1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum.</para>
111 <para>New reserved words: <literal>foreign</literal>.</para>
117 <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
120 <para> These two flags control how generalisation is done.
121 See <xref linkend="monomorphism"/>.
128 <option>-fextended-default-rules</option>:
129 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
132 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
133 Independent of the <option>-fglasgow-exts</option>
140 <option>-fallow-overlapping-instances</option>
141 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
144 <option>-fallow-undecidable-instances</option>
145 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
148 <option>-fallow-incoherent-instances</option>
149 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
152 <option>-fcontext-stack=N</option>
153 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
156 <para> See <xref linkend="instance-decls"/>. Only relevant
157 if you also use <option>-fglasgow-exts</option>.</para>
163 <option>-finline-phase</option>
164 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
167 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
168 you also use <option>-fglasgow-exts</option>.</para>
174 <option>-farrows</option>
175 <indexterm><primary><option>-farrows</option></primary></indexterm>
178 <para>See <xref linkend="arrow-notation"/>. Independent of
179 <option>-fglasgow-exts</option>.</para>
181 <para>New reserved words/symbols: <literal>rec</literal>,
182 <literal>proc</literal>, <literal>-<</literal>,
183 <literal>>-</literal>, <literal>-<<</literal>,
184 <literal>>>-</literal>.</para>
186 <para>Other syntax stolen: <literal>(|</literal>,
187 <literal>|)</literal>.</para>
193 <option>-fgenerics</option>
194 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
197 <para>See <xref linkend="generic-classes"/>. Independent of
198 <option>-fglasgow-exts</option>.</para>
203 <term><option>-fno-implicit-prelude</option></term>
205 <para><indexterm><primary>-fno-implicit-prelude
206 option</primary></indexterm> GHC normally imports
207 <filename>Prelude.hi</filename> files for you. If you'd
208 rather it didn't, then give it a
209 <option>-fno-implicit-prelude</option> option. The idea is
210 that you can then import a Prelude of your own. (But don't
211 call it <literal>Prelude</literal>; the Haskell module
212 namespace is flat, and you must not conflict with any
213 Prelude module.)</para>
215 <para>Even though you have not imported the Prelude, most of
216 the built-in syntax still refers to the built-in Haskell
217 Prelude types and values, as specified by the Haskell
218 Report. For example, the type <literal>[Int]</literal>
219 still means <literal>Prelude.[] Int</literal>; tuples
220 continue to refer to the standard Prelude tuples; the
221 translation for list comprehensions continues to use
222 <literal>Prelude.map</literal> etc.</para>
224 <para>However, <option>-fno-implicit-prelude</option> does
225 change the handling of certain built-in syntax: see <xref
226 linkend="rebindable-syntax"/>.</para>
231 <term><option>-fimplicit-params</option></term>
233 <para>Enables implicit parameters (see <xref
234 linkend="implicit-parameters"/>). Currently also implied by
235 <option>-fglasgow-exts</option>.</para>
238 <literal>?<replaceable>varid</replaceable></literal>,
239 <literal>%<replaceable>varid</replaceable></literal>.</para>
244 <term><option>-fscoped-type-variables</option></term>
246 <para>Enables lexically-scoped type variables (see <xref
247 linkend="scoped-type-variables"/>). Implied by
248 <option>-fglasgow-exts</option>.</para>
253 <term><option>-fth</option></term>
255 <para>Enables Template Haskell (see <xref
256 linkend="template-haskell"/>). This flag must
257 be given explicitly; it is no longer implied by
258 <option>-fglasgow-exts</option>.</para>
260 <para>Syntax stolen: <literal>[|</literal>,
261 <literal>[e|</literal>, <literal>[p|</literal>,
262 <literal>[d|</literal>, <literal>[t|</literal>,
263 <literal>$(</literal>,
264 <literal>$<replaceable>varid</replaceable></literal>.</para>
271 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
272 <!-- included from primitives.sgml -->
273 <!-- &primitives; -->
274 <sect1 id="primitives">
275 <title>Unboxed types and primitive operations</title>
277 <para>GHC is built on a raft of primitive data types and operations.
278 While you really can use this stuff to write fast code,
279 we generally find it a lot less painful, and more satisfying in the
280 long run, to use higher-level language features and libraries. With
281 any luck, the code you write will be optimised to the efficient
282 unboxed version in any case. And if it isn't, we'd like to know
285 <para>We do not currently have good, up-to-date documentation about the
286 primitives, perhaps because they are mainly intended for internal use.
287 There used to be a long section about them here in the User Guide, but it
288 became out of date, and wrong information is worse than none.</para>
290 <para>The Real Truth about what primitive types there are, and what operations
291 work over those types, is held in the file
292 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
293 This file is used directly to generate GHC's primitive-operation definitions, so
294 it is always correct! It is also intended for processing into text.</para>
297 the result of such processing is part of the description of the
299 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
300 Core language</ulink>.
301 So that document is a good place to look for a type-set version.
302 We would be very happy if someone wanted to volunteer to produce an SGML
303 back end to the program that processes <filename>primops.txt</filename> so that
304 we could include the results here in the User Guide.</para>
306 <para>What follows here is a brief summary of some main points.</para>
308 <sect2 id="glasgow-unboxed">
313 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
316 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
317 that values of that type are represented by a pointer to a heap
318 object. The representation of a Haskell <literal>Int</literal>, for
319 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
320 type, however, is represented by the value itself, no pointers or heap
321 allocation are involved.
325 Unboxed types correspond to the “raw machine” types you
326 would use in C: <literal>Int#</literal> (long int),
327 <literal>Double#</literal> (double), <literal>Addr#</literal>
328 (void *), etc. The <emphasis>primitive operations</emphasis>
329 (PrimOps) on these types are what you might expect; e.g.,
330 <literal>(+#)</literal> is addition on
331 <literal>Int#</literal>s, and is the machine-addition that we all
332 know and love—usually one instruction.
336 Primitive (unboxed) types cannot be defined in Haskell, and are
337 therefore built into the language and compiler. Primitive types are
338 always unlifted; that is, a value of a primitive type cannot be
339 bottom. We use the convention that primitive types, values, and
340 operations have a <literal>#</literal> suffix.
344 Primitive values are often represented by a simple bit-pattern, such
345 as <literal>Int#</literal>, <literal>Float#</literal>,
346 <literal>Double#</literal>. But this is not necessarily the case:
347 a primitive value might be represented by a pointer to a
348 heap-allocated object. Examples include
349 <literal>Array#</literal>, the type of primitive arrays. A
350 primitive array is heap-allocated because it is too big a value to fit
351 in a register, and would be too expensive to copy around; in a sense,
352 it is accidental that it is represented by a pointer. If a pointer
353 represents a primitive value, then it really does point to that value:
354 no unevaluated thunks, no indirections…nothing can be at the
355 other end of the pointer than the primitive value.
356 A numerically-intensive program using unboxed types can
357 go a <emphasis>lot</emphasis> faster than its “standard”
358 counterpart—we saw a threefold speedup on one example.
362 There are some restrictions on the use of primitive types:
364 <listitem><para>The main restriction
365 is that you can't pass a primitive value to a polymorphic
366 function or store one in a polymorphic data type. This rules out
367 things like <literal>[Int#]</literal> (i.e. lists of primitive
368 integers). The reason for this restriction is that polymorphic
369 arguments and constructor fields are assumed to be pointers: if an
370 unboxed integer is stored in one of these, the garbage collector would
371 attempt to follow it, leading to unpredictable space leaks. Or a
372 <function>seq</function> operation on the polymorphic component may
373 attempt to dereference the pointer, with disastrous results. Even
374 worse, the unboxed value might be larger than a pointer
375 (<literal>Double#</literal> for instance).
378 <listitem><para> You cannot bind a variable with an unboxed type
379 in a <emphasis>top-level</emphasis> binding.
381 <listitem><para> You cannot bind a variable with an unboxed type
382 in a <emphasis>recursive</emphasis> binding.
384 <listitem><para> You may bind unboxed variables in a (non-recursive,
385 non-top-level) pattern binding, but any such variable causes the entire
387 to become strict. For example:
389 data Foo = Foo Int Int#
391 f x = let (Foo a b, w) = ..rhs.. in ..body..
393 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
395 is strict, and the program behaves as if you had written
397 data Foo = Foo Int Int#
399 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
408 <sect2 id="unboxed-tuples">
409 <title>Unboxed Tuples
413 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
414 they're available by default with <option>-fglasgow-exts</option>. An
415 unboxed tuple looks like this:
427 where <literal>e_1..e_n</literal> are expressions of any
428 type (primitive or non-primitive). The type of an unboxed tuple looks
433 Unboxed tuples are used for functions that need to return multiple
434 values, but they avoid the heap allocation normally associated with
435 using fully-fledged tuples. When an unboxed tuple is returned, the
436 components are put directly into registers or on the stack; the
437 unboxed tuple itself does not have a composite representation. Many
438 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
440 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
441 tuples to avoid unnecessary allocation during sequences of operations.
445 There are some pretty stringent restrictions on the use of unboxed tuples:
450 Values of unboxed tuple types are subject to the same restrictions as
451 other unboxed types; i.e. they may not be stored in polymorphic data
452 structures or passed to polymorphic functions.
459 No variable can have an unboxed tuple type, nor may a constructor or function
460 argument have an unboxed tuple type. The following are all illegal:
464 data Foo = Foo (# Int, Int #)
466 f :: (# Int, Int #) -> (# Int, Int #)
469 g :: (# Int, Int #) -> Int
472 h x = let y = (# x,x #) in ...
479 The typical use of unboxed tuples is simply to return multiple values,
480 binding those multiple results with a <literal>case</literal> expression, thus:
482 f x y = (# x+1, y-1 #)
483 g x = case f x x of { (# a, b #) -> a + b }
485 You can have an unboxed tuple in a pattern binding, thus
487 f x = let (# p,q #) = h x in ..body..
489 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
490 the resulting binding is lazy like any other Haskell pattern binding. The
491 above example desugars like this:
493 f x = let t = case h x o f{ (# p,q #) -> (p,q)
498 Indeed, the bindings can even be recursive.
505 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
507 <sect1 id="syntax-extns">
508 <title>Syntactic extensions</title>
510 <!-- ====================== HIERARCHICAL MODULES ======================= -->
512 <sect2 id="hierarchical-modules">
513 <title>Hierarchical Modules</title>
515 <para>GHC supports a small extension to the syntax of module
516 names: a module name is allowed to contain a dot
517 <literal>‘.’</literal>. This is also known as the
518 “hierarchical module namespace” extension, because
519 it extends the normally flat Haskell module namespace into a
520 more flexible hierarchy of modules.</para>
522 <para>This extension has very little impact on the language
523 itself; modules names are <emphasis>always</emphasis> fully
524 qualified, so you can just think of the fully qualified module
525 name as <quote>the module name</quote>. In particular, this
526 means that the full module name must be given after the
527 <literal>module</literal> keyword at the beginning of the
528 module; for example, the module <literal>A.B.C</literal> must
531 <programlisting>module A.B.C</programlisting>
534 <para>It is a common strategy to use the <literal>as</literal>
535 keyword to save some typing when using qualified names with
536 hierarchical modules. For example:</para>
539 import qualified Control.Monad.ST.Strict as ST
542 <para>For details on how GHC searches for source and interface
543 files in the presence of hierarchical modules, see <xref
544 linkend="search-path"/>.</para>
546 <para>GHC comes with a large collection of libraries arranged
547 hierarchically; see the accompanying library documentation.
548 There is an ongoing project to create and maintain a stable set
549 of <quote>core</quote> libraries used by several Haskell
550 compilers, and the libraries that GHC comes with represent the
551 current status of that project. For more details, see <ulink
552 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
553 Libraries</ulink>.</para>
557 <!-- ====================== PATTERN GUARDS ======================= -->
559 <sect2 id="pattern-guards">
560 <title>Pattern guards</title>
563 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
564 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
568 Suppose we have an abstract data type of finite maps, with a
572 lookup :: FiniteMap -> Int -> Maybe Int
575 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
576 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
580 clunky env var1 var2 | ok1 && ok2 = val1 + val2
581 | otherwise = var1 + var2
592 The auxiliary functions are
596 maybeToBool :: Maybe a -> Bool
597 maybeToBool (Just x) = True
598 maybeToBool Nothing = False
600 expectJust :: Maybe a -> a
601 expectJust (Just x) = x
602 expectJust Nothing = error "Unexpected Nothing"
606 What is <function>clunky</function> doing? The guard <literal>ok1 &&
607 ok2</literal> checks that both lookups succeed, using
608 <function>maybeToBool</function> to convert the <function>Maybe</function>
609 types to booleans. The (lazily evaluated) <function>expectJust</function>
610 calls extract the values from the results of the lookups, and binds the
611 returned values to <varname>val1</varname> and <varname>val2</varname>
612 respectively. If either lookup fails, then clunky takes the
613 <literal>otherwise</literal> case and returns the sum of its arguments.
617 This is certainly legal Haskell, but it is a tremendously verbose and
618 un-obvious way to achieve the desired effect. Arguably, a more direct way
619 to write clunky would be to use case expressions:
623 clunky env var1 var1 = case lookup env var1 of
625 Just val1 -> case lookup env var2 of
627 Just val2 -> val1 + val2
633 This is a bit shorter, but hardly better. Of course, we can rewrite any set
634 of pattern-matching, guarded equations as case expressions; that is
635 precisely what the compiler does when compiling equations! The reason that
636 Haskell provides guarded equations is because they allow us to write down
637 the cases we want to consider, one at a time, independently of each other.
638 This structure is hidden in the case version. Two of the right-hand sides
639 are really the same (<function>fail</function>), and the whole expression
640 tends to become more and more indented.
644 Here is how I would write clunky:
649 | Just val1 <- lookup env var1
650 , Just val2 <- lookup env var2
652 ...other equations for clunky...
656 The semantics should be clear enough. The qualifiers are matched in order.
657 For a <literal><-</literal> qualifier, which I call a pattern guard, the
658 right hand side is evaluated and matched against the pattern on the left.
659 If the match fails then the whole guard fails and the next equation is
660 tried. If it succeeds, then the appropriate binding takes place, and the
661 next qualifier is matched, in the augmented environment. Unlike list
662 comprehensions, however, the type of the expression to the right of the
663 <literal><-</literal> is the same as the type of the pattern to its
664 left. The bindings introduced by pattern guards scope over all the
665 remaining guard qualifiers, and over the right hand side of the equation.
669 Just as with list comprehensions, boolean expressions can be freely mixed
670 with among the pattern guards. For example:
681 Haskell's current guards therefore emerge as a special case, in which the
682 qualifier list has just one element, a boolean expression.
686 <!-- ===================== Recursive do-notation =================== -->
688 <sect2 id="mdo-notation">
689 <title>The recursive do-notation
692 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
693 "A recursive do for Haskell",
694 Levent Erkok, John Launchbury",
695 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
698 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
699 that is, the variables bound in a do-expression are visible only in the textually following
700 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
701 group. It turns out that several applications can benefit from recursive bindings in
702 the do-notation, and this extension provides the necessary syntactic support.
705 Here is a simple (yet contrived) example:
708 import Control.Monad.Fix
710 justOnes = mdo xs <- Just (1:xs)
714 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
718 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
721 class Monad m => MonadFix m where
722 mfix :: (a -> m a) -> m a
725 The function <literal>mfix</literal>
726 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
727 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
728 For details, see the above mentioned reference.
731 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
732 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
733 for Haskell's internal state monad (strict and lazy, respectively).
736 There are three important points in using the recursive-do notation:
739 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
740 than <literal>do</literal>).
744 You should <literal>import Control.Monad.Fix</literal>.
745 (Note: Strictly speaking, this import is required only when you need to refer to the name
746 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
747 are encouraged to always import this module when using the mdo-notation.)
751 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
757 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
758 contains up to date information on recursive monadic bindings.
762 Historical note: The old implementation of the mdo-notation (and most
763 of the existing documents) used the name
764 <literal>MonadRec</literal> for the class and the corresponding library.
765 This name is not supported by GHC.
771 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
773 <sect2 id="parallel-list-comprehensions">
774 <title>Parallel List Comprehensions</title>
775 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
777 <indexterm><primary>parallel list comprehensions</primary>
780 <para>Parallel list comprehensions are a natural extension to list
781 comprehensions. List comprehensions can be thought of as a nice
782 syntax for writing maps and filters. Parallel comprehensions
783 extend this to include the zipWith family.</para>
785 <para>A parallel list comprehension has multiple independent
786 branches of qualifier lists, each separated by a `|' symbol. For
787 example, the following zips together two lists:</para>
790 [ (x, y) | x <- xs | y <- ys ]
793 <para>The behavior of parallel list comprehensions follows that of
794 zip, in that the resulting list will have the same length as the
795 shortest branch.</para>
797 <para>We can define parallel list comprehensions by translation to
798 regular comprehensions. Here's the basic idea:</para>
800 <para>Given a parallel comprehension of the form: </para>
803 [ e | p1 <- e11, p2 <- e12, ...
804 | q1 <- e21, q2 <- e22, ...
809 <para>This will be translated to: </para>
812 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
813 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
818 <para>where `zipN' is the appropriate zip for the given number of
823 <sect2 id="rebindable-syntax">
824 <title>Rebindable syntax</title>
827 <para>GHC allows most kinds of built-in syntax to be rebound by
828 the user, to facilitate replacing the <literal>Prelude</literal>
829 with a home-grown version, for example.</para>
831 <para>You may want to define your own numeric class
832 hierarchy. It completely defeats that purpose if the
833 literal "1" means "<literal>Prelude.fromInteger
834 1</literal>", which is what the Haskell Report specifies.
835 So the <option>-fno-implicit-prelude</option> flag causes
836 the following pieces of built-in syntax to refer to
837 <emphasis>whatever is in scope</emphasis>, not the Prelude
842 <para>An integer literal <literal>368</literal> means
843 "<literal>fromInteger (368::Integer)</literal>", rather than
844 "<literal>Prelude.fromInteger (368::Integer)</literal>".
847 <listitem><para>Fractional literals are handed in just the same way,
848 except that the translation is
849 <literal>fromRational (3.68::Rational)</literal>.
852 <listitem><para>The equality test in an overloaded numeric pattern
853 uses whatever <literal>(==)</literal> is in scope.
856 <listitem><para>The subtraction operation, and the
857 greater-than-or-equal test, in <literal>n+k</literal> patterns
858 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
862 <para>Negation (e.g. "<literal>- (f x)</literal>")
863 means "<literal>negate (f x)</literal>", both in numeric
864 patterns, and expressions.
868 <para>"Do" notation is translated using whatever
869 functions <literal>(>>=)</literal>,
870 <literal>(>>)</literal>, and <literal>fail</literal>,
871 are in scope (not the Prelude
872 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
873 comprehensions, are unaffected. </para></listitem>
877 notation (see <xref linkend="arrow-notation"/>)
878 uses whatever <literal>arr</literal>,
879 <literal>(>>>)</literal>, <literal>first</literal>,
880 <literal>app</literal>, <literal>(|||)</literal> and
881 <literal>loop</literal> functions are in scope. But unlike the
882 other constructs, the types of these functions must match the
883 Prelude types very closely. Details are in flux; if you want
887 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
888 even if that is a little unexpected. For emample, the
889 static semantics of the literal <literal>368</literal>
890 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
891 <literal>fromInteger</literal> to have any of the types:
893 fromInteger :: Integer -> Integer
894 fromInteger :: forall a. Foo a => Integer -> a
895 fromInteger :: Num a => a -> Integer
896 fromInteger :: Integer -> Bool -> Bool
900 <para>Be warned: this is an experimental facility, with
901 fewer checks than usual. Use <literal>-dcore-lint</literal>
902 to typecheck the desugared program. If Core Lint is happy
903 you should be all right.</para>
907 <sect2 id="postfix-operators">
908 <title>Postfix operators</title>
911 GHC allows a small extension to the syntax of left operator sections, which
912 allows you to define postfix operators. The extension is this: the left section
916 is equivalent (from the point of view of both type checking and execution) to the expression
920 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
921 The strict Haskell 98 interpretation is that the section is equivalent to
925 That is, the operator must be a function of two arguments. GHC allows it to
926 take only one argument, and that in turn allows you to write the function
929 <para>Since this extension goes beyond Haskell 98, it should really be enabled
930 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
931 change their behaviour, of course.)
933 <para>The extension does not extend to the left-hand side of function
934 definitions; you must define such a function in prefix form.</para>
941 <!-- TYPE SYSTEM EXTENSIONS -->
942 <sect1 id="type-extensions">
943 <title>Type system extensions</title>
947 <title>Data types and type synonyms</title>
949 <sect3 id="nullary-types">
950 <title>Data types with no constructors</title>
952 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
953 a data type with no constructors. For example:</para>
957 data T a -- T :: * -> *
960 <para>Syntactically, the declaration lacks the "= constrs" part. The
961 type can be parameterised over types of any kind, but if the kind is
962 not <literal>*</literal> then an explicit kind annotation must be used
963 (see <xref linkend="sec-kinding"/>).</para>
965 <para>Such data types have only one value, namely bottom.
966 Nevertheless, they can be useful when defining "phantom types".</para>
969 <sect3 id="infix-tycons">
970 <title>Infix type constructors, classes, and type variables</title>
973 GHC allows type constructors, classes, and type variables to be operators, and
974 to be written infix, very much like expressions. More specifically:
977 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
978 The lexical syntax is the same as that for data constructors.
981 Data type and type-synonym declarations can be written infix, parenthesised
982 if you want further arguments. E.g.
984 data a :*: b = Foo a b
985 type a :+: b = Either a b
986 class a :=: b where ...
988 data (a :**: b) x = Baz a b x
989 type (a :++: b) y = Either (a,b) y
993 Types, and class constraints, can be written infix. For example
996 f :: (a :=: b) => a -> b
1000 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1001 The lexical syntax is the same as that for variable operators, excluding "(.)",
1002 "(!)", and "(*)". In a binding position, the operator must be
1003 parenthesised. For example:
1005 type T (+) = Int + Int
1009 liftA2 :: Arrow (~>)
1010 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1016 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1017 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1020 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1021 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1022 sets the fixity for a data constructor and the corresponding type constructor. For example:
1026 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1027 and similarly for <literal>:*:</literal>.
1028 <literal>Int `a` Bool</literal>.
1031 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1038 <sect3 id="type-synonyms">
1039 <title>Liberalised type synonyms</title>
1042 Type synonyms are like macros at the type level, and
1043 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1044 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1046 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1047 in a type synonym, thus:
1049 type Discard a = forall b. Show b => a -> b -> (a, String)
1054 g :: Discard Int -> (Int,String) -- A rank-2 type
1061 You can write an unboxed tuple in a type synonym:
1063 type Pr = (# Int, Int #)
1071 You can apply a type synonym to a forall type:
1073 type Foo a = a -> a -> Bool
1075 f :: Foo (forall b. b->b)
1077 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1079 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1084 You can apply a type synonym to a partially applied type synonym:
1086 type Generic i o = forall x. i x -> o x
1089 foo :: Generic Id []
1091 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1093 foo :: forall x. x -> [x]
1101 GHC currently does kind checking before expanding synonyms (though even that
1105 After expanding type synonyms, GHC does validity checking on types, looking for
1106 the following mal-formedness which isn't detected simply by kind checking:
1109 Type constructor applied to a type involving for-alls.
1112 Unboxed tuple on left of an arrow.
1115 Partially-applied type synonym.
1119 this will be rejected:
1121 type Pr = (# Int, Int #)
1126 because GHC does not allow unboxed tuples on the left of a function arrow.
1131 <sect3 id="existential-quantification">
1132 <title>Existentially quantified data constructors
1136 The idea of using existential quantification in data type declarations
1137 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1138 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1139 London, 1991). It was later formalised by Laufer and Odersky
1140 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1141 TOPLAS, 16(5), pp1411-1430, 1994).
1142 It's been in Lennart
1143 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1144 proved very useful. Here's the idea. Consider the declaration:
1150 data Foo = forall a. MkFoo a (a -> Bool)
1157 The data type <literal>Foo</literal> has two constructors with types:
1163 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1170 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1171 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1172 For example, the following expression is fine:
1178 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1184 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1185 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1186 isUpper</function> packages a character with a compatible function. These
1187 two things are each of type <literal>Foo</literal> and can be put in a list.
1191 What can we do with a value of type <literal>Foo</literal>?. In particular,
1192 what happens when we pattern-match on <function>MkFoo</function>?
1198 f (MkFoo val fn) = ???
1204 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1205 are compatible, the only (useful) thing we can do with them is to
1206 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1213 f (MkFoo val fn) = fn val
1219 What this allows us to do is to package heterogenous values
1220 together with a bunch of functions that manipulate them, and then treat
1221 that collection of packages in a uniform manner. You can express
1222 quite a bit of object-oriented-like programming this way.
1225 <sect4 id="existential">
1226 <title>Why existential?
1230 What has this to do with <emphasis>existential</emphasis> quantification?
1231 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1237 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1243 But Haskell programmers can safely think of the ordinary
1244 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1245 adding a new existential quantification construct.
1251 <title>Type classes</title>
1254 An easy extension is to allow
1255 arbitrary contexts before the constructor. For example:
1261 data Baz = forall a. Eq a => Baz1 a a
1262 | forall b. Show b => Baz2 b (b -> b)
1268 The two constructors have the types you'd expect:
1274 Baz1 :: forall a. Eq a => a -> a -> Baz
1275 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1281 But when pattern matching on <function>Baz1</function> the matched values can be compared
1282 for equality, and when pattern matching on <function>Baz2</function> the first matched
1283 value can be converted to a string (as well as applying the function to it).
1284 So this program is legal:
1291 f (Baz1 p q) | p == q = "Yes"
1293 f (Baz2 v fn) = show (fn v)
1299 Operationally, in a dictionary-passing implementation, the
1300 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1301 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1302 extract it on pattern matching.
1306 Notice the way that the syntax fits smoothly with that used for
1307 universal quantification earlier.
1313 <title>Record Constructors</title>
1316 GHC allows existentials to be used with records syntax as well. For example:
1319 data Counter a = forall self. NewCounter
1321 , _inc :: self -> self
1322 , _display :: self -> IO ()
1326 Here <literal>tag</literal> is a public field, with a well-typed selector
1327 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1328 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1329 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1330 compile-time error. In other words, <emphasis>GHC defines a record selector function
1331 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1332 (This example used an underscore in the fields for which record selectors
1333 will not be defined, but that is only programming style; GHC ignores them.)
1337 To make use of these hidden fields, we need to create some helper functions:
1340 inc :: Counter a -> Counter a
1341 inc (NewCounter x i d t) = NewCounter
1342 { _this = i x, _inc = i, _display = d, tag = t }
1344 display :: Counter a -> IO ()
1345 display NewCounter{ _this = x, _display = d } = d x
1348 Now we can define counters with different underlying implementations:
1351 counterA :: Counter String
1352 counterA = NewCounter
1353 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1355 counterB :: Counter String
1356 counterB = NewCounter
1357 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1360 display (inc counterA) -- prints "1"
1361 display (inc (inc counterB)) -- prints "##"
1364 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1365 <literal>forall</literal> may be omitted. For example, we can express
1366 the same <literal>Counter a</literal> using GADT:
1369 data Counter a where
1370 NewCounter { _this :: self
1371 , _inc :: self -> self
1372 , _display :: self -> IO ()
1378 At the moment, record update syntax is only supported for Haskell 98 data types,
1379 so the following function does <emphasis>not</emphasis> work:
1382 -- This is invalid; use explicit NewCounter instead for now
1383 setTag :: Counter a -> a -> Counter a
1384 setTag obj t = obj{ tag = t }
1393 <title>Restrictions</title>
1396 There are several restrictions on the ways in which existentially-quantified
1397 constructors can be use.
1406 When pattern matching, each pattern match introduces a new,
1407 distinct, type for each existential type variable. These types cannot
1408 be unified with any other type, nor can they escape from the scope of
1409 the pattern match. For example, these fragments are incorrect:
1417 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1418 is the result of <function>f1</function>. One way to see why this is wrong is to
1419 ask what type <function>f1</function> has:
1423 f1 :: Foo -> a -- Weird!
1427 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1432 f1 :: forall a. Foo -> a -- Wrong!
1436 The original program is just plain wrong. Here's another sort of error
1440 f2 (Baz1 a b) (Baz1 p q) = a==q
1444 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1445 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1446 from the two <function>Baz1</function> constructors.
1454 You can't pattern-match on an existentially quantified
1455 constructor in a <literal>let</literal> or <literal>where</literal> group of
1456 bindings. So this is illegal:
1460 f3 x = a==b where { Baz1 a b = x }
1463 Instead, use a <literal>case</literal> expression:
1466 f3 x = case x of Baz1 a b -> a==b
1469 In general, you can only pattern-match
1470 on an existentially-quantified constructor in a <literal>case</literal> expression or
1471 in the patterns of a function definition.
1473 The reason for this restriction is really an implementation one.
1474 Type-checking binding groups is already a nightmare without
1475 existentials complicating the picture. Also an existential pattern
1476 binding at the top level of a module doesn't make sense, because it's
1477 not clear how to prevent the existentially-quantified type "escaping".
1478 So for now, there's a simple-to-state restriction. We'll see how
1486 You can't use existential quantification for <literal>newtype</literal>
1487 declarations. So this is illegal:
1491 newtype T = forall a. Ord a => MkT a
1495 Reason: a value of type <literal>T</literal> must be represented as a
1496 pair of a dictionary for <literal>Ord t</literal> and a value of type
1497 <literal>t</literal>. That contradicts the idea that
1498 <literal>newtype</literal> should have no concrete representation.
1499 You can get just the same efficiency and effect by using
1500 <literal>data</literal> instead of <literal>newtype</literal>. If
1501 there is no overloading involved, then there is more of a case for
1502 allowing an existentially-quantified <literal>newtype</literal>,
1503 because the <literal>data</literal> version does carry an
1504 implementation cost, but single-field existentially quantified
1505 constructors aren't much use. So the simple restriction (no
1506 existential stuff on <literal>newtype</literal>) stands, unless there
1507 are convincing reasons to change it.
1515 You can't use <literal>deriving</literal> to define instances of a
1516 data type with existentially quantified data constructors.
1518 Reason: in most cases it would not make sense. For example:#
1521 data T = forall a. MkT [a] deriving( Eq )
1524 To derive <literal>Eq</literal> in the standard way we would need to have equality
1525 between the single component of two <function>MkT</function> constructors:
1529 (MkT a) == (MkT b) = ???
1532 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1533 It's just about possible to imagine examples in which the derived instance
1534 would make sense, but it seems altogether simpler simply to prohibit such
1535 declarations. Define your own instances!
1550 <sect2 id="multi-param-type-classes">
1551 <title>Class declarations</title>
1554 This section, and the next one, documents GHC's type-class extensions.
1555 There's lots of background in the paper <ulink
1556 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1557 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1558 Jones, Erik Meijer).
1561 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1565 <title>Multi-parameter type classes</title>
1567 Multi-parameter type classes are permitted. For example:
1571 class Collection c a where
1572 union :: c a -> c a -> c a
1580 <title>The superclasses of a class declaration</title>
1583 There are no restrictions on the context in a class declaration
1584 (which introduces superclasses), except that the class hierarchy must
1585 be acyclic. So these class declarations are OK:
1589 class Functor (m k) => FiniteMap m k where
1592 class (Monad m, Monad (t m)) => Transform t m where
1593 lift :: m a -> (t m) a
1599 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1600 of "acyclic" involves only the superclass relationships. For example,
1606 op :: D b => a -> b -> b
1609 class C a => D a where { ... }
1613 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1614 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1615 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1622 <sect3 id="class-method-types">
1623 <title>Class method types</title>
1626 Haskell 98 prohibits class method types to mention constraints on the
1627 class type variable, thus:
1630 fromList :: [a] -> s a
1631 elem :: Eq a => a -> s a -> Bool
1633 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1634 contains the constraint <literal>Eq a</literal>, constrains only the
1635 class type variable (in this case <literal>a</literal>).
1636 GHC lifts this restriction.
1643 <sect2 id="functional-dependencies">
1644 <title>Functional dependencies
1647 <para> Functional dependencies are implemented as described by Mark Jones
1648 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1649 In Proceedings of the 9th European Symposium on Programming,
1650 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1654 Functional dependencies are introduced by a vertical bar in the syntax of a
1655 class declaration; e.g.
1657 class (Monad m) => MonadState s m | m -> s where ...
1659 class Foo a b c | a b -> c where ...
1661 There should be more documentation, but there isn't (yet). Yell if you need it.
1664 <sect3><title>Rules for functional dependencies </title>
1666 In a class declaration, all of the class type variables must be reachable (in the sense
1667 mentioned in <xref linkend="type-restrictions"/>)
1668 from the free variables of each method type.
1672 class Coll s a where
1674 insert :: s -> a -> s
1677 is not OK, because the type of <literal>empty</literal> doesn't mention
1678 <literal>a</literal>. Functional dependencies can make the type variable
1681 class Coll s a | s -> a where
1683 insert :: s -> a -> s
1686 Alternatively <literal>Coll</literal> might be rewritten
1689 class Coll s a where
1691 insert :: s a -> a -> s a
1695 which makes the connection between the type of a collection of
1696 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1697 Occasionally this really doesn't work, in which case you can split the
1705 class CollE s => Coll s a where
1706 insert :: s -> a -> s
1713 <title>Background on functional dependencies</title>
1715 <para>The following description of the motivation and use of functional dependencies is taken
1716 from the Hugs user manual, reproduced here (with minor changes) by kind
1717 permission of Mark Jones.
1720 Consider the following class, intended as part of a
1721 library for collection types:
1723 class Collects e ce where
1725 insert :: e -> ce -> ce
1726 member :: e -> ce -> Bool
1728 The type variable e used here represents the element type, while ce is the type
1729 of the container itself. Within this framework, we might want to define
1730 instances of this class for lists or characteristic functions (both of which
1731 can be used to represent collections of any equality type), bit sets (which can
1732 be used to represent collections of characters), or hash tables (which can be
1733 used to represent any collection whose elements have a hash function). Omitting
1734 standard implementation details, this would lead to the following declarations:
1736 instance Eq e => Collects e [e] where ...
1737 instance Eq e => Collects e (e -> Bool) where ...
1738 instance Collects Char BitSet where ...
1739 instance (Hashable e, Collects a ce)
1740 => Collects e (Array Int ce) where ...
1742 All this looks quite promising; we have a class and a range of interesting
1743 implementations. Unfortunately, there are some serious problems with the class
1744 declaration. First, the empty function has an ambiguous type:
1746 empty :: Collects e ce => ce
1748 By "ambiguous" we mean that there is a type variable e that appears on the left
1749 of the <literal>=></literal> symbol, but not on the right. The problem with
1750 this is that, according to the theoretical foundations of Haskell overloading,
1751 we cannot guarantee a well-defined semantics for any term with an ambiguous
1755 We can sidestep this specific problem by removing the empty member from the
1756 class declaration. However, although the remaining members, insert and member,
1757 do not have ambiguous types, we still run into problems when we try to use
1758 them. For example, consider the following two functions:
1760 f x y = insert x . insert y
1763 for which GHC infers the following types:
1765 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1766 g :: (Collects Bool c, Collects Char c) => c -> c
1768 Notice that the type for f allows the two parameters x and y to be assigned
1769 different types, even though it attempts to insert each of the two values, one
1770 after the other, into the same collection. If we're trying to model collections
1771 that contain only one type of value, then this is clearly an inaccurate
1772 type. Worse still, the definition for g is accepted, without causing a type
1773 error. As a result, the error in this code will not be flagged at the point
1774 where it appears. Instead, it will show up only when we try to use g, which
1775 might even be in a different module.
1778 <sect4><title>An attempt to use constructor classes</title>
1781 Faced with the problems described above, some Haskell programmers might be
1782 tempted to use something like the following version of the class declaration:
1784 class Collects e c where
1786 insert :: e -> c e -> c e
1787 member :: e -> c e -> Bool
1789 The key difference here is that we abstract over the type constructor c that is
1790 used to form the collection type c e, and not over that collection type itself,
1791 represented by ce in the original class declaration. This avoids the immediate
1792 problems that we mentioned above: empty has type <literal>Collects e c => c
1793 e</literal>, which is not ambiguous.
1796 The function f from the previous section has a more accurate type:
1798 f :: (Collects e c) => e -> e -> c e -> c e
1800 The function g from the previous section is now rejected with a type error as
1801 we would hope because the type of f does not allow the two arguments to have
1803 This, then, is an example of a multiple parameter class that does actually work
1804 quite well in practice, without ambiguity problems.
1805 There is, however, a catch. This version of the Collects class is nowhere near
1806 as general as the original class seemed to be: only one of the four instances
1807 for <literal>Collects</literal>
1808 given above can be used with this version of Collects because only one of
1809 them---the instance for lists---has a collection type that can be written in
1810 the form c e, for some type constructor c, and element type e.
1814 <sect4><title>Adding functional dependencies</title>
1817 To get a more useful version of the Collects class, Hugs provides a mechanism
1818 that allows programmers to specify dependencies between the parameters of a
1819 multiple parameter class (For readers with an interest in theoretical
1820 foundations and previous work: The use of dependency information can be seen
1821 both as a generalization of the proposal for `parametric type classes' that was
1822 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1823 later framework for "improvement" of qualified types. The
1824 underlying ideas are also discussed in a more theoretical and abstract setting
1825 in a manuscript [implparam], where they are identified as one point in a
1826 general design space for systems of implicit parameterization.).
1828 To start with an abstract example, consider a declaration such as:
1830 class C a b where ...
1832 which tells us simply that C can be thought of as a binary relation on types
1833 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1834 included in the definition of classes to add information about dependencies
1835 between parameters, as in the following examples:
1837 class D a b | a -> b where ...
1838 class E a b | a -> b, b -> a where ...
1840 The notation <literal>a -> b</literal> used here between the | and where
1841 symbols --- not to be
1842 confused with a function type --- indicates that the a parameter uniquely
1843 determines the b parameter, and might be read as "a determines b." Thus D is
1844 not just a relation, but actually a (partial) function. Similarly, from the two
1845 dependencies that are included in the definition of E, we can see that E
1846 represents a (partial) one-one mapping between types.
1849 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1850 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1851 m>=0, meaning that the y parameters are uniquely determined by the x
1852 parameters. Spaces can be used as separators if more than one variable appears
1853 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1854 annotated with multiple dependencies using commas as separators, as in the
1855 definition of E above. Some dependencies that we can write in this notation are
1856 redundant, and will be rejected because they don't serve any useful
1857 purpose, and may instead indicate an error in the program. Examples of
1858 dependencies like this include <literal>a -> a </literal>,
1859 <literal>a -> a a </literal>,
1860 <literal>a -> </literal>, etc. There can also be
1861 some redundancy if multiple dependencies are given, as in
1862 <literal>a->b</literal>,
1863 <literal>b->c </literal>, <literal>a->c </literal>, and
1864 in which some subset implies the remaining dependencies. Examples like this are
1865 not treated as errors. Note that dependencies appear only in class
1866 declarations, and not in any other part of the language. In particular, the
1867 syntax for instance declarations, class constraints, and types is completely
1871 By including dependencies in a class declaration, we provide a mechanism for
1872 the programmer to specify each multiple parameter class more precisely. The
1873 compiler, on the other hand, is responsible for ensuring that the set of
1874 instances that are in scope at any given point in the program is consistent
1875 with any declared dependencies. For example, the following pair of instance
1876 declarations cannot appear together in the same scope because they violate the
1877 dependency for D, even though either one on its own would be acceptable:
1879 instance D Bool Int where ...
1880 instance D Bool Char where ...
1882 Note also that the following declaration is not allowed, even by itself:
1884 instance D [a] b where ...
1886 The problem here is that this instance would allow one particular choice of [a]
1887 to be associated with more than one choice for b, which contradicts the
1888 dependency specified in the definition of D. More generally, this means that,
1889 in any instance of the form:
1891 instance D t s where ...
1893 for some particular types t and s, the only variables that can appear in s are
1894 the ones that appear in t, and hence, if the type t is known, then s will be
1895 uniquely determined.
1898 The benefit of including dependency information is that it allows us to define
1899 more general multiple parameter classes, without ambiguity problems, and with
1900 the benefit of more accurate types. To illustrate this, we return to the
1901 collection class example, and annotate the original definition of <literal>Collects</literal>
1902 with a simple dependency:
1904 class Collects e ce | ce -> e where
1906 insert :: e -> ce -> ce
1907 member :: e -> ce -> Bool
1909 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1910 determined by the type of the collection ce. Note that both parameters of
1911 Collects are of kind *; there are no constructor classes here. Note too that
1912 all of the instances of Collects that we gave earlier can be used
1913 together with this new definition.
1916 What about the ambiguity problems that we encountered with the original
1917 definition? The empty function still has type Collects e ce => ce, but it is no
1918 longer necessary to regard that as an ambiguous type: Although the variable e
1919 does not appear on the right of the => symbol, the dependency for class
1920 Collects tells us that it is uniquely determined by ce, which does appear on
1921 the right of the => symbol. Hence the context in which empty is used can still
1922 give enough information to determine types for both ce and e, without
1923 ambiguity. More generally, we need only regard a type as ambiguous if it
1924 contains a variable on the left of the => that is not uniquely determined
1925 (either directly or indirectly) by the variables on the right.
1928 Dependencies also help to produce more accurate types for user defined
1929 functions, and hence to provide earlier detection of errors, and less cluttered
1930 types for programmers to work with. Recall the previous definition for a
1933 f x y = insert x y = insert x . insert y
1935 for which we originally obtained a type:
1937 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1939 Given the dependency information that we have for Collects, however, we can
1940 deduce that a and b must be equal because they both appear as the second
1941 parameter in a Collects constraint with the same first parameter c. Hence we
1942 can infer a shorter and more accurate type for f:
1944 f :: (Collects a c) => a -> a -> c -> c
1946 In a similar way, the earlier definition of g will now be flagged as a type error.
1949 Although we have given only a few examples here, it should be clear that the
1950 addition of dependency information can help to make multiple parameter classes
1951 more useful in practice, avoiding ambiguity problems, and allowing more general
1952 sets of instance declarations.
1958 <sect2 id="instance-decls">
1959 <title>Instance declarations</title>
1961 <sect3 id="instance-rules">
1962 <title>Relaxed rules for instance declarations</title>
1964 <para>An instance declaration has the form
1966 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 ...
1968 The part before the "<literal>=></literal>" is the
1969 <emphasis>context</emphasis>, while the part after the
1970 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1974 In Haskell 98 the head of an instance declaration
1975 must be of the form <literal>C (T a1 ... an)</literal>, where
1976 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1977 and the <literal>a1 ... an</literal> are distinct type variables.
1978 Furthermore, the assertions in the context of the instance declaration
1979 must be of the form <literal>C a</literal> where <literal>a</literal>
1980 is a type variable that occurs in the head.
1983 The <option>-fglasgow-exts</option> flag loosens these restrictions
1984 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1985 the context and head of the instance declaration can each consist of arbitrary
1986 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1990 For each assertion in the context:
1992 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1993 <listitem><para>The assertion has fewer constructors and variables (taken together
1994 and counting repetitions) than the head</para></listitem>
1998 <listitem><para>The coverage condition. For each functional dependency,
1999 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2000 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2001 every type variable in
2002 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2003 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2004 substitution mapping each type variable in the class declaration to the
2005 corresponding type in the instance declaration.
2008 These restrictions ensure that context reduction terminates: each reduction
2009 step makes the problem smaller by at least one
2010 constructor. For example, the following would make the type checker
2011 loop if it wasn't excluded:
2013 instance C a => C a where ...
2015 For example, these are OK:
2017 instance C Int [a] -- Multiple parameters
2018 instance Eq (S [a]) -- Structured type in head
2020 -- Repeated type variable in head
2021 instance C4 a a => C4 [a] [a]
2022 instance Stateful (ST s) (MutVar s)
2024 -- Head can consist of type variables only
2026 instance (Eq a, Show b) => C2 a b
2028 -- Non-type variables in context
2029 instance Show (s a) => Show (Sized s a)
2030 instance C2 Int a => C3 Bool [a]
2031 instance C2 Int a => C3 [a] b
2035 -- Context assertion no smaller than head
2036 instance C a => C a where ...
2037 -- (C b b) has more more occurrences of b than the head
2038 instance C b b => Foo [b] where ...
2043 The same restrictions apply to instances generated by
2044 <literal>deriving</literal> clauses. Thus the following is accepted:
2046 data MinHeap h a = H a (h a)
2049 because the derived instance
2051 instance (Show a, Show (h a)) => Show (MinHeap h a)
2053 conforms to the above rules.
2057 A useful idiom permitted by the above rules is as follows.
2058 If one allows overlapping instance declarations then it's quite
2059 convenient to have a "default instance" declaration that applies if
2060 something more specific does not:
2066 <para>You can find lots of background material about the reason for these
2067 restrictions in the paper <ulink
2068 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2069 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2073 <sect3 id="undecidable-instances">
2074 <title>Undecidable instances</title>
2077 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2078 For example, sometimes you might want to use the following to get the
2079 effect of a "class synonym":
2081 class (C1 a, C2 a, C3 a) => C a where { }
2083 instance (C1 a, C2 a, C3 a) => C a where { }
2085 This allows you to write shorter signatures:
2091 f :: (C1 a, C2 a, C3 a) => ...
2093 The restrictions on functional dependencies (<xref
2094 linkend="functional-dependencies"/>) are particularly troublesome.
2095 It is tempting to introduce type variables in the context that do not appear in
2096 the head, something that is excluded by the normal rules. For example:
2098 class HasConverter a b | a -> b where
2101 data Foo a = MkFoo a
2103 instance (HasConverter a b,Show b) => Show (Foo a) where
2104 show (MkFoo value) = show (convert value)
2106 This is dangerous territory, however. Here, for example, is a program that would make the
2111 instance F [a] [[a]]
2112 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2114 Similarly, it can be tempting to lift the coverage condition:
2116 class Mul a b c | a b -> c where
2117 (.*.) :: a -> b -> c
2119 instance Mul Int Int Int where (.*.) = (*)
2120 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2121 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2123 The third instance declaration does not obey the coverage condition;
2124 and indeed the (somewhat strange) definition:
2126 f = \ b x y -> if b then x .*. [y] else y
2128 makes instance inference go into a loop, because it requires the constraint
2129 <literal>(Mul a [b] b)</literal>.
2132 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2133 the experimental flag <option>-fallow-undecidable-instances</option>
2134 <indexterm><primary>-fallow-undecidable-instances
2135 option</primary></indexterm>, you can use arbitrary
2136 types in both an instance context and instance head. Termination is ensured by having a
2137 fixed-depth recursion stack. If you exceed the stack depth you get a
2138 sort of backtrace, and the opportunity to increase the stack depth
2139 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2145 <sect3 id="instance-overlap">
2146 <title>Overlapping instances</title>
2148 In general, <emphasis>GHC requires that that it be unambiguous which instance
2150 should be used to resolve a type-class constraint</emphasis>. This behaviour
2151 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2152 <indexterm><primary>-fallow-overlapping-instances
2153 </primary></indexterm>
2154 and <option>-fallow-incoherent-instances</option>
2155 <indexterm><primary>-fallow-incoherent-instances
2156 </primary></indexterm>, as this section discusses. Both these
2157 flags are dynamic flags, and can be set on a per-module basis, using
2158 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2160 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2161 it tries to match every instance declaration against the
2163 by instantiating the head of the instance declaration. For example, consider
2166 instance context1 => C Int a where ... -- (A)
2167 instance context2 => C a Bool where ... -- (B)
2168 instance context3 => C Int [a] where ... -- (C)
2169 instance context4 => C Int [Int] where ... -- (D)
2171 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2172 but (C) and (D) do not. When matching, GHC takes
2173 no account of the context of the instance declaration
2174 (<literal>context1</literal> etc).
2175 GHC's default behaviour is that <emphasis>exactly one instance must match the
2176 constraint it is trying to resolve</emphasis>.
2177 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2178 including both declarations (A) and (B), say); an error is only reported if a
2179 particular constraint matches more than one.
2183 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2184 more than one instance to match, provided there is a most specific one. For
2185 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2186 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2187 most-specific match, the program is rejected.
2190 However, GHC is conservative about committing to an overlapping instance. For example:
2195 Suppose that from the RHS of <literal>f</literal> we get the constraint
2196 <literal>C Int [b]</literal>. But
2197 GHC does not commit to instance (C), because in a particular
2198 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2199 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2200 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2201 GHC will instead pick (C), without complaining about
2202 the problem of subsequent instantiations.
2205 The willingness to be overlapped or incoherent is a property of
2206 the <emphasis>instance declaration</emphasis> itself, controlled by the
2207 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2208 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2209 being defined. Neither flag is required in a module that imports and uses the
2210 instance declaration. Specifically, during the lookup process:
2213 An instance declaration is ignored during the lookup process if (a) a more specific
2214 match is found, and (b) the instance declaration was compiled with
2215 <option>-fallow-overlapping-instances</option>. The flag setting for the
2216 more-specific instance does not matter.
2219 Suppose an instance declaration does not matche the constraint being looked up, but
2220 does unify with it, so that it might match when the constraint is further
2221 instantiated. Usually GHC will regard this as a reason for not committing to
2222 some other constraint. But if the instance declaration was compiled with
2223 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2224 check for that declaration.
2227 These rules make it possible for a library author to design a library that relies on
2228 overlapping instances without the library client having to know.
2231 If an instance declaration is compiled without
2232 <option>-fallow-overlapping-instances</option>,
2233 then that instance can never be overlapped. This could perhaps be
2234 inconvenient. Perhaps the rule should instead say that the
2235 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2236 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2237 at a usage site should be permitted regardless of how the instance declarations
2238 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2239 used at the usage site. (Mind you, the exact usage site can occasionally be
2240 hard to pin down.) We are interested to receive feedback on these points.
2242 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2243 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2248 <title>Type synonyms in the instance head</title>
2251 <emphasis>Unlike Haskell 98, instance heads may use type
2252 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2253 As always, using a type synonym is just shorthand for
2254 writing the RHS of the type synonym definition. For example:
2258 type Point = (Int,Int)
2259 instance C Point where ...
2260 instance C [Point] where ...
2264 is legal. However, if you added
2268 instance C (Int,Int) where ...
2272 as well, then the compiler will complain about the overlapping
2273 (actually, identical) instance declarations. As always, type synonyms
2274 must be fully applied. You cannot, for example, write:
2279 instance Monad P where ...
2283 This design decision is independent of all the others, and easily
2284 reversed, but it makes sense to me.
2292 <sect2 id="type-restrictions">
2293 <title>Type signatures</title>
2295 <sect3><title>The context of a type signature</title>
2297 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2298 the form <emphasis>(class type-variable)</emphasis> or
2299 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2300 these type signatures are perfectly OK
2303 g :: Ord (T a ()) => ...
2307 GHC imposes the following restrictions on the constraints in a type signature.
2311 forall tv1..tvn (c1, ...,cn) => type
2314 (Here, we write the "foralls" explicitly, although the Haskell source
2315 language omits them; in Haskell 98, all the free type variables of an
2316 explicit source-language type signature are universally quantified,
2317 except for the class type variables in a class declaration. However,
2318 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2327 <emphasis>Each universally quantified type variable
2328 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2330 A type variable <literal>a</literal> is "reachable" if it it appears
2331 in the same constraint as either a type variable free in in
2332 <literal>type</literal>, or another reachable type variable.
2333 A value with a type that does not obey
2334 this reachability restriction cannot be used without introducing
2335 ambiguity; that is why the type is rejected.
2336 Here, for example, is an illegal type:
2340 forall a. Eq a => Int
2344 When a value with this type was used, the constraint <literal>Eq tv</literal>
2345 would be introduced where <literal>tv</literal> is a fresh type variable, and
2346 (in the dictionary-translation implementation) the value would be
2347 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2348 can never know which instance of <literal>Eq</literal> to use because we never
2349 get any more information about <literal>tv</literal>.
2353 that the reachability condition is weaker than saying that <literal>a</literal> is
2354 functionally dependent on a type variable free in
2355 <literal>type</literal> (see <xref
2356 linkend="functional-dependencies"/>). The reason for this is there
2357 might be a "hidden" dependency, in a superclass perhaps. So
2358 "reachable" is a conservative approximation to "functionally dependent".
2359 For example, consider:
2361 class C a b | a -> b where ...
2362 class C a b => D a b where ...
2363 f :: forall a b. D a b => a -> a
2365 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2366 but that is not immediately apparent from <literal>f</literal>'s type.
2372 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2373 universally quantified type variables <literal>tvi</literal></emphasis>.
2375 For example, this type is OK because <literal>C a b</literal> mentions the
2376 universally quantified type variable <literal>b</literal>:
2380 forall a. C a b => burble
2384 The next type is illegal because the constraint <literal>Eq b</literal> does not
2385 mention <literal>a</literal>:
2389 forall a. Eq b => burble
2393 The reason for this restriction is milder than the other one. The
2394 excluded types are never useful or necessary (because the offending
2395 context doesn't need to be witnessed at this point; it can be floated
2396 out). Furthermore, floating them out increases sharing. Lastly,
2397 excluding them is a conservative choice; it leaves a patch of
2398 territory free in case we need it later.
2409 <title>For-all hoisting</title>
2411 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2412 end of an arrow, thus:
2414 type Discard a = forall b. a -> b -> a
2416 g :: Int -> Discard Int
2419 Simply expanding the type synonym would give
2421 g :: Int -> (forall b. Int -> b -> Int)
2423 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2425 g :: forall b. Int -> Int -> b -> Int
2427 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2428 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2429 performs the transformation:</emphasis>
2431 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2433 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2435 (In fact, GHC tries to retain as much synonym information as possible for use in
2436 error messages, but that is a usability issue.) This rule applies, of course, whether
2437 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2438 valid way to write <literal>g</literal>'s type signature:
2440 g :: Int -> Int -> forall b. b -> Int
2444 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2447 type Foo a = (?x::Int) => Bool -> a
2452 g :: (?x::Int) => Bool -> Bool -> Int
2460 <sect2 id="implicit-parameters">
2461 <title>Implicit parameters</title>
2463 <para> Implicit parameters are implemented as described in
2464 "Implicit parameters: dynamic scoping with static types",
2465 J Lewis, MB Shields, E Meijer, J Launchbury,
2466 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2470 <para>(Most of the following, stil rather incomplete, documentation is
2471 due to Jeff Lewis.)</para>
2473 <para>Implicit parameter support is enabled with the option
2474 <option>-fimplicit-params</option>.</para>
2477 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2478 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2479 context. In Haskell, all variables are statically bound. Dynamic
2480 binding of variables is a notion that goes back to Lisp, but was later
2481 discarded in more modern incarnations, such as Scheme. Dynamic binding
2482 can be very confusing in an untyped language, and unfortunately, typed
2483 languages, in particular Hindley-Milner typed languages like Haskell,
2484 only support static scoping of variables.
2487 However, by a simple extension to the type class system of Haskell, we
2488 can support dynamic binding. Basically, we express the use of a
2489 dynamically bound variable as a constraint on the type. These
2490 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2491 function uses a dynamically-bound variable <literal>?x</literal>
2492 of type <literal>t'</literal>". For
2493 example, the following expresses the type of a sort function,
2494 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2496 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2498 The dynamic binding constraints are just a new form of predicate in the type class system.
2501 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2502 where <literal>x</literal> is
2503 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2504 Use of this construct also introduces a new
2505 dynamic-binding constraint in the type of the expression.
2506 For example, the following definition
2507 shows how we can define an implicitly parameterized sort function in
2508 terms of an explicitly parameterized <literal>sortBy</literal> function:
2510 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2512 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2518 <title>Implicit-parameter type constraints</title>
2520 Dynamic binding constraints behave just like other type class
2521 constraints in that they are automatically propagated. Thus, when a
2522 function is used, its implicit parameters are inherited by the
2523 function that called it. For example, our <literal>sort</literal> function might be used
2524 to pick out the least value in a list:
2526 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2527 least xs = head (sort xs)
2529 Without lifting a finger, the <literal>?cmp</literal> parameter is
2530 propagated to become a parameter of <literal>least</literal> as well. With explicit
2531 parameters, the default is that parameters must always be explicit
2532 propagated. With implicit parameters, the default is to always
2536 An implicit-parameter type constraint differs from other type class constraints in the
2537 following way: All uses of a particular implicit parameter must have
2538 the same type. This means that the type of <literal>(?x, ?x)</literal>
2539 is <literal>(?x::a) => (a,a)</literal>, and not
2540 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2544 <para> You can't have an implicit parameter in the context of a class or instance
2545 declaration. For example, both these declarations are illegal:
2547 class (?x::Int) => C a where ...
2548 instance (?x::a) => Foo [a] where ...
2550 Reason: exactly which implicit parameter you pick up depends on exactly where
2551 you invoke a function. But the ``invocation'' of instance declarations is done
2552 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2553 Easiest thing is to outlaw the offending types.</para>
2555 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2557 f :: (?x :: [a]) => Int -> Int
2560 g :: (Read a, Show a) => String -> String
2563 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2564 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2565 quite unambiguous, and fixes the type <literal>a</literal>.
2570 <title>Implicit-parameter bindings</title>
2573 An implicit parameter is <emphasis>bound</emphasis> using the standard
2574 <literal>let</literal> or <literal>where</literal> binding forms.
2575 For example, we define the <literal>min</literal> function by binding
2576 <literal>cmp</literal>.
2579 min = let ?cmp = (<=) in least
2583 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2584 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2585 (including in a list comprehension, or do-notation, or pattern guards),
2586 or a <literal>where</literal> clause.
2587 Note the following points:
2590 An implicit-parameter binding group must be a
2591 collection of simple bindings to implicit-style variables (no
2592 function-style bindings, and no type signatures); these bindings are
2593 neither polymorphic or recursive.
2596 You may not mix implicit-parameter bindings with ordinary bindings in a
2597 single <literal>let</literal>
2598 expression; use two nested <literal>let</literal>s instead.
2599 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2603 You may put multiple implicit-parameter bindings in a
2604 single binding group; but they are <emphasis>not</emphasis> treated
2605 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2606 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2607 parameter. The bindings are not nested, and may be re-ordered without changing
2608 the meaning of the program.
2609 For example, consider:
2611 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2613 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2614 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2616 f :: (?x::Int) => Int -> Int
2624 <sect3><title>Implicit parameters and polymorphic recursion</title>
2627 Consider these two definitions:
2630 len1 xs = let ?acc = 0 in len_acc1 xs
2633 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2638 len2 xs = let ?acc = 0 in len_acc2 xs
2640 len_acc2 :: (?acc :: Int) => [a] -> Int
2642 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2644 The only difference between the two groups is that in the second group
2645 <literal>len_acc</literal> is given a type signature.
2646 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2647 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2648 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2649 has a type signature, the recursive call is made to the
2650 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2651 as an implicit parameter. So we get the following results in GHCi:
2658 Adding a type signature dramatically changes the result! This is a rather
2659 counter-intuitive phenomenon, worth watching out for.
2663 <sect3><title>Implicit parameters and monomorphism</title>
2665 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2666 Haskell Report) to implicit parameters. For example, consider:
2674 Since the binding for <literal>y</literal> falls under the Monomorphism
2675 Restriction it is not generalised, so the type of <literal>y</literal> is
2676 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2677 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2678 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2679 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2680 <literal>y</literal> in the body of the <literal>let</literal> will see the
2681 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2682 <literal>14</literal>.
2687 <!-- ======================= COMMENTED OUT ========================
2689 We intend to remove linear implicit parameters, so I'm at least removing
2690 them from the 6.6 user manual
2692 <sect2 id="linear-implicit-parameters">
2693 <title>Linear implicit parameters</title>
2695 Linear implicit parameters are an idea developed by Koen Claessen,
2696 Mark Shields, and Simon PJ. They address the long-standing
2697 problem that monads seem over-kill for certain sorts of problem, notably:
2700 <listitem> <para> distributing a supply of unique names </para> </listitem>
2701 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2702 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2706 Linear implicit parameters are just like ordinary implicit parameters,
2707 except that they are "linear"; that is, they cannot be copied, and
2708 must be explicitly "split" instead. Linear implicit parameters are
2709 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2710 (The '/' in the '%' suggests the split!)
2715 import GHC.Exts( Splittable )
2717 data NameSupply = ...
2719 splitNS :: NameSupply -> (NameSupply, NameSupply)
2720 newName :: NameSupply -> Name
2722 instance Splittable NameSupply where
2726 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2727 f env (Lam x e) = Lam x' (f env e)
2730 env' = extend env x x'
2731 ...more equations for f...
2733 Notice that the implicit parameter %ns is consumed
2735 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2736 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2740 So the translation done by the type checker makes
2741 the parameter explicit:
2743 f :: NameSupply -> Env -> Expr -> Expr
2744 f ns env (Lam x e) = Lam x' (f ns1 env e)
2746 (ns1,ns2) = splitNS ns
2748 env = extend env x x'
2750 Notice the call to 'split' introduced by the type checker.
2751 How did it know to use 'splitNS'? Because what it really did
2752 was to introduce a call to the overloaded function 'split',
2753 defined by the class <literal>Splittable</literal>:
2755 class Splittable a where
2758 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2759 split for name supplies. But we can simply write
2765 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2767 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2768 <literal>GHC.Exts</literal>.
2773 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2774 are entirely distinct implicit parameters: you
2775 can use them together and they won't intefere with each other. </para>
2778 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2780 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2781 in the context of a class or instance declaration. </para></listitem>
2785 <sect3><title>Warnings</title>
2788 The monomorphism restriction is even more important than usual.
2789 Consider the example above:
2791 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2792 f env (Lam x e) = Lam x' (f env e)
2795 env' = extend env x x'
2797 If we replaced the two occurrences of x' by (newName %ns), which is
2798 usually a harmless thing to do, we get:
2800 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2801 f env (Lam x e) = Lam (newName %ns) (f env e)
2803 env' = extend env x (newName %ns)
2805 But now the name supply is consumed in <emphasis>three</emphasis> places
2806 (the two calls to newName,and the recursive call to f), so
2807 the result is utterly different. Urk! We don't even have
2811 Well, this is an experimental change. With implicit
2812 parameters we have already lost beta reduction anyway, and
2813 (as John Launchbury puts it) we can't sensibly reason about
2814 Haskell programs without knowing their typing.
2819 <sect3><title>Recursive functions</title>
2820 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2823 foo :: %x::T => Int -> [Int]
2825 foo n = %x : foo (n-1)
2827 where T is some type in class Splittable.</para>
2829 Do you get a list of all the same T's or all different T's
2830 (assuming that split gives two distinct T's back)?
2832 If you supply the type signature, taking advantage of polymorphic
2833 recursion, you get what you'd probably expect. Here's the
2834 translated term, where the implicit param is made explicit:
2837 foo x n = let (x1,x2) = split x
2838 in x1 : foo x2 (n-1)
2840 But if you don't supply a type signature, GHC uses the Hindley
2841 Milner trick of using a single monomorphic instance of the function
2842 for the recursive calls. That is what makes Hindley Milner type inference
2843 work. So the translation becomes
2847 foom n = x : foom (n-1)
2851 Result: 'x' is not split, and you get a list of identical T's. So the
2852 semantics of the program depends on whether or not foo has a type signature.
2855 You may say that this is a good reason to dislike linear implicit parameters
2856 and you'd be right. That is why they are an experimental feature.
2862 ================ END OF Linear Implicit Parameters commented out -->
2864 <sect2 id="sec-kinding">
2865 <title>Explicitly-kinded quantification</title>
2868 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2869 to give the kind explicitly as (machine-checked) documentation,
2870 just as it is nice to give a type signature for a function. On some occasions,
2871 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2872 John Hughes had to define the data type:
2874 data Set cxt a = Set [a]
2875 | Unused (cxt a -> ())
2877 The only use for the <literal>Unused</literal> constructor was to force the correct
2878 kind for the type variable <literal>cxt</literal>.
2881 GHC now instead allows you to specify the kind of a type variable directly, wherever
2882 a type variable is explicitly bound. Namely:
2884 <listitem><para><literal>data</literal> declarations:
2886 data Set (cxt :: * -> *) a = Set [a]
2887 </screen></para></listitem>
2888 <listitem><para><literal>type</literal> declarations:
2890 type T (f :: * -> *) = f Int
2891 </screen></para></listitem>
2892 <listitem><para><literal>class</literal> declarations:
2894 class (Eq a) => C (f :: * -> *) a where ...
2895 </screen></para></listitem>
2896 <listitem><para><literal>forall</literal>'s in type signatures:
2898 f :: forall (cxt :: * -> *). Set cxt Int
2899 </screen></para></listitem>
2904 The parentheses are required. Some of the spaces are required too, to
2905 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2906 will get a parse error, because "<literal>::*->*</literal>" is a
2907 single lexeme in Haskell.
2911 As part of the same extension, you can put kind annotations in types
2914 f :: (Int :: *) -> Int
2915 g :: forall a. a -> (a :: *)
2919 atype ::= '(' ctype '::' kind ')
2921 The parentheses are required.
2926 <sect2 id="universal-quantification">
2927 <title>Arbitrary-rank polymorphism
2931 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2932 allows us to say exactly what this means. For example:
2940 g :: forall b. (b -> b)
2942 The two are treated identically.
2946 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2947 explicit universal quantification in
2949 For example, all the following types are legal:
2951 f1 :: forall a b. a -> b -> a
2952 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2954 f2 :: (forall a. a->a) -> Int -> Int
2955 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2957 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2959 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2960 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2961 The <literal>forall</literal> makes explicit the universal quantification that
2962 is implicitly added by Haskell.
2965 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2966 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2967 shows, the polymorphic type on the left of the function arrow can be overloaded.
2970 The function <literal>f3</literal> has a rank-3 type;
2971 it has rank-2 types on the left of a function arrow.
2974 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2975 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2976 that restriction has now been lifted.)
2977 In particular, a forall-type (also called a "type scheme"),
2978 including an operational type class context, is legal:
2980 <listitem> <para> On the left of a function arrow </para> </listitem>
2981 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2982 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2983 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2984 field type signatures.</para> </listitem>
2985 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2986 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2988 There is one place you cannot put a <literal>forall</literal>:
2989 you cannot instantiate a type variable with a forall-type. So you cannot
2990 make a forall-type the argument of a type constructor. So these types are illegal:
2992 x1 :: [forall a. a->a]
2993 x2 :: (forall a. a->a, Int)
2994 x3 :: Maybe (forall a. a->a)
2996 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2997 a type variable any more!
3006 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3007 the types of the constructor arguments. Here are several examples:
3013 data T a = T1 (forall b. b -> b -> b) a
3015 data MonadT m = MkMonad { return :: forall a. a -> m a,
3016 bind :: forall a b. m a -> (a -> m b) -> m b
3019 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3025 The constructors have rank-2 types:
3031 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3032 MkMonad :: forall m. (forall a. a -> m a)
3033 -> (forall a b. m a -> (a -> m b) -> m b)
3035 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3041 Notice that you don't need to use a <literal>forall</literal> if there's an
3042 explicit context. For example in the first argument of the
3043 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3044 prefixed to the argument type. The implicit <literal>forall</literal>
3045 quantifies all type variables that are not already in scope, and are
3046 mentioned in the type quantified over.
3050 As for type signatures, implicit quantification happens for non-overloaded
3051 types too. So if you write this:
3054 data T a = MkT (Either a b) (b -> b)
3057 it's just as if you had written this:
3060 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3063 That is, since the type variable <literal>b</literal> isn't in scope, it's
3064 implicitly universally quantified. (Arguably, it would be better
3065 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3066 where that is what is wanted. Feedback welcomed.)
3070 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3071 the constructor to suitable values, just as usual. For example,
3082 a3 = MkSwizzle reverse
3085 a4 = let r x = Just x
3092 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3093 mkTs f x y = [T1 f x, T1 f y]
3099 The type of the argument can, as usual, be more general than the type
3100 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3101 does not need the <literal>Ord</literal> constraint.)
3105 When you use pattern matching, the bound variables may now have
3106 polymorphic types. For example:
3112 f :: T a -> a -> (a, Char)
3113 f (T1 w k) x = (w k x, w 'c' 'd')
3115 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3116 g (MkSwizzle s) xs f = s (map f (s xs))
3118 h :: MonadT m -> [m a] -> m [a]
3119 h m [] = return m []
3120 h m (x:xs) = bind m x $ \y ->
3121 bind m (h m xs) $ \ys ->
3128 In the function <function>h</function> we use the record selectors <literal>return</literal>
3129 and <literal>bind</literal> to extract the polymorphic bind and return functions
3130 from the <literal>MonadT</literal> data structure, rather than using pattern
3136 <title>Type inference</title>
3139 In general, type inference for arbitrary-rank types is undecidable.
3140 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3141 to get a decidable algorithm by requiring some help from the programmer.
3142 We do not yet have a formal specification of "some help" but the rule is this:
3145 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3146 provides an explicit polymorphic type for x, or GHC's type inference will assume
3147 that x's type has no foralls in it</emphasis>.
3150 What does it mean to "provide" an explicit type for x? You can do that by
3151 giving a type signature for x directly, using a pattern type signature
3152 (<xref linkend="scoped-type-variables"/>), thus:
3154 \ f :: (forall a. a->a) -> (f True, f 'c')
3156 Alternatively, you can give a type signature to the enclosing
3157 context, which GHC can "push down" to find the type for the variable:
3159 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3161 Here the type signature on the expression can be pushed inwards
3162 to give a type signature for f. Similarly, and more commonly,
3163 one can give a type signature for the function itself:
3165 h :: (forall a. a->a) -> (Bool,Char)
3166 h f = (f True, f 'c')
3168 You don't need to give a type signature if the lambda bound variable
3169 is a constructor argument. Here is an example we saw earlier:
3171 f :: T a -> a -> (a, Char)
3172 f (T1 w k) x = (w k x, w 'c' 'd')
3174 Here we do not need to give a type signature to <literal>w</literal>, because
3175 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3182 <sect3 id="implicit-quant">
3183 <title>Implicit quantification</title>
3186 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3187 user-written types, if and only if there is no explicit <literal>forall</literal>,
3188 GHC finds all the type variables mentioned in the type that are not already
3189 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3193 f :: forall a. a -> a
3200 h :: forall b. a -> b -> b
3206 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3209 f :: (a -> a) -> Int
3211 f :: forall a. (a -> a) -> Int
3213 f :: (forall a. a -> a) -> Int
3216 g :: (Ord a => a -> a) -> Int
3217 -- MEANS the illegal type
3218 g :: forall a. (Ord a => a -> a) -> Int
3220 g :: (forall a. Ord a => a -> a) -> Int
3222 The latter produces an illegal type, which you might think is silly,
3223 but at least the rule is simple. If you want the latter type, you
3224 can write your for-alls explicitly. Indeed, doing so is strongly advised
3231 <sect2 id="impredicative-polymorphism">
3232 <title>Impredicative polymorphism
3234 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3235 that you can call a polymorphic function at a polymorphic type, and
3236 parameterise data structures over polymorphic types. For example:
3238 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3239 f (Just g) = Just (g [3], g "hello")
3242 Notice here that the <literal>Maybe</literal> type is parameterised by the
3243 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3246 <para>The technical details of this extension are described in the paper
3247 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3248 type inference for higher-rank types and impredicativity</ulink>,
3249 which appeared at ICFP 2006.
3253 <sect2 id="scoped-type-variables">
3254 <title>Lexically scoped type variables
3258 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3259 which some type signatures are simply impossible to write. For example:
3261 f :: forall a. [a] -> [a]
3267 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3268 the entire definition of <literal>f</literal>.
3269 In particular, it is in scope at the type signature for <varname>ys</varname>.
3270 In Haskell 98 it is not possible to declare
3271 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3272 it becomes possible to do so.
3274 <para>Lexically-scoped type variables are enabled by
3275 <option>-fglasgow-exts</option>.
3277 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3278 variables work, compared to earlier releases. Read this section
3282 <title>Overview</title>
3284 <para>The design follows the following principles
3286 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3287 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3288 design.)</para></listitem>
3289 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3290 type variables. This means that every programmer-written type signature
3291 (includin one that contains free scoped type variables) denotes a
3292 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3293 checker, and no inference is involved.</para></listitem>
3294 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3295 changing the program.</para></listitem>
3299 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3301 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3302 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3303 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3304 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3308 In Haskell, a programmer-written type signature is implicitly quantifed over
3309 its free type variables (<ulink
3310 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3312 of the Haskel Report).
3313 Lexically scoped type variables affect this implicit quantification rules
3314 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3315 quantified. For example, if type variable <literal>a</literal> is in scope,
3318 (e :: a -> a) means (e :: a -> a)
3319 (e :: b -> b) means (e :: forall b. b->b)
3320 (e :: a -> b) means (e :: forall b. a->b)
3328 <sect3 id="decl-type-sigs">
3329 <title>Declaration type signatures</title>
3330 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3331 quantification (using <literal>forall</literal>) brings into scope the
3332 explicitly-quantified
3333 type variables, in the definition of the named function(s). For example:
3335 f :: forall a. [a] -> [a]
3336 f (x:xs) = xs ++ [ x :: a ]
3338 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3339 the definition of "<literal>f</literal>".
3341 <para>This only happens if the quantification in <literal>f</literal>'s type
3342 signature is explicit. For example:
3345 g (x:xs) = xs ++ [ x :: a ]
3347 This program will be rejected, because "<literal>a</literal>" does not scope
3348 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3349 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3350 quantification rules.
3354 <sect3 id="exp-type-sigs">
3355 <title>Expression type signatures</title>
3357 <para>An expression type signature that has <emphasis>explicit</emphasis>
3358 quantification (using <literal>forall</literal>) brings into scope the
3359 explicitly-quantified
3360 type variables, in the annotated expression. For example:
3362 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3364 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3365 type variable <literal>s</literal> into scope, in the annotated expression
3366 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3371 <sect3 id="pattern-type-sigs">
3372 <title>Pattern type signatures</title>
3374 A type signature may occur in any pattern; this is a <emphasis>pattern type
3375 signature</emphasis>.
3378 -- f and g assume that 'a' is already in scope
3379 f = \(x::Int, y::a) -> x
3381 h ((x,y) :: (Int,Bool)) = (y,x)
3383 In the case where all the type variables in the pattern type sigature are
3384 already in scope (i.e. bound by the enclosing context), matters are simple: the
3385 signature simply constrains the type of the pattern in the obvious way.
3388 There is only one situation in which you can write a pattern type signature that
3389 mentions a type variable that is not already in scope, namely in pattern match
3390 of an existential data constructor. For example:
3392 data T = forall a. MkT [a]
3395 k (MkT [t::a]) = MkT t3
3399 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3400 variable that is not already in scope. Indeed, it cannot already be in scope,
3401 because it is bound by the pattern match. GHC's rule is that in this situation
3402 (and only then), a pattern type signature can mention a type variable that is
3403 not already in scope; the effect is to bring it into scope, standing for the
3404 existentially-bound type variable.
3407 If this seems a little odd, we think so too. But we must have
3408 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3409 could not name existentially-bound type variables in subequent type signatures.
3412 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3413 signature is allowed to mention a lexical variable that is not already in
3415 For example, both <literal>f</literal> and <literal>g</literal> would be
3416 illegal if <literal>a</literal> was not already in scope.
3422 <!-- ==================== Commented out part about result type signatures
3424 <sect3 id="result-type-sigs">
3425 <title>Result type signatures</title>
3428 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3431 {- f assumes that 'a' is already in scope -}
3432 f x y :: [a] = [x,y,x]
3434 g = \ x :: [Int] -> [3,4]
3436 h :: forall a. [a] -> a
3440 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3441 the result of the function. Similarly, the body of the lambda in the RHS of
3442 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3443 alternative in <literal>h</literal> is <literal>a</literal>.
3445 <para> A result type signature never brings new type variables into scope.</para>
3447 There are a couple of syntactic wrinkles. First, notice that all three
3448 examples would parse quite differently with parentheses:
3450 {- f assumes that 'a' is already in scope -}
3451 f x (y :: [a]) = [x,y,x]
3453 g = \ (x :: [Int]) -> [3,4]
3455 h :: forall a. [a] -> a
3459 Now the signature is on the <emphasis>pattern</emphasis>; and
3460 <literal>h</literal> would certainly be ill-typed (since the pattern
3461 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3463 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3464 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3465 token or a parenthesised type of some sort). To see why,
3466 consider how one would parse this:
3475 <sect3 id="cls-inst-scoped-tyvars">
3476 <title>Class and instance declarations</title>
3479 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3480 scope over the methods defined in the <literal>where</literal> part. For example:
3497 <sect2 id="deriving-typeable">
3498 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3501 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3502 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3503 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3504 classes <literal>Eq</literal>, <literal>Ord</literal>,
3505 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3508 GHC extends this list with two more classes that may be automatically derived
3509 (provided the <option>-fglasgow-exts</option> flag is specified):
3510 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3511 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3512 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3514 <para>An instance of <literal>Typeable</literal> can only be derived if the
3515 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3516 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3518 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3519 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3521 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3522 are used, and only <literal>Typeable1</literal> up to
3523 <literal>Typeable7</literal> are provided in the library.)
3524 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3525 class, whose kind suits that of the data type constructor, and
3526 then writing the data type instance by hand.
3530 <sect2 id="newtype-deriving">
3531 <title>Generalised derived instances for newtypes</title>
3534 When you define an abstract type using <literal>newtype</literal>, you may want
3535 the new type to inherit some instances from its representation. In
3536 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3537 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3538 other classes you have to write an explicit instance declaration. For
3539 example, if you define
3542 newtype Dollars = Dollars Int
3545 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3546 explicitly define an instance of <literal>Num</literal>:
3549 instance Num Dollars where
3550 Dollars a + Dollars b = Dollars (a+b)
3553 All the instance does is apply and remove the <literal>newtype</literal>
3554 constructor. It is particularly galling that, since the constructor
3555 doesn't appear at run-time, this instance declaration defines a
3556 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3557 dictionary, only slower!
3561 <sect3> <title> Generalising the deriving clause </title>
3563 GHC now permits such instances to be derived instead, so one can write
3565 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3568 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3569 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3570 derives an instance declaration of the form
3573 instance Num Int => Num Dollars
3576 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3580 We can also derive instances of constructor classes in a similar
3581 way. For example, suppose we have implemented state and failure monad
3582 transformers, such that
3585 instance Monad m => Monad (State s m)
3586 instance Monad m => Monad (Failure m)
3588 In Haskell 98, we can define a parsing monad by
3590 type Parser tok m a = State [tok] (Failure m) a
3593 which is automatically a monad thanks to the instance declarations
3594 above. With the extension, we can make the parser type abstract,
3595 without needing to write an instance of class <literal>Monad</literal>, via
3598 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3601 In this case the derived instance declaration is of the form
3603 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3606 Notice that, since <literal>Monad</literal> is a constructor class, the
3607 instance is a <emphasis>partial application</emphasis> of the new type, not the
3608 entire left hand side. We can imagine that the type declaration is
3609 ``eta-converted'' to generate the context of the instance
3614 We can even derive instances of multi-parameter classes, provided the
3615 newtype is the last class parameter. In this case, a ``partial
3616 application'' of the class appears in the <literal>deriving</literal>
3617 clause. For example, given the class
3620 class StateMonad s m | m -> s where ...
3621 instance Monad m => StateMonad s (State s m) where ...
3623 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3625 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3626 deriving (Monad, StateMonad [tok])
3629 The derived instance is obtained by completing the application of the
3630 class to the new type:
3633 instance StateMonad [tok] (State [tok] (Failure m)) =>
3634 StateMonad [tok] (Parser tok m)
3639 As a result of this extension, all derived instances in newtype
3640 declarations are treated uniformly (and implemented just by reusing
3641 the dictionary for the representation type), <emphasis>except</emphasis>
3642 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3643 the newtype and its representation.
3647 <sect3> <title> A more precise specification </title>
3649 Derived instance declarations are constructed as follows. Consider the
3650 declaration (after expansion of any type synonyms)
3653 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3659 The <literal>ci</literal> are partial applications of
3660 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3661 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3664 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3667 The type <literal>t</literal> is an arbitrary type.
3670 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3671 nor in the <literal>ci</literal>, and
3674 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3675 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3676 should not "look through" the type or its constructor. You can still
3677 derive these classes for a newtype, but it happens in the usual way, not
3678 via this new mechanism.
3681 Then, for each <literal>ci</literal>, the derived instance
3684 instance ci t => ci (T v1...vk)
3686 As an example which does <emphasis>not</emphasis> work, consider
3688 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3690 Here we cannot derive the instance
3692 instance Monad (State s m) => Monad (NonMonad m)
3695 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3696 and so cannot be "eta-converted" away. It is a good thing that this
3697 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3698 not, in fact, a monad --- for the same reason. Try defining
3699 <literal>>>=</literal> with the correct type: you won't be able to.
3703 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3704 important, since we can only derive instances for the last one. If the
3705 <literal>StateMonad</literal> class above were instead defined as
3708 class StateMonad m s | m -> s where ...
3711 then we would not have been able to derive an instance for the
3712 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3713 classes usually have one "main" parameter for which deriving new
3714 instances is most interesting.
3716 <para>Lastly, all of this applies only for classes other than
3717 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3718 and <literal>Data</literal>, for which the built-in derivation applies (section
3719 4.3.3. of the Haskell Report).
3720 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3721 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3722 the standard method is used or the one described here.)
3728 <sect2 id="stand-alone-deriving">
3729 <title>Stand-alone deriving declarations</title>
3732 GHC now allows stand-alone <literal>deriving</literal> declarations:
3736 data Foo = Bar Int | Baz String
3741 <para>Deriving instances of multi-parameter type classes for newtypes is
3742 also allowed:</para>
3745 newtype Foo a = MkFoo (State Int a)
3747 deriving (MonadState Int) for Foo
3755 <sect2 id="typing-binds">
3756 <title>Generalised typing of mutually recursive bindings</title>
3759 The Haskell Report specifies that a group of bindings (at top level, or in a
3760 <literal>let</literal> or <literal>where</literal>) should be sorted into
3761 strongly-connected components, and then type-checked in dependency order
3762 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3763 Report, Section 4.5.1</ulink>).
3764 As each group is type-checked, any binders of the group that
3766 an explicit type signature are put in the type environment with the specified
3768 and all others are monomorphic until the group is generalised
3769 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3772 <para>Following a suggestion of Mark Jones, in his paper
3773 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3775 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3777 <emphasis>the dependency analysis ignores references to variables that have an explicit
3778 type signature</emphasis>.
3779 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3780 typecheck. For example, consider:
3782 f :: Eq a => a -> Bool
3783 f x = (x == x) || g True || g "Yes"
3785 g y = (y <= y) || f True
3787 This is rejected by Haskell 98, but under Jones's scheme the definition for
3788 <literal>g</literal> is typechecked first, separately from that for
3789 <literal>f</literal>,
3790 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3791 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3792 type is generalised, to get
3794 g :: Ord a => a -> Bool
3796 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3797 <literal>g</literal> in the type environment.
3801 The same refined dependency analysis also allows the type signatures of
3802 mutually-recursive functions to have different contexts, something that is illegal in
3803 Haskell 98 (Section 4.5.2, last sentence). With
3804 <option>-fglasgow-exts</option>
3805 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3806 type signatures; in practice this means that only variables bound by the same
3807 pattern binding must have the same context. For example, this is fine:
3809 f :: Eq a => a -> Bool
3810 f x = (x == x) || g True
3812 g :: Ord a => a -> Bool
3813 g y = (y <= y) || f True
3819 <!-- ==================== End of type system extensions ================= -->
3821 <!-- ====================== Generalised algebraic data types ======================= -->
3824 <title>Generalised Algebraic Data Types (GADTs)</title>
3826 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types by allowing you
3827 to give the type signatures of constructors explicitly. For example:
3830 Lit :: Int -> Term Int
3831 Succ :: Term Int -> Term Int
3832 IsZero :: Term Int -> Term Bool
3833 If :: Term Bool -> Term a -> Term a -> Term a
3834 Pair :: Term a -> Term b -> Term (a,b)
3836 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3837 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3838 for these <literal>Terms</literal>:
3842 eval (Succ t) = 1 + eval t
3843 eval (IsZero t) = eval t == 0
3844 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3845 eval (Pair e1 e2) = (eval e1, eval e2)
3847 These and many other examples are given in papers by Hongwei Xi, and
3848 Tim Sheard. There is a longer introduction
3849 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3851 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
3852 may use different notation to that implemented in GHC.
3855 The rest of this section outlines the extensions to GHC that support GADTs.
3856 It is far from comprehensive, but the design closely follows that described in
3858 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
3859 unification-based type inference for GADTs</ulink>,
3860 which appeared in ICFP 2006.
3863 Data type declarations have a 'where' form, as exemplified above. The type signature of
3864 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3865 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3866 have no scope. Indeed, one can write a kind signature instead:
3868 data Term :: * -> * where ...
3870 or even a mixture of the two:
3872 data Foo a :: (* -> *) -> * where ...
3874 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3877 data Foo a (b :: * -> *) where ...
3882 There are no restrictions on the type of the data constructor, except that the result
3883 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3884 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3888 You can use record syntax on a GADT-style data type declaration:
3892 Lit { val :: Int } :: Term Int
3893 Succ { num :: Term Int } :: Term Int
3894 Pred { num :: Term Int } :: Term Int
3895 IsZero { arg :: Term Int } :: Term Bool
3896 Pair { arg1 :: Term a
3899 If { cnd :: Term Bool
3904 For every constructor that has a field <literal>f</literal>, (a) the type of
3905 field <literal>f</literal> must be the same; and (b) the
3906 result type of the constructor must be the same; both modulo alpha conversion.
3907 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3909 single name. Although their field types are both <literal>Term Int</literal>,
3910 their selector functions actually have different types:
3913 num :: Term Int -> Term Int
3914 arg :: Term Bool -> Term Int
3917 At the moment, record updates are not yet possible with GADT, so support is
3918 limited to record construction, selection and pattern matching:
3921 someTerm :: Term Bool
3922 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3925 eval Lit { val = i } = i
3926 eval Succ { num = t } = eval t + 1
3927 eval Pred { num = t } = eval t - 1
3928 eval IsZero { arg = t } = eval t == 0
3929 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3930 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3936 You can use strictness annotations, in the obvious places
3937 in the constructor type:
3940 Lit :: !Int -> Term Int
3941 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3942 Pair :: Term a -> Term b -> Term (a,b)
3947 You can use a <literal>deriving</literal> clause on a GADT-style data type
3948 declaration, but only if the data type could also have been declared in
3949 Haskell-98 syntax. For example, these two declarations are equivalent
3951 data Maybe1 a where {
3952 Nothing1 :: Maybe1 a ;
3953 Just1 :: a -> Maybe1 a
3954 } deriving( Eq, Ord )
3956 data Maybe2 a = Nothing2 | Just2 a
3959 This simply allows you to declare a vanilla Haskell-98 data type using the
3960 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3964 Pattern matching causes type refinement. For example, in the right hand side of the equation
3969 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3970 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3971 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3973 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3974 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3975 occur. However, the refinement is quite general. For example, if we had:
3977 eval :: Term a -> a -> a
3978 eval (Lit i) j = i+j
3980 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3981 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3982 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3988 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3990 data T a = forall b. MkT b (b->a)
3991 data T' a where { MKT :: b -> (b->a) -> T' a }
3996 <!-- ====================== End of Generalised algebraic data types ======================= -->
3998 <!-- ====================== TEMPLATE HASKELL ======================= -->
4000 <sect1 id="template-haskell">
4001 <title>Template Haskell</title>
4003 <para>Template Haskell allows you to do compile-time meta-programming in
4006 the main technical innovations is discussed in "<ulink
4007 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4008 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4011 There is a Wiki page about
4012 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4013 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4017 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4018 Haskell library reference material</ulink>
4019 (search for the type ExpQ).
4020 [Temporary: many changes to the original design are described in
4021 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4022 Not all of these changes are in GHC 6.6.]
4025 <para> The first example from that paper is set out below as a worked example to help get you started.
4029 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4030 Tim Sheard is going to expand it.)
4034 <title>Syntax</title>
4036 <para> Template Haskell has the following new syntactic
4037 constructions. You need to use the flag
4038 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4039 </indexterm>to switch these syntactic extensions on
4040 (<option>-fth</option> is no longer implied by
4041 <option>-fglasgow-exts</option>).</para>
4045 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4046 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4047 There must be no space between the "$" and the identifier or parenthesis. This use
4048 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4049 of "." as an infix operator. If you want the infix operator, put spaces around it.
4051 <para> A splice can occur in place of
4053 <listitem><para> an expression; the spliced expression must
4054 have type <literal>Q Exp</literal></para></listitem>
4055 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4056 <listitem><para> [Planned, but not implemented yet.] a
4057 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4059 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4060 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4066 A expression quotation is written in Oxford brackets, thus:
4068 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4069 the quotation has type <literal>Expr</literal>.</para></listitem>
4070 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4071 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4072 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4073 the quotation has type <literal>Type</literal>.</para></listitem>
4074 </itemizedlist></para></listitem>
4077 Reification is written thus:
4079 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4080 has type <literal>Dec</literal>. </para></listitem>
4081 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4082 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4083 <listitem><para> Still to come: fixities </para></listitem>
4085 </itemizedlist></para>
4092 <sect2> <title> Using Template Haskell </title>
4096 The data types and monadic constructor functions for Template Haskell are in the library
4097 <literal>Language.Haskell.THSyntax</literal>.
4101 You can only run a function at compile time if it is imported from another module. That is,
4102 you can't define a function in a module, and call it from within a splice in the same module.
4103 (It would make sense to do so, but it's hard to implement.)
4107 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4110 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4111 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4112 compiles and runs a program, and then looks at the result. So it's important that
4113 the program it compiles produces results whose representations are identical to
4114 those of the compiler itself.
4118 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4119 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4124 <sect2> <title> A Template Haskell Worked Example </title>
4125 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4126 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4133 -- Import our template "pr"
4134 import Printf ( pr )
4136 -- The splice operator $ takes the Haskell source code
4137 -- generated at compile time by "pr" and splices it into
4138 -- the argument of "putStrLn".
4139 main = putStrLn ( $(pr "Hello") )
4145 -- Skeletal printf from the paper.
4146 -- It needs to be in a separate module to the one where
4147 -- you intend to use it.
4149 -- Import some Template Haskell syntax
4150 import Language.Haskell.TH
4152 -- Describe a format string
4153 data Format = D | S | L String
4155 -- Parse a format string. This is left largely to you
4156 -- as we are here interested in building our first ever
4157 -- Template Haskell program and not in building printf.
4158 parse :: String -> [Format]
4161 -- Generate Haskell source code from a parsed representation
4162 -- of the format string. This code will be spliced into
4163 -- the module which calls "pr", at compile time.
4164 gen :: [Format] -> ExpQ
4165 gen [D] = [| \n -> show n |]
4166 gen [S] = [| \s -> s |]
4167 gen [L s] = stringE s
4169 -- Here we generate the Haskell code for the splice
4170 -- from an input format string.
4171 pr :: String -> ExpQ
4172 pr s = gen (parse s)
4175 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4178 $ ghc --make -fth main.hs -o main.exe
4181 <para>Run "main.exe" and here is your output:</para>
4191 <title>Using Template Haskell with Profiling</title>
4192 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4194 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4195 interpreter to run the splice expressions. The bytecode interpreter
4196 runs the compiled expression on top of the same runtime on which GHC
4197 itself is running; this means that the compiled code referred to by
4198 the interpreted expression must be compatible with this runtime, and
4199 in particular this means that object code that is compiled for
4200 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4201 expression, because profiled object code is only compatible with the
4202 profiling version of the runtime.</para>
4204 <para>This causes difficulties if you have a multi-module program
4205 containing Template Haskell code and you need to compile it for
4206 profiling, because GHC cannot load the profiled object code and use it
4207 when executing the splices. Fortunately GHC provides a workaround.
4208 The basic idea is to compile the program twice:</para>
4212 <para>Compile the program or library first the normal way, without
4213 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4216 <para>Then compile it again with <option>-prof</option>, and
4217 additionally use <option>-osuf
4218 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4219 to name the object files differentliy (you can choose any suffix
4220 that isn't the normal object suffix here). GHC will automatically
4221 load the object files built in the first step when executing splice
4222 expressions. If you omit the <option>-osuf</option> flag when
4223 building with <option>-prof</option> and Template Haskell is used,
4224 GHC will emit an error message. </para>
4231 <!-- ===================== Arrow notation =================== -->
4233 <sect1 id="arrow-notation">
4234 <title>Arrow notation
4237 <para>Arrows are a generalization of monads introduced by John Hughes.
4238 For more details, see
4243 “Generalising Monads to Arrows”,
4244 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4245 pp67–111, May 2000.
4251 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4252 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4258 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4259 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4265 and the arrows web page at
4266 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4267 With the <option>-farrows</option> flag, GHC supports the arrow
4268 notation described in the second of these papers.
4269 What follows is a brief introduction to the notation;
4270 it won't make much sense unless you've read Hughes's paper.
4271 This notation is translated to ordinary Haskell,
4272 using combinators from the
4273 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4277 <para>The extension adds a new kind of expression for defining arrows:
4279 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4280 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4282 where <literal>proc</literal> is a new keyword.
4283 The variables of the pattern are bound in the body of the
4284 <literal>proc</literal>-expression,
4285 which is a new sort of thing called a <firstterm>command</firstterm>.
4286 The syntax of commands is as follows:
4288 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4289 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4290 | <replaceable>cmd</replaceable><superscript>0</superscript>
4292 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4293 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4294 infix operators as for expressions, and
4296 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4297 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4298 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4299 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4300 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4301 | <replaceable>fcmd</replaceable>
4303 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4304 | ( <replaceable>cmd</replaceable> )
4305 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4307 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4308 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4309 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4310 | <replaceable>cmd</replaceable>
4312 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4313 except that the bodies are commands instead of expressions.
4317 Commands produce values, but (like monadic computations)
4318 may yield more than one value,
4319 or none, and may do other things as well.
4320 For the most part, familiarity with monadic notation is a good guide to
4322 However the values of expressions, even monadic ones,
4323 are determined by the values of the variables they contain;
4324 this is not necessarily the case for commands.
4328 A simple example of the new notation is the expression
4330 proc x -> f -< x+1
4332 We call this a <firstterm>procedure</firstterm> or
4333 <firstterm>arrow abstraction</firstterm>.
4334 As with a lambda expression, the variable <literal>x</literal>
4335 is a new variable bound within the <literal>proc</literal>-expression.
4336 It refers to the input to the arrow.
4337 In the above example, <literal>-<</literal> is not an identifier but an
4338 new reserved symbol used for building commands from an expression of arrow
4339 type and an expression to be fed as input to that arrow.
4340 (The weird look will make more sense later.)
4341 It may be read as analogue of application for arrows.
4342 The above example is equivalent to the Haskell expression
4344 arr (\ x -> x+1) >>> f
4346 That would make no sense if the expression to the left of
4347 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4348 More generally, the expression to the left of <literal>-<</literal>
4349 may not involve any <firstterm>local variable</firstterm>,
4350 i.e. a variable bound in the current arrow abstraction.
4351 For such a situation there is a variant <literal>-<<</literal>, as in
4353 proc x -> f x -<< x+1
4355 which is equivalent to
4357 arr (\ x -> (f x, x+1)) >>> app
4359 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4361 Such an arrow is equivalent to a monad, so if you're using this form
4362 you may find a monadic formulation more convenient.
4366 <title>do-notation for commands</title>
4369 Another form of command is a form of <literal>do</literal>-notation.
4370 For example, you can write
4379 You can read this much like ordinary <literal>do</literal>-notation,
4380 but with commands in place of monadic expressions.
4381 The first line sends the value of <literal>x+1</literal> as an input to
4382 the arrow <literal>f</literal>, and matches its output against
4383 <literal>y</literal>.
4384 In the next line, the output is discarded.
4385 The arrow <function>returnA</function> is defined in the
4386 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4387 module as <literal>arr id</literal>.
4388 The above example is treated as an abbreviation for
4390 arr (\ x -> (x, x)) >>>
4391 first (arr (\ x -> x+1) >>> f) >>>
4392 arr (\ (y, x) -> (y, (x, y))) >>>
4393 first (arr (\ y -> 2*y) >>> g) >>>
4395 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4396 first (arr (\ (x, z) -> x*z) >>> h) >>>
4397 arr (\ (t, z) -> t+z) >>>
4400 Note that variables not used later in the composition are projected out.
4401 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4403 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4404 module, this reduces to
4406 arr (\ x -> (x+1, x)) >>>
4408 arr (\ (y, x) -> (2*y, (x, y))) >>>
4410 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4412 arr (\ (t, z) -> t+z)
4414 which is what you might have written by hand.
4415 With arrow notation, GHC keeps track of all those tuples of variables for you.
4419 Note that although the above translation suggests that
4420 <literal>let</literal>-bound variables like <literal>z</literal> must be
4421 monomorphic, the actual translation produces Core,
4422 so polymorphic variables are allowed.
4426 It's also possible to have mutually recursive bindings,
4427 using the new <literal>rec</literal> keyword, as in the following example:
4429 counter :: ArrowCircuit a => a Bool Int
4430 counter = proc reset -> do
4431 rec output <- returnA -< if reset then 0 else next
4432 next <- delay 0 -< output+1
4433 returnA -< output
4435 The translation of such forms uses the <function>loop</function> combinator,
4436 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4442 <title>Conditional commands</title>
4445 In the previous example, we used a conditional expression to construct the
4447 Sometimes we want to conditionally execute different commands, as in
4454 which is translated to
4456 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4457 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4459 Since the translation uses <function>|||</function>,
4460 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4464 There are also <literal>case</literal> commands, like
4470 y <- h -< (x1, x2)
4474 The syntax is the same as for <literal>case</literal> expressions,
4475 except that the bodies of the alternatives are commands rather than expressions.
4476 The translation is similar to that of <literal>if</literal> commands.
4482 <title>Defining your own control structures</title>
4485 As we're seen, arrow notation provides constructs,
4486 modelled on those for expressions,
4487 for sequencing, value recursion and conditionals.
4488 But suitable combinators,
4489 which you can define in ordinary Haskell,
4490 may also be used to build new commands out of existing ones.
4491 The basic idea is that a command defines an arrow from environments to values.
4492 These environments assign values to the free local variables of the command.
4493 Thus combinators that produce arrows from arrows
4494 may also be used to build commands from commands.
4495 For example, the <literal>ArrowChoice</literal> class includes a combinator
4497 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4499 so we can use it to build commands:
4501 expr' = proc x -> do
4504 symbol Plus -< ()
4505 y <- term -< ()
4508 symbol Minus -< ()
4509 y <- term -< ()
4512 (The <literal>do</literal> on the first line is needed to prevent the first
4513 <literal><+> ...</literal> from being interpreted as part of the
4514 expression on the previous line.)
4515 This is equivalent to
4517 expr' = (proc x -> returnA -< x)
4518 <+> (proc x -> do
4519 symbol Plus -< ()
4520 y <- term -< ()
4522 <+> (proc x -> do
4523 symbol Minus -< ()
4524 y <- term -< ()
4527 It is essential that this operator be polymorphic in <literal>e</literal>
4528 (representing the environment input to the command
4529 and thence to its subcommands)
4530 and satisfy the corresponding naturality property
4532 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4534 at least for strict <literal>k</literal>.
4535 (This should be automatic if you're not using <function>seq</function>.)
4536 This ensures that environments seen by the subcommands are environments
4537 of the whole command,
4538 and also allows the translation to safely trim these environments.
4539 The operator must also not use any variable defined within the current
4544 We could define our own operator
4546 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4547 untilA body cond = proc x ->
4548 if cond x then returnA -< ()
4551 untilA body cond -< x
4553 and use it in the same way.
4554 Of course this infix syntax only makes sense for binary operators;
4555 there is also a more general syntax involving special brackets:
4559 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4566 <title>Primitive constructs</title>
4569 Some operators will need to pass additional inputs to their subcommands.
4570 For example, in an arrow type supporting exceptions,
4571 the operator that attaches an exception handler will wish to pass the
4572 exception that occurred to the handler.
4573 Such an operator might have a type
4575 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4577 where <literal>Ex</literal> is the type of exceptions handled.
4578 You could then use this with arrow notation by writing a command
4580 body `handleA` \ ex -> handler
4582 so that if an exception is raised in the command <literal>body</literal>,
4583 the variable <literal>ex</literal> is bound to the value of the exception
4584 and the command <literal>handler</literal>,
4585 which typically refers to <literal>ex</literal>, is entered.
4586 Though the syntax here looks like a functional lambda,
4587 we are talking about commands, and something different is going on.
4588 The input to the arrow represented by a command consists of values for
4589 the free local variables in the command, plus a stack of anonymous values.
4590 In all the prior examples, this stack was empty.
4591 In the second argument to <function>handleA</function>,
4592 this stack consists of one value, the value of the exception.
4593 The command form of lambda merely gives this value a name.
4598 the values on the stack are paired to the right of the environment.
4599 So operators like <function>handleA</function> that pass
4600 extra inputs to their subcommands can be designed for use with the notation
4601 by pairing the values with the environment in this way.
4602 More precisely, the type of each argument of the operator (and its result)
4603 should have the form
4605 a (...(e,t1), ... tn) t
4607 where <replaceable>e</replaceable> is a polymorphic variable
4608 (representing the environment)
4609 and <replaceable>ti</replaceable> are the types of the values on the stack,
4610 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4611 The polymorphic variable <replaceable>e</replaceable> must not occur in
4612 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4613 <replaceable>t</replaceable>.
4614 However the arrows involved need not be the same.
4615 Here are some more examples of suitable operators:
4617 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4618 runReader :: ... => a e c -> a' (e,State) c
4619 runState :: ... => a e c -> a' (e,State) (c,State)
4621 We can supply the extra input required by commands built with the last two
4622 by applying them to ordinary expressions, as in
4626 (|runReader (do { ... })|) s
4628 which adds <literal>s</literal> to the stack of inputs to the command
4629 built using <function>runReader</function>.
4633 The command versions of lambda abstraction and application are analogous to
4634 the expression versions.
4635 In particular, the beta and eta rules describe equivalences of commands.
4636 These three features (operators, lambda abstraction and application)
4637 are the core of the notation; everything else can be built using them,
4638 though the results would be somewhat clumsy.
4639 For example, we could simulate <literal>do</literal>-notation by defining
4641 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4642 u `bind` f = returnA &&& u >>> f
4644 bind_ :: Arrow a => a e b -> a e c -> a e c
4645 u `bind_` f = u `bind` (arr fst >>> f)
4647 We could simulate <literal>if</literal> by defining
4649 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4650 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4657 <title>Differences with the paper</title>
4662 <para>Instead of a single form of arrow application (arrow tail) with two
4663 translations, the implementation provides two forms
4664 <quote><literal>-<</literal></quote> (first-order)
4665 and <quote><literal>-<<</literal></quote> (higher-order).
4670 <para>User-defined operators are flagged with banana brackets instead of
4671 a new <literal>form</literal> keyword.
4680 <title>Portability</title>
4683 Although only GHC implements arrow notation directly,
4684 there is also a preprocessor
4686 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4687 that translates arrow notation into Haskell 98
4688 for use with other Haskell systems.
4689 You would still want to check arrow programs with GHC;
4690 tracing type errors in the preprocessor output is not easy.
4691 Modules intended for both GHC and the preprocessor must observe some
4692 additional restrictions:
4697 The module must import
4698 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4704 The preprocessor cannot cope with other Haskell extensions.
4705 These would have to go in separate modules.
4711 Because the preprocessor targets Haskell (rather than Core),
4712 <literal>let</literal>-bound variables are monomorphic.
4723 <!-- ==================== BANG PATTERNS ================= -->
4725 <sect1 id="sec-bang-patterns">
4726 <title>Bang patterns
4727 <indexterm><primary>Bang patterns</primary></indexterm>
4729 <para>GHC supports an extension of pattern matching called <emphasis>bang
4730 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4732 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4733 prime feature description</ulink> contains more discussion and examples
4734 than the material below.
4737 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4740 <sect2 id="sec-bang-patterns-informal">
4741 <title>Informal description of bang patterns
4744 The main idea is to add a single new production to the syntax of patterns:
4748 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4749 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4754 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4755 whereas without the bang it would be lazy.
4756 Bang patterns can be nested of course:
4760 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4761 <literal>y</literal>.
4762 A bang only really has an effect if it precedes a variable or wild-card pattern:
4767 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4768 forces evaluation anyway does nothing.
4770 Bang patterns work in <literal>case</literal> expressions too, of course:
4772 g5 x = let y = f x in body
4773 g6 x = case f x of { y -> body }
4774 g7 x = case f x of { !y -> body }
4776 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4777 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4778 result, and then evaluates <literal>body</literal>.
4780 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4781 definitions too. For example:
4785 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4786 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4787 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4788 in a function argument <literal>![x,y]</literal> means the
4789 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4790 is part of the syntax of <literal>let</literal> bindings.
4795 <sect2 id="sec-bang-patterns-sem">
4796 <title>Syntax and semantics
4800 We add a single new production to the syntax of patterns:
4804 There is one problem with syntactic ambiguity. Consider:
4808 Is this a definition of the infix function "<literal>(!)</literal>",
4809 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4810 ambiguity in favour of the latter. If you want to define
4811 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4816 The semantics of Haskell pattern matching is described in <ulink
4817 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4818 Section 3.17.2</ulink> of the Haskell Report. To this description add
4819 one extra item 10, saying:
4820 <itemizedlist><listitem><para>Matching
4821 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4822 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4823 <listitem><para>otherwise, <literal>pat</literal> is matched against
4824 <literal>v</literal></para></listitem>
4826 </para></listitem></itemizedlist>
4827 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4828 Section 3.17.3</ulink>, add a new case (t):
4830 case v of { !pat -> e; _ -> e' }
4831 = v `seq` case v of { pat -> e; _ -> e' }
4834 That leaves let expressions, whose translation is given in
4835 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4837 of the Haskell Report.
4838 In the translation box, first apply
4839 the following transformation: for each pattern <literal>pi</literal> that is of
4840 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4841 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4842 have a bang at the top, apply the rules in the existing box.
4844 <para>The effect of the let rule is to force complete matching of the pattern
4845 <literal>qi</literal> before evaluation of the body is begun. The bang is
4846 retained in the translated form in case <literal>qi</literal> is a variable,
4854 The let-binding can be recursive. However, it is much more common for
4855 the let-binding to be non-recursive, in which case the following law holds:
4856 <literal>(let !p = rhs in body)</literal>
4858 <literal>(case rhs of !p -> body)</literal>
4861 A pattern with a bang at the outermost level is not allowed at the top level of
4867 <!-- ==================== ASSERTIONS ================= -->
4869 <sect1 id="sec-assertions">
4871 <indexterm><primary>Assertions</primary></indexterm>
4875 If you want to make use of assertions in your standard Haskell code, you
4876 could define a function like the following:
4882 assert :: Bool -> a -> a
4883 assert False x = error "assertion failed!"
4890 which works, but gives you back a less than useful error message --
4891 an assertion failed, but which and where?
4895 One way out is to define an extended <function>assert</function> function which also
4896 takes a descriptive string to include in the error message and
4897 perhaps combine this with the use of a pre-processor which inserts
4898 the source location where <function>assert</function> was used.
4902 Ghc offers a helping hand here, doing all of this for you. For every
4903 use of <function>assert</function> in the user's source:
4909 kelvinToC :: Double -> Double
4910 kelvinToC k = assert (k >= 0.0) (k+273.15)
4916 Ghc will rewrite this to also include the source location where the
4923 assert pred val ==> assertError "Main.hs|15" pred val
4929 The rewrite is only performed by the compiler when it spots
4930 applications of <function>Control.Exception.assert</function>, so you
4931 can still define and use your own versions of
4932 <function>assert</function>, should you so wish. If not, import
4933 <literal>Control.Exception</literal> to make use
4934 <function>assert</function> in your code.
4938 GHC ignores assertions when optimisation is turned on with the
4939 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4940 <literal>assert pred e</literal> will be rewritten to
4941 <literal>e</literal>. You can also disable assertions using the
4942 <option>-fignore-asserts</option>
4943 option<indexterm><primary><option>-fignore-asserts</option></primary>
4944 </indexterm>.</para>
4947 Assertion failures can be caught, see the documentation for the
4948 <literal>Control.Exception</literal> library for the details.
4954 <!-- =============================== PRAGMAS =========================== -->
4956 <sect1 id="pragmas">
4957 <title>Pragmas</title>
4959 <indexterm><primary>pragma</primary></indexterm>
4961 <para>GHC supports several pragmas, or instructions to the
4962 compiler placed in the source code. Pragmas don't normally affect
4963 the meaning of the program, but they might affect the efficiency
4964 of the generated code.</para>
4966 <para>Pragmas all take the form
4968 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4970 where <replaceable>word</replaceable> indicates the type of
4971 pragma, and is followed optionally by information specific to that
4972 type of pragma. Case is ignored in
4973 <replaceable>word</replaceable>. The various values for
4974 <replaceable>word</replaceable> that GHC understands are described
4975 in the following sections; any pragma encountered with an
4976 unrecognised <replaceable>word</replaceable> is (silently)
4979 <sect2 id="deprecated-pragma">
4980 <title>DEPRECATED pragma</title>
4981 <indexterm><primary>DEPRECATED</primary>
4984 <para>The DEPRECATED pragma lets you specify that a particular
4985 function, class, or type, is deprecated. There are two
4990 <para>You can deprecate an entire module thus:</para>
4992 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4995 <para>When you compile any module that import
4996 <literal>Wibble</literal>, GHC will print the specified
5001 <para>You can deprecate a function, class, type, or data constructor, with the
5002 following top-level declaration:</para>
5004 {-# DEPRECATED f, C, T "Don't use these" #-}
5006 <para>When you compile any module that imports and uses any
5007 of the specified entities, GHC will print the specified
5009 <para> You can only depecate entities declared at top level in the module
5010 being compiled, and you can only use unqualified names in the list of
5011 entities being deprecated. A capitalised name, such as <literal>T</literal>
5012 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5013 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5014 both are in scope. If both are in scope, there is currently no way to deprecate
5015 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5018 Any use of the deprecated item, or of anything from a deprecated
5019 module, will be flagged with an appropriate message. However,
5020 deprecations are not reported for
5021 (a) uses of a deprecated function within its defining module, and
5022 (b) uses of a deprecated function in an export list.
5023 The latter reduces spurious complaints within a library
5024 in which one module gathers together and re-exports
5025 the exports of several others.
5027 <para>You can suppress the warnings with the flag
5028 <option>-fno-warn-deprecations</option>.</para>
5031 <sect2 id="include-pragma">
5032 <title>INCLUDE pragma</title>
5034 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5035 of C header files that should be <literal>#include</literal>'d into
5036 the C source code generated by the compiler for the current module (if
5037 compiling via C). For example:</para>
5040 {-# INCLUDE "foo.h" #-}
5041 {-# INCLUDE <stdio.h> #-}</programlisting>
5043 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5044 your source file with any <literal>OPTIONS_GHC</literal>
5047 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5048 to the <option>-#include</option> option (<xref
5049 linkend="options-C-compiler" />), because the
5050 <literal>INCLUDE</literal> pragma is understood by other
5051 compilers. Yet another alternative is to add the include file to each
5052 <literal>foreign import</literal> declaration in your code, but we
5053 don't recommend using this approach with GHC.</para>
5056 <sect2 id="inline-noinline-pragma">
5057 <title>INLINE and NOINLINE pragmas</title>
5059 <para>These pragmas control the inlining of function
5062 <sect3 id="inline-pragma">
5063 <title>INLINE pragma</title>
5064 <indexterm><primary>INLINE</primary></indexterm>
5066 <para>GHC (with <option>-O</option>, as always) tries to
5067 inline (or “unfold”) functions/values that are
5068 “small enough,” thus avoiding the call overhead
5069 and possibly exposing other more-wonderful optimisations.
5070 Normally, if GHC decides a function is “too
5071 expensive” to inline, it will not do so, nor will it
5072 export that unfolding for other modules to use.</para>
5074 <para>The sledgehammer you can bring to bear is the
5075 <literal>INLINE</literal><indexterm><primary>INLINE
5076 pragma</primary></indexterm> pragma, used thusly:</para>
5079 key_function :: Int -> String -> (Bool, Double)
5081 #ifdef __GLASGOW_HASKELL__
5082 {-# INLINE key_function #-}
5086 <para>(You don't need to do the C pre-processor carry-on
5087 unless you're going to stick the code through HBC—it
5088 doesn't like <literal>INLINE</literal> pragmas.)</para>
5090 <para>The major effect of an <literal>INLINE</literal> pragma
5091 is to declare a function's “cost” to be very low.
5092 The normal unfolding machinery will then be very keen to
5095 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5096 function can be put anywhere its type signature could be
5099 <para><literal>INLINE</literal> pragmas are a particularly
5101 <literal>then</literal>/<literal>return</literal> (or
5102 <literal>bind</literal>/<literal>unit</literal>) functions in
5103 a monad. For example, in GHC's own
5104 <literal>UniqueSupply</literal> monad code, we have:</para>
5107 #ifdef __GLASGOW_HASKELL__
5108 {-# INLINE thenUs #-}
5109 {-# INLINE returnUs #-}
5113 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5114 linkend="noinline-pragma"/>).</para>
5117 <sect3 id="noinline-pragma">
5118 <title>NOINLINE pragma</title>
5120 <indexterm><primary>NOINLINE</primary></indexterm>
5121 <indexterm><primary>NOTINLINE</primary></indexterm>
5123 <para>The <literal>NOINLINE</literal> pragma does exactly what
5124 you'd expect: it stops the named function from being inlined
5125 by the compiler. You shouldn't ever need to do this, unless
5126 you're very cautious about code size.</para>
5128 <para><literal>NOTINLINE</literal> is a synonym for
5129 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5130 specified by Haskell 98 as the standard way to disable
5131 inlining, so it should be used if you want your code to be
5135 <sect3 id="phase-control">
5136 <title>Phase control</title>
5138 <para> Sometimes you want to control exactly when in GHC's
5139 pipeline the INLINE pragma is switched on. Inlining happens
5140 only during runs of the <emphasis>simplifier</emphasis>. Each
5141 run of the simplifier has a different <emphasis>phase
5142 number</emphasis>; the phase number decreases towards zero.
5143 If you use <option>-dverbose-core2core</option> you'll see the
5144 sequence of phase numbers for successive runs of the
5145 simplifier. In an INLINE pragma you can optionally specify a
5149 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5150 <literal>f</literal>
5151 until phase <literal>k</literal>, but from phase
5152 <literal>k</literal> onwards be very keen to inline it.
5155 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5156 <literal>f</literal>
5157 until phase <literal>k</literal>, but from phase
5158 <literal>k</literal> onwards do not inline it.
5161 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5162 <literal>f</literal>
5163 until phase <literal>k</literal>, but from phase
5164 <literal>k</literal> onwards be willing to inline it (as if
5165 there was no pragma).
5168 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5169 <literal>f</literal>
5170 until phase <literal>k</literal>, but from phase
5171 <literal>k</literal> onwards do not inline it.
5174 The same information is summarised here:
5176 -- Before phase 2 Phase 2 and later
5177 {-# INLINE [2] f #-} -- No Yes
5178 {-# INLINE [~2] f #-} -- Yes No
5179 {-# NOINLINE [2] f #-} -- No Maybe
5180 {-# NOINLINE [~2] f #-} -- Maybe No
5182 {-# INLINE f #-} -- Yes Yes
5183 {-# NOINLINE f #-} -- No No
5185 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5186 function body is small, or it is applied to interesting-looking arguments etc).
5187 Another way to understand the semantics is this:
5189 <listitem><para>For both INLINE and NOINLINE, the phase number says
5190 when inlining is allowed at all.</para></listitem>
5191 <listitem><para>The INLINE pragma has the additional effect of making the
5192 function body look small, so that when inlining is allowed it is very likely to
5197 <para>The same phase-numbering control is available for RULES
5198 (<xref linkend="rewrite-rules"/>).</para>
5202 <sect2 id="language-pragma">
5203 <title>LANGUAGE pragma</title>
5205 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5206 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5208 <para>This allows language extensions to be enabled in a portable way.
5209 It is the intention that all Haskell compilers support the
5210 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5211 all extensions are supported by all compilers, of
5212 course. The <literal>LANGUAGE</literal> pragma should be used instead
5213 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5215 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5217 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5219 <para>Any extension from the <literal>Extension</literal> type defined in
5221 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>
5225 <sect2 id="line-pragma">
5226 <title>LINE pragma</title>
5228 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5229 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5230 <para>This pragma is similar to C's <literal>#line</literal>
5231 pragma, and is mainly for use in automatically generated Haskell
5232 code. It lets you specify the line number and filename of the
5233 original code; for example</para>
5235 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5237 <para>if you'd generated the current file from something called
5238 <filename>Foo.vhs</filename> and this line corresponds to line
5239 42 in the original. GHC will adjust its error messages to refer
5240 to the line/file named in the <literal>LINE</literal>
5244 <sect2 id="options-pragma">
5245 <title>OPTIONS_GHC pragma</title>
5246 <indexterm><primary>OPTIONS_GHC</primary>
5248 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5251 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5252 additional options that are given to the compiler when compiling
5253 this source file. See <xref linkend="source-file-options"/> for
5256 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5257 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5261 <title>RULES pragma</title>
5263 <para>The RULES pragma lets you specify rewrite rules. It is
5264 described in <xref linkend="rewrite-rules"/>.</para>
5267 <sect2 id="specialize-pragma">
5268 <title>SPECIALIZE pragma</title>
5270 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5271 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5272 <indexterm><primary>overloading, death to</primary></indexterm>
5274 <para>(UK spelling also accepted.) For key overloaded
5275 functions, you can create extra versions (NB: more code space)
5276 specialised to particular types. Thus, if you have an
5277 overloaded function:</para>
5280 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5283 <para>If it is heavily used on lists with
5284 <literal>Widget</literal> keys, you could specialise it as
5288 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5291 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5292 be put anywhere its type signature could be put.</para>
5294 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5295 (a) a specialised version of the function and (b) a rewrite rule
5296 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5297 un-specialised function into a call to the specialised one.</para>
5299 <para>The type in a SPECIALIZE pragma can be any type that is less
5300 polymorphic than the type of the original function. In concrete terms,
5301 if the original function is <literal>f</literal> then the pragma
5303 {-# SPECIALIZE f :: <type> #-}
5305 is valid if and only if the defintion
5307 f_spec :: <type>
5310 is valid. Here are some examples (where we only give the type signature
5311 for the original function, not its code):
5313 f :: Eq a => a -> b -> b
5314 {-# SPECIALISE f :: Int -> b -> b #-}
5316 g :: (Eq a, Ix b) => a -> b -> b
5317 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5319 h :: Eq a => a -> a -> a
5320 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5322 The last of these examples will generate a
5323 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5324 well. If you use this kind of specialisation, let us know how well it works.
5327 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5328 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5329 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5330 The <literal>INLINE</literal> pragma affects the specialised verison of the
5331 function (only), and applies even if the function is recursive. The motivating
5334 -- A GADT for arrays with type-indexed representation
5336 ArrInt :: !Int -> ByteArray# -> Arr Int
5337 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5339 (!:) :: Arr e -> Int -> e
5340 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5341 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5342 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5343 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5345 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5346 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5347 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5348 the specialised function will be inlined. It has two calls to
5349 <literal>(!:)</literal>,
5350 both at type <literal>Int</literal>. Both these calls fire the first
5351 specialisation, whose body is also inlined. The result is a type-based
5352 unrolling of the indexing function.</para>
5353 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5354 on an ordinarily-recursive function.</para>
5356 <para>Note: In earlier versions of GHC, it was possible to provide your own
5357 specialised function for a given type:
5360 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5363 This feature has been removed, as it is now subsumed by the
5364 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5368 <sect2 id="specialize-instance-pragma">
5369 <title>SPECIALIZE instance pragma
5373 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5374 <indexterm><primary>overloading, death to</primary></indexterm>
5375 Same idea, except for instance declarations. For example:
5378 instance (Eq a) => Eq (Foo a) where {
5379 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5383 The pragma must occur inside the <literal>where</literal> part
5384 of the instance declaration.
5387 Compatible with HBC, by the way, except perhaps in the placement
5393 <sect2 id="unpack-pragma">
5394 <title>UNPACK pragma</title>
5396 <indexterm><primary>UNPACK</primary></indexterm>
5398 <para>The <literal>UNPACK</literal> indicates to the compiler
5399 that it should unpack the contents of a constructor field into
5400 the constructor itself, removing a level of indirection. For
5404 data T = T {-# UNPACK #-} !Float
5405 {-# UNPACK #-} !Float
5408 <para>will create a constructor <literal>T</literal> containing
5409 two unboxed floats. This may not always be an optimisation: if
5410 the <function>T</function> constructor is scrutinised and the
5411 floats passed to a non-strict function for example, they will
5412 have to be reboxed (this is done automatically by the
5415 <para>Unpacking constructor fields should only be used in
5416 conjunction with <option>-O</option>, in order to expose
5417 unfoldings to the compiler so the reboxing can be removed as
5418 often as possible. For example:</para>
5422 f (T f1 f2) = f1 + f2
5425 <para>The compiler will avoid reboxing <function>f1</function>
5426 and <function>f2</function> by inlining <function>+</function>
5427 on floats, but only when <option>-O</option> is on.</para>
5429 <para>Any single-constructor data is eligible for unpacking; for
5433 data T = T {-# UNPACK #-} !(Int,Int)
5436 <para>will store the two <literal>Int</literal>s directly in the
5437 <function>T</function> constructor, by flattening the pair.
5438 Multi-level unpacking is also supported:</para>
5441 data T = T {-# UNPACK #-} !S
5442 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5445 <para>will store two unboxed <literal>Int#</literal>s
5446 directly in the <function>T</function> constructor. The
5447 unpacker can see through newtypes, too.</para>
5449 <para>If a field cannot be unpacked, you will not get a warning,
5450 so it might be an idea to check the generated code with
5451 <option>-ddump-simpl</option>.</para>
5453 <para>See also the <option>-funbox-strict-fields</option> flag,
5454 which essentially has the effect of adding
5455 <literal>{-# UNPACK #-}</literal> to every strict
5456 constructor field.</para>
5461 <!-- ======================= REWRITE RULES ======================== -->
5463 <sect1 id="rewrite-rules">
5464 <title>Rewrite rules
5466 <indexterm><primary>RULES pragma</primary></indexterm>
5467 <indexterm><primary>pragma, RULES</primary></indexterm>
5468 <indexterm><primary>rewrite rules</primary></indexterm></title>
5471 The programmer can specify rewrite rules as part of the source program
5472 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5473 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5474 and (b) the <option>-frules-off</option> flag
5475 (<xref linkend="options-f"/>) is not specified, and (c) the
5476 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5485 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5492 <title>Syntax</title>
5495 From a syntactic point of view:
5501 There may be zero or more rules in a <literal>RULES</literal> pragma.
5508 Each rule has a name, enclosed in double quotes. The name itself has
5509 no significance at all. It is only used when reporting how many times the rule fired.
5515 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5516 immediately after the name of the rule. Thus:
5519 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5522 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5523 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5532 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5533 is set, so you must lay out your rules starting in the same column as the
5534 enclosing definitions.
5541 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5542 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5543 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5544 by spaces, just like in a type <literal>forall</literal>.
5550 A pattern variable may optionally have a type signature.
5551 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5552 For example, here is the <literal>foldr/build</literal> rule:
5555 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5556 foldr k z (build g) = g k z
5559 Since <function>g</function> has a polymorphic type, it must have a type signature.
5566 The left hand side of a rule must consist of a top-level variable applied
5567 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5570 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5571 "wrong2" forall f. f True = True
5574 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5581 A rule does not need to be in the same module as (any of) the
5582 variables it mentions, though of course they need to be in scope.
5588 Rules are automatically exported from a module, just as instance declarations are.
5599 <title>Semantics</title>
5602 From a semantic point of view:
5608 Rules are only applied if you use the <option>-O</option> flag.
5614 Rules are regarded as left-to-right rewrite rules.
5615 When GHC finds an expression that is a substitution instance of the LHS
5616 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5617 By "a substitution instance" we mean that the LHS can be made equal to the
5618 expression by substituting for the pattern variables.
5625 The LHS and RHS of a rule are typechecked, and must have the
5633 GHC makes absolutely no attempt to verify that the LHS and RHS
5634 of a rule have the same meaning. That is undecidable in general, and
5635 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5642 GHC makes no attempt to make sure that the rules are confluent or
5643 terminating. For example:
5646 "loop" forall x,y. f x y = f y x
5649 This rule will cause the compiler to go into an infinite loop.
5656 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5662 GHC currently uses a very simple, syntactic, matching algorithm
5663 for matching a rule LHS with an expression. It seeks a substitution
5664 which makes the LHS and expression syntactically equal modulo alpha
5665 conversion. The pattern (rule), but not the expression, is eta-expanded if
5666 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5667 But not beta conversion (that's called higher-order matching).
5671 Matching is carried out on GHC's intermediate language, which includes
5672 type abstractions and applications. So a rule only matches if the
5673 types match too. See <xref linkend="rule-spec"/> below.
5679 GHC keeps trying to apply the rules as it optimises the program.
5680 For example, consider:
5689 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5690 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5691 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5692 not be substituted, and the rule would not fire.
5699 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5700 that appears on the LHS of a rule</emphasis>, because once you have substituted
5701 for something you can't match against it (given the simple minded
5702 matching). So if you write the rule
5705 "map/map" forall f,g. map f . map g = map (f.g)
5708 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5709 It will only match something written with explicit use of ".".
5710 Well, not quite. It <emphasis>will</emphasis> match the expression
5716 where <function>wibble</function> is defined:
5719 wibble f g = map f . map g
5722 because <function>wibble</function> will be inlined (it's small).
5724 Later on in compilation, GHC starts inlining even things on the
5725 LHS of rules, but still leaves the rules enabled. This inlining
5726 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5733 All rules are implicitly exported from the module, and are therefore
5734 in force in any module that imports the module that defined the rule, directly
5735 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5736 in force when compiling A.) The situation is very similar to that for instance
5748 <title>List fusion</title>
5751 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5752 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5753 intermediate list should be eliminated entirely.
5757 The following are good producers:
5769 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5775 Explicit lists (e.g. <literal>[True, False]</literal>)
5781 The cons constructor (e.g <literal>3:4:[]</literal>)
5787 <function>++</function>
5793 <function>map</function>
5799 <function>take</function>, <function>filter</function>
5805 <function>iterate</function>, <function>repeat</function>
5811 <function>zip</function>, <function>zipWith</function>
5820 The following are good consumers:
5832 <function>array</function> (on its second argument)
5838 <function>length</function>
5844 <function>++</function> (on its first argument)
5850 <function>foldr</function>
5856 <function>map</function>
5862 <function>take</function>, <function>filter</function>
5868 <function>concat</function>
5874 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5880 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5881 will fuse with one but not the other)
5887 <function>partition</function>
5893 <function>head</function>
5899 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5905 <function>sequence_</function>
5911 <function>msum</function>
5917 <function>sortBy</function>
5926 So, for example, the following should generate no intermediate lists:
5929 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5935 This list could readily be extended; if there are Prelude functions that you use
5936 a lot which are not included, please tell us.
5940 If you want to write your own good consumers or producers, look at the
5941 Prelude definitions of the above functions to see how to do so.
5946 <sect2 id="rule-spec">
5947 <title>Specialisation
5951 Rewrite rules can be used to get the same effect as a feature
5952 present in earlier versions of GHC.
5953 For example, suppose that:
5956 genericLookup :: Ord a => Table a b -> a -> b
5957 intLookup :: Table Int b -> Int -> b
5960 where <function>intLookup</function> is an implementation of
5961 <function>genericLookup</function> that works very fast for
5962 keys of type <literal>Int</literal>. You might wish
5963 to tell GHC to use <function>intLookup</function> instead of
5964 <function>genericLookup</function> whenever the latter was called with
5965 type <literal>Table Int b -> Int -> b</literal>.
5966 It used to be possible to write
5969 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5972 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5975 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5978 This slightly odd-looking rule instructs GHC to replace
5979 <function>genericLookup</function> by <function>intLookup</function>
5980 <emphasis>whenever the types match</emphasis>.
5981 What is more, this rule does not need to be in the same
5982 file as <function>genericLookup</function>, unlike the
5983 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5984 have an original definition available to specialise).
5987 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5988 <function>intLookup</function> really behaves as a specialised version
5989 of <function>genericLookup</function>!!!</para>
5991 <para>An example in which using <literal>RULES</literal> for
5992 specialisation will Win Big:
5995 toDouble :: Real a => a -> Double
5996 toDouble = fromRational . toRational
5998 {-# RULES "toDouble/Int" toDouble = i2d #-}
5999 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6002 The <function>i2d</function> function is virtually one machine
6003 instruction; the default conversion—via an intermediate
6004 <literal>Rational</literal>—is obscenely expensive by
6011 <title>Controlling what's going on</title>
6019 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6025 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6026 If you add <option>-dppr-debug</option> you get a more detailed listing.
6032 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6035 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6036 {-# INLINE build #-}
6040 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6041 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6042 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6043 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6050 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6051 see how to write rules that will do fusion and yet give an efficient
6052 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6062 <sect2 id="core-pragma">
6063 <title>CORE pragma</title>
6065 <indexterm><primary>CORE pragma</primary></indexterm>
6066 <indexterm><primary>pragma, CORE</primary></indexterm>
6067 <indexterm><primary>core, annotation</primary></indexterm>
6070 The external core format supports <quote>Note</quote> annotations;
6071 the <literal>CORE</literal> pragma gives a way to specify what these
6072 should be in your Haskell source code. Syntactically, core
6073 annotations are attached to expressions and take a Haskell string
6074 literal as an argument. The following function definition shows an
6078 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6081 Semantically, this is equivalent to:
6089 However, when external for is generated (via
6090 <option>-fext-core</option>), there will be Notes attached to the
6091 expressions <function>show</function> and <varname>x</varname>.
6092 The core function declaration for <function>f</function> is:
6096 f :: %forall a . GHCziShow.ZCTShow a ->
6097 a -> GHCziBase.ZMZN GHCziBase.Char =
6098 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6100 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6102 (tpl1::GHCziBase.Int ->
6104 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6106 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6107 (tpl3::GHCziBase.ZMZN a ->
6108 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6116 Here, we can see that the function <function>show</function> (which
6117 has been expanded out to a case expression over the Show dictionary)
6118 has a <literal>%note</literal> attached to it, as does the
6119 expression <varname>eta</varname> (which used to be called
6120 <varname>x</varname>).
6127 <sect1 id="special-ids">
6128 <title>Special built-in functions</title>
6129 <para>GHC has a few built-in funcions with special behaviour,
6130 described in this section. All are exported by
6131 <literal>GHC.Exts</literal>.</para>
6133 <sect2> <title>The <literal>seq</literal> function </title>
6135 The function <literal>seq</literal> is as described in the Haskell98 Report.
6139 It evaluates its first argument to head normal form, and then returns its
6140 second argument as the result. The reason that it is documented here is
6141 that, despite <literal>seq</literal>'s polymorphism, its
6142 second argument can have an unboxed type, or
6143 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6144 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6145 to be instantiated to an unboxed type, which is not usually allowed.
6149 <sect2> <title>The <literal>inline</literal> function </title>
6151 The <literal>inline</literal> function is somewhat experimental.
6155 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6156 is inlined, regardless of its size. More precisely, the call
6157 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6159 This allows the programmer to control inlining from
6160 a particular <emphasis>call site</emphasis>
6161 rather than the <emphasis>definition site</emphasis> of the function
6162 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6165 This inlining occurs regardless of the argument to the call
6166 or the size of <literal>f</literal>'s definition; it is unconditional.
6167 The main caveat is that <literal>f</literal>'s definition must be
6168 visible to the compiler. That is, <literal>f</literal> must be
6169 let-bound in the current scope.
6170 If no inlining takes place, the <literal>inline</literal> function
6171 expands to the identity function in Phase zero; so its use imposes
6174 <para> If the function is defined in another
6175 module, GHC only exposes its inlining in the interface file if the
6176 function is sufficiently small that it <emphasis>might</emphasis> be
6177 inlined by the automatic mechanism. There is currently no way to tell
6178 GHC to expose arbitrarily-large functions in the interface file. (This
6179 shortcoming is something that could be fixed, with some kind of pragma.)
6183 <sect2> <title>The <literal>lazy</literal> function </title>
6185 The <literal>lazy</literal> function restrains strictness analysis a little:
6189 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6190 but <literal>lazy</literal> has a magical property so far as strictness
6191 analysis is concerned: it is lazy in its first argument,
6192 even though its semantics is strict. After strictness analysis has run,
6193 calls to <literal>lazy</literal> are inlined to be the identity function.
6196 This behaviour is occasionally useful when controlling evaluation order.
6197 Notably, <literal>lazy</literal> is used in the library definition of
6198 <literal>Control.Parallel.par</literal>:
6201 par x y = case (par# x) of { _ -> lazy y }
6203 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6204 look strict in <literal>y</literal> which would defeat the whole
6205 purpose of <literal>par</literal>.
6208 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6214 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6216 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6217 typechecker entirely. It has type
6219 unsafeCoerce# :: a -> b
6221 That is, it allows you to coerce any type into any other type. If you use this
6222 function, you had better get it right, otherwise segmentation faults await.
6223 It is generally used when you want to write a program that you know is
6224 well-typed, but where Haskell's type system is not expressive enough to prove
6225 that it is well typed.
6228 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6229 although extremely bad things will happen if you coerce a boxed type
6238 <sect1 id="generic-classes">
6239 <title>Generic classes</title>
6242 The ideas behind this extension are described in detail in "Derivable type classes",
6243 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6244 An example will give the idea:
6252 fromBin :: [Int] -> (a, [Int])
6254 toBin {| Unit |} Unit = []
6255 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6256 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6257 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6259 fromBin {| Unit |} bs = (Unit, bs)
6260 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6261 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6262 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6263 (y,bs'') = fromBin bs'
6266 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6267 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6268 which are defined thus in the library module <literal>Generics</literal>:
6272 data a :+: b = Inl a | Inr b
6273 data a :*: b = a :*: b
6276 Now you can make a data type into an instance of Bin like this:
6278 instance (Bin a, Bin b) => Bin (a,b)
6279 instance Bin a => Bin [a]
6281 That is, just leave off the "where" clause. Of course, you can put in the
6282 where clause and over-ride whichever methods you please.
6286 <title> Using generics </title>
6287 <para>To use generics you need to</para>
6290 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6291 <option>-fgenerics</option> (to generate extra per-data-type code),
6292 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6296 <para>Import the module <literal>Generics</literal> from the
6297 <literal>lang</literal> package. This import brings into
6298 scope the data types <literal>Unit</literal>,
6299 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6300 don't need this import if you don't mention these types
6301 explicitly; for example, if you are simply giving instance
6302 declarations.)</para>
6307 <sect2> <title> Changes wrt the paper </title>
6309 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6310 can be written infix (indeed, you can now use
6311 any operator starting in a colon as an infix type constructor). Also note that
6312 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6313 Finally, note that the syntax of the type patterns in the class declaration
6314 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6315 alone would ambiguous when they appear on right hand sides (an extension we
6316 anticipate wanting).
6320 <sect2> <title>Terminology and restrictions</title>
6322 Terminology. A "generic default method" in a class declaration
6323 is one that is defined using type patterns as above.
6324 A "polymorphic default method" is a default method defined as in Haskell 98.
6325 A "generic class declaration" is a class declaration with at least one
6326 generic default method.
6334 Alas, we do not yet implement the stuff about constructor names and
6341 A generic class can have only one parameter; you can't have a generic
6342 multi-parameter class.
6348 A default method must be defined entirely using type patterns, or entirely
6349 without. So this is illegal:
6352 op :: a -> (a, Bool)
6353 op {| Unit |} Unit = (Unit, True)
6356 However it is perfectly OK for some methods of a generic class to have
6357 generic default methods and others to have polymorphic default methods.
6363 The type variable(s) in the type pattern for a generic method declaration
6364 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:
6368 op {| p :*: q |} (x :*: y) = op (x :: p)
6376 The type patterns in a generic default method must take one of the forms:
6382 where "a" and "b" are type variables. Furthermore, all the type patterns for
6383 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6384 must use the same type variables. So this is illegal:
6388 op {| a :+: b |} (Inl x) = True
6389 op {| p :+: q |} (Inr y) = False
6391 The type patterns must be identical, even in equations for different methods of the class.
6392 So this too is illegal:
6396 op1 {| a :*: b |} (x :*: y) = True
6399 op2 {| p :*: q |} (x :*: y) = False
6401 (The reason for this restriction is that we gather all the equations for a particular type consructor
6402 into a single generic instance declaration.)
6408 A generic method declaration must give a case for each of the three type constructors.
6414 The type for a generic method can be built only from:
6416 <listitem> <para> Function arrows </para> </listitem>
6417 <listitem> <para> Type variables </para> </listitem>
6418 <listitem> <para> Tuples </para> </listitem>
6419 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6421 Here are some example type signatures for generic methods:
6424 op2 :: Bool -> (a,Bool)
6425 op3 :: [Int] -> a -> a
6428 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6432 This restriction is an implementation restriction: we just havn't got around to
6433 implementing the necessary bidirectional maps over arbitrary type constructors.
6434 It would be relatively easy to add specific type constructors, such as Maybe and list,
6435 to the ones that are allowed.</para>
6440 In an instance declaration for a generic class, the idea is that the compiler
6441 will fill in the methods for you, based on the generic templates. However it can only
6446 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6451 No constructor of the instance type has unboxed fields.
6455 (Of course, these things can only arise if you are already using GHC extensions.)
6456 However, you can still give an instance declarations for types which break these rules,
6457 provided you give explicit code to override any generic default methods.
6465 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6466 what the compiler does with generic declarations.
6471 <sect2> <title> Another example </title>
6473 Just to finish with, here's another example I rather like:
6477 nCons {| Unit |} _ = 1
6478 nCons {| a :*: b |} _ = 1
6479 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6482 tag {| Unit |} _ = 1
6483 tag {| a :*: b |} _ = 1
6484 tag {| a :+: b |} (Inl x) = tag x
6485 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6491 <sect1 id="monomorphism">
6492 <title>Control over monomorphism</title>
6494 <para>GHC supports two flags that control the way in which generalisation is
6495 carried out at let and where bindings.
6499 <title>Switching off the dreaded Monomorphism Restriction</title>
6500 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6502 <para>Haskell's monomorphism restriction (see
6503 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6505 of the Haskell Report)
6506 can be completely switched off by
6507 <option>-fno-monomorphism-restriction</option>.
6512 <title>Monomorphic pattern bindings</title>
6513 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6514 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6516 <para> As an experimental change, we are exploring the possibility of
6517 making pattern bindings monomorphic; that is, not generalised at all.
6518 A pattern binding is a binding whose LHS has no function arguments,
6519 and is not a simple variable. For example:
6521 f x = x -- Not a pattern binding
6522 f = \x -> x -- Not a pattern binding
6523 f :: Int -> Int = \x -> x -- Not a pattern binding
6525 (g,h) = e -- A pattern binding
6526 (f) = e -- A pattern binding
6527 [x] = e -- A pattern binding
6529 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6530 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6539 ;;; Local Variables: ***
6541 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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