stack consists of one value, the value of the exception.
4680 The command form of lambda merely gives this value a name.
4685 the values on the stack are paired to the right of the environment.
4686 So operators like <function>handleA</function> that pass
4687 extra inputs to their subcommands can be designed for use with the notation
4688 by pairing the values with the environment in this way.
4689 More precisely, the type of each argument of the operator (and its result)
4690 should have the form
4692 a (...(e,t1), ... tn) t
4694 where <replaceable>e</replaceable> is a polymorphic variable
4695 (representing the environment)
4696 and <replaceable>ti</replaceable> are the types of the values on the stack,
4697 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4698 The polymorphic variable <replaceable>e</replaceable> must not occur in
4699 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4700 <replaceable>t</replaceable>.
4701 However the arrows involved need not be the same.
4702 Here are some more examples of suitable operators:
4704 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4705 runReader :: ... => a e c -> a' (e,State) c
4706 runState :: ... => a e c -> a' (e,State) (c,State)
4708 We can supply the extra input required by commands built with the last two
4709 by applying them to ordinary expressions, as in
4713 (|runReader (do { ... })|) s
4715 which adds <literal>s</literal> to the stack of inputs to the command
4716 built using <function>runReader</function>.
4720 The command versions of lambda abstraction and application are analogous to
4721 the expression versions.
4722 In particular, the beta and eta rules describe equivalences of commands.
4723 These three features (operators, lambda abstraction and application)
4724 are the core of the notation; everything else can be built using them,
4725 though the results would be somewhat clumsy.
4726 For example, we could simulate <literal>do</literal>-notation by defining
4728 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4729 u `bind` f = returnA &&& u >>> f
4731 bind_ :: Arrow a => a e b -> a e c -> a e c
4732 u `bind_` f = u `bind` (arr fst >>> f)
4734 We could simulate <literal>if</literal> by defining
4736 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4737 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4744 <title>Differences with the paper</title>
4749 <para>Instead of a single form of arrow application (arrow tail) with two
4750 translations, the implementation provides two forms
4751 <quote><literal>-<</literal></quote> (first-order)
4752 and <quote><literal>-<<</literal></quote> (higher-order).
4757 <para>User-defined operators are flagged with banana brackets instead of
4758 a new <literal>form</literal> keyword.
4767 <title>Portability</title>
4770 Although only GHC implements arrow notation directly,
4771 there is also a preprocessor
4773 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4774 that translates arrow notation into Haskell 98
4775 for use with other Haskell systems.
4776 You would still want to check arrow programs with GHC;
4777 tracing type errors in the preprocessor output is not easy.
4778 Modules intended for both GHC and the preprocessor must observe some
4779 additional restrictions:
4784 The module must import
4785 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4791 The preprocessor cannot cope with other Haskell extensions.
4792 These would have to go in separate modules.
4798 Because the preprocessor targets Haskell (rather than Core),
4799 <literal>let</literal>-bound variables are monomorphic.
4810 <!-- ==================== BANG PATTERNS ================= -->
4812 <sect1 id="sec-bang-patterns">
4813 <title>Bang patterns
4814 <indexterm><primary>Bang patterns</primary></indexterm>
4816 <para>GHC supports an extension of pattern matching called <emphasis>bang
4817 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4819 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4820 prime feature description</ulink> contains more discussion and examples
4821 than the material below.
4824 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4827 <sect2 id="sec-bang-patterns-informal">
4828 <title>Informal description of bang patterns
4831 The main idea is to add a single new production to the syntax of patterns:
4835 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4836 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4841 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4842 whereas without the bang it would be lazy.
4843 Bang patterns can be nested of course:
4847 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4848 <literal>y</literal>.
4849 A bang only really has an effect if it precedes a variable or wild-card pattern:
4854 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4855 forces evaluation anyway does nothing.
4857 Bang patterns work in <literal>case</literal> expressions too, of course:
4859 g5 x = let y = f x in body
4860 g6 x = case f x of { y -> body }
4861 g7 x = case f x of { !y -> body }
4863 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4864 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4865 result, and then evaluates <literal>body</literal>.
4867 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4868 definitions too. For example:
4872 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4873 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4874 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4875 in a function argument <literal>![x,y]</literal> means the
4876 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4877 is part of the syntax of <literal>let</literal> bindings.
4882 <sect2 id="sec-bang-patterns-sem">
4883 <title>Syntax and semantics
4887 We add a single new production to the syntax of patterns:
4891 There is one problem with syntactic ambiguity. Consider:
4895 Is this a definition of the infix function "<literal>(!)</literal>",
4896 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4897 ambiguity inf favour of the latter. If you want to define
4898 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4903 The semantics of Haskell pattern matching is described in <ulink
4904 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4905 Section 3.17.2</ulink> of the Haskell Report. To this description add
4906 one extra item 10, saying:
4907 <itemizedlist><listitem><para>Matching
4908 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4909 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4910 <listitem><para>otherwise, <literal>pat</literal> is matched against
4911 <literal>v</literal></para></listitem>
4913 </para></listitem></itemizedlist>
4914 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4915 Section 3.17.3</ulink>, add a new case (t):
4917 case v of { !pat -> e; _ -> e' }
4918 = v `seq` case v of { pat -> e; _ -> e' }
4921 That leaves let expressions, whose translation is given in
4922 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4924 of the Haskell Report.
4925 In the translation box, first apply
4926 the following transformation: for each pattern <literal>pi</literal> that is of
4927 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4928 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4929 have a bang at the top, apply the rules in the existing box.
4931 <para>The effect of the let rule is to force complete matching of the pattern
4932 <literal>qi</literal> before evaluation of the body is begun. The bang is
4933 retained in the translated form in case <literal>qi</literal> is a variable,
4941 The let-binding can be recursive. However, it is much more common for
4942 the let-binding to be non-recursive, in which case the following law holds:
4943 <literal>(let !p = rhs in body)</literal>
4945 <literal>(case rhs of !p -> body)</literal>
4948 A pattern with a bang at the outermost level is not allowed at the top level of
4954 <!-- ==================== ASSERTIONS ================= -->
4956 <sect1 id="sec-assertions">
4958 <indexterm><primary>Assertions</primary></indexterm>
4962 If you want to make use of assertions in your standard Haskell code, you
4963 could define a function like the following:
4969 assert :: Bool -> a -> a
4970 assert False x = error "assertion failed!"
4977 which works, but gives you back a less than useful error message --
4978 an assertion failed, but which and where?
4982 One way out is to define an extended <function>assert</function> function which also
4983 takes a descriptive string to include in the error message and
4984 perhaps combine this with the use of a pre-processor which inserts
4985 the source location where <function>assert</function> was used.
4989 Ghc offers a helping hand here, doing all of this for you. For every
4990 use of <function>assert</function> in the user's source:
4996 kelvinToC :: Double -> Double
4997 kelvinToC k = assert (k >= 0.0) (k+273.15)
5003 Ghc will rewrite this to also include the source location where the
5010 assert pred val ==> assertError "Main.hs|15" pred val
5016 The rewrite is only performed by the compiler when it spots
5017 applications of <function>Control.Exception.assert</function>, so you
5018 can still define and use your own versions of
5019 <function>assert</function>, should you so wish. If not, import
5020 <literal>Control.Exception</literal> to make use
5021 <function>assert</function> in your code.
5025 GHC ignores assertions when optimisation is turned on with the
5026 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5027 <literal>assert pred e</literal> will be rewritten to
5028 <literal>e</literal>. You can also disable assertions using the
5029 <option>-fignore-asserts</option>
5030 option<indexterm><primary><option>-fignore-asserts</option></primary>
5031 </indexterm>.</para>
5034 Assertion failures can be caught, see the documentation for the
5035 <literal>Control.Exception</literal> library for the details.
5041 <!-- =============================== PRAGMAS =========================== -->
5043 <sect1 id="pragmas">
5044 <title>Pragmas</title>
5046 <indexterm><primary>pragma</primary></indexterm>
5048 <para>GHC supports several pragmas, or instructions to the
5049 compiler placed in the source code. Pragmas don't normally affect
5050 the meaning of the program, but they might affect the efficiency
5051 of the generated code.</para>
5053 <para>Pragmas all take the form
5055 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5057 where <replaceable>word</replaceable> indicates the type of
5058 pragma, and is followed optionally by information specific to that
5059 type of pragma. Case is ignored in
5060 <replaceable>word</replaceable>. The various values for
5061 <replaceable>word</replaceable> that GHC understands are described
5062 in the following sections; any pragma encountered with an
5063 unrecognised <replaceable>word</replaceable> is (silently)
5066 <sect2 id="deprecated-pragma">
5067 <title>DEPRECATED pragma</title>
5068 <indexterm><primary>DEPRECATED</primary>
5071 <para>The DEPRECATED pragma lets you specify that a particular
5072 function, class, or type, is deprecated. There are two
5077 <para>You can deprecate an entire module thus:</para>
5079 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5082 <para>When you compile any module that import
5083 <literal>Wibble</literal>, GHC will print the specified
5088 <para>You can deprecate a function, class, type, or data constructor, with the
5089 following top-level declaration:</para>
5091 {-# DEPRECATED f, C, T "Don't use these" #-}
5093 <para>When you compile any module that imports and uses any
5094 of the specified entities, GHC will print the specified
5096 <para> You can only depecate entities declared at top level in the module
5097 being compiled, and you can only use unqualified names in the list of
5098 entities being deprecated. A capitalised name, such as <literal>T</literal>
5099 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5100 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5101 both are in scope. If both are in scope, there is currently no way to deprecate
5102 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5105 Any use of the deprecated item, or of anything from a deprecated
5106 module, will be flagged with an appropriate message. However,
5107 deprecations are not reported for
5108 (a) uses of a deprecated function within its defining module, and
5109 (b) uses of a deprecated function in an export list.
5110 The latter reduces spurious complaints within a library
5111 in which one module gathers together and re-exports
5112 the exports of several others.
5114 <para>You can suppress the warnings with the flag
5115 <option>-fno-warn-deprecations</option>.</para>
5118 <sect2 id="include-pragma">
5119 <title>INCLUDE pragma</title>
5121 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5122 of C header files that should be <literal>#include</literal>'d into
5123 the C source code generated by the compiler for the current module (if
5124 compiling via C). For example:</para>
5127 {-# INCLUDE "foo.h" #-}
5128 {-# INCLUDE <stdio.h> #-}</programlisting>
5130 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5131 your source file with any <literal>OPTIONS_GHC</literal>
5134 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5135 to the <option>-#include</option> option (<xref
5136 linkend="options-C-compiler" />), because the
5137 <literal>INCLUDE</literal> pragma is understood by other
5138 compilers. Yet another alternative is to add the include file to each
5139 <literal>foreign import</literal> declaration in your code, but we
5140 don't recommend using this approach with GHC.</para>
5143 <sect2 id="inline-noinline-pragma">
5144 <title>INLINE and NOINLINE pragmas</title>
5146 <para>These pragmas control the inlining of function
5149 <sect3 id="inline-pragma">
5150 <title>INLINE pragma</title>
5151 <indexterm><primary>INLINE</primary></indexterm>
5153 <para>GHC (with <option>-O</option>, as always) tries to
5154 inline (or “unfold”) functions/values that are
5155 “small enough,” thus avoiding the call overhead
5156 and possibly exposing other more-wonderful optimisations.
5157 Normally, if GHC decides a function is “too
5158 expensive” to inline, it will not do so, nor will it
5159 export that unfolding for other modules to use.</para>
5161 <para>The sledgehammer you can bring to bear is the
5162 <literal>INLINE</literal><indexterm><primary>INLINE
5163 pragma</primary></indexterm> pragma, used thusly:</para>
5166 key_function :: Int -> String -> (Bool, Double)
5168 #ifdef __GLASGOW_HASKELL__
5169 {-# INLINE key_function #-}
5173 <para>(You don't need to do the C pre-processor carry-on
5174 unless you're going to stick the code through HBC—it
5175 doesn't like <literal>INLINE</literal> pragmas.)</para>
5177 <para>The major effect of an <literal>INLINE</literal> pragma
5178 is to declare a function's “cost” to be very low.
5179 The normal unfolding machinery will then be very keen to
5182 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5183 function can be put anywhere its type signature could be
5186 <para><literal>INLINE</literal> pragmas are a particularly
5188 <literal>then</literal>/<literal>return</literal> (or
5189 <literal>bind</literal>/<literal>unit</literal>) functions in
5190 a monad. For example, in GHC's own
5191 <literal>UniqueSupply</literal> monad code, we have:</para>
5194 #ifdef __GLASGOW_HASKELL__
5195 {-# INLINE thenUs #-}
5196 {-# INLINE returnUs #-}
5200 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5201 linkend="noinline-pragma"/>).</para>
5204 <sect3 id="noinline-pragma">
5205 <title>NOINLINE pragma</title>
5207 <indexterm><primary>NOINLINE</primary></indexterm>
5208 <indexterm><primary>NOTINLINE</primary></indexterm>
5210 <para>The <literal>NOINLINE</literal> pragma does exactly what
5211 you'd expect: it stops the named function from being inlined
5212 by the compiler. You shouldn't ever need to do this, unless
5213 you're very cautious about code size.</para>
5215 <para><literal>NOTINLINE</literal> is a synonym for
5216 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5217 specified by Haskell 98 as the standard way to disable
5218 inlining, so it should be used if you want your code to be
5222 <sect3 id="phase-control">
5223 <title>Phase control</title>
5225 <para> Sometimes you want to control exactly when in GHC's
5226 pipeline the INLINE pragma is switched on. Inlining happens
5227 only during runs of the <emphasis>simplifier</emphasis>. Each
5228 run of the simplifier has a different <emphasis>phase
5229 number</emphasis>; the phase number decreases towards zero.
5230 If you use <option>-dverbose-core2core</option> you'll see the
5231 sequence of phase numbers for successive runs of the
5232 simplifier. In an INLINE pragma you can optionally specify a
5236 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5237 <literal>f</literal>
5238 until phase <literal>k</literal>, but from phase
5239 <literal>k</literal> onwards be very keen to inline it.
5242 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5243 <literal>f</literal>
5244 until phase <literal>k</literal>, but from phase
5245 <literal>k</literal> onwards do not inline it.
5248 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5249 <literal>f</literal>
5250 until phase <literal>k</literal>, but from phase
5251 <literal>k</literal> onwards be willing to inline it (as if
5252 there was no pragma).
5255 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5256 <literal>f</literal>
5257 until phase <literal>k</literal>, but from phase
5258 <literal>k</literal> onwards do not inline it.
5261 The same information is summarised here:
5263 -- Before phase 2 Phase 2 and later
5264 {-# INLINE [2] f #-} -- No Yes
5265 {-# INLINE [~2] f #-} -- Yes No
5266 {-# NOINLINE [2] f #-} -- No Maybe
5267 {-# NOINLINE [~2] f #-} -- Maybe No
5269 {-# INLINE f #-} -- Yes Yes
5270 {-# NOINLINE f #-} -- No No
5272 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5273 function body is small, or it is applied to interesting-looking arguments etc).
5274 Another way to understand the semantics is this:
5276 <listitem><para>For both INLINE and NOINLINE, the phase number says
5277 when inlining is allowed at all.</para></listitem>
5278 <listitem><para>The INLINE pragma has the additional effect of making the
5279 function body look small, so that when inlining is allowed it is very likely to
5284 <para>The same phase-numbering control is available for RULES
5285 (<xref linkend="rewrite-rules"/>).</para>
5289 <sect2 id="language-pragma">
5290 <title>LANGUAGE pragma</title>
5292 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5293 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5295 <para>This allows language extensions to be enabled in a portable way.
5296 It is the intention that all Haskell compilers support the
5297 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5298 all extensions are supported by all compilers, of
5299 course. The <literal>LANGUAGE</literal> pragma should be used instead
5300 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5302 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5304 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5306 <para>Any extension from the <literal>Extension</literal> type defined in
5308 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>
5312 <sect2 id="line-pragma">
5313 <title>LINE pragma</title>
5315 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5316 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5317 <para>This pragma is similar to C's <literal>#line</literal>
5318 pragma, and is mainly for use in automatically generated Haskell
5319 code. It lets you specify the line number and filename of the
5320 original code; for example</para>
5322 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5324 <para>if you'd generated the current file from something called
5325 <filename>Foo.vhs</filename> and this line corresponds to line
5326 42 in the original. GHC will adjust its error messages to refer
5327 to the line/file named in the <literal>LINE</literal>
5331 <sect2 id="options-pragma">
5332 <title>OPTIONS_GHC pragma</title>
5333 <indexterm><primary>OPTIONS_GHC</primary>
5335 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5338 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5339 additional options that are given to the compiler when compiling
5340 this source file. See <xref linkend="source-file-options"/> for
5343 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5344 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5348 <title>RULES pragma</title>
5350 <para>The RULES pragma lets you specify rewrite rules. It is
5351 described in <xref linkend="rewrite-rules"/>.</para>
5354 <sect2 id="specialize-pragma">
5355 <title>SPECIALIZE pragma</title>
5357 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5358 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5359 <indexterm><primary>overloading, death to</primary></indexterm>
5361 <para>(UK spelling also accepted.) For key overloaded
5362 functions, you can create extra versions (NB: more code space)
5363 specialised to particular types. Thus, if you have an
5364 overloaded function:</para>
5367 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5370 <para>If it is heavily used on lists with
5371 <literal>Widget</literal> keys, you could specialise it as
5375 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5378 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5379 be put anywhere its type signature could be put.</para>
5381 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5382 (a) a specialised version of the function and (b) a rewrite rule
5383 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5384 un-specialised function into a call to the specialised one.</para>
5386 <para>The type in a SPECIALIZE pragma can be any type that is less
5387 polymorphic than the type of the original function. In concrete terms,
5388 if the original function is <literal>f</literal> then the pragma
5390 {-# SPECIALIZE f :: <type> #-}
5392 is valid if and only if the defintion
5394 f_spec :: <type>
5397 is valid. Here are some examples (where we only give the type signature
5398 for the original function, not its code):
5400 f :: Eq a => a -> b -> b
5401 {-# SPECIALISE f :: Int -> b -> b #-}
5403 g :: (Eq a, Ix b) => a -> b -> b
5404 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5406 h :: Eq a => a -> a -> a
5407 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5409 The last of these examples will generate a
5410 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5411 well. If you use this kind of specialisation, let us know how well it works.
5414 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5415 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5416 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5417 The <literal>INLINE</literal> pragma affects the specialised verison of the
5418 function (only), and applies even if the function is recursive. The motivating
5421 -- A GADT for arrays with type-indexed representation
5423 ArrInt :: !Int -> ByteArray# -> Arr Int
5424 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5426 (!:) :: Arr e -> Int -> e
5427 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5428 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5429 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5430 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5432 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5433 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5434 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5435 the specialised function will be inlined. It has two calls to
5436 <literal>(!:)</literal>,
5437 both at type <literal>Int</literal>. Both these calls fire the first
5438 specialisation, whose body is also inlined. The result is a type-based
5439 unrolling of the indexing function.</para>
5440 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5441 on an ordinarily-recursive function.</para>
5443 <para>Note: In earlier versions of GHC, it was possible to provide your own
5444 specialised function for a given type:
5447 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5450 This feature has been removed, as it is now subsumed by the
5451 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5455 <sect2 id="specialize-instance-pragma">
5456 <title>SPECIALIZE instance pragma
5460 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5461 <indexterm><primary>overloading, death to</primary></indexterm>
5462 Same idea, except for instance declarations. For example:
5465 instance (Eq a) => Eq (Foo a) where {
5466 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5470 The pragma must occur inside the <literal>where</literal> part
5471 of the instance declaration.
5474 Compatible with HBC, by the way, except perhaps in the placement
5480 <sect2 id="unpack-pragma">
5481 <title>UNPACK pragma</title>
5483 <indexterm><primary>UNPACK</primary></indexterm>
5485 <para>The <literal>UNPACK</literal> indicates to the compiler
5486 that it should unpack the contents of a constructor field into
5487 the constructor itself, removing a level of indirection. For
5491 data T = T {-# UNPACK #-} !Float
5492 {-# UNPACK #-} !Float
5495 <para>will create a constructor <literal>T</literal> containing
5496 two unboxed floats. This may not always be an optimisation: if
5497 the <function>T</function> constructor is scrutinised and the
5498 floats passed to a non-strict function for example, they will
5499 have to be reboxed (this is done automatically by the
5502 <para>Unpacking constructor fields should only be used in
5503 conjunction with <option>-O</option>, in order to expose
5504 unfoldings to the compiler so the reboxing can be removed as
5505 often as possible. For example:</para>
5509 f (T f1 f2) = f1 + f2
5512 <para>The compiler will avoid reboxing <function>f1</function>
5513 and <function>f2</function> by inlining <function>+</function>
5514 on floats, but only when <option>-O</option> is on.</para>
5516 <para>Any single-constructor data is eligible for unpacking; for
5520 data T = T {-# UNPACK #-} !(Int,Int)
5523 <para>will store the two <literal>Int</literal>s directly in the
5524 <function>T</function> constructor, by flattening the pair.
5525 Multi-level unpacking is also supported:</para>
5528 data T = T {-# UNPACK #-} !S
5529 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5532 <para>will store two unboxed <literal>Int#</literal>s
5533 directly in the <function>T</function> constructor. The
5534 unpacker can see through newtypes, too.</para>
5536 <para>If a field cannot be unpacked, you will not get a warning,
5537 so it might be an idea to check the generated code with
5538 <option>-ddump-simpl</option>.</para>
5540 <para>See also the <option>-funbox-strict-fields</option> flag,
5541 which essentially has the effect of adding
5542 <literal>{-# UNPACK #-}</literal> to every strict
5543 constructor field.</para>
5548 <!-- ======================= REWRITE RULES ======================== -->
5550 <sect1 id="rewrite-rules">
5551 <title>Rewrite rules
5553 <indexterm><primary>RULES pragma</primary></indexterm>
5554 <indexterm><primary>pragma, RULES</primary></indexterm>
5555 <indexterm><primary>rewrite rules</primary></indexterm></title>
5558 The programmer can specify rewrite rules as part of the source program
5559 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5560 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5561 and (b) the <option>-frules-off</option> flag
5562 (<xref linkend="options-f"/>) is not specified, and (c) the
5563 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5572 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5579 <title>Syntax</title>
5582 From a syntactic point of view:
5588 There may be zero or more rules in a <literal>RULES</literal> pragma.
5595 Each rule has a name, enclosed in double quotes. The name itself has
5596 no significance at all. It is only used when reporting how many times the rule fired.
5602 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5603 immediately after the name of the rule. Thus:
5606 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5609 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5610 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5619 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5620 is set, so you must lay out your rules starting in the same column as the
5621 enclosing definitions.
5628 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5629 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5630 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5631 by spaces, just like in a type <literal>forall</literal>.
5637 A pattern variable may optionally have a type signature.
5638 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5639 For example, here is the <literal>foldr/build</literal> rule:
5642 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5643 foldr k z (build g) = g k z
5646 Since <function>g</function> has a polymorphic type, it must have a type signature.
5653 The left hand side of a rule must consist of a top-level variable applied
5654 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5657 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5658 "wrong2" forall f. f True = True
5661 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5668 A rule does not need to be in the same module as (any of) the
5669 variables it mentions, though of course they need to be in scope.
5675 Rules are automatically exported from a module, just as instance declarations are.
5686 <title>Semantics</title>
5689 From a semantic point of view:
5695 Rules are only applied if you use the <option>-O</option> flag.
5701 Rules are regarded as left-to-right rewrite rules.
5702 When GHC finds an expression that is a substitution instance of the LHS
5703 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5704 By "a substitution instance" we mean that the LHS can be made equal to the
5705 expression by substituting for the pattern variables.
5712 The LHS and RHS of a rule are typechecked, and must have the
5720 GHC makes absolutely no attempt to verify that the LHS and RHS
5721 of a rule have the same meaning. That is undecidable in general, and
5722 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5729 GHC makes no attempt to make sure that the rules are confluent or
5730 terminating. For example:
5733 "loop" forall x,y. f x y = f y x
5736 This rule will cause the compiler to go into an infinite loop.
5743 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5749 GHC currently uses a very simple, syntactic, matching algorithm
5750 for matching a rule LHS with an expression. It seeks a substitution
5751 which makes the LHS and expression syntactically equal modulo alpha
5752 conversion. The pattern (rule), but not the expression, is eta-expanded if
5753 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5754 But not beta conversion (that's called higher-order matching).
5758 Matching is carried out on GHC's intermediate language, which includes
5759 type abstractions and applications. So a rule only matches if the
5760 types match too. See <xref linkend="rule-spec"/> below.
5766 GHC keeps trying to apply the rules as it optimises the program.
5767 For example, consider:
5776 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5777 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5778 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5779 not be substituted, and the rule would not fire.
5786 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5787 that appears on the LHS of a rule</emphasis>, because once you have substituted
5788 for something you can't match against it (given the simple minded
5789 matching). So if you write the rule
5792 "map/map" forall f,g. map f . map g = map (f.g)
5795 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5796 It will only match something written with explicit use of ".".
5797 Well, not quite. It <emphasis>will</emphasis> match the expression
5803 where <function>wibble</function> is defined:
5806 wibble f g = map f . map g
5809 because <function>wibble</function> will be inlined (it's small).
5811 Later on in compilation, GHC starts inlining even things on the
5812 LHS of rules, but still leaves the rules enabled. This inlining
5813 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5820 All rules are implicitly exported from the module, and are therefore
5821 in force in any module that imports the module that defined the rule, directly
5822 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5823 in force when compiling A.) The situation is very similar to that for instance
5835 <title>List fusion</title>
5838 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5839 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5840 intermediate list should be eliminated entirely.
5844 The following are good producers:
5856 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5862 Explicit lists (e.g. <literal>[True, False]</literal>)
5868 The cons constructor (e.g <literal>3:4:[]</literal>)
5874 <function>++</function>
5880 <function>map</function>
5886 <function>take</function>, <function>filter</function>
5892 <function>iterate</function>, <function>repeat</function>
5898 <function>zip</function>, <function>zipWith</function>
5907 The following are good consumers:
5919 <function>array</function> (on its second argument)
5925 <function>length</function>
5931 <function>++</function> (on its first argument)
5937 <function>foldr</function>
5943 <function>map</function>
5949 <function>take</function>, <function>filter</function>
5955 <function>concat</function>
5961 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5967 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5968 will fuse with one but not the other)
5974 <function>partition</function>
5980 <function>head</function>
5986 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5992 <function>sequence_</function>
5998 <function>msum</function>
6004 <function>sortBy</function>
6013 So, for example, the following should generate no intermediate lists:
6016 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6022 This list could readily be extended; if there are Prelude functions that you use
6023 a lot which are not included, please tell us.
6027 If you want to write your own good consumers or producers, look at the
6028 Prelude definitions of the above functions to see how to do so.
6033 <sect2 id="rule-spec">
6034 <title>Specialisation
6038 Rewrite rules can be used to get the same effect as a feature
6039 present in earlier versions of GHC.
6040 For example, suppose that:
6043 genericLookup :: Ord a => Table a b -> a -> b
6044 intLookup :: Table Int b -> Int -> b
6047 where <function>intLookup</function> is an implementation of
6048 <function>genericLookup</function> that works very fast for
6049 keys of type <literal>Int</literal>. You might wish
6050 to tell GHC to use <function>intLookup</function> instead of
6051 <function>genericLookup</function> whenever the latter was called with
6052 type <literal>Table Int b -> Int -> b</literal>.
6053 It used to be possible to write
6056 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6059 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6062 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6065 This slightly odd-looking rule instructs GHC to replace
6066 <function>genericLookup</function> by <function>intLookup</function>
6067 <emphasis>whenever the types match</emphasis>.
6068 What is more, this rule does not need to be in the same
6069 file as <function>genericLookup</function>, unlike the
6070 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6071 have an original definition available to specialise).
6074 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6075 <function>intLookup</function> really behaves as a specialised version
6076 of <function>genericLookup</function>!!!</para>
6078 <para>An example in which using <literal>RULES</literal> for
6079 specialisation will Win Big:
6082 toDouble :: Real a => a -> Double
6083 toDouble = fromRational . toRational
6085 {-# RULES "toDouble/Int" toDouble = i2d #-}
6086 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6089 The <function>i2d</function> function is virtually one machine
6090 instruction; the default conversion—via an intermediate
6091 <literal>Rational</literal>—is obscenely expensive by
6098 <title>Controlling what's going on</title>
6106 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6112 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6113 If you add <option>-dppr-debug</option> you get a more detailed listing.
6119 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6122 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6123 {-# INLINE build #-}
6127 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6128 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6129 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6130 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6137 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6138 see how to write rules that will do fusion and yet give an efficient
6139 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6149 <sect2 id="core-pragma">
6150 <title>CORE pragma</title>
6152 <indexterm><primary>CORE pragma</primary></indexterm>
6153 <indexterm><primary>pragma, CORE</primary></indexterm>
6154 <indexterm><primary>core, annotation</primary></indexterm>
6157 The external core format supports <quote>Note</quote> annotations;
6158 the <literal>CORE</literal> pragma gives a way to specify what these
6159 should be in your Haskell source code. Syntactically, core
6160 annotations are attached to expressions and take a Haskell string
6161 literal as an argument. The following function definition shows an
6165 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6168 Semantically, this is equivalent to:
6176 However, when external for is generated (via
6177 <option>-fext-core</option>), there will be Notes attached to the
6178 expressions <function>show</function> and <varname>x</varname>.
6179 The core function declaration for <function>f</function> is:
6183 f :: %forall a . GHCziShow.ZCTShow a ->
6184 a -> GHCziBase.ZMZN GHCziBase.Char =
6185 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6187 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6189 (tpl1::GHCziBase.Int ->
6191 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6193 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6194 (tpl3::GHCziBase.ZMZN a ->
6195 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6203 Here, we can see that the function <function>show</function> (which
6204 has been expanded out to a case expression over the Show dictionary)
6205 has a <literal>%note</literal> attached to it, as does the
6206 expression <varname>eta</varname> (which used to be called
6207 <varname>x</varname>).
6214 <sect1 id="special-ids">
6215 <title>Special built-in functions</title>
6216 <para>GHC has a few built-in funcions with special behaviour,
6217 described in this section. All are exported by
6218 <literal>GHC.Exts</literal>.</para>
6220 <sect2> <title>The <literal>inline</literal> function </title>
6222 The <literal>inline</literal> function is somewhat experimental.
6226 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6227 is inlined, regardless of its size. More precisely, the call
6228 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6230 This allows the programmer to control inlining from
6231 a particular <emphasis>call site</emphasis>
6232 rather than the <emphasis>definition site</emphasis> of the function
6233 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6236 This inlining occurs regardless of the argument to the call
6237 or the size of <literal>f</literal>'s definition; it is unconditional.
6238 The main caveat is that <literal>f</literal>'s definition must be
6239 visible to the compiler. That is, <literal>f</literal> must be
6240 let-bound in the current scope.
6241 If no inlining takes place, the <literal>inline</literal> function
6242 expands to the identity function in Phase zero; so its use imposes
6245 <para> If the function is defined in another
6246 module, GHC only exposes its inlining in the interface file if the
6247 function is sufficiently small that it <emphasis>might</emphasis> be
6248 inlined by the automatic mechanism. There is currently no way to tell
6249 GHC to expose arbitrarily-large functions in the interface file. (This
6250 shortcoming is something that could be fixed, with some kind of pragma.)
6254 <sect2> <title>The <literal>lazy</literal> function </title>
6256 The <literal>lazy</literal> function restrains strictness analysis a little:
6260 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6261 but <literal>lazy</literal> has a magical property so far as strictness
6262 analysis is concerned: it is lazy in its first argument,
6263 even though its semantics is strict. After strictness analysis has run,
6264 calls to <literal>lazy</literal> are inlined to be the identity function.
6267 This behaviour is occasionally useful when controlling evaluation order.
6268 Notably, <literal>lazy</literal> is used in the library definition of
6269 <literal>Control.Parallel.par</literal>:
6272 par x y = case (par# x) of { _ -> lazy y }
6274 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6275 look strict in <literal>y</literal> which would defeat the whole
6276 purpose of <literal>par</literal>.
6280 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6282 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6283 typechecker entirely. It has type
6285 unsafeCoerce# :: a -> b
6287 That is, it allows you to coerce any type into any other type. If you use this
6288 function, you had better get it right, otherwise segmentation faults await.
6289 It is generally used when you want to write a program that you know is
6290 well-typed, but where Haskell's type system is not expressive enough to prove
6291 that it is well typed.
6297 <sect1 id="generic-classes">
6298 <title>Generic classes</title>
6300 <para>(Note: support for generic classes is currently broken in
6304 The ideas behind this extension are described in detail in "Derivable type classes",
6305 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6306 An example will give the idea:
6314 fromBin :: [Int] -> (a, [Int])
6316 toBin {| Unit |} Unit = []
6317 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6318 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6319 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6321 fromBin {| Unit |} bs = (Unit, bs)
6322 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6323 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6324 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6325 (y,bs'') = fromBin bs'
6328 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6329 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6330 which are defined thus in the library module <literal>Generics</literal>:
6334 data a :+: b = Inl a | Inr b
6335 data a :*: b = a :*: b
6338 Now you can make a data type into an instance of Bin like this:
6340 instance (Bin a, Bin b) => Bin (a,b)
6341 instance Bin a => Bin [a]
6343 That is, just leave off the "where" clause. Of course, you can put in the
6344 where clause and over-ride whichever methods you please.
6348 <title> Using generics </title>
6349 <para>To use generics you need to</para>
6352 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6353 <option>-fgenerics</option> (to generate extra per-data-type code),
6354 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6358 <para>Import the module <literal>Generics</literal> from the
6359 <literal>lang</literal> package. This import brings into
6360 scope the data types <literal>Unit</literal>,
6361 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6362 don't need this import if you don't mention these types
6363 explicitly; for example, if you are simply giving instance
6364 declarations.)</para>
6369 <sect2> <title> Changes wrt the paper </title>
6371 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6372 can be written infix (indeed, you can now use
6373 any operator starting in a colon as an infix type constructor). Also note that
6374 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6375 Finally, note that the syntax of the type patterns in the class declaration
6376 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6377 alone would ambiguous when they appear on right hand sides (an extension we
6378 anticipate wanting).
6382 <sect2> <title>Terminology and restrictions</title>
6384 Terminology. A "generic default method" in a class declaration
6385 is one that is defined using type patterns as above.
6386 A "polymorphic default method" is a default method defined as in Haskell 98.
6387 A "generic class declaration" is a class declaration with at least one
6388 generic default method.
6396 Alas, we do not yet implement the stuff about constructor names and
6403 A generic class can have only one parameter; you can't have a generic
6404 multi-parameter class.
6410 A default method must be defined entirely using type patterns, or entirely
6411 without. So this is illegal:
6414 op :: a -> (a, Bool)
6415 op {| Unit |} Unit = (Unit, True)
6418 However it is perfectly OK for some methods of a generic class to have
6419 generic default methods and others to have polymorphic default methods.
6425 The type variable(s) in the type pattern for a generic method declaration
6426 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:
6430 op {| p :*: q |} (x :*: y) = op (x :: p)
6438 The type patterns in a generic default method must take one of the forms:
6444 where "a" and "b" are type variables. Furthermore, all the type patterns for
6445 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6446 must use the same type variables. So this is illegal:
6450 op {| a :+: b |} (Inl x) = True
6451 op {| p :+: q |} (Inr y) = False
6453 The type patterns must be identical, even in equations for different methods of the class.
6454 So this too is illegal:
6458 op1 {| a :*: b |} (x :*: y) = True
6461 op2 {| p :*: q |} (x :*: y) = False
6463 (The reason for this restriction is that we gather all the equations for a particular type consructor
6464 into a single generic instance declaration.)
6470 A generic method declaration must give a case for each of the three type constructors.
6476 The type for a generic method can be built only from:
6478 <listitem> <para> Function arrows </para> </listitem>
6479 <listitem> <para> Type variables </para> </listitem>
6480 <listitem> <para> Tuples </para> </listitem>
6481 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6483 Here are some example type signatures for generic methods:
6486 op2 :: Bool -> (a,Bool)
6487 op3 :: [Int] -> a -> a
6490 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6494 This restriction is an implementation restriction: we just havn't got around to
6495 implementing the necessary bidirectional maps over arbitrary type constructors.
6496 It would be relatively easy to add specific type constructors, such as Maybe and list,
6497 to the ones that are allowed.</para>
6502 In an instance declaration for a generic class, the idea is that the compiler
6503 will fill in the methods for you, based on the generic templates. However it can only
6508 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6513 No constructor of the instance type has unboxed fields.
6517 (Of course, these things can only arise if you are already using GHC extensions.)
6518 However, you can still give an instance declarations for types which break these rules,
6519 provided you give explicit code to override any generic default methods.
6527 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6528 what the compiler does with generic declarations.
6533 <sect2> <title> Another example </title>
6535 Just to finish with, here's another example I rather like:
6539 nCons {| Unit |} _ = 1
6540 nCons {| a :*: b |} _ = 1
6541 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6544 tag {| Unit |} _ = 1
6545 tag {| a :*: b |} _ = 1
6546 tag {| a :+: b |} (Inl x) = tag x
6547 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6553 <sect1 id="monomorphism">
6554 <title>Control over monomorphism</title>
6556 <para>GHC supports two flags that control the way in which generalisation is
6557 carried out at let and where bindings.
6561 <title>Switching off the dreaded Monomorphism Restriction</title>
6562 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6564 <para>Haskell's monomorphism restriction (see
6565 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6567 of the Haskell Report)
6568 can be completely switched off by
6569 <option>-fno-monomorphism-restriction</option>.
6574 <title>Monomorphic pattern bindings</title>
6575 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6576 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6578 <para> As an experimental change, we are exploring the possibility of
6579 making pattern bindings monomorphic; that is, not generalised at all.
6580 A pattern binding is a binding whose LHS has no function arguments,
6581 and is not a simple variable. For example:
6583 f x = x -- Not a pattern binding
6584 f = \x -> x -- Not a pattern binding
6585 f :: Int -> Int = \x -> x -- Not a pattern binding
6587 (g,h) = e -- A pattern binding
6588 (f) = e -- A pattern binding
6589 [x] = e -- A pattern binding
6591 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6592 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
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