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.
1312 <sect4 id="existential-records">
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 At the moment, record update syntax is only supported for Haskell 98 data types,
1365 so the following function does <emphasis>not</emphasis> work:
1368 -- This is invalid; use explicit NewCounter instead for now
1369 setTag :: Counter a -> a -> Counter a
1370 setTag obj t = obj{ tag = t }
1379 <title>Restrictions</title>
1382 There are several restrictions on the ways in which existentially-quantified
1383 constructors can be use.
1392 When pattern matching, each pattern match introduces a new,
1393 distinct, type for each existential type variable. These types cannot
1394 be unified with any other type, nor can they escape from the scope of
1395 the pattern match. For example, these fragments are incorrect:
1403 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1404 is the result of <function>f1</function>. One way to see why this is wrong is to
1405 ask what type <function>f1</function> has:
1409 f1 :: Foo -> a -- Weird!
1413 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1418 f1 :: forall a. Foo -> a -- Wrong!
1422 The original program is just plain wrong. Here's another sort of error
1426 f2 (Baz1 a b) (Baz1 p q) = a==q
1430 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1431 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1432 from the two <function>Baz1</function> constructors.
1440 You can't pattern-match on an existentially quantified
1441 constructor in a <literal>let</literal> or <literal>where</literal> group of
1442 bindings. So this is illegal:
1446 f3 x = a==b where { Baz1 a b = x }
1449 Instead, use a <literal>case</literal> expression:
1452 f3 x = case x of Baz1 a b -> a==b
1455 In general, you can only pattern-match
1456 on an existentially-quantified constructor in a <literal>case</literal> expression or
1457 in the patterns of a function definition.
1459 The reason for this restriction is really an implementation one.
1460 Type-checking binding groups is already a nightmare without
1461 existentials complicating the picture. Also an existential pattern
1462 binding at the top level of a module doesn't make sense, because it's
1463 not clear how to prevent the existentially-quantified type "escaping".
1464 So for now, there's a simple-to-state restriction. We'll see how
1472 You can't use existential quantification for <literal>newtype</literal>
1473 declarations. So this is illegal:
1477 newtype T = forall a. Ord a => MkT a
1481 Reason: a value of type <literal>T</literal> must be represented as a
1482 pair of a dictionary for <literal>Ord t</literal> and a value of type
1483 <literal>t</literal>. That contradicts the idea that
1484 <literal>newtype</literal> should have no concrete representation.
1485 You can get just the same efficiency and effect by using
1486 <literal>data</literal> instead of <literal>newtype</literal>. If
1487 there is no overloading involved, then there is more of a case for
1488 allowing an existentially-quantified <literal>newtype</literal>,
1489 because the <literal>data</literal> version does carry an
1490 implementation cost, but single-field existentially quantified
1491 constructors aren't much use. So the simple restriction (no
1492 existential stuff on <literal>newtype</literal>) stands, unless there
1493 are convincing reasons to change it.
1501 You can't use <literal>deriving</literal> to define instances of a
1502 data type with existentially quantified data constructors.
1504 Reason: in most cases it would not make sense. For example:;
1507 data T = forall a. MkT [a] deriving( Eq )
1510 To derive <literal>Eq</literal> in the standard way we would need to have equality
1511 between the single component of two <function>MkT</function> constructors:
1515 (MkT a) == (MkT b) = ???
1518 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1519 It's just about possible to imagine examples in which the derived instance
1520 would make sense, but it seems altogether simpler simply to prohibit such
1521 declarations. Define your own instances!
1532 <!-- ====================== Generalised algebraic data types ======================= -->
1534 <sect3 id="gadt-style">
1535 <title>Declaring data types with explicit constructor signatures</title>
1537 <para>GHC allows you to declare an algebraic data type by
1538 giving the type signatures of constructors explicitly. For example:
1542 Just :: a -> Maybe a
1544 The form is called a "GADT-style declaration"
1545 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1546 can only be declared using this form.</para>
1547 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1548 For example, these two declarations are equivalent:
1550 data Foo = forall a. MkFoo a (a -> Bool)
1551 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1554 <para>Any data type that can be declared in standard Haskell-98 syntax
1555 can also be declared using GADT-style syntax.
1556 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1557 they treat class constraints on the data constructors differently.
1558 Specifically, if the constructor is given a type-class context, that
1559 context is made available by pattern matching. For example:
1562 MkSet :: Eq a => [a] -> Set a
1564 makeSet :: Eq a => [a] -> Set a
1565 makeSet xs = MkSet (nub xs)
1567 insert :: a -> Set a -> Set a
1568 insert a (MkSet as) | a `elem` as = MkSet as
1569 | otherwise = MkSet (a:as)
1571 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1572 gives rise to a <literal>(Eq a)</literal>
1573 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1574 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1575 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1576 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1577 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1578 In the example, the equality dictionary is used to satisfy the equality constraint
1579 generated by the call to <literal>elem</literal>, so that the type of
1580 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1582 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1583 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1584 In Haskell 98 the defintion
1586 data Eq a => Set' a = MkSet' [a]
1588 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1589 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1590 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1591 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1592 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1594 For example, a possible application of GHC's behaviour is to reify dictionaries:
1596 data NumInst a where
1597 MkNumInst :: Num a => NumInst a
1599 intInst :: NumInst Int
1602 plus :: NumInst a -> a -> a -> a
1603 plus MkNumInst p q = p + q
1605 Here, a value of type <literal>NumInst a</literal> is equivalent
1606 to an explicit <literal>(Num a)</literal> dictionary.
1610 The rest of this section gives further details about GADT-style data
1615 The result type of each data constructor must begin with the type constructor being defined.
1616 If the result type of all constructors
1617 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1618 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1619 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1623 The type signature of
1624 each constructor is independent, and is implicitly universally quantified as usual.
1625 Different constructors may have different universally-quantified type variables
1626 and different type-class constraints.
1627 For example, this is fine:
1630 T1 :: Eq b => b -> T b
1631 T2 :: (Show c, Ix c) => c -> [c] -> T c
1636 Unlike a Haskell-98-style
1637 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1638 have no scope. Indeed, one can write a kind signature instead:
1640 data Set :: * -> * where ...
1642 or even a mixture of the two:
1644 data Foo a :: (* -> *) -> * where ...
1646 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1649 data Foo a (b :: * -> *) where ...
1655 You can use strictness annotations, in the obvious places
1656 in the constructor type:
1659 Lit :: !Int -> Term Int
1660 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1661 Pair :: Term a -> Term b -> Term (a,b)
1666 You can use a <literal>deriving</literal> clause on a GADT-style data type
1667 declaration. For example, these two declarations are equivalent
1669 data Maybe1 a where {
1670 Nothing1 :: Maybe1 a ;
1671 Just1 :: a -> Maybe1 a
1672 } deriving( Eq, Ord )
1674 data Maybe2 a = Nothing2 | Just2 a
1680 You can use record syntax on a GADT-style data type declaration:
1684 Adult { name :: String, children :: [Person] } :: Person
1685 Child { name :: String } :: Person
1687 As usual, for every constructor that has a field <literal>f</literal>, the type of
1688 field <literal>f</literal> must be the same (modulo alpha conversion).
1691 At the moment, record updates are not yet possible with GADT-style declarations,
1692 so support is limited to record construction, selection and pattern matching.
1695 aPerson = Adult { name = "Fred", children = [] }
1697 shortName :: Person -> Bool
1698 hasChildren (Adult { children = kids }) = not (null kids)
1699 hasChildren (Child {}) = False
1704 As in the case of existentials declared using the Haskell-98-like record syntax
1705 (<xref linkend="existential-records"/>),
1706 record-selector functions are generated only for those fields that have well-typed
1708 Here is the example of that section, in GADT-style syntax:
1710 data Counter a where
1711 NewCounter { _this :: self
1712 , _inc :: self -> self
1713 , _display :: self -> IO ()
1718 As before, only one selector function is generated here, that for <literal>tag</literal>.
1719 Nevertheless, you can still use all the field names in pattern matching and record construction.
1721 </itemizedlist></para>
1725 <title>Generalised Algebraic Data Types (GADTs)</title>
1727 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1728 by allowing constructors to have richer return types. Here is an example:
1731 Lit :: Int -> Term Int
1732 Succ :: Term Int -> Term Int
1733 IsZero :: Term Int -> Term Bool
1734 If :: Term Bool -> Term a -> Term a -> Term a
1735 Pair :: Term a -> Term b -> Term (a,b)
1737 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1738 case with ordinary data types. This generality allows us to
1739 write a well-typed <literal>eval</literal> function
1740 for these <literal>Terms</literal>:
1744 eval (Succ t) = 1 + eval t
1745 eval (IsZero t) = eval t == 0
1746 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1747 eval (Pair e1 e2) = (eval e1, eval e2)
1749 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1750 For example, in the right hand side of the equation
1755 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1756 A precise specification of the type rules is beyond what this user manual aspires to,
1757 but the design closely follows that described in
1759 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1760 unification-based type inference for GADTs</ulink>,
1762 The general principle is this: <emphasis>type refinement is only carried out
1763 based on user-supplied type annotations</emphasis>.
1764 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1765 and lots of obscure error messages will
1766 occur. However, the refinement is quite general. For example, if we had:
1768 eval :: Term a -> a -> a
1769 eval (Lit i) j = i+j
1771 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1772 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1773 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1776 These and many other examples are given in papers by Hongwei Xi, and
1777 Tim Sheard. There is a longer introduction
1778 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1780 <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
1781 may use different notation to that implemented in GHC.
1784 The rest of this section outlines the extensions to GHC that support GADTs.
1787 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1788 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1789 The result type of each constructor must begin with the type constructor being defined,
1790 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1791 For example, in the <literal>Term</literal> data
1792 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1793 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1798 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1799 an ordianary data type.
1803 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1807 Lit { val :: Int } :: Term Int
1808 Succ { num :: Term Int } :: Term Int
1809 Pred { num :: Term Int } :: Term Int
1810 IsZero { arg :: Term Int } :: Term Bool
1811 Pair { arg1 :: Term a
1814 If { cnd :: Term Bool
1819 However, for GADTs there is the following additional constraint:
1820 every constructor that has a field <literal>f</literal> must have
1821 the same result type (modulo alpha conversion)
1822 Hence, in the above example, we cannot merge the <literal>num</literal>
1823 and <literal>arg</literal> fields above into a
1824 single name. Although their field types are both <literal>Term Int</literal>,
1825 their selector functions actually have different types:
1828 num :: Term Int -> Term Int
1829 arg :: Term Bool -> Term Int
1838 <!-- ====================== End of Generalised algebraic data types ======================= -->
1845 <sect2 id="multi-param-type-classes">
1846 <title>Class declarations</title>
1849 This section, and the next one, documents GHC's type-class extensions.
1850 There's lots of background in the paper <ulink
1851 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1852 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1853 Jones, Erik Meijer).
1856 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1860 <title>Multi-parameter type classes</title>
1862 Multi-parameter type classes are permitted. For example:
1866 class Collection c a where
1867 union :: c a -> c a -> c a
1875 <title>The superclasses of a class declaration</title>
1878 There are no restrictions on the context in a class declaration
1879 (which introduces superclasses), except that the class hierarchy must
1880 be acyclic. So these class declarations are OK:
1884 class Functor (m k) => FiniteMap m k where
1887 class (Monad m, Monad (t m)) => Transform t m where
1888 lift :: m a -> (t m) a
1894 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1895 of "acyclic" involves only the superclass relationships. For example,
1901 op :: D b => a -> b -> b
1904 class C a => D a where { ... }
1908 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1909 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1910 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1917 <sect3 id="class-method-types">
1918 <title>Class method types</title>
1921 Haskell 98 prohibits class method types to mention constraints on the
1922 class type variable, thus:
1925 fromList :: [a] -> s a
1926 elem :: Eq a => a -> s a -> Bool
1928 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1929 contains the constraint <literal>Eq a</literal>, constrains only the
1930 class type variable (in this case <literal>a</literal>).
1931 GHC lifts this restriction.
1938 <sect2 id="functional-dependencies">
1939 <title>Functional dependencies
1942 <para> Functional dependencies are implemented as described by Mark Jones
1943 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1944 In Proceedings of the 9th European Symposium on Programming,
1945 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1949 Functional dependencies are introduced by a vertical bar in the syntax of a
1950 class declaration; e.g.
1952 class (Monad m) => MonadState s m | m -> s where ...
1954 class Foo a b c | a b -> c where ...
1956 There should be more documentation, but there isn't (yet). Yell if you need it.
1959 <sect3><title>Rules for functional dependencies </title>
1961 In a class declaration, all of the class type variables must be reachable (in the sense
1962 mentioned in <xref linkend="type-restrictions"/>)
1963 from the free variables of each method type.
1967 class Coll s a where
1969 insert :: s -> a -> s
1972 is not OK, because the type of <literal>empty</literal> doesn't mention
1973 <literal>a</literal>. Functional dependencies can make the type variable
1976 class Coll s a | s -> a where
1978 insert :: s -> a -> s
1981 Alternatively <literal>Coll</literal> might be rewritten
1984 class Coll s a where
1986 insert :: s a -> a -> s a
1990 which makes the connection between the type of a collection of
1991 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1992 Occasionally this really doesn't work, in which case you can split the
2000 class CollE s => Coll s a where
2001 insert :: s -> a -> s
2008 <title>Background on functional dependencies</title>
2010 <para>The following description of the motivation and use of functional dependencies is taken
2011 from the Hugs user manual, reproduced here (with minor changes) by kind
2012 permission of Mark Jones.
2015 Consider the following class, intended as part of a
2016 library for collection types:
2018 class Collects e ce where
2020 insert :: e -> ce -> ce
2021 member :: e -> ce -> Bool
2023 The type variable e used here represents the element type, while ce is the type
2024 of the container itself. Within this framework, we might want to define
2025 instances of this class for lists or characteristic functions (both of which
2026 can be used to represent collections of any equality type), bit sets (which can
2027 be used to represent collections of characters), or hash tables (which can be
2028 used to represent any collection whose elements have a hash function). Omitting
2029 standard implementation details, this would lead to the following declarations:
2031 instance Eq e => Collects e [e] where ...
2032 instance Eq e => Collects e (e -> Bool) where ...
2033 instance Collects Char BitSet where ...
2034 instance (Hashable e, Collects a ce)
2035 => Collects e (Array Int ce) where ...
2037 All this looks quite promising; we have a class and a range of interesting
2038 implementations. Unfortunately, there are some serious problems with the class
2039 declaration. First, the empty function has an ambiguous type:
2041 empty :: Collects e ce => ce
2043 By "ambiguous" we mean that there is a type variable e that appears on the left
2044 of the <literal>=></literal> symbol, but not on the right. The problem with
2045 this is that, according to the theoretical foundations of Haskell overloading,
2046 we cannot guarantee a well-defined semantics for any term with an ambiguous
2050 We can sidestep this specific problem by removing the empty member from the
2051 class declaration. However, although the remaining members, insert and member,
2052 do not have ambiguous types, we still run into problems when we try to use
2053 them. For example, consider the following two functions:
2055 f x y = insert x . insert y
2058 for which GHC infers the following types:
2060 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2061 g :: (Collects Bool c, Collects Char c) => c -> c
2063 Notice that the type for f allows the two parameters x and y to be assigned
2064 different types, even though it attempts to insert each of the two values, one
2065 after the other, into the same collection. If we're trying to model collections
2066 that contain only one type of value, then this is clearly an inaccurate
2067 type. Worse still, the definition for g is accepted, without causing a type
2068 error. As a result, the error in this code will not be flagged at the point
2069 where it appears. Instead, it will show up only when we try to use g, which
2070 might even be in a different module.
2073 <sect4><title>An attempt to use constructor classes</title>
2076 Faced with the problems described above, some Haskell programmers might be
2077 tempted to use something like the following version of the class declaration:
2079 class Collects e c where
2081 insert :: e -> c e -> c e
2082 member :: e -> c e -> Bool
2084 The key difference here is that we abstract over the type constructor c that is
2085 used to form the collection type c e, and not over that collection type itself,
2086 represented by ce in the original class declaration. This avoids the immediate
2087 problems that we mentioned above: empty has type <literal>Collects e c => c
2088 e</literal>, which is not ambiguous.
2091 The function f from the previous section has a more accurate type:
2093 f :: (Collects e c) => e -> e -> c e -> c e
2095 The function g from the previous section is now rejected with a type error as
2096 we would hope because the type of f does not allow the two arguments to have
2098 This, then, is an example of a multiple parameter class that does actually work
2099 quite well in practice, without ambiguity problems.
2100 There is, however, a catch. This version of the Collects class is nowhere near
2101 as general as the original class seemed to be: only one of the four instances
2102 for <literal>Collects</literal>
2103 given above can be used with this version of Collects because only one of
2104 them---the instance for lists---has a collection type that can be written in
2105 the form c e, for some type constructor c, and element type e.
2109 <sect4><title>Adding functional dependencies</title>
2112 To get a more useful version of the Collects class, Hugs provides a mechanism
2113 that allows programmers to specify dependencies between the parameters of a
2114 multiple parameter class (For readers with an interest in theoretical
2115 foundations and previous work: The use of dependency information can be seen
2116 both as a generalization of the proposal for `parametric type classes' that was
2117 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2118 later framework for "improvement" of qualified types. The
2119 underlying ideas are also discussed in a more theoretical and abstract setting
2120 in a manuscript [implparam], where they are identified as one point in a
2121 general design space for systems of implicit parameterization.).
2123 To start with an abstract example, consider a declaration such as:
2125 class C a b where ...
2127 which tells us simply that C can be thought of as a binary relation on types
2128 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2129 included in the definition of classes to add information about dependencies
2130 between parameters, as in the following examples:
2132 class D a b | a -> b where ...
2133 class E a b | a -> b, b -> a where ...
2135 The notation <literal>a -> b</literal> used here between the | and where
2136 symbols --- not to be
2137 confused with a function type --- indicates that the a parameter uniquely
2138 determines the b parameter, and might be read as "a determines b." Thus D is
2139 not just a relation, but actually a (partial) function. Similarly, from the two
2140 dependencies that are included in the definition of E, we can see that E
2141 represents a (partial) one-one mapping between types.
2144 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2145 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2146 m>=0, meaning that the y parameters are uniquely determined by the x
2147 parameters. Spaces can be used as separators if more than one variable appears
2148 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2149 annotated with multiple dependencies using commas as separators, as in the
2150 definition of E above. Some dependencies that we can write in this notation are
2151 redundant, and will be rejected because they don't serve any useful
2152 purpose, and may instead indicate an error in the program. Examples of
2153 dependencies like this include <literal>a -> a </literal>,
2154 <literal>a -> a a </literal>,
2155 <literal>a -> </literal>, etc. There can also be
2156 some redundancy if multiple dependencies are given, as in
2157 <literal>a->b</literal>,
2158 <literal>b->c </literal>, <literal>a->c </literal>, and
2159 in which some subset implies the remaining dependencies. Examples like this are
2160 not treated as errors. Note that dependencies appear only in class
2161 declarations, and not in any other part of the language. In particular, the
2162 syntax for instance declarations, class constraints, and types is completely
2166 By including dependencies in a class declaration, we provide a mechanism for
2167 the programmer to specify each multiple parameter class more precisely. The
2168 compiler, on the other hand, is responsible for ensuring that the set of
2169 instances that are in scope at any given point in the program is consistent
2170 with any declared dependencies. For example, the following pair of instance
2171 declarations cannot appear together in the same scope because they violate the
2172 dependency for D, even though either one on its own would be acceptable:
2174 instance D Bool Int where ...
2175 instance D Bool Char where ...
2177 Note also that the following declaration is not allowed, even by itself:
2179 instance D [a] b where ...
2181 The problem here is that this instance would allow one particular choice of [a]
2182 to be associated with more than one choice for b, which contradicts the
2183 dependency specified in the definition of D. More generally, this means that,
2184 in any instance of the form:
2186 instance D t s where ...
2188 for some particular types t and s, the only variables that can appear in s are
2189 the ones that appear in t, and hence, if the type t is known, then s will be
2190 uniquely determined.
2193 The benefit of including dependency information is that it allows us to define
2194 more general multiple parameter classes, without ambiguity problems, and with
2195 the benefit of more accurate types. To illustrate this, we return to the
2196 collection class example, and annotate the original definition of <literal>Collects</literal>
2197 with a simple dependency:
2199 class Collects e ce | ce -> e where
2201 insert :: e -> ce -> ce
2202 member :: e -> ce -> Bool
2204 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2205 determined by the type of the collection ce. Note that both parameters of
2206 Collects are of kind *; there are no constructor classes here. Note too that
2207 all of the instances of Collects that we gave earlier can be used
2208 together with this new definition.
2211 What about the ambiguity problems that we encountered with the original
2212 definition? The empty function still has type Collects e ce => ce, but it is no
2213 longer necessary to regard that as an ambiguous type: Although the variable e
2214 does not appear on the right of the => symbol, the dependency for class
2215 Collects tells us that it is uniquely determined by ce, which does appear on
2216 the right of the => symbol. Hence the context in which empty is used can still
2217 give enough information to determine types for both ce and e, without
2218 ambiguity. More generally, we need only regard a type as ambiguous if it
2219 contains a variable on the left of the => that is not uniquely determined
2220 (either directly or indirectly) by the variables on the right.
2223 Dependencies also help to produce more accurate types for user defined
2224 functions, and hence to provide earlier detection of errors, and less cluttered
2225 types for programmers to work with. Recall the previous definition for a
2228 f x y = insert x y = insert x . insert y
2230 for which we originally obtained a type:
2232 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2234 Given the dependency information that we have for Collects, however, we can
2235 deduce that a and b must be equal because they both appear as the second
2236 parameter in a Collects constraint with the same first parameter c. Hence we
2237 can infer a shorter and more accurate type for f:
2239 f :: (Collects a c) => a -> a -> c -> c
2241 In a similar way, the earlier definition of g will now be flagged as a type error.
2244 Although we have given only a few examples here, it should be clear that the
2245 addition of dependency information can help to make multiple parameter classes
2246 more useful in practice, avoiding ambiguity problems, and allowing more general
2247 sets of instance declarations.
2253 <sect2 id="instance-decls">
2254 <title>Instance declarations</title>
2256 <sect3 id="instance-rules">
2257 <title>Relaxed rules for instance declarations</title>
2259 <para>An instance declaration has the form
2261 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 ...
2263 The part before the "<literal>=></literal>" is the
2264 <emphasis>context</emphasis>, while the part after the
2265 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2269 In Haskell 98 the head of an instance declaration
2270 must be of the form <literal>C (T a1 ... an)</literal>, where
2271 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2272 and the <literal>a1 ... an</literal> are distinct type variables.
2273 Furthermore, the assertions in the context of the instance declaration
2274 must be of the form <literal>C a</literal> where <literal>a</literal>
2275 is a type variable that occurs in the head.
2278 The <option>-fglasgow-exts</option> flag loosens these restrictions
2279 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2280 the context and head of the instance declaration can each consist of arbitrary
2281 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2285 For each assertion in the context:
2287 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2288 <listitem><para>The assertion has fewer constructors and variables (taken together
2289 and counting repetitions) than the head</para></listitem>
2293 <listitem><para>The coverage condition. For each functional dependency,
2294 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2295 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2296 every type variable in
2297 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2298 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2299 substitution mapping each type variable in the class declaration to the
2300 corresponding type in the instance declaration.
2303 These restrictions ensure that context reduction terminates: each reduction
2304 step makes the problem smaller by at least one
2305 constructor. For example, the following would make the type checker
2306 loop if it wasn't excluded:
2308 instance C a => C a where ...
2310 For example, these are OK:
2312 instance C Int [a] -- Multiple parameters
2313 instance Eq (S [a]) -- Structured type in head
2315 -- Repeated type variable in head
2316 instance C4 a a => C4 [a] [a]
2317 instance Stateful (ST s) (MutVar s)
2319 -- Head can consist of type variables only
2321 instance (Eq a, Show b) => C2 a b
2323 -- Non-type variables in context
2324 instance Show (s a) => Show (Sized s a)
2325 instance C2 Int a => C3 Bool [a]
2326 instance C2 Int a => C3 [a] b
2330 -- Context assertion no smaller than head
2331 instance C a => C a where ...
2332 -- (C b b) has more more occurrences of b than the head
2333 instance C b b => Foo [b] where ...
2338 The same restrictions apply to instances generated by
2339 <literal>deriving</literal> clauses. Thus the following is accepted:
2341 data MinHeap h a = H a (h a)
2344 because the derived instance
2346 instance (Show a, Show (h a)) => Show (MinHeap h a)
2348 conforms to the above rules.
2352 A useful idiom permitted by the above rules is as follows.
2353 If one allows overlapping instance declarations then it's quite
2354 convenient to have a "default instance" declaration that applies if
2355 something more specific does not:
2361 <para>You can find lots of background material about the reason for these
2362 restrictions in the paper <ulink
2363 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2364 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2368 <sect3 id="undecidable-instances">
2369 <title>Undecidable instances</title>
2372 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2373 For example, sometimes you might want to use the following to get the
2374 effect of a "class synonym":
2376 class (C1 a, C2 a, C3 a) => C a where { }
2378 instance (C1 a, C2 a, C3 a) => C a where { }
2380 This allows you to write shorter signatures:
2386 f :: (C1 a, C2 a, C3 a) => ...
2388 The restrictions on functional dependencies (<xref
2389 linkend="functional-dependencies"/>) are particularly troublesome.
2390 It is tempting to introduce type variables in the context that do not appear in
2391 the head, something that is excluded by the normal rules. For example:
2393 class HasConverter a b | a -> b where
2396 data Foo a = MkFoo a
2398 instance (HasConverter a b,Show b) => Show (Foo a) where
2399 show (MkFoo value) = show (convert value)
2401 This is dangerous territory, however. Here, for example, is a program that would make the
2406 instance F [a] [[a]]
2407 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2409 Similarly, it can be tempting to lift the coverage condition:
2411 class Mul a b c | a b -> c where
2412 (.*.) :: a -> b -> c
2414 instance Mul Int Int Int where (.*.) = (*)
2415 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2416 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2418 The third instance declaration does not obey the coverage condition;
2419 and indeed the (somewhat strange) definition:
2421 f = \ b x y -> if b then x .*. [y] else y
2423 makes instance inference go into a loop, because it requires the constraint
2424 <literal>(Mul a [b] b)</literal>.
2427 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2428 the experimental flag <option>-fallow-undecidable-instances</option>
2429 <indexterm><primary>-fallow-undecidable-instances
2430 option</primary></indexterm>, you can use arbitrary
2431 types in both an instance context and instance head. Termination is ensured by having a
2432 fixed-depth recursion stack. If you exceed the stack depth you get a
2433 sort of backtrace, and the opportunity to increase the stack depth
2434 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2440 <sect3 id="instance-overlap">
2441 <title>Overlapping instances</title>
2443 In general, <emphasis>GHC requires that that it be unambiguous which instance
2445 should be used to resolve a type-class constraint</emphasis>. This behaviour
2446 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2447 <indexterm><primary>-fallow-overlapping-instances
2448 </primary></indexterm>
2449 and <option>-fallow-incoherent-instances</option>
2450 <indexterm><primary>-fallow-incoherent-instances
2451 </primary></indexterm>, as this section discusses. Both these
2452 flags are dynamic flags, and can be set on a per-module basis, using
2453 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2455 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2456 it tries to match every instance declaration against the
2458 by instantiating the head of the instance declaration. For example, consider
2461 instance context1 => C Int a where ... -- (A)
2462 instance context2 => C a Bool where ... -- (B)
2463 instance context3 => C Int [a] where ... -- (C)
2464 instance context4 => C Int [Int] where ... -- (D)
2466 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2467 but (C) and (D) do not. When matching, GHC takes
2468 no account of the context of the instance declaration
2469 (<literal>context1</literal> etc).
2470 GHC's default behaviour is that <emphasis>exactly one instance must match the
2471 constraint it is trying to resolve</emphasis>.
2472 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2473 including both declarations (A) and (B), say); an error is only reported if a
2474 particular constraint matches more than one.
2478 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2479 more than one instance to match, provided there is a most specific one. For
2480 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2481 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2482 most-specific match, the program is rejected.
2485 However, GHC is conservative about committing to an overlapping instance. For example:
2490 Suppose that from the RHS of <literal>f</literal> we get the constraint
2491 <literal>C Int [b]</literal>. But
2492 GHC does not commit to instance (C), because in a particular
2493 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2494 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2495 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2496 GHC will instead pick (C), without complaining about
2497 the problem of subsequent instantiations.
2500 The willingness to be overlapped or incoherent is a property of
2501 the <emphasis>instance declaration</emphasis> itself, controlled by the
2502 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2503 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2504 being defined. Neither flag is required in a module that imports and uses the
2505 instance declaration. Specifically, during the lookup process:
2508 An instance declaration is ignored during the lookup process if (a) a more specific
2509 match is found, and (b) the instance declaration was compiled with
2510 <option>-fallow-overlapping-instances</option>. The flag setting for the
2511 more-specific instance does not matter.
2514 Suppose an instance declaration does not matche the constraint being looked up, but
2515 does unify with it, so that it might match when the constraint is further
2516 instantiated. Usually GHC will regard this as a reason for not committing to
2517 some other constraint. But if the instance declaration was compiled with
2518 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2519 check for that declaration.
2522 These rules make it possible for a library author to design a library that relies on
2523 overlapping instances without the library client having to know.
2526 If an instance declaration is compiled without
2527 <option>-fallow-overlapping-instances</option>,
2528 then that instance can never be overlapped. This could perhaps be
2529 inconvenient. Perhaps the rule should instead say that the
2530 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2531 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2532 at a usage site should be permitted regardless of how the instance declarations
2533 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2534 used at the usage site. (Mind you, the exact usage site can occasionally be
2535 hard to pin down.) We are interested to receive feedback on these points.
2537 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2538 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2543 <title>Type synonyms in the instance head</title>
2546 <emphasis>Unlike Haskell 98, instance heads may use type
2547 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2548 As always, using a type synonym is just shorthand for
2549 writing the RHS of the type synonym definition. For example:
2553 type Point = (Int,Int)
2554 instance C Point where ...
2555 instance C [Point] where ...
2559 is legal. However, if you added
2563 instance C (Int,Int) where ...
2567 as well, then the compiler will complain about the overlapping
2568 (actually, identical) instance declarations. As always, type synonyms
2569 must be fully applied. You cannot, for example, write:
2574 instance Monad P where ...
2578 This design decision is independent of all the others, and easily
2579 reversed, but it makes sense to me.
2587 <sect2 id="type-restrictions">
2588 <title>Type signatures</title>
2590 <sect3><title>The context of a type signature</title>
2592 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2593 the form <emphasis>(class type-variable)</emphasis> or
2594 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2595 these type signatures are perfectly OK
2598 g :: Ord (T a ()) => ...
2602 GHC imposes the following restrictions on the constraints in a type signature.
2606 forall tv1..tvn (c1, ...,cn) => type
2609 (Here, we write the "foralls" explicitly, although the Haskell source
2610 language omits them; in Haskell 98, all the free type variables of an
2611 explicit source-language type signature are universally quantified,
2612 except for the class type variables in a class declaration. However,
2613 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2622 <emphasis>Each universally quantified type variable
2623 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2625 A type variable <literal>a</literal> is "reachable" if it it appears
2626 in the same constraint as either a type variable free in in
2627 <literal>type</literal>, or another reachable type variable.
2628 A value with a type that does not obey
2629 this reachability restriction cannot be used without introducing
2630 ambiguity; that is why the type is rejected.
2631 Here, for example, is an illegal type:
2635 forall a. Eq a => Int
2639 When a value with this type was used, the constraint <literal>Eq tv</literal>
2640 would be introduced where <literal>tv</literal> is a fresh type variable, and
2641 (in the dictionary-translation implementation) the value would be
2642 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2643 can never know which instance of <literal>Eq</literal> to use because we never
2644 get any more information about <literal>tv</literal>.
2648 that the reachability condition is weaker than saying that <literal>a</literal> is
2649 functionally dependent on a type variable free in
2650 <literal>type</literal> (see <xref
2651 linkend="functional-dependencies"/>). The reason for this is there
2652 might be a "hidden" dependency, in a superclass perhaps. So
2653 "reachable" is a conservative approximation to "functionally dependent".
2654 For example, consider:
2656 class C a b | a -> b where ...
2657 class C a b => D a b where ...
2658 f :: forall a b. D a b => a -> a
2660 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2661 but that is not immediately apparent from <literal>f</literal>'s type.
2667 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2668 universally quantified type variables <literal>tvi</literal></emphasis>.
2670 For example, this type is OK because <literal>C a b</literal> mentions the
2671 universally quantified type variable <literal>b</literal>:
2675 forall a. C a b => burble
2679 The next type is illegal because the constraint <literal>Eq b</literal> does not
2680 mention <literal>a</literal>:
2684 forall a. Eq b => burble
2688 The reason for this restriction is milder than the other one. The
2689 excluded types are never useful or necessary (because the offending
2690 context doesn't need to be witnessed at this point; it can be floated
2691 out). Furthermore, floating them out increases sharing. Lastly,
2692 excluding them is a conservative choice; it leaves a patch of
2693 territory free in case we need it later.
2704 <title>For-all hoisting</title>
2706 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2707 end of an arrow, thus:
2709 type Discard a = forall b. a -> b -> a
2711 g :: Int -> Discard Int
2714 Simply expanding the type synonym would give
2716 g :: Int -> (forall b. Int -> b -> Int)
2718 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2720 g :: forall b. Int -> Int -> b -> Int
2722 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2723 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2724 performs the transformation:</emphasis>
2726 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2728 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2730 (In fact, GHC tries to retain as much synonym information as possible for use in
2731 error messages, but that is a usability issue.) This rule applies, of course, whether
2732 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2733 valid way to write <literal>g</literal>'s type signature:
2735 g :: Int -> Int -> forall b. b -> Int
2739 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2742 type Foo a = (?x::Int) => Bool -> a
2747 g :: (?x::Int) => Bool -> Bool -> Int
2755 <sect2 id="implicit-parameters">
2756 <title>Implicit parameters</title>
2758 <para> Implicit parameters are implemented as described in
2759 "Implicit parameters: dynamic scoping with static types",
2760 J Lewis, MB Shields, E Meijer, J Launchbury,
2761 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2765 <para>(Most of the following, stil rather incomplete, documentation is
2766 due to Jeff Lewis.)</para>
2768 <para>Implicit parameter support is enabled with the option
2769 <option>-fimplicit-params</option>.</para>
2772 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2773 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2774 context. In Haskell, all variables are statically bound. Dynamic
2775 binding of variables is a notion that goes back to Lisp, but was later
2776 discarded in more modern incarnations, such as Scheme. Dynamic binding
2777 can be very confusing in an untyped language, and unfortunately, typed
2778 languages, in particular Hindley-Milner typed languages like Haskell,
2779 only support static scoping of variables.
2782 However, by a simple extension to the type class system of Haskell, we
2783 can support dynamic binding. Basically, we express the use of a
2784 dynamically bound variable as a constraint on the type. These
2785 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2786 function uses a dynamically-bound variable <literal>?x</literal>
2787 of type <literal>t'</literal>". For
2788 example, the following expresses the type of a sort function,
2789 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2791 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2793 The dynamic binding constraints are just a new form of predicate in the type class system.
2796 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2797 where <literal>x</literal> is
2798 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2799 Use of this construct also introduces a new
2800 dynamic-binding constraint in the type of the expression.
2801 For example, the following definition
2802 shows how we can define an implicitly parameterized sort function in
2803 terms of an explicitly parameterized <literal>sortBy</literal> function:
2805 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2807 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2813 <title>Implicit-parameter type constraints</title>
2815 Dynamic binding constraints behave just like other type class
2816 constraints in that they are automatically propagated. Thus, when a
2817 function is used, its implicit parameters are inherited by the
2818 function that called it. For example, our <literal>sort</literal> function might be used
2819 to pick out the least value in a list:
2821 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2822 least xs = head (sort xs)
2824 Without lifting a finger, the <literal>?cmp</literal> parameter is
2825 propagated to become a parameter of <literal>least</literal> as well. With explicit
2826 parameters, the default is that parameters must always be explicit
2827 propagated. With implicit parameters, the default is to always
2831 An implicit-parameter type constraint differs from other type class constraints in the
2832 following way: All uses of a particular implicit parameter must have
2833 the same type. This means that the type of <literal>(?x, ?x)</literal>
2834 is <literal>(?x::a) => (a,a)</literal>, and not
2835 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2839 <para> You can't have an implicit parameter in the context of a class or instance
2840 declaration. For example, both these declarations are illegal:
2842 class (?x::Int) => C a where ...
2843 instance (?x::a) => Foo [a] where ...
2845 Reason: exactly which implicit parameter you pick up depends on exactly where
2846 you invoke a function. But the ``invocation'' of instance declarations is done
2847 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2848 Easiest thing is to outlaw the offending types.</para>
2850 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2852 f :: (?x :: [a]) => Int -> Int
2855 g :: (Read a, Show a) => String -> String
2858 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2859 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2860 quite unambiguous, and fixes the type <literal>a</literal>.
2865 <title>Implicit-parameter bindings</title>
2868 An implicit parameter is <emphasis>bound</emphasis> using the standard
2869 <literal>let</literal> or <literal>where</literal> binding forms.
2870 For example, we define the <literal>min</literal> function by binding
2871 <literal>cmp</literal>.
2874 min = let ?cmp = (<=) in least
2878 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2879 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2880 (including in a list comprehension, or do-notation, or pattern guards),
2881 or a <literal>where</literal> clause.
2882 Note the following points:
2885 An implicit-parameter binding group must be a
2886 collection of simple bindings to implicit-style variables (no
2887 function-style bindings, and no type signatures); these bindings are
2888 neither polymorphic or recursive.
2891 You may not mix implicit-parameter bindings with ordinary bindings in a
2892 single <literal>let</literal>
2893 expression; use two nested <literal>let</literal>s instead.
2894 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2898 You may put multiple implicit-parameter bindings in a
2899 single binding group; but they are <emphasis>not</emphasis> treated
2900 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2901 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2902 parameter. The bindings are not nested, and may be re-ordered without changing
2903 the meaning of the program.
2904 For example, consider:
2906 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2908 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2909 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2911 f :: (?x::Int) => Int -> Int
2919 <sect3><title>Implicit parameters and polymorphic recursion</title>
2922 Consider these two definitions:
2925 len1 xs = let ?acc = 0 in len_acc1 xs
2928 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2933 len2 xs = let ?acc = 0 in len_acc2 xs
2935 len_acc2 :: (?acc :: Int) => [a] -> Int
2937 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2939 The only difference between the two groups is that in the second group
2940 <literal>len_acc</literal> is given a type signature.
2941 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2942 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2943 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2944 has a type signature, the recursive call is made to the
2945 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2946 as an implicit parameter. So we get the following results in GHCi:
2953 Adding a type signature dramatically changes the result! This is a rather
2954 counter-intuitive phenomenon, worth watching out for.
2958 <sect3><title>Implicit parameters and monomorphism</title>
2960 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2961 Haskell Report) to implicit parameters. For example, consider:
2969 Since the binding for <literal>y</literal> falls under the Monomorphism
2970 Restriction it is not generalised, so the type of <literal>y</literal> is
2971 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2972 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2973 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2974 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2975 <literal>y</literal> in the body of the <literal>let</literal> will see the
2976 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2977 <literal>14</literal>.
2982 <!-- ======================= COMMENTED OUT ========================
2984 We intend to remove linear implicit parameters, so I'm at least removing
2985 them from the 6.6 user manual
2987 <sect2 id="linear-implicit-parameters">
2988 <title>Linear implicit parameters</title>
2990 Linear implicit parameters are an idea developed by Koen Claessen,
2991 Mark Shields, and Simon PJ. They address the long-standing
2992 problem that monads seem over-kill for certain sorts of problem, notably:
2995 <listitem> <para> distributing a supply of unique names </para> </listitem>
2996 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2997 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3001 Linear implicit parameters are just like ordinary implicit parameters,
3002 except that they are "linear"; that is, they cannot be copied, and
3003 must be explicitly "split" instead. Linear implicit parameters are
3004 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3005 (The '/' in the '%' suggests the split!)
3010 import GHC.Exts( Splittable )
3012 data NameSupply = ...
3014 splitNS :: NameSupply -> (NameSupply, NameSupply)
3015 newName :: NameSupply -> Name
3017 instance Splittable NameSupply where
3021 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3022 f env (Lam x e) = Lam x' (f env e)
3025 env' = extend env x x'
3026 ...more equations for f...
3028 Notice that the implicit parameter %ns is consumed
3030 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3031 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3035 So the translation done by the type checker makes
3036 the parameter explicit:
3038 f :: NameSupply -> Env -> Expr -> Expr
3039 f ns env (Lam x e) = Lam x' (f ns1 env e)
3041 (ns1,ns2) = splitNS ns
3043 env = extend env x x'
3045 Notice the call to 'split' introduced by the type checker.
3046 How did it know to use 'splitNS'? Because what it really did
3047 was to introduce a call to the overloaded function 'split',
3048 defined by the class <literal>Splittable</literal>:
3050 class Splittable a where
3053 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3054 split for name supplies. But we can simply write
3060 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3062 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3063 <literal>GHC.Exts</literal>.
3068 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3069 are entirely distinct implicit parameters: you
3070 can use them together and they won't intefere with each other. </para>
3073 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3075 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3076 in the context of a class or instance declaration. </para></listitem>
3080 <sect3><title>Warnings</title>
3083 The monomorphism restriction is even more important than usual.
3084 Consider the example above:
3086 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3087 f env (Lam x e) = Lam x' (f env e)
3090 env' = extend env x x'
3092 If we replaced the two occurrences of x' by (newName %ns), which is
3093 usually a harmless thing to do, we get:
3095 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3096 f env (Lam x e) = Lam (newName %ns) (f env e)
3098 env' = extend env x (newName %ns)
3100 But now the name supply is consumed in <emphasis>three</emphasis> places
3101 (the two calls to newName,and the recursive call to f), so
3102 the result is utterly different. Urk! We don't even have
3106 Well, this is an experimental change. With implicit
3107 parameters we have already lost beta reduction anyway, and
3108 (as John Launchbury puts it) we can't sensibly reason about
3109 Haskell programs without knowing their typing.
3114 <sect3><title>Recursive functions</title>
3115 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3118 foo :: %x::T => Int -> [Int]
3120 foo n = %x : foo (n-1)
3122 where T is some type in class Splittable.</para>
3124 Do you get a list of all the same T's or all different T's
3125 (assuming that split gives two distinct T's back)?
3127 If you supply the type signature, taking advantage of polymorphic
3128 recursion, you get what you'd probably expect. Here's the
3129 translated term, where the implicit param is made explicit:
3132 foo x n = let (x1,x2) = split x
3133 in x1 : foo x2 (n-1)
3135 But if you don't supply a type signature, GHC uses the Hindley
3136 Milner trick of using a single monomorphic instance of the function
3137 for the recursive calls. That is what makes Hindley Milner type inference
3138 work. So the translation becomes
3142 foom n = x : foom (n-1)
3146 Result: 'x' is not split, and you get a list of identical T's. So the
3147 semantics of the program depends on whether or not foo has a type signature.
3150 You may say that this is a good reason to dislike linear implicit parameters
3151 and you'd be right. That is why they are an experimental feature.
3157 ================ END OF Linear Implicit Parameters commented out -->
3159 <sect2 id="sec-kinding">
3160 <title>Explicitly-kinded quantification</title>
3163 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3164 to give the kind explicitly as (machine-checked) documentation,
3165 just as it is nice to give a type signature for a function. On some occasions,
3166 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3167 John Hughes had to define the data type:
3169 data Set cxt a = Set [a]
3170 | Unused (cxt a -> ())
3172 The only use for the <literal>Unused</literal> constructor was to force the correct
3173 kind for the type variable <literal>cxt</literal>.
3176 GHC now instead allows you to specify the kind of a type variable directly, wherever
3177 a type variable is explicitly bound. Namely:
3179 <listitem><para><literal>data</literal> declarations:
3181 data Set (cxt :: * -> *) a = Set [a]
3182 </screen></para></listitem>
3183 <listitem><para><literal>type</literal> declarations:
3185 type T (f :: * -> *) = f Int
3186 </screen></para></listitem>
3187 <listitem><para><literal>class</literal> declarations:
3189 class (Eq a) => C (f :: * -> *) a where ...
3190 </screen></para></listitem>
3191 <listitem><para><literal>forall</literal>'s in type signatures:
3193 f :: forall (cxt :: * -> *). Set cxt Int
3194 </screen></para></listitem>
3199 The parentheses are required. Some of the spaces are required too, to
3200 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3201 will get a parse error, because "<literal>::*->*</literal>" is a
3202 single lexeme in Haskell.
3206 As part of the same extension, you can put kind annotations in types
3209 f :: (Int :: *) -> Int
3210 g :: forall a. a -> (a :: *)
3214 atype ::= '(' ctype '::' kind ')
3216 The parentheses are required.
3221 <sect2 id="universal-quantification">
3222 <title>Arbitrary-rank polymorphism
3226 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3227 allows us to say exactly what this means. For example:
3235 g :: forall b. (b -> b)
3237 The two are treated identically.
3241 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3242 explicit universal quantification in
3244 For example, all the following types are legal:
3246 f1 :: forall a b. a -> b -> a
3247 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3249 f2 :: (forall a. a->a) -> Int -> Int
3250 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3252 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3254 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3255 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3256 The <literal>forall</literal> makes explicit the universal quantification that
3257 is implicitly added by Haskell.
3260 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3261 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3262 shows, the polymorphic type on the left of the function arrow can be overloaded.
3265 The function <literal>f3</literal> has a rank-3 type;
3266 it has rank-2 types on the left of a function arrow.
3269 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3270 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3271 that restriction has now been lifted.)
3272 In particular, a forall-type (also called a "type scheme"),
3273 including an operational type class context, is legal:
3275 <listitem> <para> On the left of a function arrow </para> </listitem>
3276 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
3277 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3278 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3279 field type signatures.</para> </listitem>
3280 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3281 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3283 There is one place you cannot put a <literal>forall</literal>:
3284 you cannot instantiate a type variable with a forall-type. So you cannot
3285 make a forall-type the argument of a type constructor. So these types are illegal:
3287 x1 :: [forall a. a->a]
3288 x2 :: (forall a. a->a, Int)
3289 x3 :: Maybe (forall a. a->a)
3291 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3292 a type variable any more!
3301 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3302 the types of the constructor arguments. Here are several examples:
3308 data T a = T1 (forall b. b -> b -> b) a
3310 data MonadT m = MkMonad { return :: forall a. a -> m a,
3311 bind :: forall a b. m a -> (a -> m b) -> m b
3314 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3320 The constructors have rank-2 types:
3326 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3327 MkMonad :: forall m. (forall a. a -> m a)
3328 -> (forall a b. m a -> (a -> m b) -> m b)
3330 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3336 Notice that you don't need to use a <literal>forall</literal> if there's an
3337 explicit context. For example in the first argument of the
3338 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3339 prefixed to the argument type. The implicit <literal>forall</literal>
3340 quantifies all type variables that are not already in scope, and are
3341 mentioned in the type quantified over.
3345 As for type signatures, implicit quantification happens for non-overloaded
3346 types too. So if you write this:
3349 data T a = MkT (Either a b) (b -> b)
3352 it's just as if you had written this:
3355 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3358 That is, since the type variable <literal>b</literal> isn't in scope, it's
3359 implicitly universally quantified. (Arguably, it would be better
3360 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3361 where that is what is wanted. Feedback welcomed.)
3365 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3366 the constructor to suitable values, just as usual. For example,
3377 a3 = MkSwizzle reverse
3380 a4 = let r x = Just x
3387 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3388 mkTs f x y = [T1 f x, T1 f y]
3394 The type of the argument can, as usual, be more general than the type
3395 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3396 does not need the <literal>Ord</literal> constraint.)
3400 When you use pattern matching, the bound variables may now have
3401 polymorphic types. For example:
3407 f :: T a -> a -> (a, Char)
3408 f (T1 w k) x = (w k x, w 'c' 'd')
3410 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3411 g (MkSwizzle s) xs f = s (map f (s xs))
3413 h :: MonadT m -> [m a] -> m [a]
3414 h m [] = return m []
3415 h m (x:xs) = bind m x $ \y ->
3416 bind m (h m xs) $ \ys ->
3423 In the function <function>h</function> we use the record selectors <literal>return</literal>
3424 and <literal>bind</literal> to extract the polymorphic bind and return functions
3425 from the <literal>MonadT</literal> data structure, rather than using pattern
3431 <title>Type inference</title>
3434 In general, type inference for arbitrary-rank types is undecidable.
3435 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3436 to get a decidable algorithm by requiring some help from the programmer.
3437 We do not yet have a formal specification of "some help" but the rule is this:
3440 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3441 provides an explicit polymorphic type for x, or GHC's type inference will assume
3442 that x's type has no foralls in it</emphasis>.
3445 What does it mean to "provide" an explicit type for x? You can do that by
3446 giving a type signature for x directly, using a pattern type signature
3447 (<xref linkend="scoped-type-variables"/>), thus:
3449 \ f :: (forall a. a->a) -> (f True, f 'c')
3451 Alternatively, you can give a type signature to the enclosing
3452 context, which GHC can "push down" to find the type for the variable:
3454 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3456 Here the type signature on the expression can be pushed inwards
3457 to give a type signature for f. Similarly, and more commonly,
3458 one can give a type signature for the function itself:
3460 h :: (forall a. a->a) -> (Bool,Char)
3461 h f = (f True, f 'c')
3463 You don't need to give a type signature if the lambda bound variable
3464 is a constructor argument. Here is an example we saw earlier:
3466 f :: T a -> a -> (a, Char)
3467 f (T1 w k) x = (w k x, w 'c' 'd')
3469 Here we do not need to give a type signature to <literal>w</literal>, because
3470 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3477 <sect3 id="implicit-quant">
3478 <title>Implicit quantification</title>
3481 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3482 user-written types, if and only if there is no explicit <literal>forall</literal>,
3483 GHC finds all the type variables mentioned in the type that are not already
3484 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3488 f :: forall a. a -> a
3495 h :: forall b. a -> b -> b
3501 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3504 f :: (a -> a) -> Int
3506 f :: forall a. (a -> a) -> Int
3508 f :: (forall a. a -> a) -> Int
3511 g :: (Ord a => a -> a) -> Int
3512 -- MEANS the illegal type
3513 g :: forall a. (Ord a => a -> a) -> Int
3515 g :: (forall a. Ord a => a -> a) -> Int
3517 The latter produces an illegal type, which you might think is silly,
3518 but at least the rule is simple. If you want the latter type, you
3519 can write your for-alls explicitly. Indeed, doing so is strongly advised
3526 <sect2 id="impredicative-polymorphism">
3527 <title>Impredicative polymorphism
3529 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3530 that you can call a polymorphic function at a polymorphic type, and
3531 parameterise data structures over polymorphic types. For example:
3533 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3534 f (Just g) = Just (g [3], g "hello")
3537 Notice here that the <literal>Maybe</literal> type is parameterised by the
3538 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3541 <para>The technical details of this extension are described in the paper
3542 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3543 type inference for higher-rank types and impredicativity</ulink>,
3544 which appeared at ICFP 2006.
3548 <sect2 id="scoped-type-variables">
3549 <title>Lexically scoped type variables
3553 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3554 which some type signatures are simply impossible to write. For example:
3556 f :: forall a. [a] -> [a]
3562 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3563 the entire definition of <literal>f</literal>.
3564 In particular, it is in scope at the type signature for <varname>ys</varname>.
3565 In Haskell 98 it is not possible to declare
3566 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3567 it becomes possible to do so.
3569 <para>Lexically-scoped type variables are enabled by
3570 <option>-fglasgow-exts</option>.
3572 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3573 variables work, compared to earlier releases. Read this section
3577 <title>Overview</title>
3579 <para>The design follows the following principles
3581 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3582 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3583 design.)</para></listitem>
3584 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3585 type variables. This means that every programmer-written type signature
3586 (includin one that contains free scoped type variables) denotes a
3587 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3588 checker, and no inference is involved.</para></listitem>
3589 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3590 changing the program.</para></listitem>
3594 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3596 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3597 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3598 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3599 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3603 In Haskell, a programmer-written type signature is implicitly quantifed over
3604 its free type variables (<ulink
3605 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3607 of the Haskel Report).
3608 Lexically scoped type variables affect this implicit quantification rules
3609 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3610 quantified. For example, if type variable <literal>a</literal> is in scope,
3613 (e :: a -> a) means (e :: a -> a)
3614 (e :: b -> b) means (e :: forall b. b->b)
3615 (e :: a -> b) means (e :: forall b. a->b)
3623 <sect3 id="decl-type-sigs">
3624 <title>Declaration type signatures</title>
3625 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3626 quantification (using <literal>forall</literal>) brings into scope the
3627 explicitly-quantified
3628 type variables, in the definition of the named function(s). For example:
3630 f :: forall a. [a] -> [a]
3631 f (x:xs) = xs ++ [ x :: a ]
3633 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3634 the definition of "<literal>f</literal>".
3636 <para>This only happens if the quantification in <literal>f</literal>'s type
3637 signature is explicit. For example:
3640 g (x:xs) = xs ++ [ x :: a ]
3642 This program will be rejected, because "<literal>a</literal>" does not scope
3643 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3644 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3645 quantification rules.
3649 <sect3 id="exp-type-sigs">
3650 <title>Expression type signatures</title>
3652 <para>An expression type signature that has <emphasis>explicit</emphasis>
3653 quantification (using <literal>forall</literal>) brings into scope the
3654 explicitly-quantified
3655 type variables, in the annotated expression. For example:
3657 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3659 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3660 type variable <literal>s</literal> into scope, in the annotated expression
3661 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3666 <sect3 id="pattern-type-sigs">
3667 <title>Pattern type signatures</title>
3669 A type signature may occur in any pattern; this is a <emphasis>pattern type
3670 signature</emphasis>.
3673 -- f and g assume that 'a' is already in scope
3674 f = \(x::Int, y::a) -> x
3676 h ((x,y) :: (Int,Bool)) = (y,x)
3678 In the case where all the type variables in the pattern type sigature are
3679 already in scope (i.e. bound by the enclosing context), matters are simple: the
3680 signature simply constrains the type of the pattern in the obvious way.
3683 There is only one situation in which you can write a pattern type signature that
3684 mentions a type variable that is not already in scope, namely in pattern match
3685 of an existential data constructor. For example:
3687 data T = forall a. MkT [a]
3690 k (MkT [t::a]) = MkT t3
3694 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3695 variable that is not already in scope. Indeed, it cannot already be in scope,
3696 because it is bound by the pattern match. GHC's rule is that in this situation
3697 (and only then), a pattern type signature can mention a type variable that is
3698 not already in scope; the effect is to bring it into scope, standing for the
3699 existentially-bound type variable.
3702 If this seems a little odd, we think so too. But we must have
3703 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3704 could not name existentially-bound type variables in subequent type signatures.
3707 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3708 signature is allowed to mention a lexical variable that is not already in
3710 For example, both <literal>f</literal> and <literal>g</literal> would be
3711 illegal if <literal>a</literal> was not already in scope.
3717 <!-- ==================== Commented out part about result type signatures
3719 <sect3 id="result-type-sigs">
3720 <title>Result type signatures</title>
3723 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3726 {- f assumes that 'a' is already in scope -}
3727 f x y :: [a] = [x,y,x]
3729 g = \ x :: [Int] -> [3,4]
3731 h :: forall a. [a] -> a
3735 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3736 the result of the function. Similarly, the body of the lambda in the RHS of
3737 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3738 alternative in <literal>h</literal> is <literal>a</literal>.
3740 <para> A result type signature never brings new type variables into scope.</para>
3742 There are a couple of syntactic wrinkles. First, notice that all three
3743 examples would parse quite differently with parentheses:
3745 {- f assumes that 'a' is already in scope -}
3746 f x (y :: [a]) = [x,y,x]
3748 g = \ (x :: [Int]) -> [3,4]
3750 h :: forall a. [a] -> a
3754 Now the signature is on the <emphasis>pattern</emphasis>; and
3755 <literal>h</literal> would certainly be ill-typed (since the pattern
3756 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3758 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3759 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3760 token or a parenthesised type of some sort). To see why,
3761 consider how one would parse this:
3770 <sect3 id="cls-inst-scoped-tyvars">
3771 <title>Class and instance declarations</title>
3774 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3775 scope over the methods defined in the <literal>where</literal> part. For example:
3792 <sect2 id="deriving-typeable">
3793 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3796 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3797 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3798 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3799 classes <literal>Eq</literal>, <literal>Ord</literal>,
3800 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3803 GHC extends this list with two more classes that may be automatically derived
3804 (provided the <option>-fglasgow-exts</option> flag is specified):
3805 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3806 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3807 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3809 <para>An instance of <literal>Typeable</literal> can only be derived if the
3810 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3811 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3813 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3814 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3816 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3817 are used, and only <literal>Typeable1</literal> up to
3818 <literal>Typeable7</literal> are provided in the library.)
3819 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3820 class, whose kind suits that of the data type constructor, and
3821 then writing the data type instance by hand.
3825 <sect2 id="newtype-deriving">
3826 <title>Generalised derived instances for newtypes</title>
3829 When you define an abstract type using <literal>newtype</literal>, you may want
3830 the new type to inherit some instances from its representation. In
3831 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3832 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3833 other classes you have to write an explicit instance declaration. For
3834 example, if you define
3837 newtype Dollars = Dollars Int
3840 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3841 explicitly define an instance of <literal>Num</literal>:
3844 instance Num Dollars where
3845 Dollars a + Dollars b = Dollars (a+b)
3848 All the instance does is apply and remove the <literal>newtype</literal>
3849 constructor. It is particularly galling that, since the constructor
3850 doesn't appear at run-time, this instance declaration defines a
3851 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3852 dictionary, only slower!
3856 <sect3> <title> Generalising the deriving clause </title>
3858 GHC now permits such instances to be derived instead, so one can write
3860 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3863 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3864 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3865 derives an instance declaration of the form
3868 instance Num Int => Num Dollars
3871 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3875 We can also derive instances of constructor classes in a similar
3876 way. For example, suppose we have implemented state and failure monad
3877 transformers, such that
3880 instance Monad m => Monad (State s m)
3881 instance Monad m => Monad (Failure m)
3883 In Haskell 98, we can define a parsing monad by
3885 type Parser tok m a = State [tok] (Failure m) a
3888 which is automatically a monad thanks to the instance declarations
3889 above. With the extension, we can make the parser type abstract,
3890 without needing to write an instance of class <literal>Monad</literal>, via
3893 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3896 In this case the derived instance declaration is of the form
3898 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3901 Notice that, since <literal>Monad</literal> is a constructor class, the
3902 instance is a <emphasis>partial application</emphasis> of the new type, not the
3903 entire left hand side. We can imagine that the type declaration is
3904 ``eta-converted'' to generate the context of the instance
3909 We can even derive instances of multi-parameter classes, provided the
3910 newtype is the last class parameter. In this case, a ``partial
3911 application'' of the class appears in the <literal>deriving</literal>
3912 clause. For example, given the class
3915 class StateMonad s m | m -> s where ...
3916 instance Monad m => StateMonad s (State s m) where ...
3918 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3920 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3921 deriving (Monad, StateMonad [tok])
3924 The derived instance is obtained by completing the application of the
3925 class to the new type:
3928 instance StateMonad [tok] (State [tok] (Failure m)) =>
3929 StateMonad [tok] (Parser tok m)
3934 As a result of this extension, all derived instances in newtype
3935 declarations are treated uniformly (and implemented just by reusing
3936 the dictionary for the representation type), <emphasis>except</emphasis>
3937 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3938 the newtype and its representation.
3942 <sect3> <title> A more precise specification </title>
3944 Derived instance declarations are constructed as follows. Consider the
3945 declaration (after expansion of any type synonyms)
3948 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3954 The <literal>ci</literal> are partial applications of
3955 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3956 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3959 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3962 The type <literal>t</literal> is an arbitrary type.
3965 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3966 nor in the <literal>ci</literal>, and
3969 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3970 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3971 should not "look through" the type or its constructor. You can still
3972 derive these classes for a newtype, but it happens in the usual way, not
3973 via this new mechanism.
3976 Then, for each <literal>ci</literal>, the derived instance
3979 instance ci t => ci (T v1...vk)
3981 As an example which does <emphasis>not</emphasis> work, consider
3983 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3985 Here we cannot derive the instance
3987 instance Monad (State s m) => Monad (NonMonad m)
3990 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3991 and so cannot be "eta-converted" away. It is a good thing that this
3992 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3993 not, in fact, a monad --- for the same reason. Try defining
3994 <literal>>>=</literal> with the correct type: you won't be able to.
3998 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3999 important, since we can only derive instances for the last one. If the
4000 <literal>StateMonad</literal> class above were instead defined as
4003 class StateMonad m s | m -> s where ...
4006 then we would not have been able to derive an instance for the
4007 <literal>Parser</literal> type above. We hypothesise that multi-parameter
4008 classes usually have one "main" parameter for which deriving new
4009 instances is most interesting.
4011 <para>Lastly, all of this applies only for classes other than
4012 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
4013 and <literal>Data</literal>, for which the built-in derivation applies (section
4014 4.3.3. of the Haskell Report).
4015 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
4016 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
4017 the standard method is used or the one described here.)
4023 <sect2 id="stand-alone-deriving">
4024 <title>Stand-alone deriving declarations</title>
4027 GHC now allows stand-alone <literal>deriving</literal> declarations:
4031 data Foo = Bar Int | Baz String
4036 <para>Deriving instances of multi-parameter type classes for newtypes is
4037 also allowed:</para>
4040 newtype Foo a = MkFoo (State Int a)
4042 deriving (MonadState Int) for Foo
4050 <sect2 id="typing-binds">
4051 <title>Generalised typing of mutually recursive bindings</title>
4054 The Haskell Report specifies that a group of bindings (at top level, or in a
4055 <literal>let</literal> or <literal>where</literal>) should be sorted into
4056 strongly-connected components, and then type-checked in dependency order
4057 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4058 Report, Section 4.5.1</ulink>).
4059 As each group is type-checked, any binders of the group that
4061 an explicit type signature are put in the type environment with the specified
4063 and all others are monomorphic until the group is generalised
4064 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4067 <para>Following a suggestion of Mark Jones, in his paper
4068 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4070 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4072 <emphasis>the dependency analysis ignores references to variables that have an explicit
4073 type signature</emphasis>.
4074 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4075 typecheck. For example, consider:
4077 f :: Eq a => a -> Bool
4078 f x = (x == x) || g True || g "Yes"
4080 g y = (y <= y) || f True
4082 This is rejected by Haskell 98, but under Jones's scheme the definition for
4083 <literal>g</literal> is typechecked first, separately from that for
4084 <literal>f</literal>,
4085 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4086 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4087 type is generalised, to get
4089 g :: Ord a => a -> Bool
4091 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4092 <literal>g</literal> in the type environment.
4096 The same refined dependency analysis also allows the type signatures of
4097 mutually-recursive functions to have different contexts, something that is illegal in
4098 Haskell 98 (Section 4.5.2, last sentence). With
4099 <option>-fglasgow-exts</option>
4100 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4101 type signatures; in practice this means that only variables bound by the same
4102 pattern binding must have the same context. For example, this is fine:
4104 f :: Eq a => a -> Bool
4105 f x = (x == x) || g True
4107 g :: Ord a => a -> Bool
4108 g y = (y <= y) || f True
4114 <!-- ==================== End of type system extensions ================= -->
4116 <!-- ====================== TEMPLATE HASKELL ======================= -->
4118 <sect1 id="template-haskell">
4119 <title>Template Haskell</title>
4121 <para>Template Haskell allows you to do compile-time meta-programming in
4124 the main technical innovations is discussed in "<ulink
4125 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4126 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4129 There is a Wiki page about
4130 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4131 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4135 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4136 Haskell library reference material</ulink>
4137 (search for the type ExpQ).
4138 [Temporary: many changes to the original design are described in
4139 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4140 Not all of these changes are in GHC 6.6.]
4143 <para> The first example from that paper is set out below as a worked example to help get you started.
4147 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4148 Tim Sheard is going to expand it.)
4152 <title>Syntax</title>
4154 <para> Template Haskell has the following new syntactic
4155 constructions. You need to use the flag
4156 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4157 </indexterm>to switch these syntactic extensions on
4158 (<option>-fth</option> is no longer implied by
4159 <option>-fglasgow-exts</option>).</para>
4163 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4164 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4165 There must be no space between the "$" and the identifier or parenthesis. This use
4166 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4167 of "." as an infix operator. If you want the infix operator, put spaces around it.
4169 <para> A splice can occur in place of
4171 <listitem><para> an expression; the spliced expression must
4172 have type <literal>Q Exp</literal></para></listitem>
4173 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4174 <listitem><para> [Planned, but not implemented yet.] a
4175 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4177 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4178 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4184 A expression quotation is written in Oxford brackets, thus:
4186 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4187 the quotation has type <literal>Expr</literal>.</para></listitem>
4188 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4189 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4190 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4191 the quotation has type <literal>Type</literal>.</para></listitem>
4192 </itemizedlist></para></listitem>
4195 Reification is written thus:
4197 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4198 has type <literal>Dec</literal>. </para></listitem>
4199 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4200 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4201 <listitem><para> Still to come: fixities </para></listitem>
4203 </itemizedlist></para>
4210 <sect2> <title> Using Template Haskell </title>
4214 The data types and monadic constructor functions for Template Haskell are in the library
4215 <literal>Language.Haskell.THSyntax</literal>.
4219 You can only run a function at compile time if it is imported from another module. That is,
4220 you can't define a function in a module, and call it from within a splice in the same module.
4221 (It would make sense to do so, but it's hard to implement.)
4225 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4228 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4229 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4230 compiles and runs a program, and then looks at the result. So it's important that
4231 the program it compiles produces results whose representations are identical to
4232 those of the compiler itself.
4236 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4237 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4242 <sect2> <title> A Template Haskell Worked Example </title>
4243 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4244 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4251 -- Import our template "pr"
4252 import Printf ( pr )
4254 -- The splice operator $ takes the Haskell source code
4255 -- generated at compile time by "pr" and splices it into
4256 -- the argument of "putStrLn".
4257 main = putStrLn ( $(pr "Hello") )
4263 -- Skeletal printf from the paper.
4264 -- It needs to be in a separate module to the one where
4265 -- you intend to use it.
4267 -- Import some Template Haskell syntax
4268 import Language.Haskell.TH
4270 -- Describe a format string
4271 data Format = D | S | L String
4273 -- Parse a format string. This is left largely to you
4274 -- as we are here interested in building our first ever
4275 -- Template Haskell program and not in building printf.
4276 parse :: String -> [Format]
4279 -- Generate Haskell source code from a parsed representation
4280 -- of the format string. This code will be spliced into
4281 -- the module which calls "pr", at compile time.
4282 gen :: [Format] -> ExpQ
4283 gen [D] = [| \n -> show n |]
4284 gen [S] = [| \s -> s |]
4285 gen [L s] = stringE s
4287 -- Here we generate the Haskell code for the splice
4288 -- from an input format string.
4289 pr :: String -> ExpQ
4290 pr s = gen (parse s)
4293 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4296 $ ghc --make -fth main.hs -o main.exe
4299 <para>Run "main.exe" and here is your output:</para>
4309 <title>Using Template Haskell with Profiling</title>
4310 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4312 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4313 interpreter to run the splice expressions. The bytecode interpreter
4314 runs the compiled expression on top of the same runtime on which GHC
4315 itself is running; this means that the compiled code referred to by
4316 the interpreted expression must be compatible with this runtime, and
4317 in particular this means that object code that is compiled for
4318 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4319 expression, because profiled object code is only compatible with the
4320 profiling version of the runtime.</para>
4322 <para>This causes difficulties if you have a multi-module program
4323 containing Template Haskell code and you need to compile it for
4324 profiling, because GHC cannot load the profiled object code and use it
4325 when executing the splices. Fortunately GHC provides a workaround.
4326 The basic idea is to compile the program twice:</para>
4330 <para>Compile the program or library first the normal way, without
4331 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4334 <para>Then compile it again with <option>-prof</option>, and
4335 additionally use <option>-osuf
4336 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4337 to name the object files differentliy (you can choose any suffix
4338 that isn't the normal object suffix here). GHC will automatically
4339 load the object files built in the first step when executing splice
4340 expressions. If you omit the <option>-osuf</option> flag when
4341 building with <option>-prof</option> and Template Haskell is used,
4342 GHC will emit an error message. </para>
4349 <!-- ===================== Arrow notation =================== -->
4351 <sect1 id="arrow-notation">
4352 <title>Arrow notation
4355 <para>Arrows are a generalization of monads introduced by John Hughes.
4356 For more details, see
4361 “Generalising Monads to Arrows”,
4362 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4363 pp67–111, May 2000.
4369 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4370 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4376 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4377 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4383 and the arrows web page at
4384 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4385 With the <option>-farrows</option> flag, GHC supports the arrow
4386 notation described in the second of these papers.
4387 What follows is a brief introduction to the notation;
4388 it won't make much sense unless you've read Hughes's paper.
4389 This notation is translated to ordinary Haskell,
4390 using combinators from the
4391 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4395 <para>The extension adds a new kind of expression for defining arrows:
4397 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4398 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4400 where <literal>proc</literal> is a new keyword.
4401 The variables of the pattern are bound in the body of the
4402 <literal>proc</literal>-expression,
4403 which is a new sort of thing called a <firstterm>command</firstterm>.
4404 The syntax of commands is as follows:
4406 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4407 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4408 | <replaceable>cmd</replaceable><superscript>0</superscript>
4410 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4411 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4412 infix operators as for expressions, and
4414 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4415 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4416 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4417 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4418 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4419 | <replaceable>fcmd</replaceable>
4421 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4422 | ( <replaceable>cmd</replaceable> )
4423 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4425 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4426 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4427 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4428 | <replaceable>cmd</replaceable>
4430 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4431 except that the bodies are commands instead of expressions.
4435 Commands produce values, but (like monadic computations)
4436 may yield more than one value,
4437 or none, and may do other things as well.
4438 For the most part, familiarity with monadic notation is a good guide to
4440 However the values of expressions, even monadic ones,
4441 are determined by the values of the variables they contain;
4442 this is not necessarily the case for commands.
4446 A simple example of the new notation is the expression
4448 proc x -> f -< x+1
4450 We call this a <firstterm>procedure</firstterm> or
4451 <firstterm>arrow abstraction</firstterm>.
4452 As with a lambda expression, the variable <literal>x</literal>
4453 is a new variable bound within the <literal>proc</literal>-expression.
4454 It refers to the input to the arrow.
4455 In the above example, <literal>-<</literal> is not an identifier but an
4456 new reserved symbol used for building commands from an expression of arrow
4457 type and an expression to be fed as input to that arrow.
4458 (The weird look will make more sense later.)
4459 It may be read as analogue of application for arrows.
4460 The above example is equivalent to the Haskell expression
4462 arr (\ x -> x+1) >>> f
4464 That would make no sense if the expression to the left of
4465 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4466 More generally, the expression to the left of <literal>-<</literal>
4467 may not involve any <firstterm>local variable</firstterm>,
4468 i.e. a variable bound in the current arrow abstraction.
4469 For such a situation there is a variant <literal>-<<</literal>, as in
4471 proc x -> f x -<< x+1
4473 which is equivalent to
4475 arr (\ x -> (f x, x+1)) >>> app
4477 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4479 Such an arrow is equivalent to a monad, so if you're using this form
4480 you may find a monadic formulation more convenient.
4484 <title>do-notation for commands</title>
4487 Another form of command is a form of <literal>do</literal>-notation.
4488 For example, you can write
4497 You can read this much like ordinary <literal>do</literal>-notation,
4498 but with commands in place of monadic expressions.
4499 The first line sends the value of <literal>x+1</literal> as an input to
4500 the arrow <literal>f</literal>, and matches its output against
4501 <literal>y</literal>.
4502 In the next line, the output is discarded.
4503 The arrow <function>returnA</function> is defined in the
4504 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4505 module as <literal>arr id</literal>.
4506 The above example is treated as an abbreviation for
4508 arr (\ x -> (x, x)) >>>
4509 first (arr (\ x -> x+1) >>> f) >>>
4510 arr (\ (y, x) -> (y, (x, y))) >>>
4511 first (arr (\ y -> 2*y) >>> g) >>>
4513 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4514 first (arr (\ (x, z) -> x*z) >>> h) >>>
4515 arr (\ (t, z) -> t+z) >>>
4518 Note that variables not used later in the composition are projected out.
4519 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4521 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4522 module, this reduces to
4524 arr (\ x -> (x+1, x)) >>>
4526 arr (\ (y, x) -> (2*y, (x, y))) >>>
4528 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4530 arr (\ (t, z) -> t+z)
4532 which is what you might have written by hand.
4533 With arrow notation, GHC keeps track of all those tuples of variables for you.
4537 Note that although the above translation suggests that
4538 <literal>let</literal>-bound variables like <literal>z</literal> must be
4539 monomorphic, the actual translation produces Core,
4540 so polymorphic variables are allowed.
4544 It's also possible to have mutually recursive bindings,
4545 using the new <literal>rec</literal> keyword, as in the following example:
4547 counter :: ArrowCircuit a => a Bool Int
4548 counter = proc reset -> do
4549 rec output <- returnA -< if reset then 0 else next
4550 next <- delay 0 -< output+1
4551 returnA -< output
4553 The translation of such forms uses the <function>loop</function> combinator,
4554 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4560 <title>Conditional commands</title>
4563 In the previous example, we used a conditional expression to construct the
4565 Sometimes we want to conditionally execute different commands, as in
4572 which is translated to
4574 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4575 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4577 Since the translation uses <function>|||</function>,
4578 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4582 There are also <literal>case</literal> commands, like
4588 y <- h -< (x1, x2)
4592 The syntax is the same as for <literal>case</literal> expressions,
4593 except that the bodies of the alternatives are commands rather than expressions.
4594 The translation is similar to that of <literal>if</literal> commands.
4600 <title>Defining your own control structures</title>
4603 As we're seen, arrow notation provides constructs,
4604 modelled on those for expressions,
4605 for sequencing, value recursion and conditionals.
4606 But suitable combinators,
4607 which you can define in ordinary Haskell,
4608 may also be used to build new commands out of existing ones.
4609 The basic idea is that a command defines an arrow from environments to values.
4610 These environments assign values to the free local variables of the command.
4611 Thus combinators that produce arrows from arrows
4612 may also be used to build commands from commands.
4613 For example, the <literal>ArrowChoice</literal> class includes a combinator
4615 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4617 so we can use it to build commands:
4619 expr' = proc x -> do
4622 symbol Plus -< ()
4623 y <- term -< ()
4626 symbol Minus -< ()
4627 y <- term -< ()
4630 (The <literal>do</literal> on the first line is needed to prevent the first
4631 <literal><+> ...</literal> from being interpreted as part of the
4632 expression on the previous line.)
4633 This is equivalent to
4635 expr' = (proc x -> returnA -< x)
4636 <+> (proc x -> do
4637 symbol Plus -< ()
4638 y <- term -< ()
4640 <+> (proc x -> do
4641 symbol Minus -< ()
4642 y <- term -< ()
4645 It is essential that this operator be polymorphic in <literal>e</literal>
4646 (representing the environment input to the command
4647 and thence to its subcommands)
4648 and satisfy the corresponding naturality property
4650 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4652 at least for strict <literal>k</literal>.
4653 (This should be automatic if you're not using <function>seq</function>.)
4654 This ensures that environments seen by the subcommands are environments
4655 of the whole command,
4656 and also allows the translation to safely trim these environments.
4657 The operator must also not use any variable defined within the current
4662 We could define our own operator
4664 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4665 untilA body cond = proc x ->
4666 if cond x then returnA -< ()
4669 untilA body cond -< x
4671 and use it in the same way.
4672 Of course this infix syntax only makes sense for binary operators;
4673 there is also a more general syntax involving special brackets:
4677 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4684 <title>Primitive constructs</title>
4687 Some operators will need to pass additional inputs to their subcommands.
4688 For example, in an arrow type supporting exceptions,
4689 the operator that attaches an exception handler will wish to pass the
4690 exception that occurred to the handler.
4691 Such an operator might have a type
4693 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4695 where <literal>Ex</literal> is the type of exceptions handled.
4696 You could then use this with arrow notation by writing a command
4698 body `handleA` \ ex -> handler
4700 so that if an exception is raised in the command <literal>body</literal>,
4701 the variable <literal>ex</literal> is bound to the value of the exception
4702 and the command <literal>handler</literal>,
4703 which typically refers to <literal>ex</literal>, is entered.
4704 Though the syntax here looks like a functional lambda,
4705 we are talking about commands, and something different is going on.
4706 The input to the arrow represented by a command consists of values for
4707 the free local variables in the command, plus a stack of anonymous values.
4708 In all the prior examples, this stack was empty.
4709 In the second argument to <function>handleA</function>,
4710 this stack consists of one value, the value of the exception.
4711 The command form of lambda merely gives this value a name.
4716 the values on the stack are paired to the right of the environment.
4717 So operators like <function>handleA</function> that pass
4718 extra inputs to their subcommands can be designed for use with the notation
4719 by pairing the values with the environment in this way.
4720 More precisely, the type of each argument of the operator (and its result)
4721 should have the form
4723 a (...(e,t1), ... tn) t
4725 where <replaceable>e</replaceable> is a polymorphic variable
4726 (representing the environment)
4727 and <replaceable>ti</replaceable> are the types of the values on the stack,
4728 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4729 The polymorphic variable <replaceable>e</replaceable> must not occur in
4730 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4731 <replaceable>t</replaceable>.
4732 However the arrows involved need not be the same.
4733 Here are some more examples of suitable operators:
4735 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4736 runReader :: ... => a e c -> a' (e,State) c
4737 runState :: ... => a e c -> a' (e,State) (c,State)
4739 We can supply the extra input required by commands built with the last two
4740 by applying them to ordinary expressions, as in
4744 (|runReader (do { ... })|) s
4746 which adds <literal>s</literal> to the stack of inputs to the command
4747 built using <function>runReader</function>.
4751 The command versions of lambda abstraction and application are analogous to
4752 the expression versions.
4753 In particular, the beta and eta rules describe equivalences of commands.
4754 These three features (operators, lambda abstraction and application)
4755 are the core of the notation; everything else can be built using them,
4756 though the results would be somewhat clumsy.
4757 For example, we could simulate <literal>do</literal>-notation by defining
4759 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4760 u `bind` f = returnA &&& u >>> f
4762 bind_ :: Arrow a => a e b -> a e c -> a e c
4763 u `bind_` f = u `bind` (arr fst >>> f)
4765 We could simulate <literal>if</literal> by defining
4767 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4768 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4775 <title>Differences with the paper</title>
4780 <para>Instead of a single form of arrow application (arrow tail) with two
4781 translations, the implementation provides two forms
4782 <quote><literal>-<</literal></quote> (first-order)
4783 and <quote><literal>-<<</literal></quote> (higher-order).
4788 <para>User-defined operators are flagged with banana brackets instead of
4789 a new <literal>form</literal> keyword.
4798 <title>Portability</title>
4801 Although only GHC implements arrow notation directly,
4802 there is also a preprocessor
4804 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4805 that translates arrow notation into Haskell 98
4806 for use with other Haskell systems.
4807 You would still want to check arrow programs with GHC;
4808 tracing type errors in the preprocessor output is not easy.
4809 Modules intended for both GHC and the preprocessor must observe some
4810 additional restrictions:
4815 The module must import
4816 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4822 The preprocessor cannot cope with other Haskell extensions.
4823 These would have to go in separate modules.
4829 Because the preprocessor targets Haskell (rather than Core),
4830 <literal>let</literal>-bound variables are monomorphic.
4841 <!-- ==================== BANG PATTERNS ================= -->
4843 <sect1 id="sec-bang-patterns">
4844 <title>Bang patterns
4845 <indexterm><primary>Bang patterns</primary></indexterm>
4847 <para>GHC supports an extension of pattern matching called <emphasis>bang
4848 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4850 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4851 prime feature description</ulink> contains more discussion and examples
4852 than the material below.
4855 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4858 <sect2 id="sec-bang-patterns-informal">
4859 <title>Informal description of bang patterns
4862 The main idea is to add a single new production to the syntax of patterns:
4866 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4867 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4872 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4873 whereas without the bang it would be lazy.
4874 Bang patterns can be nested of course:
4878 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4879 <literal>y</literal>.
4880 A bang only really has an effect if it precedes a variable or wild-card pattern:
4885 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4886 forces evaluation anyway does nothing.
4888 Bang patterns work in <literal>case</literal> expressions too, of course:
4890 g5 x = let y = f x in body
4891 g6 x = case f x of { y -> body }
4892 g7 x = case f x of { !y -> body }
4894 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4895 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4896 result, and then evaluates <literal>body</literal>.
4898 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4899 definitions too. For example:
4903 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4904 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4905 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4906 in a function argument <literal>![x,y]</literal> means the
4907 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4908 is part of the syntax of <literal>let</literal> bindings.
4913 <sect2 id="sec-bang-patterns-sem">
4914 <title>Syntax and semantics
4918 We add a single new production to the syntax of patterns:
4922 There is one problem with syntactic ambiguity. Consider:
4926 Is this a definition of the infix function "<literal>(!)</literal>",
4927 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4928 ambiguity in favour of the latter. If you want to define
4929 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4934 The semantics of Haskell pattern matching is described in <ulink
4935 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4936 Section 3.17.2</ulink> of the Haskell Report. To this description add
4937 one extra item 10, saying:
4938 <itemizedlist><listitem><para>Matching
4939 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4940 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4941 <listitem><para>otherwise, <literal>pat</literal> is matched against
4942 <literal>v</literal></para></listitem>
4944 </para></listitem></itemizedlist>
4945 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4946 Section 3.17.3</ulink>, add a new case (t):
4948 case v of { !pat -> e; _ -> e' }
4949 = v `seq` case v of { pat -> e; _ -> e' }
4952 That leaves let expressions, whose translation is given in
4953 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4955 of the Haskell Report.
4956 In the translation box, first apply
4957 the following transformation: for each pattern <literal>pi</literal> that is of
4958 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4959 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4960 have a bang at the top, apply the rules in the existing box.
4962 <para>The effect of the let rule is to force complete matching of the pattern
4963 <literal>qi</literal> before evaluation of the body is begun. The bang is
4964 retained in the translated form in case <literal>qi</literal> is a variable,
4972 The let-binding can be recursive. However, it is much more common for
4973 the let-binding to be non-recursive, in which case the following law holds:
4974 <literal>(let !p = rhs in body)</literal>
4976 <literal>(case rhs of !p -> body)</literal>
4979 A pattern with a bang at the outermost level is not allowed at the top level of
4985 <!-- ==================== ASSERTIONS ================= -->
4987 <sect1 id="sec-assertions">
4989 <indexterm><primary>Assertions</primary></indexterm>
4993 If you want to make use of assertions in your standard Haskell code, you
4994 could define a function like the following:
5000 assert :: Bool -> a -> a
5001 assert False x = error "assertion failed!"
5008 which works, but gives you back a less than useful error message --
5009 an assertion failed, but which and where?
5013 One way out is to define an extended <function>assert</function> function which also
5014 takes a descriptive string to include in the error message and
5015 perhaps combine this with the use of a pre-processor which inserts
5016 the source location where <function>assert</function> was used.
5020 Ghc offers a helping hand here, doing all of this for you. For every
5021 use of <function>assert</function> in the user's source:
5027 kelvinToC :: Double -> Double
5028 kelvinToC k = assert (k >= 0.0) (k+273.15)
5034 Ghc will rewrite this to also include the source location where the
5041 assert pred val ==> assertError "Main.hs|15" pred val
5047 The rewrite is only performed by the compiler when it spots
5048 applications of <function>Control.Exception.assert</function>, so you
5049 can still define and use your own versions of
5050 <function>assert</function>, should you so wish. If not, import
5051 <literal>Control.Exception</literal> to make use
5052 <function>assert</function> in your code.
5056 GHC ignores assertions when optimisation is turned on with the
5057 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5058 <literal>assert pred e</literal> will be rewritten to
5059 <literal>e</literal>. You can also disable assertions using the
5060 <option>-fignore-asserts</option>
5061 option<indexterm><primary><option>-fignore-asserts</option></primary>
5062 </indexterm>.</para>
5065 Assertion failures can be caught, see the documentation for the
5066 <literal>Control.Exception</literal> library for the details.
5072 <!-- =============================== PRAGMAS =========================== -->
5074 <sect1 id="pragmas">
5075 <title>Pragmas</title>
5077 <indexterm><primary>pragma</primary></indexterm>
5079 <para>GHC supports several pragmas, or instructions to the
5080 compiler placed in the source code. Pragmas don't normally affect
5081 the meaning of the program, but they might affect the efficiency
5082 of the generated code.</para>
5084 <para>Pragmas all take the form
5086 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5088 where <replaceable>word</replaceable> indicates the type of
5089 pragma, and is followed optionally by information specific to that
5090 type of pragma. Case is ignored in
5091 <replaceable>word</replaceable>. The various values for
5092 <replaceable>word</replaceable> that GHC understands are described
5093 in the following sections; any pragma encountered with an
5094 unrecognised <replaceable>word</replaceable> is (silently)
5097 <sect2 id="deprecated-pragma">
5098 <title>DEPRECATED pragma</title>
5099 <indexterm><primary>DEPRECATED</primary>
5102 <para>The DEPRECATED pragma lets you specify that a particular
5103 function, class, or type, is deprecated. There are two
5108 <para>You can deprecate an entire module thus:</para>
5110 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5113 <para>When you compile any module that import
5114 <literal>Wibble</literal>, GHC will print the specified
5119 <para>You can deprecate a function, class, type, or data constructor, with the
5120 following top-level declaration:</para>
5122 {-# DEPRECATED f, C, T "Don't use these" #-}
5124 <para>When you compile any module that imports and uses any
5125 of the specified entities, GHC will print the specified
5127 <para> You can only depecate entities declared at top level in the module
5128 being compiled, and you can only use unqualified names in the list of
5129 entities being deprecated. A capitalised name, such as <literal>T</literal>
5130 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5131 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5132 both are in scope. If both are in scope, there is currently no way to deprecate
5133 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5136 Any use of the deprecated item, or of anything from a deprecated
5137 module, will be flagged with an appropriate message. However,
5138 deprecations are not reported for
5139 (a) uses of a deprecated function within its defining module, and
5140 (b) uses of a deprecated function in an export list.
5141 The latter reduces spurious complaints within a library
5142 in which one module gathers together and re-exports
5143 the exports of several others.
5145 <para>You can suppress the warnings with the flag
5146 <option>-fno-warn-deprecations</option>.</para>
5149 <sect2 id="include-pragma">
5150 <title>INCLUDE pragma</title>
5152 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5153 of C header files that should be <literal>#include</literal>'d into
5154 the C source code generated by the compiler for the current module (if
5155 compiling via C). For example:</para>
5158 {-# INCLUDE "foo.h" #-}
5159 {-# INCLUDE <stdio.h> #-}</programlisting>
5161 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5162 your source file with any <literal>OPTIONS_GHC</literal>
5165 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5166 to the <option>-#include</option> option (<xref
5167 linkend="options-C-compiler" />), because the
5168 <literal>INCLUDE</literal> pragma is understood by other
5169 compilers. Yet another alternative is to add the include file to each
5170 <literal>foreign import</literal> declaration in your code, but we
5171 don't recommend using this approach with GHC.</para>
5174 <sect2 id="inline-noinline-pragma">
5175 <title>INLINE and NOINLINE pragmas</title>
5177 <para>These pragmas control the inlining of function
5180 <sect3 id="inline-pragma">
5181 <title>INLINE pragma</title>
5182 <indexterm><primary>INLINE</primary></indexterm>
5184 <para>GHC (with <option>-O</option>, as always) tries to
5185 inline (or “unfold”) functions/values that are
5186 “small enough,” thus avoiding the call overhead
5187 and possibly exposing other more-wonderful optimisations.
5188 Normally, if GHC decides a function is “too
5189 expensive” to inline, it will not do so, nor will it
5190 export that unfolding for other modules to use.</para>
5192 <para>The sledgehammer you can bring to bear is the
5193 <literal>INLINE</literal><indexterm><primary>INLINE
5194 pragma</primary></indexterm> pragma, used thusly:</para>
5197 key_function :: Int -> String -> (Bool, Double)
5199 #ifdef __GLASGOW_HASKELL__
5200 {-# INLINE key_function #-}
5204 <para>(You don't need to do the C pre-processor carry-on
5205 unless you're going to stick the code through HBC—it
5206 doesn't like <literal>INLINE</literal> pragmas.)</para>
5208 <para>The major effect of an <literal>INLINE</literal> pragma
5209 is to declare a function's “cost” to be very low.
5210 The normal unfolding machinery will then be very keen to
5213 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5214 function can be put anywhere its type signature could be
5217 <para><literal>INLINE</literal> pragmas are a particularly
5219 <literal>then</literal>/<literal>return</literal> (or
5220 <literal>bind</literal>/<literal>unit</literal>) functions in
5221 a monad. For example, in GHC's own
5222 <literal>UniqueSupply</literal> monad code, we have:</para>
5225 #ifdef __GLASGOW_HASKELL__
5226 {-# INLINE thenUs #-}
5227 {-# INLINE returnUs #-}
5231 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5232 linkend="noinline-pragma"/>).</para>
5235 <sect3 id="noinline-pragma">
5236 <title>NOINLINE pragma</title>
5238 <indexterm><primary>NOINLINE</primary></indexterm>
5239 <indexterm><primary>NOTINLINE</primary></indexterm>
5241 <para>The <literal>NOINLINE</literal> pragma does exactly what
5242 you'd expect: it stops the named function from being inlined
5243 by the compiler. You shouldn't ever need to do this, unless
5244 you're very cautious about code size.</para>
5246 <para><literal>NOTINLINE</literal> is a synonym for
5247 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5248 specified by Haskell 98 as the standard way to disable
5249 inlining, so it should be used if you want your code to be
5253 <sect3 id="phase-control">
5254 <title>Phase control</title>
5256 <para> Sometimes you want to control exactly when in GHC's
5257 pipeline the INLINE pragma is switched on. Inlining happens
5258 only during runs of the <emphasis>simplifier</emphasis>. Each
5259 run of the simplifier has a different <emphasis>phase
5260 number</emphasis>; the phase number decreases towards zero.
5261 If you use <option>-dverbose-core2core</option> you'll see the
5262 sequence of phase numbers for successive runs of the
5263 simplifier. In an INLINE pragma you can optionally specify a
5267 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5268 <literal>f</literal>
5269 until phase <literal>k</literal>, but from phase
5270 <literal>k</literal> onwards be very keen to inline it.
5273 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5274 <literal>f</literal>
5275 until phase <literal>k</literal>, but from phase
5276 <literal>k</literal> onwards do not inline it.
5279 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5280 <literal>f</literal>
5281 until phase <literal>k</literal>, but from phase
5282 <literal>k</literal> onwards be willing to inline it (as if
5283 there was no pragma).
5286 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5287 <literal>f</literal>
5288 until phase <literal>k</literal>, but from phase
5289 <literal>k</literal> onwards do not inline it.
5292 The same information is summarised here:
5294 -- Before phase 2 Phase 2 and later
5295 {-# INLINE [2] f #-} -- No Yes
5296 {-# INLINE [~2] f #-} -- Yes No
5297 {-# NOINLINE [2] f #-} -- No Maybe
5298 {-# NOINLINE [~2] f #-} -- Maybe No
5300 {-# INLINE f #-} -- Yes Yes
5301 {-# NOINLINE f #-} -- No No
5303 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5304 function body is small, or it is applied to interesting-looking arguments etc).
5305 Another way to understand the semantics is this:
5307 <listitem><para>For both INLINE and NOINLINE, the phase number says
5308 when inlining is allowed at all.</para></listitem>
5309 <listitem><para>The INLINE pragma has the additional effect of making the
5310 function body look small, so that when inlining is allowed it is very likely to
5315 <para>The same phase-numbering control is available for RULES
5316 (<xref linkend="rewrite-rules"/>).</para>
5320 <sect2 id="language-pragma">
5321 <title>LANGUAGE pragma</title>
5323 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5324 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5326 <para>This allows language extensions to be enabled in a portable way.
5327 It is the intention that all Haskell compilers support the
5328 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5329 all extensions are supported by all compilers, of
5330 course. The <literal>LANGUAGE</literal> pragma should be used instead
5331 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5333 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5335 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5337 <para>Any extension from the <literal>Extension</literal> type defined in
5339 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>
5343 <sect2 id="line-pragma">
5344 <title>LINE pragma</title>
5346 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5347 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5348 <para>This pragma is similar to C's <literal>#line</literal>
5349 pragma, and is mainly for use in automatically generated Haskell
5350 code. It lets you specify the line number and filename of the
5351 original code; for example</para>
5353 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5355 <para>if you'd generated the current file from something called
5356 <filename>Foo.vhs</filename> and this line corresponds to line
5357 42 in the original. GHC will adjust its error messages to refer
5358 to the line/file named in the <literal>LINE</literal>
5362 <sect2 id="options-pragma">
5363 <title>OPTIONS_GHC pragma</title>
5364 <indexterm><primary>OPTIONS_GHC</primary>
5366 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5369 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5370 additional options that are given to the compiler when compiling
5371 this source file. See <xref linkend="source-file-options"/> for
5374 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5375 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5379 <title>RULES pragma</title>
5381 <para>The RULES pragma lets you specify rewrite rules. It is
5382 described in <xref linkend="rewrite-rules"/>.</para>
5385 <sect2 id="specialize-pragma">
5386 <title>SPECIALIZE pragma</title>
5388 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5389 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5390 <indexterm><primary>overloading, death to</primary></indexterm>
5392 <para>(UK spelling also accepted.) For key overloaded
5393 functions, you can create extra versions (NB: more code space)
5394 specialised to particular types. Thus, if you have an
5395 overloaded function:</para>
5398 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5401 <para>If it is heavily used on lists with
5402 <literal>Widget</literal> keys, you could specialise it as
5406 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5409 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5410 be put anywhere its type signature could be put.</para>
5412 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5413 (a) a specialised version of the function and (b) a rewrite rule
5414 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5415 un-specialised function into a call to the specialised one.</para>
5417 <para>The type in a SPECIALIZE pragma can be any type that is less
5418 polymorphic than the type of the original function. In concrete terms,
5419 if the original function is <literal>f</literal> then the pragma
5421 {-# SPECIALIZE f :: <type> #-}
5423 is valid if and only if the defintion
5425 f_spec :: <type>
5428 is valid. Here are some examples (where we only give the type signature
5429 for the original function, not its code):
5431 f :: Eq a => a -> b -> b
5432 {-# SPECIALISE f :: Int -> b -> b #-}
5434 g :: (Eq a, Ix b) => a -> b -> b
5435 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5437 h :: Eq a => a -> a -> a
5438 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5440 The last of these examples will generate a
5441 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5442 well. If you use this kind of specialisation, let us know how well it works.
5445 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5446 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5447 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5448 The <literal>INLINE</literal> pragma affects the specialised verison of the
5449 function (only), and applies even if the function is recursive. The motivating
5452 -- A GADT for arrays with type-indexed representation
5454 ArrInt :: !Int -> ByteArray# -> Arr Int
5455 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5457 (!:) :: Arr e -> Int -> e
5458 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5459 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5460 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5461 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5463 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5464 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5465 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5466 the specialised function will be inlined. It has two calls to
5467 <literal>(!:)</literal>,
5468 both at type <literal>Int</literal>. Both these calls fire the first
5469 specialisation, whose body is also inlined. The result is a type-based
5470 unrolling of the indexing function.</para>
5471 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5472 on an ordinarily-recursive function.</para>
5474 <para>Note: In earlier versions of GHC, it was possible to provide your own
5475 specialised function for a given type:
5478 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5481 This feature has been removed, as it is now subsumed by the
5482 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5486 <sect2 id="specialize-instance-pragma">
5487 <title>SPECIALIZE instance pragma
5491 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5492 <indexterm><primary>overloading, death to</primary></indexterm>
5493 Same idea, except for instance declarations. For example:
5496 instance (Eq a) => Eq (Foo a) where {
5497 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5501 The pragma must occur inside the <literal>where</literal> part
5502 of the instance declaration.
5505 Compatible with HBC, by the way, except perhaps in the placement
5511 <sect2 id="unpack-pragma">
5512 <title>UNPACK pragma</title>
5514 <indexterm><primary>UNPACK</primary></indexterm>
5516 <para>The <literal>UNPACK</literal> indicates to the compiler
5517 that it should unpack the contents of a constructor field into
5518 the constructor itself, removing a level of indirection. For
5522 data T = T {-# UNPACK #-} !Float
5523 {-# UNPACK #-} !Float
5526 <para>will create a constructor <literal>T</literal> containing
5527 two unboxed floats. This may not always be an optimisation: if
5528 the <function>T</function> constructor is scrutinised and the
5529 floats passed to a non-strict function for example, they will
5530 have to be reboxed (this is done automatically by the
5533 <para>Unpacking constructor fields should only be used in
5534 conjunction with <option>-O</option>, in order to expose
5535 unfoldings to the compiler so the reboxing can be removed as
5536 often as possible. For example:</para>
5540 f (T f1 f2) = f1 + f2
5543 <para>The compiler will avoid reboxing <function>f1</function>
5544 and <function>f2</function> by inlining <function>+</function>
5545 on floats, but only when <option>-O</option> is on.</para>
5547 <para>Any single-constructor data is eligible for unpacking; for
5551 data T = T {-# UNPACK #-} !(Int,Int)
5554 <para>will store the two <literal>Int</literal>s directly in the
5555 <function>T</function> constructor, by flattening the pair.
5556 Multi-level unpacking is also supported:</para>
5559 data T = T {-# UNPACK #-} !S
5560 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5563 <para>will store two unboxed <literal>Int#</literal>s
5564 directly in the <function>T</function> constructor. The
5565 unpacker can see through newtypes, too.</para>
5567 <para>If a field cannot be unpacked, you will not get a warning,
5568 so it might be an idea to check the generated code with
5569 <option>-ddump-simpl</option>.</para>
5571 <para>See also the <option>-funbox-strict-fields</option> flag,
5572 which essentially has the effect of adding
5573 <literal>{-# UNPACK #-}</literal> to every strict
5574 constructor field.</para>
5579 <!-- ======================= REWRITE RULES ======================== -->
5581 <sect1 id="rewrite-rules">
5582 <title>Rewrite rules
5584 <indexterm><primary>RULES pragma</primary></indexterm>
5585 <indexterm><primary>pragma, RULES</primary></indexterm>
5586 <indexterm><primary>rewrite rules</primary></indexterm></title>
5589 The programmer can specify rewrite rules as part of the source program
5590 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5591 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5592 and (b) the <option>-frules-off</option> flag
5593 (<xref linkend="options-f"/>) is not specified, and (c) the
5594 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5603 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5610 <title>Syntax</title>
5613 From a syntactic point of view:
5619 There may be zero or more rules in a <literal>RULES</literal> pragma.
5626 Each rule has a name, enclosed in double quotes. The name itself has
5627 no significance at all. It is only used when reporting how many times the rule fired.
5633 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5634 immediately after the name of the rule. Thus:
5637 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5640 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5641 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5650 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5651 is set, so you must lay out your rules starting in the same column as the
5652 enclosing definitions.
5659 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5660 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5661 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5662 by spaces, just like in a type <literal>forall</literal>.
5668 A pattern variable may optionally have a type signature.
5669 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5670 For example, here is the <literal>foldr/build</literal> rule:
5673 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5674 foldr k z (build g) = g k z
5677 Since <function>g</function> has a polymorphic type, it must have a type signature.
5684 The left hand side of a rule must consist of a top-level variable applied
5685 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5688 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5689 "wrong2" forall f. f True = True
5692 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5699 A rule does not need to be in the same module as (any of) the
5700 variables it mentions, though of course they need to be in scope.
5706 Rules are automatically exported from a module, just as instance declarations are.
5717 <title>Semantics</title>
5720 From a semantic point of view:
5726 Rules are only applied if you use the <option>-O</option> flag.
5732 Rules are regarded as left-to-right rewrite rules.
5733 When GHC finds an expression that is a substitution instance of the LHS
5734 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5735 By "a substitution instance" we mean that the LHS can be made equal to the
5736 expression by substituting for the pattern variables.
5743 The LHS and RHS of a rule are typechecked, and must have the
5751 GHC makes absolutely no attempt to verify that the LHS and RHS
5752 of a rule have the same meaning. That is undecidable in general, and
5753 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5760 GHC makes no attempt to make sure that the rules are confluent or
5761 terminating. For example:
5764 "loop" forall x,y. f x y = f y x
5767 This rule will cause the compiler to go into an infinite loop.
5774 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5780 GHC currently uses a very simple, syntactic, matching algorithm
5781 for matching a rule LHS with an expression. It seeks a substitution
5782 which makes the LHS and expression syntactically equal modulo alpha
5783 conversion. The pattern (rule), but not the expression, is eta-expanded if
5784 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5785 But not beta conversion (that's called higher-order matching).
5789 Matching is carried out on GHC's intermediate language, which includes
5790 type abstractions and applications. So a rule only matches if the
5791 types match too. See <xref linkend="rule-spec"/> below.
5797 GHC keeps trying to apply the rules as it optimises the program.
5798 For example, consider:
5807 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5808 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5809 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5810 not be substituted, and the rule would not fire.
5817 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5818 that appears on the LHS of a rule</emphasis>, because once you have substituted
5819 for something you can't match against it (given the simple minded
5820 matching). So if you write the rule
5823 "map/map" forall f,g. map f . map g = map (f.g)
5826 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5827 It will only match something written with explicit use of ".".
5828 Well, not quite. It <emphasis>will</emphasis> match the expression
5834 where <function>wibble</function> is defined:
5837 wibble f g = map f . map g
5840 because <function>wibble</function> will be inlined (it's small).
5842 Later on in compilation, GHC starts inlining even things on the
5843 LHS of rules, but still leaves the rules enabled. This inlining
5844 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5851 All rules are implicitly exported from the module, and are therefore
5852 in force in any module that imports the module that defined the rule, directly
5853 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5854 in force when compiling A.) The situation is very similar to that for instance
5866 <title>List fusion</title>
5869 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5870 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5871 intermediate list should be eliminated entirely.
5875 The following are good producers:
5887 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5893 Explicit lists (e.g. <literal>[True, False]</literal>)
5899 The cons constructor (e.g <literal>3:4:[]</literal>)
5905 <function>++</function>
5911 <function>map</function>
5917 <function>take</function>, <function>filter</function>
5923 <function>iterate</function>, <function>repeat</function>
5929 <function>zip</function>, <function>zipWith</function>
5938 The following are good consumers:
5950 <function>array</function> (on its second argument)
5956 <function>length</function>
5962 <function>++</function> (on its first argument)
5968 <function>foldr</function>
5974 <function>map</function>
5980 <function>take</function>, <function>filter</function>
5986 <function>concat</function>
5992 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5998 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5999 will fuse with one but not the other)
6005 <function>partition</function>
6011 <function>head</function>
6017 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6023 <function>sequence_</function>
6029 <function>msum</function>
6035 <function>sortBy</function>
6044 So, for example, the following should generate no intermediate lists:
6047 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6053 This list could readily be extended; if there are Prelude functions that you use
6054 a lot which are not included, please tell us.
6058 If you want to write your own good consumers or producers, look at the
6059 Prelude definitions of the above functions to see how to do so.
6064 <sect2 id="rule-spec">
6065 <title>Specialisation
6069 Rewrite rules can be used to get the same effect as a feature
6070 present in earlier versions of GHC.
6071 For example, suppose that:
6074 genericLookup :: Ord a => Table a b -> a -> b
6075 intLookup :: Table Int b -> Int -> b
6078 where <function>intLookup</function> is an implementation of
6079 <function>genericLookup</function> that works very fast for
6080 keys of type <literal>Int</literal>. You might wish
6081 to tell GHC to use <function>intLookup</function> instead of
6082 <function>genericLookup</function> whenever the latter was called with
6083 type <literal>Table Int b -> Int -> b</literal>.
6084 It used to be possible to write
6087 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6090 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6093 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6096 This slightly odd-looking rule instructs GHC to replace
6097 <function>genericLookup</function> by <function>intLookup</function>
6098 <emphasis>whenever the types match</emphasis>.
6099 What is more, this rule does not need to be in the same
6100 file as <function>genericLookup</function>, unlike the
6101 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6102 have an original definition available to specialise).
6105 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6106 <function>intLookup</function> really behaves as a specialised version
6107 of <function>genericLookup</function>!!!</para>
6109 <para>An example in which using <literal>RULES</literal> for
6110 specialisation will Win Big:
6113 toDouble :: Real a => a -> Double
6114 toDouble = fromRational . toRational
6116 {-# RULES "toDouble/Int" toDouble = i2d #-}
6117 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6120 The <function>i2d</function> function is virtually one machine
6121 instruction; the default conversion—via an intermediate
6122 <literal>Rational</literal>—is obscenely expensive by
6129 <title>Controlling what's going on</title>
6137 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6143 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6144 If you add <option>-dppr-debug</option> you get a more detailed listing.
6150 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6153 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6154 {-# INLINE build #-}
6158 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6159 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6160 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6161 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6168 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6169 see how to write rules that will do fusion and yet give an efficient
6170 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6180 <sect2 id="core-pragma">
6181 <title>CORE pragma</title>
6183 <indexterm><primary>CORE pragma</primary></indexterm>
6184 <indexterm><primary>pragma, CORE</primary></indexterm>
6185 <indexterm><primary>core, annotation</primary></indexterm>
6188 The external core format supports <quote>Note</quote> annotations;
6189 the <literal>CORE</literal> pragma gives a way to specify what these
6190 should be in your Haskell source code. Syntactically, core
6191 annotations are attached to expressions and take a Haskell string
6192 literal as an argument. The following function definition shows an
6196 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6199 Semantically, this is equivalent to:
6207 However, when external for is generated (via
6208 <option>-fext-core</option>), there will be Notes attached to the
6209 expressions <function>show</function> and <varname>x</varname>.
6210 The core function declaration for <function>f</function> is:
6214 f :: %forall a . GHCziShow.ZCTShow a ->
6215 a -> GHCziBase.ZMZN GHCziBase.Char =
6216 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6218 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6220 (tpl1::GHCziBase.Int ->
6222 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6224 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6225 (tpl3::GHCziBase.ZMZN a ->
6226 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6234 Here, we can see that the function <function>show</function> (which
6235 has been expanded out to a case expression over the Show dictionary)
6236 has a <literal>%note</literal> attached to it, as does the
6237 expression <varname>eta</varname> (which used to be called
6238 <varname>x</varname>).
6245 <sect1 id="special-ids">
6246 <title>Special built-in functions</title>
6247 <para>GHC has a few built-in funcions with special behaviour,
6248 described in this section. All are exported by
6249 <literal>GHC.Exts</literal>.</para>
6251 <sect2> <title>The <literal>seq</literal> function </title>
6253 The function <literal>seq</literal> is as described in the Haskell98 Report.
6257 It evaluates its first argument to head normal form, and then returns its
6258 second argument as the result. The reason that it is documented here is
6259 that, despite <literal>seq</literal>'s polymorphism, its
6260 second argument can have an unboxed type, or
6261 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6262 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6263 to be instantiated to an unboxed type, which is not usually allowed.
6267 <sect2> <title>The <literal>inline</literal> function </title>
6269 The <literal>inline</literal> function is somewhat experimental.
6273 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6274 is inlined, regardless of its size. More precisely, the call
6275 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6277 This allows the programmer to control inlining from
6278 a particular <emphasis>call site</emphasis>
6279 rather than the <emphasis>definition site</emphasis> of the function
6280 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6283 This inlining occurs regardless of the argument to the call
6284 or the size of <literal>f</literal>'s definition; it is unconditional.
6285 The main caveat is that <literal>f</literal>'s definition must be
6286 visible to the compiler. That is, <literal>f</literal> must be
6287 let-bound in the current scope.
6288 If no inlining takes place, the <literal>inline</literal> function
6289 expands to the identity function in Phase zero; so its use imposes
6292 <para> If the function is defined in another
6293 module, GHC only exposes its inlining in the interface file if the
6294 function is sufficiently small that it <emphasis>might</emphasis> be
6295 inlined by the automatic mechanism. There is currently no way to tell
6296 GHC to expose arbitrarily-large functions in the interface file. (This
6297 shortcoming is something that could be fixed, with some kind of pragma.)
6301 <sect2> <title>The <literal>lazy</literal> function </title>
6303 The <literal>lazy</literal> function restrains strictness analysis a little:
6307 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6308 but <literal>lazy</literal> has a magical property so far as strictness
6309 analysis is concerned: it is lazy in its first argument,
6310 even though its semantics is strict. After strictness analysis has run,
6311 calls to <literal>lazy</literal> are inlined to be the identity function.
6314 This behaviour is occasionally useful when controlling evaluation order.
6315 Notably, <literal>lazy</literal> is used in the library definition of
6316 <literal>Control.Parallel.par</literal>:
6319 par x y = case (par# x) of { _ -> lazy y }
6321 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6322 look strict in <literal>y</literal> which would defeat the whole
6323 purpose of <literal>par</literal>.
6326 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6332 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6334 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6335 typechecker entirely. It has type
6337 unsafeCoerce# :: a -> b
6339 That is, it allows you to coerce any type into any other type. If you use this
6340 function, you had better get it right, otherwise segmentation faults await.
6341 It is generally used when you want to write a program that you know is
6342 well-typed, but where Haskell's type system is not expressive enough to prove
6343 that it is well typed.
6346 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6347 although extremely bad things will happen if you coerce a boxed type
6356 <sect1 id="generic-classes">
6357 <title>Generic classes</title>
6360 The ideas behind this extension are described in detail in "Derivable type classes",
6361 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6362 An example will give the idea:
6370 fromBin :: [Int] -> (a, [Int])
6372 toBin {| Unit |} Unit = []
6373 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6374 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6375 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6377 fromBin {| Unit |} bs = (Unit, bs)
6378 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6379 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6380 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6381 (y,bs'') = fromBin bs'
6384 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6385 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6386 which are defined thus in the library module <literal>Generics</literal>:
6390 data a :+: b = Inl a | Inr b
6391 data a :*: b = a :*: b
6394 Now you can make a data type into an instance of Bin like this:
6396 instance (Bin a, Bin b) => Bin (a,b)
6397 instance Bin a => Bin [a]
6399 That is, just leave off the "where" clause. Of course, you can put in the
6400 where clause and over-ride whichever methods you please.
6404 <title> Using generics </title>
6405 <para>To use generics you need to</para>
6408 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6409 <option>-fgenerics</option> (to generate extra per-data-type code),
6410 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6414 <para>Import the module <literal>Generics</literal> from the
6415 <literal>lang</literal> package. This import brings into
6416 scope the data types <literal>Unit</literal>,
6417 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6418 don't need this import if you don't mention these types
6419 explicitly; for example, if you are simply giving instance
6420 declarations.)</para>
6425 <sect2> <title> Changes wrt the paper </title>
6427 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6428 can be written infix (indeed, you can now use
6429 any operator starting in a colon as an infix type constructor). Also note that
6430 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6431 Finally, note that the syntax of the type patterns in the class declaration
6432 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6433 alone would ambiguous when they appear on right hand sides (an extension we
6434 anticipate wanting).
6438 <sect2> <title>Terminology and restrictions</title>
6440 Terminology. A "generic default method" in a class declaration
6441 is one that is defined using type patterns as above.
6442 A "polymorphic default method" is a default method defined as in Haskell 98.
6443 A "generic class declaration" is a class declaration with at least one
6444 generic default method.
6452 Alas, we do not yet implement the stuff about constructor names and
6459 A generic class can have only one parameter; you can't have a generic
6460 multi-parameter class.
6466 A default method must be defined entirely using type patterns, or entirely
6467 without. So this is illegal:
6470 op :: a -> (a, Bool)
6471 op {| Unit |} Unit = (Unit, True)
6474 However it is perfectly OK for some methods of a generic class to have
6475 generic default methods and others to have polymorphic default methods.
6481 The type variable(s) in the type pattern for a generic method declaration
6482 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:
6486 op {| p :*: q |} (x :*: y) = op (x :: p)
6494 The type patterns in a generic default method must take one of the forms:
6500 where "a" and "b" are type variables. Furthermore, all the type patterns for
6501 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6502 must use the same type variables. So this is illegal:
6506 op {| a :+: b |} (Inl x) = True
6507 op {| p :+: q |} (Inr y) = False
6509 The type patterns must be identical, even in equations for different methods of the class.
6510 So this too is illegal:
6514 op1 {| a :*: b |} (x :*: y) = True
6517 op2 {| p :*: q |} (x :*: y) = False
6519 (The reason for this restriction is that we gather all the equations for a particular type consructor
6520 into a single generic instance declaration.)
6526 A generic method declaration must give a case for each of the three type constructors.
6532 The type for a generic method can be built only from:
6534 <listitem> <para> Function arrows </para> </listitem>
6535 <listitem> <para> Type variables </para> </listitem>
6536 <listitem> <para> Tuples </para> </listitem>
6537 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6539 Here are some example type signatures for generic methods:
6542 op2 :: Bool -> (a,Bool)
6543 op3 :: [Int] -> a -> a
6546 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6550 This restriction is an implementation restriction: we just havn't got around to
6551 implementing the necessary bidirectional maps over arbitrary type constructors.
6552 It would be relatively easy to add specific type constructors, such as Maybe and list,
6553 to the ones that are allowed.</para>
6558 In an instance declaration for a generic class, the idea is that the compiler
6559 will fill in the methods for you, based on the generic templates. However it can only
6564 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6569 No constructor of the instance type has unboxed fields.
6573 (Of course, these things can only arise if you are already using GHC extensions.)
6574 However, you can still give an instance declarations for types which break these rules,
6575 provided you give explicit code to override any generic default methods.
6583 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6584 what the compiler does with generic declarations.
6589 <sect2> <title> Another example </title>
6591 Just to finish with, here's another example I rather like:
6595 nCons {| Unit |} _ = 1
6596 nCons {| a :*: b |} _ = 1
6597 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6600 tag {| Unit |} _ = 1
6601 tag {| a :*: b |} _ = 1
6602 tag {| a :+: b |} (Inl x) = tag x
6603 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6609 <sect1 id="monomorphism">
6610 <title>Control over monomorphism</title>
6612 <para>GHC supports two flags that control the way in which generalisation is
6613 carried out at let and where bindings.
6617 <title>Switching off the dreaded Monomorphism Restriction</title>
6618 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6620 <para>Haskell's monomorphism restriction (see
6621 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6623 of the Haskell Report)
6624 can be completely switched off by
6625 <option>-fno-monomorphism-restriction</option>.
6630 <title>Monomorphic pattern bindings</title>
6631 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6632 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6634 <para> As an experimental change, we are exploring the possibility of
6635 making pattern bindings monomorphic; that is, not generalised at all.
6636 A pattern binding is a binding whose LHS has no function arguments,
6637 and is not a simple variable. For example:
6639 f x = x -- Not a pattern binding
6640 f = \x -> x -- Not a pattern binding
6641 f :: Int -> Int = \x -> x -- Not a pattern binding
6643 (g,h) = e -- A pattern binding
6644 (f) = e -- A pattern binding
6645 [x] = e -- A pattern binding
6647 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6648 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6657 ;;; Local Variables: ***
6659 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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