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>-foverloaded-strings</option></term>
246 <para>Enables overloaded string literals (see <xref
247 linkend="overloaded-strings"/>).</para>
252 <term><option>-fscoped-type-variables</option></term>
254 <para>Enables lexically-scoped type variables (see <xref
255 linkend="scoped-type-variables"/>). Implied by
256 <option>-fglasgow-exts</option>.</para>
261 <term><option>-fth</option></term>
263 <para>Enables Template Haskell (see <xref
264 linkend="template-haskell"/>). This flag must
265 be given explicitly; it is no longer implied by
266 <option>-fglasgow-exts</option>.</para>
268 <para>Syntax stolen: <literal>[|</literal>,
269 <literal>[e|</literal>, <literal>[p|</literal>,
270 <literal>[d|</literal>, <literal>[t|</literal>,
271 <literal>$(</literal>,
272 <literal>$<replaceable>varid</replaceable></literal>.</para>
279 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
280 <sect1 id="primitives">
281 <title>Unboxed types and primitive operations</title>
283 <para>GHC is built on a raft of primitive data types and operations.
284 While you really can use this stuff to write fast code,
285 we generally find it a lot less painful, and more satisfying in the
286 long run, to use higher-level language features and libraries. With
287 any luck, the code you write will be optimised to the efficient
288 unboxed version in any case. And if it isn't, we'd like to know
291 <para>We do not currently have good, up-to-date documentation about the
292 primitives, perhaps because they are mainly intended for internal use.
293 There used to be a long section about them here in the User Guide, but it
294 became out of date, and wrong information is worse than none.</para>
296 <para>The Real Truth about what primitive types there are, and what operations
297 work over those types, is held in the file
298 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
299 This file is used directly to generate GHC's primitive-operation definitions, so
300 it is always correct! It is also intended for processing into text.</para>
303 the result of such processing is part of the description of the
305 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
306 Core language</ulink>.
307 So that document is a good place to look for a type-set version.
308 We would be very happy if someone wanted to volunteer to produce an SGML
309 back end to the program that processes <filename>primops.txt</filename> so that
310 we could include the results here in the User Guide.</para>
312 <para>What follows here is a brief summary of some main points.</para>
314 <sect2 id="glasgow-unboxed">
319 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
322 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
323 that values of that type are represented by a pointer to a heap
324 object. The representation of a Haskell <literal>Int</literal>, for
325 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
326 type, however, is represented by the value itself, no pointers or heap
327 allocation are involved.
331 Unboxed types correspond to the “raw machine” types you
332 would use in C: <literal>Int#</literal> (long int),
333 <literal>Double#</literal> (double), <literal>Addr#</literal>
334 (void *), etc. The <emphasis>primitive operations</emphasis>
335 (PrimOps) on these types are what you might expect; e.g.,
336 <literal>(+#)</literal> is addition on
337 <literal>Int#</literal>s, and is the machine-addition that we all
338 know and love—usually one instruction.
342 Primitive (unboxed) types cannot be defined in Haskell, and are
343 therefore built into the language and compiler. Primitive types are
344 always unlifted; that is, a value of a primitive type cannot be
345 bottom. We use the convention that primitive types, values, and
346 operations have a <literal>#</literal> suffix.
350 Primitive values are often represented by a simple bit-pattern, such
351 as <literal>Int#</literal>, <literal>Float#</literal>,
352 <literal>Double#</literal>. But this is not necessarily the case:
353 a primitive value might be represented by a pointer to a
354 heap-allocated object. Examples include
355 <literal>Array#</literal>, the type of primitive arrays. A
356 primitive array is heap-allocated because it is too big a value to fit
357 in a register, and would be too expensive to copy around; in a sense,
358 it is accidental that it is represented by a pointer. If a pointer
359 represents a primitive value, then it really does point to that value:
360 no unevaluated thunks, no indirections…nothing can be at the
361 other end of the pointer than the primitive value.
362 A numerically-intensive program using unboxed types can
363 go a <emphasis>lot</emphasis> faster than its “standard”
364 counterpart—we saw a threefold speedup on one example.
368 There are some restrictions on the use of primitive types:
370 <listitem><para>The main restriction
371 is that you can't pass a primitive value to a polymorphic
372 function or store one in a polymorphic data type. This rules out
373 things like <literal>[Int#]</literal> (i.e. lists of primitive
374 integers). The reason for this restriction is that polymorphic
375 arguments and constructor fields are assumed to be pointers: if an
376 unboxed integer is stored in one of these, the garbage collector would
377 attempt to follow it, leading to unpredictable space leaks. Or a
378 <function>seq</function> operation on the polymorphic component may
379 attempt to dereference the pointer, with disastrous results. Even
380 worse, the unboxed value might be larger than a pointer
381 (<literal>Double#</literal> for instance).
384 <listitem><para> You cannot define a newtype whose representation type
385 (the argument type of the data constructor) is an unboxed type. Thus,
391 <listitem><para> You cannot bind a variable with an unboxed type
392 in a <emphasis>top-level</emphasis> binding.
394 <listitem><para> You cannot bind a variable with an unboxed type
395 in a <emphasis>recursive</emphasis> binding.
397 <listitem><para> You may bind unboxed variables in a (non-recursive,
398 non-top-level) pattern binding, but any such variable causes the entire
400 to become strict. For example:
402 data Foo = Foo Int Int#
404 f x = let (Foo a b, w) = ..rhs.. in ..body..
406 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
408 is strict, and the program behaves as if you had written
410 data Foo = Foo Int Int#
412 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
421 <sect2 id="unboxed-tuples">
422 <title>Unboxed Tuples
426 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
427 they're available by default with <option>-fglasgow-exts</option>. An
428 unboxed tuple looks like this:
440 where <literal>e_1..e_n</literal> are expressions of any
441 type (primitive or non-primitive). The type of an unboxed tuple looks
446 Unboxed tuples are used for functions that need to return multiple
447 values, but they avoid the heap allocation normally associated with
448 using fully-fledged tuples. When an unboxed tuple is returned, the
449 components are put directly into registers or on the stack; the
450 unboxed tuple itself does not have a composite representation. Many
451 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
453 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
454 tuples to avoid unnecessary allocation during sequences of operations.
458 There are some pretty stringent restrictions on the use of unboxed tuples:
463 Values of unboxed tuple types are subject to the same restrictions as
464 other unboxed types; i.e. they may not be stored in polymorphic data
465 structures or passed to polymorphic functions.
472 No variable can have an unboxed tuple type, nor may a constructor or function
473 argument have an unboxed tuple type. The following are all illegal:
477 data Foo = Foo (# Int, Int #)
479 f :: (# Int, Int #) -> (# Int, Int #)
482 g :: (# Int, Int #) -> Int
485 h x = let y = (# x,x #) in ...
492 The typical use of unboxed tuples is simply to return multiple values,
493 binding those multiple results with a <literal>case</literal> expression, thus:
495 f x y = (# x+1, y-1 #)
496 g x = case f x x of { (# a, b #) -> a + b }
498 You can have an unboxed tuple in a pattern binding, thus
500 f x = let (# p,q #) = h x in ..body..
502 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
503 the resulting binding is lazy like any other Haskell pattern binding. The
504 above example desugars like this:
506 f x = let t = case h x o f{ (# p,q #) -> (p,q)
511 Indeed, the bindings can even be recursive.
518 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
520 <sect1 id="syntax-extns">
521 <title>Syntactic extensions</title>
523 <!-- ====================== HIERARCHICAL MODULES ======================= -->
525 <sect2 id="hierarchical-modules">
526 <title>Hierarchical Modules</title>
528 <para>GHC supports a small extension to the syntax of module
529 names: a module name is allowed to contain a dot
530 <literal>‘.’</literal>. This is also known as the
531 “hierarchical module namespace” extension, because
532 it extends the normally flat Haskell module namespace into a
533 more flexible hierarchy of modules.</para>
535 <para>This extension has very little impact on the language
536 itself; modules names are <emphasis>always</emphasis> fully
537 qualified, so you can just think of the fully qualified module
538 name as <quote>the module name</quote>. In particular, this
539 means that the full module name must be given after the
540 <literal>module</literal> keyword at the beginning of the
541 module; for example, the module <literal>A.B.C</literal> must
544 <programlisting>module A.B.C</programlisting>
547 <para>It is a common strategy to use the <literal>as</literal>
548 keyword to save some typing when using qualified names with
549 hierarchical modules. For example:</para>
552 import qualified Control.Monad.ST.Strict as ST
555 <para>For details on how GHC searches for source and interface
556 files in the presence of hierarchical modules, see <xref
557 linkend="search-path"/>.</para>
559 <para>GHC comes with a large collection of libraries arranged
560 hierarchically; see the accompanying <ulink
561 url="../libraries/index.html">library
562 documentation</ulink>. More libraries to install are available
564 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
567 <!-- ====================== PATTERN GUARDS ======================= -->
569 <sect2 id="pattern-guards">
570 <title>Pattern guards</title>
573 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
574 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.)
578 Suppose we have an abstract data type of finite maps, with a
582 lookup :: FiniteMap -> Int -> Maybe Int
585 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
586 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
590 clunky env var1 var2 | ok1 && ok2 = val1 + val2
591 | otherwise = var1 + var2
602 The auxiliary functions are
606 maybeToBool :: Maybe a -> Bool
607 maybeToBool (Just x) = True
608 maybeToBool Nothing = False
610 expectJust :: Maybe a -> a
611 expectJust (Just x) = x
612 expectJust Nothing = error "Unexpected Nothing"
616 What is <function>clunky</function> doing? The guard <literal>ok1 &&
617 ok2</literal> checks that both lookups succeed, using
618 <function>maybeToBool</function> to convert the <function>Maybe</function>
619 types to booleans. The (lazily evaluated) <function>expectJust</function>
620 calls extract the values from the results of the lookups, and binds the
621 returned values to <varname>val1</varname> and <varname>val2</varname>
622 respectively. If either lookup fails, then clunky takes the
623 <literal>otherwise</literal> case and returns the sum of its arguments.
627 This is certainly legal Haskell, but it is a tremendously verbose and
628 un-obvious way to achieve the desired effect. Arguably, a more direct way
629 to write clunky would be to use case expressions:
633 clunky env var1 var2 = case lookup env var1 of
635 Just val1 -> case lookup env var2 of
637 Just val2 -> val1 + val2
643 This is a bit shorter, but hardly better. Of course, we can rewrite any set
644 of pattern-matching, guarded equations as case expressions; that is
645 precisely what the compiler does when compiling equations! The reason that
646 Haskell provides guarded equations is because they allow us to write down
647 the cases we want to consider, one at a time, independently of each other.
648 This structure is hidden in the case version. Two of the right-hand sides
649 are really the same (<function>fail</function>), and the whole expression
650 tends to become more and more indented.
654 Here is how I would write clunky:
659 | Just val1 <- lookup env var1
660 , Just val2 <- lookup env var2
662 ...other equations for clunky...
666 The semantics should be clear enough. The qualifiers are matched in order.
667 For a <literal><-</literal> qualifier, which I call a pattern guard, the
668 right hand side is evaluated and matched against the pattern on the left.
669 If the match fails then the whole guard fails and the next equation is
670 tried. If it succeeds, then the appropriate binding takes place, and the
671 next qualifier is matched, in the augmented environment. Unlike list
672 comprehensions, however, the type of the expression to the right of the
673 <literal><-</literal> is the same as the type of the pattern to its
674 left. The bindings introduced by pattern guards scope over all the
675 remaining guard qualifiers, and over the right hand side of the equation.
679 Just as with list comprehensions, boolean expressions can be freely mixed
680 with among the pattern guards. For example:
691 Haskell's current guards therefore emerge as a special case, in which the
692 qualifier list has just one element, a boolean expression.
696 <!-- ===================== Recursive do-notation =================== -->
698 <sect2 id="mdo-notation">
699 <title>The recursive do-notation
702 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
703 "A recursive do for Haskell",
704 Levent Erkok, John Launchbury",
705 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
708 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
709 that is, the variables bound in a do-expression are visible only in the textually following
710 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
711 group. It turns out that several applications can benefit from recursive bindings in
712 the do-notation, and this extension provides the necessary syntactic support.
715 Here is a simple (yet contrived) example:
718 import Control.Monad.Fix
720 justOnes = mdo xs <- Just (1:xs)
724 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
728 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
731 class Monad m => MonadFix m where
732 mfix :: (a -> m a) -> m a
735 The function <literal>mfix</literal>
736 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
737 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
738 For details, see the above mentioned reference.
741 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
742 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
743 for Haskell's internal state monad (strict and lazy, respectively).
746 There are three important points in using the recursive-do notation:
749 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
750 than <literal>do</literal>).
754 You should <literal>import Control.Monad.Fix</literal>.
755 (Note: Strictly speaking, this import is required only when you need to refer to the name
756 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
757 are encouraged to always import this module when using the mdo-notation.)
761 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
767 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
768 contains up to date information on recursive monadic bindings.
772 Historical note: The old implementation of the mdo-notation (and most
773 of the existing documents) used the name
774 <literal>MonadRec</literal> for the class and the corresponding library.
775 This name is not supported by GHC.
781 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
783 <sect2 id="parallel-list-comprehensions">
784 <title>Parallel List Comprehensions</title>
785 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
787 <indexterm><primary>parallel list comprehensions</primary>
790 <para>Parallel list comprehensions are a natural extension to list
791 comprehensions. List comprehensions can be thought of as a nice
792 syntax for writing maps and filters. Parallel comprehensions
793 extend this to include the zipWith family.</para>
795 <para>A parallel list comprehension has multiple independent
796 branches of qualifier lists, each separated by a `|' symbol. For
797 example, the following zips together two lists:</para>
800 [ (x, y) | x <- xs | y <- ys ]
803 <para>The behavior of parallel list comprehensions follows that of
804 zip, in that the resulting list will have the same length as the
805 shortest branch.</para>
807 <para>We can define parallel list comprehensions by translation to
808 regular comprehensions. Here's the basic idea:</para>
810 <para>Given a parallel comprehension of the form: </para>
813 [ e | p1 <- e11, p2 <- e12, ...
814 | q1 <- e21, q2 <- e22, ...
819 <para>This will be translated to: </para>
822 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
823 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
828 <para>where `zipN' is the appropriate zip for the given number of
833 <sect2 id="rebindable-syntax">
834 <title>Rebindable syntax</title>
837 <para>GHC allows most kinds of built-in syntax to be rebound by
838 the user, to facilitate replacing the <literal>Prelude</literal>
839 with a home-grown version, for example.</para>
841 <para>You may want to define your own numeric class
842 hierarchy. It completely defeats that purpose if the
843 literal "1" means "<literal>Prelude.fromInteger
844 1</literal>", which is what the Haskell Report specifies.
845 So the <option>-fno-implicit-prelude</option> flag causes
846 the following pieces of built-in syntax to refer to
847 <emphasis>whatever is in scope</emphasis>, not the Prelude
852 <para>An integer literal <literal>368</literal> means
853 "<literal>fromInteger (368::Integer)</literal>", rather than
854 "<literal>Prelude.fromInteger (368::Integer)</literal>".
857 <listitem><para>Fractional literals are handed in just the same way,
858 except that the translation is
859 <literal>fromRational (3.68::Rational)</literal>.
862 <listitem><para>The equality test in an overloaded numeric pattern
863 uses whatever <literal>(==)</literal> is in scope.
866 <listitem><para>The subtraction operation, and the
867 greater-than-or-equal test, in <literal>n+k</literal> patterns
868 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
872 <para>Negation (e.g. "<literal>- (f x)</literal>")
873 means "<literal>negate (f x)</literal>", both in numeric
874 patterns, and expressions.
878 <para>"Do" notation is translated using whatever
879 functions <literal>(>>=)</literal>,
880 <literal>(>>)</literal>, and <literal>fail</literal>,
881 are in scope (not the Prelude
882 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
883 comprehensions, are unaffected. </para></listitem>
887 notation (see <xref linkend="arrow-notation"/>)
888 uses whatever <literal>arr</literal>,
889 <literal>(>>>)</literal>, <literal>first</literal>,
890 <literal>app</literal>, <literal>(|||)</literal> and
891 <literal>loop</literal> functions are in scope. But unlike the
892 other constructs, the types of these functions must match the
893 Prelude types very closely. Details are in flux; if you want
897 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
898 even if that is a little unexpected. For emample, the
899 static semantics of the literal <literal>368</literal>
900 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
901 <literal>fromInteger</literal> to have any of the types:
903 fromInteger :: Integer -> Integer
904 fromInteger :: forall a. Foo a => Integer -> a
905 fromInteger :: Num a => a -> Integer
906 fromInteger :: Integer -> Bool -> Bool
910 <para>Be warned: this is an experimental facility, with
911 fewer checks than usual. Use <literal>-dcore-lint</literal>
912 to typecheck the desugared program. If Core Lint is happy
913 you should be all right.</para>
917 <sect2 id="postfix-operators">
918 <title>Postfix operators</title>
921 GHC allows a small extension to the syntax of left operator sections, which
922 allows you to define postfix operators. The extension is this: the left section
926 is equivalent (from the point of view of both type checking and execution) to the expression
930 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
931 The strict Haskell 98 interpretation is that the section is equivalent to
935 That is, the operator must be a function of two arguments. GHC allows it to
936 take only one argument, and that in turn allows you to write the function
939 <para>Since this extension goes beyond Haskell 98, it should really be enabled
940 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
941 change their behaviour, of course.)
943 <para>The extension does not extend to the left-hand side of function
944 definitions; you must define such a function in prefix form.</para>
951 <!-- TYPE SYSTEM EXTENSIONS -->
952 <sect1 id="data-type-extensions">
953 <title>Extensions to data types and type synonyms</title>
955 <sect2 id="nullary-types">
956 <title>Data types with no constructors</title>
958 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
959 a data type with no constructors. For example:</para>
963 data T a -- T :: * -> *
966 <para>Syntactically, the declaration lacks the "= constrs" part. The
967 type can be parameterised over types of any kind, but if the kind is
968 not <literal>*</literal> then an explicit kind annotation must be used
969 (see <xref linkend="kinding"/>).</para>
971 <para>Such data types have only one value, namely bottom.
972 Nevertheless, they can be useful when defining "phantom types".</para>
975 <sect2 id="infix-tycons">
976 <title>Infix type constructors, classes, and type variables</title>
979 GHC allows type constructors, classes, and type variables to be operators, and
980 to be written infix, very much like expressions. More specifically:
983 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
984 The lexical syntax is the same as that for data constructors.
987 Data type and type-synonym declarations can be written infix, parenthesised
988 if you want further arguments. E.g.
990 data a :*: b = Foo a b
991 type a :+: b = Either a b
992 class a :=: b where ...
994 data (a :**: b) x = Baz a b x
995 type (a :++: b) y = Either (a,b) y
999 Types, and class constraints, can be written infix. For example
1002 f :: (a :=: b) => a -> b
1006 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1007 The lexical syntax is the same as that for variable operators, excluding "(.)",
1008 "(!)", and "(*)". In a binding position, the operator must be
1009 parenthesised. For example:
1011 type T (+) = Int + Int
1015 liftA2 :: Arrow (~>)
1016 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1022 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1023 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1026 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1027 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1028 sets the fixity for a data constructor and the corresponding type constructor. For example:
1032 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1033 and similarly for <literal>:*:</literal>.
1034 <literal>Int `a` Bool</literal>.
1037 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1044 <sect2 id="type-synonyms">
1045 <title>Liberalised type synonyms</title>
1048 Type synonyms are like macros at the type level, and
1049 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1050 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1052 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1053 in a type synonym, thus:
1055 type Discard a = forall b. Show b => a -> b -> (a, String)
1060 g :: Discard Int -> (Int,String) -- A rank-2 type
1067 You can write an unboxed tuple in a type synonym:
1069 type Pr = (# Int, Int #)
1077 You can apply a type synonym to a forall type:
1079 type Foo a = a -> a -> Bool
1081 f :: Foo (forall b. b->b)
1083 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1085 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1090 You can apply a type synonym to a partially applied type synonym:
1092 type Generic i o = forall x. i x -> o x
1095 foo :: Generic Id []
1097 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1099 foo :: forall x. x -> [x]
1107 GHC currently does kind checking before expanding synonyms (though even that
1111 After expanding type synonyms, GHC does validity checking on types, looking for
1112 the following mal-formedness which isn't detected simply by kind checking:
1115 Type constructor applied to a type involving for-alls.
1118 Unboxed tuple on left of an arrow.
1121 Partially-applied type synonym.
1125 this will be rejected:
1127 type Pr = (# Int, Int #)
1132 because GHC does not allow unboxed tuples on the left of a function arrow.
1137 <sect2 id="existential-quantification">
1138 <title>Existentially quantified data constructors
1142 The idea of using existential quantification in data type declarations
1143 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1144 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1145 London, 1991). It was later formalised by Laufer and Odersky
1146 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1147 TOPLAS, 16(5), pp1411-1430, 1994).
1148 It's been in Lennart
1149 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1150 proved very useful. Here's the idea. Consider the declaration:
1156 data Foo = forall a. MkFoo a (a -> Bool)
1163 The data type <literal>Foo</literal> has two constructors with types:
1169 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1176 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1177 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1178 For example, the following expression is fine:
1184 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1190 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1191 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1192 isUpper</function> packages a character with a compatible function. These
1193 two things are each of type <literal>Foo</literal> and can be put in a list.
1197 What can we do with a value of type <literal>Foo</literal>?. In particular,
1198 what happens when we pattern-match on <function>MkFoo</function>?
1204 f (MkFoo val fn) = ???
1210 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1211 are compatible, the only (useful) thing we can do with them is to
1212 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1219 f (MkFoo val fn) = fn val
1225 What this allows us to do is to package heterogenous values
1226 together with a bunch of functions that manipulate them, and then treat
1227 that collection of packages in a uniform manner. You can express
1228 quite a bit of object-oriented-like programming this way.
1231 <sect3 id="existential">
1232 <title>Why existential?
1236 What has this to do with <emphasis>existential</emphasis> quantification?
1237 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1243 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1249 But Haskell programmers can safely think of the ordinary
1250 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1251 adding a new existential quantification construct.
1257 <title>Type classes</title>
1260 An easy extension is to allow
1261 arbitrary contexts before the constructor. For example:
1267 data Baz = forall a. Eq a => Baz1 a a
1268 | forall b. Show b => Baz2 b (b -> b)
1274 The two constructors have the types you'd expect:
1280 Baz1 :: forall a. Eq a => a -> a -> Baz
1281 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1287 But when pattern matching on <function>Baz1</function> the matched values can be compared
1288 for equality, and when pattern matching on <function>Baz2</function> the first matched
1289 value can be converted to a string (as well as applying the function to it).
1290 So this program is legal:
1297 f (Baz1 p q) | p == q = "Yes"
1299 f (Baz2 v fn) = show (fn v)
1305 Operationally, in a dictionary-passing implementation, the
1306 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1307 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1308 extract it on pattern matching.
1312 Notice the way that the syntax fits smoothly with that used for
1313 universal quantification earlier.
1318 <sect3 id="existential-records">
1319 <title>Record Constructors</title>
1322 GHC allows existentials to be used with records syntax as well. For example:
1325 data Counter a = forall self. NewCounter
1327 , _inc :: self -> self
1328 , _display :: self -> IO ()
1332 Here <literal>tag</literal> is a public field, with a well-typed selector
1333 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1334 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1335 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1336 compile-time error. In other words, <emphasis>GHC defines a record selector function
1337 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1338 (This example used an underscore in the fields for which record selectors
1339 will not be defined, but that is only programming style; GHC ignores them.)
1343 To make use of these hidden fields, we need to create some helper functions:
1346 inc :: Counter a -> Counter a
1347 inc (NewCounter x i d t) = NewCounter
1348 { _this = i x, _inc = i, _display = d, tag = t }
1350 display :: Counter a -> IO ()
1351 display NewCounter{ _this = x, _display = d } = d x
1354 Now we can define counters with different underlying implementations:
1357 counterA :: Counter String
1358 counterA = NewCounter
1359 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1361 counterB :: Counter String
1362 counterB = NewCounter
1363 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1366 display (inc counterA) -- prints "1"
1367 display (inc (inc counterB)) -- prints "##"
1370 At the moment, record update syntax is only supported for Haskell 98 data types,
1371 so the following function does <emphasis>not</emphasis> work:
1374 -- This is invalid; use explicit NewCounter instead for now
1375 setTag :: Counter a -> a -> Counter a
1376 setTag obj t = obj{ tag = t }
1385 <title>Restrictions</title>
1388 There are several restrictions on the ways in which existentially-quantified
1389 constructors can be use.
1398 When pattern matching, each pattern match introduces a new,
1399 distinct, type for each existential type variable. These types cannot
1400 be unified with any other type, nor can they escape from the scope of
1401 the pattern match. For example, these fragments are incorrect:
1409 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1410 is the result of <function>f1</function>. One way to see why this is wrong is to
1411 ask what type <function>f1</function> has:
1415 f1 :: Foo -> a -- Weird!
1419 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1424 f1 :: forall a. Foo -> a -- Wrong!
1428 The original program is just plain wrong. Here's another sort of error
1432 f2 (Baz1 a b) (Baz1 p q) = a==q
1436 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1437 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1438 from the two <function>Baz1</function> constructors.
1446 You can't pattern-match on an existentially quantified
1447 constructor in a <literal>let</literal> or <literal>where</literal> group of
1448 bindings. So this is illegal:
1452 f3 x = a==b where { Baz1 a b = x }
1455 Instead, use a <literal>case</literal> expression:
1458 f3 x = case x of Baz1 a b -> a==b
1461 In general, you can only pattern-match
1462 on an existentially-quantified constructor in a <literal>case</literal> expression or
1463 in the patterns of a function definition.
1465 The reason for this restriction is really an implementation one.
1466 Type-checking binding groups is already a nightmare without
1467 existentials complicating the picture. Also an existential pattern
1468 binding at the top level of a module doesn't make sense, because it's
1469 not clear how to prevent the existentially-quantified type "escaping".
1470 So for now, there's a simple-to-state restriction. We'll see how
1478 You can't use existential quantification for <literal>newtype</literal>
1479 declarations. So this is illegal:
1483 newtype T = forall a. Ord a => MkT a
1487 Reason: a value of type <literal>T</literal> must be represented as a
1488 pair of a dictionary for <literal>Ord t</literal> and a value of type
1489 <literal>t</literal>. That contradicts the idea that
1490 <literal>newtype</literal> should have no concrete representation.
1491 You can get just the same efficiency and effect by using
1492 <literal>data</literal> instead of <literal>newtype</literal>. If
1493 there is no overloading involved, then there is more of a case for
1494 allowing an existentially-quantified <literal>newtype</literal>,
1495 because the <literal>data</literal> version does carry an
1496 implementation cost, but single-field existentially quantified
1497 constructors aren't much use. So the simple restriction (no
1498 existential stuff on <literal>newtype</literal>) stands, unless there
1499 are convincing reasons to change it.
1507 You can't use <literal>deriving</literal> to define instances of a
1508 data type with existentially quantified data constructors.
1510 Reason: in most cases it would not make sense. For example:;
1513 data T = forall a. MkT [a] deriving( Eq )
1516 To derive <literal>Eq</literal> in the standard way we would need to have equality
1517 between the single component of two <function>MkT</function> constructors:
1521 (MkT a) == (MkT b) = ???
1524 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1525 It's just about possible to imagine examples in which the derived instance
1526 would make sense, but it seems altogether simpler simply to prohibit such
1527 declarations. Define your own instances!
1538 <!-- ====================== Generalised algebraic data types ======================= -->
1540 <sect2 id="gadt-style">
1541 <title>Declaring data types with explicit constructor signatures</title>
1543 <para>GHC allows you to declare an algebraic data type by
1544 giving the type signatures of constructors explicitly. For example:
1548 Just :: a -> Maybe a
1550 The form is called a "GADT-style declaration"
1551 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1552 can only be declared using this form.</para>
1553 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1554 For example, these two declarations are equivalent:
1556 data Foo = forall a. MkFoo a (a -> Bool)
1557 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1560 <para>Any data type that can be declared in standard Haskell-98 syntax
1561 can also be declared using GADT-style syntax.
1562 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1563 they treat class constraints on the data constructors differently.
1564 Specifically, if the constructor is given a type-class context, that
1565 context is made available by pattern matching. For example:
1568 MkSet :: Eq a => [a] -> Set a
1570 makeSet :: Eq a => [a] -> Set a
1571 makeSet xs = MkSet (nub xs)
1573 insert :: a -> Set a -> Set a
1574 insert a (MkSet as) | a `elem` as = MkSet as
1575 | otherwise = MkSet (a:as)
1577 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1578 gives rise to a <literal>(Eq a)</literal>
1579 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1580 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1581 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1582 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1583 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1584 In the example, the equality dictionary is used to satisfy the equality constraint
1585 generated by the call to <literal>elem</literal>, so that the type of
1586 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1588 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1589 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1590 In Haskell 98 the defintion
1592 data Eq a => Set' a = MkSet' [a]
1594 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1595 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1596 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1597 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1598 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1600 For example, a possible application of GHC's behaviour is to reify dictionaries:
1602 data NumInst a where
1603 MkNumInst :: Num a => NumInst a
1605 intInst :: NumInst Int
1608 plus :: NumInst a -> a -> a -> a
1609 plus MkNumInst p q = p + q
1611 Here, a value of type <literal>NumInst a</literal> is equivalent
1612 to an explicit <literal>(Num a)</literal> dictionary.
1616 The rest of this section gives further details about GADT-style data
1621 The result type of each data constructor must begin with the type constructor being defined.
1622 If the result type of all constructors
1623 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1624 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1625 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1629 The type signature of
1630 each constructor is independent, and is implicitly universally quantified as usual.
1631 Different constructors may have different universally-quantified type variables
1632 and different type-class constraints.
1633 For example, this is fine:
1636 T1 :: Eq b => b -> T b
1637 T2 :: (Show c, Ix c) => c -> [c] -> T c
1642 Unlike a Haskell-98-style
1643 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1644 have no scope. Indeed, one can write a kind signature instead:
1646 data Set :: * -> * where ...
1648 or even a mixture of the two:
1650 data Foo a :: (* -> *) -> * where ...
1652 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1655 data Foo a (b :: * -> *) where ...
1661 You can use strictness annotations, in the obvious places
1662 in the constructor type:
1665 Lit :: !Int -> Term Int
1666 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1667 Pair :: Term a -> Term b -> Term (a,b)
1672 You can use a <literal>deriving</literal> clause on a GADT-style data type
1673 declaration. For example, these two declarations are equivalent
1675 data Maybe1 a where {
1676 Nothing1 :: Maybe1 a ;
1677 Just1 :: a -> Maybe1 a
1678 } deriving( Eq, Ord )
1680 data Maybe2 a = Nothing2 | Just2 a
1686 You can use record syntax on a GADT-style data type declaration:
1690 Adult { name :: String, children :: [Person] } :: Person
1691 Child { name :: String } :: Person
1693 As usual, for every constructor that has a field <literal>f</literal>, the type of
1694 field <literal>f</literal> must be the same (modulo alpha conversion).
1697 At the moment, record updates are not yet possible with GADT-style declarations,
1698 so support is limited to record construction, selection and pattern matching.
1701 aPerson = Adult { name = "Fred", children = [] }
1703 shortName :: Person -> Bool
1704 hasChildren (Adult { children = kids }) = not (null kids)
1705 hasChildren (Child {}) = False
1710 As in the case of existentials declared using the Haskell-98-like record syntax
1711 (<xref linkend="existential-records"/>),
1712 record-selector functions are generated only for those fields that have well-typed
1714 Here is the example of that section, in GADT-style syntax:
1716 data Counter a where
1717 NewCounter { _this :: self
1718 , _inc :: self -> self
1719 , _display :: self -> IO ()
1724 As before, only one selector function is generated here, that for <literal>tag</literal>.
1725 Nevertheless, you can still use all the field names in pattern matching and record construction.
1727 </itemizedlist></para>
1731 <title>Generalised Algebraic Data Types (GADTs)</title>
1733 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1734 by allowing constructors to have richer return types. Here is an example:
1737 Lit :: Int -> Term Int
1738 Succ :: Term Int -> Term Int
1739 IsZero :: Term Int -> Term Bool
1740 If :: Term Bool -> Term a -> Term a -> Term a
1741 Pair :: Term a -> Term b -> Term (a,b)
1743 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1744 case with ordinary data types. This generality allows us to
1745 write a well-typed <literal>eval</literal> function
1746 for these <literal>Terms</literal>:
1750 eval (Succ t) = 1 + eval t
1751 eval (IsZero t) = eval t == 0
1752 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1753 eval (Pair e1 e2) = (eval e1, eval e2)
1755 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1756 For example, in the right hand side of the equation
1761 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1762 A precise specification of the type rules is beyond what this user manual aspires to,
1763 but the design closely follows that described in
1765 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1766 unification-based type inference for GADTs</ulink>,
1768 The general principle is this: <emphasis>type refinement is only carried out
1769 based on user-supplied type annotations</emphasis>.
1770 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1771 and lots of obscure error messages will
1772 occur. However, the refinement is quite general. For example, if we had:
1774 eval :: Term a -> a -> a
1775 eval (Lit i) j = i+j
1777 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1778 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1779 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1782 These and many other examples are given in papers by Hongwei Xi, and
1783 Tim Sheard. There is a longer introduction
1784 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1786 <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
1787 may use different notation to that implemented in GHC.
1790 The rest of this section outlines the extensions to GHC that support GADTs.
1793 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1794 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1795 The result type of each constructor must begin with the type constructor being defined,
1796 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1797 For example, in the <literal>Term</literal> data
1798 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1799 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1804 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1805 an ordianary data type.
1809 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1813 Lit { val :: Int } :: Term Int
1814 Succ { num :: Term Int } :: Term Int
1815 Pred { num :: Term Int } :: Term Int
1816 IsZero { arg :: Term Int } :: Term Bool
1817 Pair { arg1 :: Term a
1820 If { cnd :: Term Bool
1825 However, for GADTs there is the following additional constraint:
1826 every constructor that has a field <literal>f</literal> must have
1827 the same result type (modulo alpha conversion)
1828 Hence, in the above example, we cannot merge the <literal>num</literal>
1829 and <literal>arg</literal> fields above into a
1830 single name. Although their field types are both <literal>Term Int</literal>,
1831 their selector functions actually have different types:
1834 num :: Term Int -> Term Int
1835 arg :: Term Bool -> Term Int
1844 <!-- ====================== End of Generalised algebraic data types ======================= -->
1847 <sect2 id="deriving-typeable">
1848 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1851 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1852 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1853 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1854 classes <literal>Eq</literal>, <literal>Ord</literal>,
1855 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1858 GHC extends this list with two more classes that may be automatically derived
1859 (provided the <option>-fglasgow-exts</option> flag is specified):
1860 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1861 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1862 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1864 <para>An instance of <literal>Typeable</literal> can only be derived if the
1865 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1866 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1868 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1869 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1871 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1872 are used, and only <literal>Typeable1</literal> up to
1873 <literal>Typeable7</literal> are provided in the library.)
1874 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1875 class, whose kind suits that of the data type constructor, and
1876 then writing the data type instance by hand.
1880 <sect2 id="newtype-deriving">
1881 <title>Generalised derived instances for newtypes</title>
1884 When you define an abstract type using <literal>newtype</literal>, you may want
1885 the new type to inherit some instances from its representation. In
1886 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1887 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1888 other classes you have to write an explicit instance declaration. For
1889 example, if you define
1892 newtype Dollars = Dollars Int
1895 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1896 explicitly define an instance of <literal>Num</literal>:
1899 instance Num Dollars where
1900 Dollars a + Dollars b = Dollars (a+b)
1903 All the instance does is apply and remove the <literal>newtype</literal>
1904 constructor. It is particularly galling that, since the constructor
1905 doesn't appear at run-time, this instance declaration defines a
1906 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1907 dictionary, only slower!
1911 <sect3> <title> Generalising the deriving clause </title>
1913 GHC now permits such instances to be derived instead, so one can write
1915 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1918 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1919 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1920 derives an instance declaration of the form
1923 instance Num Int => Num Dollars
1926 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1930 We can also derive instances of constructor classes in a similar
1931 way. For example, suppose we have implemented state and failure monad
1932 transformers, such that
1935 instance Monad m => Monad (State s m)
1936 instance Monad m => Monad (Failure m)
1938 In Haskell 98, we can define a parsing monad by
1940 type Parser tok m a = State [tok] (Failure m) a
1943 which is automatically a monad thanks to the instance declarations
1944 above. With the extension, we can make the parser type abstract,
1945 without needing to write an instance of class <literal>Monad</literal>, via
1948 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1951 In this case the derived instance declaration is of the form
1953 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1956 Notice that, since <literal>Monad</literal> is a constructor class, the
1957 instance is a <emphasis>partial application</emphasis> of the new type, not the
1958 entire left hand side. We can imagine that the type declaration is
1959 ``eta-converted'' to generate the context of the instance
1964 We can even derive instances of multi-parameter classes, provided the
1965 newtype is the last class parameter. In this case, a ``partial
1966 application'' of the class appears in the <literal>deriving</literal>
1967 clause. For example, given the class
1970 class StateMonad s m | m -> s where ...
1971 instance Monad m => StateMonad s (State s m) where ...
1973 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1975 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1976 deriving (Monad, StateMonad [tok])
1979 The derived instance is obtained by completing the application of the
1980 class to the new type:
1983 instance StateMonad [tok] (State [tok] (Failure m)) =>
1984 StateMonad [tok] (Parser tok m)
1989 As a result of this extension, all derived instances in newtype
1990 declarations are treated uniformly (and implemented just by reusing
1991 the dictionary for the representation type), <emphasis>except</emphasis>
1992 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
1993 the newtype and its representation.
1997 <sect3> <title> A more precise specification </title>
1999 Derived instance declarations are constructed as follows. Consider the
2000 declaration (after expansion of any type synonyms)
2003 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2009 The <literal>ci</literal> are partial applications of
2010 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2011 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2014 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2017 The type <literal>t</literal> is an arbitrary type.
2020 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2021 nor in the <literal>ci</literal>, and
2024 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2025 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2026 should not "look through" the type or its constructor. You can still
2027 derive these classes for a newtype, but it happens in the usual way, not
2028 via this new mechanism.
2031 Then, for each <literal>ci</literal>, the derived instance
2034 instance ci t => ci (T v1...vk)
2036 As an example which does <emphasis>not</emphasis> work, consider
2038 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2040 Here we cannot derive the instance
2042 instance Monad (State s m) => Monad (NonMonad m)
2045 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2046 and so cannot be "eta-converted" away. It is a good thing that this
2047 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2048 not, in fact, a monad --- for the same reason. Try defining
2049 <literal>>>=</literal> with the correct type: you won't be able to.
2053 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2054 important, since we can only derive instances for the last one. If the
2055 <literal>StateMonad</literal> class above were instead defined as
2058 class StateMonad m s | m -> s where ...
2061 then we would not have been able to derive an instance for the
2062 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2063 classes usually have one "main" parameter for which deriving new
2064 instances is most interesting.
2066 <para>Lastly, all of this applies only for classes other than
2067 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2068 and <literal>Data</literal>, for which the built-in derivation applies (section
2069 4.3.3. of the Haskell Report).
2070 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2071 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2072 the standard method is used or the one described here.)
2078 <sect2 id="stand-alone-deriving">
2079 <title>Stand-alone deriving declarations</title>
2082 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2084 data Foo a = Bar a | Baz String
2086 derive instance Eq (Foo a)
2088 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2089 you can use it as a variable name elsewhere.</para>
2090 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2091 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2094 newtype Foo a = MkFoo (State Int a)
2096 derive instance MonadState Int Foo
2098 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2099 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2107 <!-- TYPE SYSTEM EXTENSIONS -->
2108 <sect1 id="other-type-extensions">
2109 <title>Other type system extensions</title>
2111 <sect2 id="multi-param-type-classes">
2112 <title>Class declarations</title>
2115 This section, and the next one, documents GHC's type-class extensions.
2116 There's lots of background in the paper <ulink
2117 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2118 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2119 Jones, Erik Meijer).
2122 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2126 <title>Multi-parameter type classes</title>
2128 Multi-parameter type classes are permitted. For example:
2132 class Collection c a where
2133 union :: c a -> c a -> c a
2141 <title>The superclasses of a class declaration</title>
2144 There are no restrictions on the context in a class declaration
2145 (which introduces superclasses), except that the class hierarchy must
2146 be acyclic. So these class declarations are OK:
2150 class Functor (m k) => FiniteMap m k where
2153 class (Monad m, Monad (t m)) => Transform t m where
2154 lift :: m a -> (t m) a
2160 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2161 of "acyclic" involves only the superclass relationships. For example,
2167 op :: D b => a -> b -> b
2170 class C a => D a where { ... }
2174 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2175 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2176 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2183 <sect3 id="class-method-types">
2184 <title>Class method types</title>
2187 Haskell 98 prohibits class method types to mention constraints on the
2188 class type variable, thus:
2191 fromList :: [a] -> s a
2192 elem :: Eq a => a -> s a -> Bool
2194 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2195 contains the constraint <literal>Eq a</literal>, constrains only the
2196 class type variable (in this case <literal>a</literal>).
2197 GHC lifts this restriction.
2204 <sect2 id="functional-dependencies">
2205 <title>Functional dependencies
2208 <para> Functional dependencies are implemented as described by Mark Jones
2209 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2210 In Proceedings of the 9th European Symposium on Programming,
2211 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2215 Functional dependencies are introduced by a vertical bar in the syntax of a
2216 class declaration; e.g.
2218 class (Monad m) => MonadState s m | m -> s where ...
2220 class Foo a b c | a b -> c where ...
2222 There should be more documentation, but there isn't (yet). Yell if you need it.
2225 <sect3><title>Rules for functional dependencies </title>
2227 In a class declaration, all of the class type variables must be reachable (in the sense
2228 mentioned in <xref linkend="type-restrictions"/>)
2229 from the free variables of each method type.
2233 class Coll s a where
2235 insert :: s -> a -> s
2238 is not OK, because the type of <literal>empty</literal> doesn't mention
2239 <literal>a</literal>. Functional dependencies can make the type variable
2242 class Coll s a | s -> a where
2244 insert :: s -> a -> s
2247 Alternatively <literal>Coll</literal> might be rewritten
2250 class Coll s a where
2252 insert :: s a -> a -> s a
2256 which makes the connection between the type of a collection of
2257 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2258 Occasionally this really doesn't work, in which case you can split the
2266 class CollE s => Coll s a where
2267 insert :: s -> a -> s
2274 <title>Background on functional dependencies</title>
2276 <para>The following description of the motivation and use of functional dependencies is taken
2277 from the Hugs user manual, reproduced here (with minor changes) by kind
2278 permission of Mark Jones.
2281 Consider the following class, intended as part of a
2282 library for collection types:
2284 class Collects e ce where
2286 insert :: e -> ce -> ce
2287 member :: e -> ce -> Bool
2289 The type variable e used here represents the element type, while ce is the type
2290 of the container itself. Within this framework, we might want to define
2291 instances of this class for lists or characteristic functions (both of which
2292 can be used to represent collections of any equality type), bit sets (which can
2293 be used to represent collections of characters), or hash tables (which can be
2294 used to represent any collection whose elements have a hash function). Omitting
2295 standard implementation details, this would lead to the following declarations:
2297 instance Eq e => Collects e [e] where ...
2298 instance Eq e => Collects e (e -> Bool) where ...
2299 instance Collects Char BitSet where ...
2300 instance (Hashable e, Collects a ce)
2301 => Collects e (Array Int ce) where ...
2303 All this looks quite promising; we have a class and a range of interesting
2304 implementations. Unfortunately, there are some serious problems with the class
2305 declaration. First, the empty function has an ambiguous type:
2307 empty :: Collects e ce => ce
2309 By "ambiguous" we mean that there is a type variable e that appears on the left
2310 of the <literal>=></literal> symbol, but not on the right. The problem with
2311 this is that, according to the theoretical foundations of Haskell overloading,
2312 we cannot guarantee a well-defined semantics for any term with an ambiguous
2316 We can sidestep this specific problem by removing the empty member from the
2317 class declaration. However, although the remaining members, insert and member,
2318 do not have ambiguous types, we still run into problems when we try to use
2319 them. For example, consider the following two functions:
2321 f x y = insert x . insert y
2324 for which GHC infers the following types:
2326 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2327 g :: (Collects Bool c, Collects Char c) => c -> c
2329 Notice that the type for f allows the two parameters x and y to be assigned
2330 different types, even though it attempts to insert each of the two values, one
2331 after the other, into the same collection. If we're trying to model collections
2332 that contain only one type of value, then this is clearly an inaccurate
2333 type. Worse still, the definition for g is accepted, without causing a type
2334 error. As a result, the error in this code will not be flagged at the point
2335 where it appears. Instead, it will show up only when we try to use g, which
2336 might even be in a different module.
2339 <sect4><title>An attempt to use constructor classes</title>
2342 Faced with the problems described above, some Haskell programmers might be
2343 tempted to use something like the following version of the class declaration:
2345 class Collects e c where
2347 insert :: e -> c e -> c e
2348 member :: e -> c e -> Bool
2350 The key difference here is that we abstract over the type constructor c that is
2351 used to form the collection type c e, and not over that collection type itself,
2352 represented by ce in the original class declaration. This avoids the immediate
2353 problems that we mentioned above: empty has type <literal>Collects e c => c
2354 e</literal>, which is not ambiguous.
2357 The function f from the previous section has a more accurate type:
2359 f :: (Collects e c) => e -> e -> c e -> c e
2361 The function g from the previous section is now rejected with a type error as
2362 we would hope because the type of f does not allow the two arguments to have
2364 This, then, is an example of a multiple parameter class that does actually work
2365 quite well in practice, without ambiguity problems.
2366 There is, however, a catch. This version of the Collects class is nowhere near
2367 as general as the original class seemed to be: only one of the four instances
2368 for <literal>Collects</literal>
2369 given above can be used with this version of Collects because only one of
2370 them---the instance for lists---has a collection type that can be written in
2371 the form c e, for some type constructor c, and element type e.
2375 <sect4><title>Adding functional dependencies</title>
2378 To get a more useful version of the Collects class, Hugs provides a mechanism
2379 that allows programmers to specify dependencies between the parameters of a
2380 multiple parameter class (For readers with an interest in theoretical
2381 foundations and previous work: The use of dependency information can be seen
2382 both as a generalization of the proposal for `parametric type classes' that was
2383 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2384 later framework for "improvement" of qualified types. The
2385 underlying ideas are also discussed in a more theoretical and abstract setting
2386 in a manuscript [implparam], where they are identified as one point in a
2387 general design space for systems of implicit parameterization.).
2389 To start with an abstract example, consider a declaration such as:
2391 class C a b where ...
2393 which tells us simply that C can be thought of as a binary relation on types
2394 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2395 included in the definition of classes to add information about dependencies
2396 between parameters, as in the following examples:
2398 class D a b | a -> b where ...
2399 class E a b | a -> b, b -> a where ...
2401 The notation <literal>a -> b</literal> used here between the | and where
2402 symbols --- not to be
2403 confused with a function type --- indicates that the a parameter uniquely
2404 determines the b parameter, and might be read as "a determines b." Thus D is
2405 not just a relation, but actually a (partial) function. Similarly, from the two
2406 dependencies that are included in the definition of E, we can see that E
2407 represents a (partial) one-one mapping between types.
2410 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2411 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2412 m>=0, meaning that the y parameters are uniquely determined by the x
2413 parameters. Spaces can be used as separators if more than one variable appears
2414 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2415 annotated with multiple dependencies using commas as separators, as in the
2416 definition of E above. Some dependencies that we can write in this notation are
2417 redundant, and will be rejected because they don't serve any useful
2418 purpose, and may instead indicate an error in the program. Examples of
2419 dependencies like this include <literal>a -> a </literal>,
2420 <literal>a -> a a </literal>,
2421 <literal>a -> </literal>, etc. There can also be
2422 some redundancy if multiple dependencies are given, as in
2423 <literal>a->b</literal>,
2424 <literal>b->c </literal>, <literal>a->c </literal>, and
2425 in which some subset implies the remaining dependencies. Examples like this are
2426 not treated as errors. Note that dependencies appear only in class
2427 declarations, and not in any other part of the language. In particular, the
2428 syntax for instance declarations, class constraints, and types is completely
2432 By including dependencies in a class declaration, we provide a mechanism for
2433 the programmer to specify each multiple parameter class more precisely. The
2434 compiler, on the other hand, is responsible for ensuring that the set of
2435 instances that are in scope at any given point in the program is consistent
2436 with any declared dependencies. For example, the following pair of instance
2437 declarations cannot appear together in the same scope because they violate the
2438 dependency for D, even though either one on its own would be acceptable:
2440 instance D Bool Int where ...
2441 instance D Bool Char where ...
2443 Note also that the following declaration is not allowed, even by itself:
2445 instance D [a] b where ...
2447 The problem here is that this instance would allow one particular choice of [a]
2448 to be associated with more than one choice for b, which contradicts the
2449 dependency specified in the definition of D. More generally, this means that,
2450 in any instance of the form:
2452 instance D t s where ...
2454 for some particular types t and s, the only variables that can appear in s are
2455 the ones that appear in t, and hence, if the type t is known, then s will be
2456 uniquely determined.
2459 The benefit of including dependency information is that it allows us to define
2460 more general multiple parameter classes, without ambiguity problems, and with
2461 the benefit of more accurate types. To illustrate this, we return to the
2462 collection class example, and annotate the original definition of <literal>Collects</literal>
2463 with a simple dependency:
2465 class Collects e ce | ce -> e where
2467 insert :: e -> ce -> ce
2468 member :: e -> ce -> Bool
2470 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2471 determined by the type of the collection ce. Note that both parameters of
2472 Collects are of kind *; there are no constructor classes here. Note too that
2473 all of the instances of Collects that we gave earlier can be used
2474 together with this new definition.
2477 What about the ambiguity problems that we encountered with the original
2478 definition? The empty function still has type Collects e ce => ce, but it is no
2479 longer necessary to regard that as an ambiguous type: Although the variable e
2480 does not appear on the right of the => symbol, the dependency for class
2481 Collects tells us that it is uniquely determined by ce, which does appear on
2482 the right of the => symbol. Hence the context in which empty is used can still
2483 give enough information to determine types for both ce and e, without
2484 ambiguity. More generally, we need only regard a type as ambiguous if it
2485 contains a variable on the left of the => that is not uniquely determined
2486 (either directly or indirectly) by the variables on the right.
2489 Dependencies also help to produce more accurate types for user defined
2490 functions, and hence to provide earlier detection of errors, and less cluttered
2491 types for programmers to work with. Recall the previous definition for a
2494 f x y = insert x y = insert x . insert y
2496 for which we originally obtained a type:
2498 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2500 Given the dependency information that we have for Collects, however, we can
2501 deduce that a and b must be equal because they both appear as the second
2502 parameter in a Collects constraint with the same first parameter c. Hence we
2503 can infer a shorter and more accurate type for f:
2505 f :: (Collects a c) => a -> a -> c -> c
2507 In a similar way, the earlier definition of g will now be flagged as a type error.
2510 Although we have given only a few examples here, it should be clear that the
2511 addition of dependency information can help to make multiple parameter classes
2512 more useful in practice, avoiding ambiguity problems, and allowing more general
2513 sets of instance declarations.
2519 <sect2 id="instance-decls">
2520 <title>Instance declarations</title>
2522 <sect3 id="instance-rules">
2523 <title>Relaxed rules for instance declarations</title>
2525 <para>An instance declaration has the form
2527 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 ...
2529 The part before the "<literal>=></literal>" is the
2530 <emphasis>context</emphasis>, while the part after the
2531 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2535 In Haskell 98 the head of an instance declaration
2536 must be of the form <literal>C (T a1 ... an)</literal>, where
2537 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2538 and the <literal>a1 ... an</literal> are distinct type variables.
2539 Furthermore, the assertions in the context of the instance declaration
2540 must be of the form <literal>C a</literal> where <literal>a</literal>
2541 is a type variable that occurs in the head.
2544 The <option>-fglasgow-exts</option> flag loosens these restrictions
2545 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2546 the context and head of the instance declaration can each consist of arbitrary
2547 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2551 The Paterson Conditions: for each assertion in the context
2553 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2554 <listitem><para>The assertion has fewer constructors and variables (taken together
2555 and counting repetitions) than the head</para></listitem>
2559 <listitem><para>The Coverage Condition. For each functional dependency,
2560 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2561 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2562 every type variable in
2563 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2564 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2565 substitution mapping each type variable in the class declaration to the
2566 corresponding type in the instance declaration.
2569 These restrictions ensure that context reduction terminates: each reduction
2570 step makes the problem smaller by at least one
2571 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2572 if you give the <option>-fallow-undecidable-instances</option>
2573 flag (<xref linkend="undecidable-instances"/>).
2574 You can find lots of background material about the reason for these
2575 restrictions in the paper <ulink
2576 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2577 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2580 For example, these are OK:
2582 instance C Int [a] -- Multiple parameters
2583 instance Eq (S [a]) -- Structured type in head
2585 -- Repeated type variable in head
2586 instance C4 a a => C4 [a] [a]
2587 instance Stateful (ST s) (MutVar s)
2589 -- Head can consist of type variables only
2591 instance (Eq a, Show b) => C2 a b
2593 -- Non-type variables in context
2594 instance Show (s a) => Show (Sized s a)
2595 instance C2 Int a => C3 Bool [a]
2596 instance C2 Int a => C3 [a] b
2600 -- Context assertion no smaller than head
2601 instance C a => C a where ...
2602 -- (C b b) has more more occurrences of b than the head
2603 instance C b b => Foo [b] where ...
2608 The same restrictions apply to instances generated by
2609 <literal>deriving</literal> clauses. Thus the following is accepted:
2611 data MinHeap h a = H a (h a)
2614 because the derived instance
2616 instance (Show a, Show (h a)) => Show (MinHeap h a)
2618 conforms to the above rules.
2622 A useful idiom permitted by the above rules is as follows.
2623 If one allows overlapping instance declarations then it's quite
2624 convenient to have a "default instance" declaration that applies if
2625 something more specific does not:
2633 <sect3 id="undecidable-instances">
2634 <title>Undecidable instances</title>
2637 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2638 For example, sometimes you might want to use the following to get the
2639 effect of a "class synonym":
2641 class (C1 a, C2 a, C3 a) => C a where { }
2643 instance (C1 a, C2 a, C3 a) => C a where { }
2645 This allows you to write shorter signatures:
2651 f :: (C1 a, C2 a, C3 a) => ...
2653 The restrictions on functional dependencies (<xref
2654 linkend="functional-dependencies"/>) are particularly troublesome.
2655 It is tempting to introduce type variables in the context that do not appear in
2656 the head, something that is excluded by the normal rules. For example:
2658 class HasConverter a b | a -> b where
2661 data Foo a = MkFoo a
2663 instance (HasConverter a b,Show b) => Show (Foo a) where
2664 show (MkFoo value) = show (convert value)
2666 This is dangerous territory, however. Here, for example, is a program that would make the
2671 instance F [a] [[a]]
2672 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2674 Similarly, it can be tempting to lift the coverage condition:
2676 class Mul a b c | a b -> c where
2677 (.*.) :: a -> b -> c
2679 instance Mul Int Int Int where (.*.) = (*)
2680 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2681 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2683 The third instance declaration does not obey the coverage condition;
2684 and indeed the (somewhat strange) definition:
2686 f = \ b x y -> if b then x .*. [y] else y
2688 makes instance inference go into a loop, because it requires the constraint
2689 <literal>(Mul a [b] b)</literal>.
2692 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2693 the experimental flag <option>-fallow-undecidable-instances</option>
2694 <indexterm><primary>-fallow-undecidable-instances
2695 option</primary></indexterm>, both the Paterson Conditions and the Coverage Condition
2696 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2697 fixed-depth recursion stack. If you exceed the stack depth you get a
2698 sort of backtrace, and the opportunity to increase the stack depth
2699 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2705 <sect3 id="instance-overlap">
2706 <title>Overlapping instances</title>
2708 In general, <emphasis>GHC requires that that it be unambiguous which instance
2710 should be used to resolve a type-class constraint</emphasis>. This behaviour
2711 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2712 <indexterm><primary>-fallow-overlapping-instances
2713 </primary></indexterm>
2714 and <option>-fallow-incoherent-instances</option>
2715 <indexterm><primary>-fallow-incoherent-instances
2716 </primary></indexterm>, as this section discusses. Both these
2717 flags are dynamic flags, and can be set on a per-module basis, using
2718 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2720 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2721 it tries to match every instance declaration against the
2723 by instantiating the head of the instance declaration. For example, consider
2726 instance context1 => C Int a where ... -- (A)
2727 instance context2 => C a Bool where ... -- (B)
2728 instance context3 => C Int [a] where ... -- (C)
2729 instance context4 => C Int [Int] where ... -- (D)
2731 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2732 but (C) and (D) do not. When matching, GHC takes
2733 no account of the context of the instance declaration
2734 (<literal>context1</literal> etc).
2735 GHC's default behaviour is that <emphasis>exactly one instance must match the
2736 constraint it is trying to resolve</emphasis>.
2737 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2738 including both declarations (A) and (B), say); an error is only reported if a
2739 particular constraint matches more than one.
2743 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2744 more than one instance to match, provided there is a most specific one. For
2745 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2746 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2747 most-specific match, the program is rejected.
2750 However, GHC is conservative about committing to an overlapping instance. For example:
2755 Suppose that from the RHS of <literal>f</literal> we get the constraint
2756 <literal>C Int [b]</literal>. But
2757 GHC does not commit to instance (C), because in a particular
2758 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2759 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2760 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2761 GHC will instead pick (C), without complaining about
2762 the problem of subsequent instantiations.
2765 The willingness to be overlapped or incoherent is a property of
2766 the <emphasis>instance declaration</emphasis> itself, controlled by the
2767 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2768 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2769 being defined. Neither flag is required in a module that imports and uses the
2770 instance declaration. Specifically, during the lookup process:
2773 An instance declaration is ignored during the lookup process if (a) a more specific
2774 match is found, and (b) the instance declaration was compiled with
2775 <option>-fallow-overlapping-instances</option>. The flag setting for the
2776 more-specific instance does not matter.
2779 Suppose an instance declaration does not matche the constraint being looked up, but
2780 does unify with it, so that it might match when the constraint is further
2781 instantiated. Usually GHC will regard this as a reason for not committing to
2782 some other constraint. But if the instance declaration was compiled with
2783 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2784 check for that declaration.
2787 These rules make it possible for a library author to design a library that relies on
2788 overlapping instances without the library client having to know.
2791 If an instance declaration is compiled without
2792 <option>-fallow-overlapping-instances</option>,
2793 then that instance can never be overlapped. This could perhaps be
2794 inconvenient. Perhaps the rule should instead say that the
2795 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2796 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2797 at a usage site should be permitted regardless of how the instance declarations
2798 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2799 used at the usage site. (Mind you, the exact usage site can occasionally be
2800 hard to pin down.) We are interested to receive feedback on these points.
2802 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2803 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2808 <title>Type synonyms in the instance head</title>
2811 <emphasis>Unlike Haskell 98, instance heads may use type
2812 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2813 As always, using a type synonym is just shorthand for
2814 writing the RHS of the type synonym definition. For example:
2818 type Point = (Int,Int)
2819 instance C Point where ...
2820 instance C [Point] where ...
2824 is legal. However, if you added
2828 instance C (Int,Int) where ...
2832 as well, then the compiler will complain about the overlapping
2833 (actually, identical) instance declarations. As always, type synonyms
2834 must be fully applied. You cannot, for example, write:
2839 instance Monad P where ...
2843 This design decision is independent of all the others, and easily
2844 reversed, but it makes sense to me.
2852 <sect2 id="type-restrictions">
2853 <title>Type signatures</title>
2855 <sect3><title>The context of a type signature</title>
2857 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2858 the form <emphasis>(class type-variable)</emphasis> or
2859 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2860 these type signatures are perfectly OK
2863 g :: Ord (T a ()) => ...
2867 GHC imposes the following restrictions on the constraints in a type signature.
2871 forall tv1..tvn (c1, ...,cn) => type
2874 (Here, we write the "foralls" explicitly, although the Haskell source
2875 language omits them; in Haskell 98, all the free type variables of an
2876 explicit source-language type signature are universally quantified,
2877 except for the class type variables in a class declaration. However,
2878 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2887 <emphasis>Each universally quantified type variable
2888 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2890 A type variable <literal>a</literal> is "reachable" if it it appears
2891 in the same constraint as either a type variable free in in
2892 <literal>type</literal>, or another reachable type variable.
2893 A value with a type that does not obey
2894 this reachability restriction cannot be used without introducing
2895 ambiguity; that is why the type is rejected.
2896 Here, for example, is an illegal type:
2900 forall a. Eq a => Int
2904 When a value with this type was used, the constraint <literal>Eq tv</literal>
2905 would be introduced where <literal>tv</literal> is a fresh type variable, and
2906 (in the dictionary-translation implementation) the value would be
2907 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2908 can never know which instance of <literal>Eq</literal> to use because we never
2909 get any more information about <literal>tv</literal>.
2913 that the reachability condition is weaker than saying that <literal>a</literal> is
2914 functionally dependent on a type variable free in
2915 <literal>type</literal> (see <xref
2916 linkend="functional-dependencies"/>). The reason for this is there
2917 might be a "hidden" dependency, in a superclass perhaps. So
2918 "reachable" is a conservative approximation to "functionally dependent".
2919 For example, consider:
2921 class C a b | a -> b where ...
2922 class C a b => D a b where ...
2923 f :: forall a b. D a b => a -> a
2925 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2926 but that is not immediately apparent from <literal>f</literal>'s type.
2932 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2933 universally quantified type variables <literal>tvi</literal></emphasis>.
2935 For example, this type is OK because <literal>C a b</literal> mentions the
2936 universally quantified type variable <literal>b</literal>:
2940 forall a. C a b => burble
2944 The next type is illegal because the constraint <literal>Eq b</literal> does not
2945 mention <literal>a</literal>:
2949 forall a. Eq b => burble
2953 The reason for this restriction is milder than the other one. The
2954 excluded types are never useful or necessary (because the offending
2955 context doesn't need to be witnessed at this point; it can be floated
2956 out). Furthermore, floating them out increases sharing. Lastly,
2957 excluding them is a conservative choice; it leaves a patch of
2958 territory free in case we need it later.
2972 <sect2 id="implicit-parameters">
2973 <title>Implicit parameters</title>
2975 <para> Implicit parameters are implemented as described in
2976 "Implicit parameters: dynamic scoping with static types",
2977 J Lewis, MB Shields, E Meijer, J Launchbury,
2978 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2982 <para>(Most of the following, stil rather incomplete, documentation is
2983 due to Jeff Lewis.)</para>
2985 <para>Implicit parameter support is enabled with the option
2986 <option>-fimplicit-params</option>.</para>
2989 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2990 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2991 context. In Haskell, all variables are statically bound. Dynamic
2992 binding of variables is a notion that goes back to Lisp, but was later
2993 discarded in more modern incarnations, such as Scheme. Dynamic binding
2994 can be very confusing in an untyped language, and unfortunately, typed
2995 languages, in particular Hindley-Milner typed languages like Haskell,
2996 only support static scoping of variables.
2999 However, by a simple extension to the type class system of Haskell, we
3000 can support dynamic binding. Basically, we express the use of a
3001 dynamically bound variable as a constraint on the type. These
3002 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3003 function uses a dynamically-bound variable <literal>?x</literal>
3004 of type <literal>t'</literal>". For
3005 example, the following expresses the type of a sort function,
3006 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3008 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3010 The dynamic binding constraints are just a new form of predicate in the type class system.
3013 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3014 where <literal>x</literal> is
3015 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3016 Use of this construct also introduces a new
3017 dynamic-binding constraint in the type of the expression.
3018 For example, the following definition
3019 shows how we can define an implicitly parameterized sort function in
3020 terms of an explicitly parameterized <literal>sortBy</literal> function:
3022 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3024 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3030 <title>Implicit-parameter type constraints</title>
3032 Dynamic binding constraints behave just like other type class
3033 constraints in that they are automatically propagated. Thus, when a
3034 function is used, its implicit parameters are inherited by the
3035 function that called it. For example, our <literal>sort</literal> function might be used
3036 to pick out the least value in a list:
3038 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3039 least xs = head (sort xs)
3041 Without lifting a finger, the <literal>?cmp</literal> parameter is
3042 propagated to become a parameter of <literal>least</literal> as well. With explicit
3043 parameters, the default is that parameters must always be explicit
3044 propagated. With implicit parameters, the default is to always
3048 An implicit-parameter type constraint differs from other type class constraints in the
3049 following way: All uses of a particular implicit parameter must have
3050 the same type. This means that the type of <literal>(?x, ?x)</literal>
3051 is <literal>(?x::a) => (a,a)</literal>, and not
3052 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3056 <para> You can't have an implicit parameter in the context of a class or instance
3057 declaration. For example, both these declarations are illegal:
3059 class (?x::Int) => C a where ...
3060 instance (?x::a) => Foo [a] where ...
3062 Reason: exactly which implicit parameter you pick up depends on exactly where
3063 you invoke a function. But the ``invocation'' of instance declarations is done
3064 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3065 Easiest thing is to outlaw the offending types.</para>
3067 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3069 f :: (?x :: [a]) => Int -> Int
3072 g :: (Read a, Show a) => String -> String
3075 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3076 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3077 quite unambiguous, and fixes the type <literal>a</literal>.
3082 <title>Implicit-parameter bindings</title>
3085 An implicit parameter is <emphasis>bound</emphasis> using the standard
3086 <literal>let</literal> or <literal>where</literal> binding forms.
3087 For example, we define the <literal>min</literal> function by binding
3088 <literal>cmp</literal>.
3091 min = let ?cmp = (<=) in least
3095 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3096 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3097 (including in a list comprehension, or do-notation, or pattern guards),
3098 or a <literal>where</literal> clause.
3099 Note the following points:
3102 An implicit-parameter binding group must be a
3103 collection of simple bindings to implicit-style variables (no
3104 function-style bindings, and no type signatures); these bindings are
3105 neither polymorphic or recursive.
3108 You may not mix implicit-parameter bindings with ordinary bindings in a
3109 single <literal>let</literal>
3110 expression; use two nested <literal>let</literal>s instead.
3111 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3115 You may put multiple implicit-parameter bindings in a
3116 single binding group; but they are <emphasis>not</emphasis> treated
3117 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3118 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3119 parameter. The bindings are not nested, and may be re-ordered without changing
3120 the meaning of the program.
3121 For example, consider:
3123 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3125 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3126 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3128 f :: (?x::Int) => Int -> Int
3136 <sect3><title>Implicit parameters and polymorphic recursion</title>
3139 Consider these two definitions:
3142 len1 xs = let ?acc = 0 in len_acc1 xs
3145 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3150 len2 xs = let ?acc = 0 in len_acc2 xs
3152 len_acc2 :: (?acc :: Int) => [a] -> Int
3154 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3156 The only difference between the two groups is that in the second group
3157 <literal>len_acc</literal> is given a type signature.
3158 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3159 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3160 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3161 has a type signature, the recursive call is made to the
3162 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3163 as an implicit parameter. So we get the following results in GHCi:
3170 Adding a type signature dramatically changes the result! This is a rather
3171 counter-intuitive phenomenon, worth watching out for.
3175 <sect3><title>Implicit parameters and monomorphism</title>
3177 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3178 Haskell Report) to implicit parameters. For example, consider:
3186 Since the binding for <literal>y</literal> falls under the Monomorphism
3187 Restriction it is not generalised, so the type of <literal>y</literal> is
3188 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3189 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3190 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3191 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3192 <literal>y</literal> in the body of the <literal>let</literal> will see the
3193 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3194 <literal>14</literal>.
3199 <!-- ======================= COMMENTED OUT ========================
3201 We intend to remove linear implicit parameters, so I'm at least removing
3202 them from the 6.6 user manual
3204 <sect2 id="linear-implicit-parameters">
3205 <title>Linear implicit parameters</title>
3207 Linear implicit parameters are an idea developed by Koen Claessen,
3208 Mark Shields, and Simon PJ. They address the long-standing
3209 problem that monads seem over-kill for certain sorts of problem, notably:
3212 <listitem> <para> distributing a supply of unique names </para> </listitem>
3213 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3214 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3218 Linear implicit parameters are just like ordinary implicit parameters,
3219 except that they are "linear"; that is, they cannot be copied, and
3220 must be explicitly "split" instead. Linear implicit parameters are
3221 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3222 (The '/' in the '%' suggests the split!)
3227 import GHC.Exts( Splittable )
3229 data NameSupply = ...
3231 splitNS :: NameSupply -> (NameSupply, NameSupply)
3232 newName :: NameSupply -> Name
3234 instance Splittable NameSupply where
3238 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3239 f env (Lam x e) = Lam x' (f env e)
3242 env' = extend env x x'
3243 ...more equations for f...
3245 Notice that the implicit parameter %ns is consumed
3247 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3248 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3252 So the translation done by the type checker makes
3253 the parameter explicit:
3255 f :: NameSupply -> Env -> Expr -> Expr
3256 f ns env (Lam x e) = Lam x' (f ns1 env e)
3258 (ns1,ns2) = splitNS ns
3260 env = extend env x x'
3262 Notice the call to 'split' introduced by the type checker.
3263 How did it know to use 'splitNS'? Because what it really did
3264 was to introduce a call to the overloaded function 'split',
3265 defined by the class <literal>Splittable</literal>:
3267 class Splittable a where
3270 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3271 split for name supplies. But we can simply write
3277 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3279 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3280 <literal>GHC.Exts</literal>.
3285 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3286 are entirely distinct implicit parameters: you
3287 can use them together and they won't intefere with each other. </para>
3290 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3292 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3293 in the context of a class or instance declaration. </para></listitem>
3297 <sect3><title>Warnings</title>
3300 The monomorphism restriction is even more important than usual.
3301 Consider the example above:
3303 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3304 f env (Lam x e) = Lam x' (f env e)
3307 env' = extend env x x'
3309 If we replaced the two occurrences of x' by (newName %ns), which is
3310 usually a harmless thing to do, we get:
3312 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3313 f env (Lam x e) = Lam (newName %ns) (f env e)
3315 env' = extend env x (newName %ns)
3317 But now the name supply is consumed in <emphasis>three</emphasis> places
3318 (the two calls to newName,and the recursive call to f), so
3319 the result is utterly different. Urk! We don't even have
3323 Well, this is an experimental change. With implicit
3324 parameters we have already lost beta reduction anyway, and
3325 (as John Launchbury puts it) we can't sensibly reason about
3326 Haskell programs without knowing their typing.
3331 <sect3><title>Recursive functions</title>
3332 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3335 foo :: %x::T => Int -> [Int]
3337 foo n = %x : foo (n-1)
3339 where T is some type in class Splittable.</para>
3341 Do you get a list of all the same T's or all different T's
3342 (assuming that split gives two distinct T's back)?
3344 If you supply the type signature, taking advantage of polymorphic
3345 recursion, you get what you'd probably expect. Here's the
3346 translated term, where the implicit param is made explicit:
3349 foo x n = let (x1,x2) = split x
3350 in x1 : foo x2 (n-1)
3352 But if you don't supply a type signature, GHC uses the Hindley
3353 Milner trick of using a single monomorphic instance of the function
3354 for the recursive calls. That is what makes Hindley Milner type inference
3355 work. So the translation becomes
3359 foom n = x : foom (n-1)
3363 Result: 'x' is not split, and you get a list of identical T's. So the
3364 semantics of the program depends on whether or not foo has a type signature.
3367 You may say that this is a good reason to dislike linear implicit parameters
3368 and you'd be right. That is why they are an experimental feature.
3374 ================ END OF Linear Implicit Parameters commented out -->
3376 <sect2 id="kinding">
3377 <title>Explicitly-kinded quantification</title>
3380 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3381 to give the kind explicitly as (machine-checked) documentation,
3382 just as it is nice to give a type signature for a function. On some occasions,
3383 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3384 John Hughes had to define the data type:
3386 data Set cxt a = Set [a]
3387 | Unused (cxt a -> ())
3389 The only use for the <literal>Unused</literal> constructor was to force the correct
3390 kind for the type variable <literal>cxt</literal>.
3393 GHC now instead allows you to specify the kind of a type variable directly, wherever
3394 a type variable is explicitly bound. Namely:
3396 <listitem><para><literal>data</literal> declarations:
3398 data Set (cxt :: * -> *) a = Set [a]
3399 </screen></para></listitem>
3400 <listitem><para><literal>type</literal> declarations:
3402 type T (f :: * -> *) = f Int
3403 </screen></para></listitem>
3404 <listitem><para><literal>class</literal> declarations:
3406 class (Eq a) => C (f :: * -> *) a where ...
3407 </screen></para></listitem>
3408 <listitem><para><literal>forall</literal>'s in type signatures:
3410 f :: forall (cxt :: * -> *). Set cxt Int
3411 </screen></para></listitem>
3416 The parentheses are required. Some of the spaces are required too, to
3417 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3418 will get a parse error, because "<literal>::*->*</literal>" is a
3419 single lexeme in Haskell.
3423 As part of the same extension, you can put kind annotations in types
3426 f :: (Int :: *) -> Int
3427 g :: forall a. a -> (a :: *)
3431 atype ::= '(' ctype '::' kind ')
3433 The parentheses are required.
3438 <sect2 id="universal-quantification">
3439 <title>Arbitrary-rank polymorphism
3443 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3444 allows us to say exactly what this means. For example:
3452 g :: forall b. (b -> b)
3454 The two are treated identically.
3458 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3459 explicit universal quantification in
3461 For example, all the following types are legal:
3463 f1 :: forall a b. a -> b -> a
3464 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3466 f2 :: (forall a. a->a) -> Int -> Int
3467 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3469 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3471 f4 :: Int -> (forall a. a -> a)
3473 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3474 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3475 The <literal>forall</literal> makes explicit the universal quantification that
3476 is implicitly added by Haskell.
3479 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3480 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3481 shows, the polymorphic type on the left of the function arrow can be overloaded.
3484 The function <literal>f3</literal> has a rank-3 type;
3485 it has rank-2 types on the left of a function arrow.
3488 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3489 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3490 that restriction has now been lifted.)
3491 In particular, a forall-type (also called a "type scheme"),
3492 including an operational type class context, is legal:
3494 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3495 of a function arrow </para> </listitem>
3496 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3497 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3498 field type signatures.</para> </listitem>
3499 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3500 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3502 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3503 a type variable any more!
3512 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3513 the types of the constructor arguments. Here are several examples:
3519 data T a = T1 (forall b. b -> b -> b) a
3521 data MonadT m = MkMonad { return :: forall a. a -> m a,
3522 bind :: forall a b. m a -> (a -> m b) -> m b
3525 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3531 The constructors have rank-2 types:
3537 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3538 MkMonad :: forall m. (forall a. a -> m a)
3539 -> (forall a b. m a -> (a -> m b) -> m b)
3541 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3547 Notice that you don't need to use a <literal>forall</literal> if there's an
3548 explicit context. For example in the first argument of the
3549 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3550 prefixed to the argument type. The implicit <literal>forall</literal>
3551 quantifies all type variables that are not already in scope, and are
3552 mentioned in the type quantified over.
3556 As for type signatures, implicit quantification happens for non-overloaded
3557 types too. So if you write this:
3560 data T a = MkT (Either a b) (b -> b)
3563 it's just as if you had written this:
3566 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3569 That is, since the type variable <literal>b</literal> isn't in scope, it's
3570 implicitly universally quantified. (Arguably, it would be better
3571 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3572 where that is what is wanted. Feedback welcomed.)
3576 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3577 the constructor to suitable values, just as usual. For example,
3588 a3 = MkSwizzle reverse
3591 a4 = let r x = Just x
3598 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3599 mkTs f x y = [T1 f x, T1 f y]
3605 The type of the argument can, as usual, be more general than the type
3606 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3607 does not need the <literal>Ord</literal> constraint.)
3611 When you use pattern matching, the bound variables may now have
3612 polymorphic types. For example:
3618 f :: T a -> a -> (a, Char)
3619 f (T1 w k) x = (w k x, w 'c' 'd')
3621 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3622 g (MkSwizzle s) xs f = s (map f (s xs))
3624 h :: MonadT m -> [m a] -> m [a]
3625 h m [] = return m []
3626 h m (x:xs) = bind m x $ \y ->
3627 bind m (h m xs) $ \ys ->
3634 In the function <function>h</function> we use the record selectors <literal>return</literal>
3635 and <literal>bind</literal> to extract the polymorphic bind and return functions
3636 from the <literal>MonadT</literal> data structure, rather than using pattern
3642 <title>Type inference</title>
3645 In general, type inference for arbitrary-rank types is undecidable.
3646 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3647 to get a decidable algorithm by requiring some help from the programmer.
3648 We do not yet have a formal specification of "some help" but the rule is this:
3651 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3652 provides an explicit polymorphic type for x, or GHC's type inference will assume
3653 that x's type has no foralls in it</emphasis>.
3656 What does it mean to "provide" an explicit type for x? You can do that by
3657 giving a type signature for x directly, using a pattern type signature
3658 (<xref linkend="scoped-type-variables"/>), thus:
3660 \ f :: (forall a. a->a) -> (f True, f 'c')
3662 Alternatively, you can give a type signature to the enclosing
3663 context, which GHC can "push down" to find the type for the variable:
3665 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3667 Here the type signature on the expression can be pushed inwards
3668 to give a type signature for f. Similarly, and more commonly,
3669 one can give a type signature for the function itself:
3671 h :: (forall a. a->a) -> (Bool,Char)
3672 h f = (f True, f 'c')
3674 You don't need to give a type signature if the lambda bound variable
3675 is a constructor argument. Here is an example we saw earlier:
3677 f :: T a -> a -> (a, Char)
3678 f (T1 w k) x = (w k x, w 'c' 'd')
3680 Here we do not need to give a type signature to <literal>w</literal>, because
3681 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3688 <sect3 id="implicit-quant">
3689 <title>Implicit quantification</title>
3692 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3693 user-written types, if and only if there is no explicit <literal>forall</literal>,
3694 GHC finds all the type variables mentioned in the type that are not already
3695 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3699 f :: forall a. a -> a
3706 h :: forall b. a -> b -> b
3712 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3715 f :: (a -> a) -> Int
3717 f :: forall a. (a -> a) -> Int
3719 f :: (forall a. a -> a) -> Int
3722 g :: (Ord a => a -> a) -> Int
3723 -- MEANS the illegal type
3724 g :: forall a. (Ord a => a -> a) -> Int
3726 g :: (forall a. Ord a => a -> a) -> Int
3728 The latter produces an illegal type, which you might think is silly,
3729 but at least the rule is simple. If you want the latter type, you
3730 can write your for-alls explicitly. Indeed, doing so is strongly advised
3737 <sect2 id="impredicative-polymorphism">
3738 <title>Impredicative polymorphism
3740 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3741 that you can call a polymorphic function at a polymorphic type, and
3742 parameterise data structures over polymorphic types. For example:
3744 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3745 f (Just g) = Just (g [3], g "hello")
3748 Notice here that the <literal>Maybe</literal> type is parameterised by the
3749 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3752 <para>The technical details of this extension are described in the paper
3753 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3754 type inference for higher-rank types and impredicativity</ulink>,
3755 which appeared at ICFP 2006.
3759 <sect2 id="scoped-type-variables">
3760 <title>Lexically scoped type variables
3764 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3765 which some type signatures are simply impossible to write. For example:
3767 f :: forall a. [a] -> [a]
3773 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3774 the entire definition of <literal>f</literal>.
3775 In particular, it is in scope at the type signature for <varname>ys</varname>.
3776 In Haskell 98 it is not possible to declare
3777 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3778 it becomes possible to do so.
3780 <para>Lexically-scoped type variables are enabled by
3781 <option>-fglasgow-exts</option>.
3783 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3784 variables work, compared to earlier releases. Read this section
3788 <title>Overview</title>
3790 <para>The design follows the following principles
3792 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3793 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3794 design.)</para></listitem>
3795 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3796 type variables. This means that every programmer-written type signature
3797 (includin one that contains free scoped type variables) denotes a
3798 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3799 checker, and no inference is involved.</para></listitem>
3800 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3801 changing the program.</para></listitem>
3805 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3807 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3808 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3809 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3810 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3814 In Haskell, a programmer-written type signature is implicitly quantifed over
3815 its free type variables (<ulink
3816 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3818 of the Haskel Report).
3819 Lexically scoped type variables affect this implicit quantification rules
3820 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3821 quantified. For example, if type variable <literal>a</literal> is in scope,
3824 (e :: a -> a) means (e :: a -> a)
3825 (e :: b -> b) means (e :: forall b. b->b)
3826 (e :: a -> b) means (e :: forall b. a->b)
3834 <sect3 id="decl-type-sigs">
3835 <title>Declaration type signatures</title>
3836 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3837 quantification (using <literal>forall</literal>) brings into scope the
3838 explicitly-quantified
3839 type variables, in the definition of the named function(s). For example:
3841 f :: forall a. [a] -> [a]
3842 f (x:xs) = xs ++ [ x :: a ]
3844 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3845 the definition of "<literal>f</literal>".
3847 <para>This only happens if the quantification in <literal>f</literal>'s type
3848 signature is explicit. For example:
3851 g (x:xs) = xs ++ [ x :: a ]
3853 This program will be rejected, because "<literal>a</literal>" does not scope
3854 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3855 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3856 quantification rules.
3860 <sect3 id="exp-type-sigs">
3861 <title>Expression type signatures</title>
3863 <para>An expression type signature that has <emphasis>explicit</emphasis>
3864 quantification (using <literal>forall</literal>) brings into scope the
3865 explicitly-quantified
3866 type variables, in the annotated expression. For example:
3868 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3870 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3871 type variable <literal>s</literal> into scope, in the annotated expression
3872 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3877 <sect3 id="pattern-type-sigs">
3878 <title>Pattern type signatures</title>
3880 A type signature may occur in any pattern; this is a <emphasis>pattern type
3881 signature</emphasis>.
3884 -- f and g assume that 'a' is already in scope
3885 f = \(x::Int, y::a) -> x
3887 h ((x,y) :: (Int,Bool)) = (y,x)
3889 In the case where all the type variables in the pattern type sigature are
3890 already in scope (i.e. bound by the enclosing context), matters are simple: the
3891 signature simply constrains the type of the pattern in the obvious way.
3894 There is only one situation in which you can write a pattern type signature that
3895 mentions a type variable that is not already in scope, namely in pattern match
3896 of an existential data constructor. For example:
3898 data T = forall a. MkT [a]
3901 k (MkT [t::a]) = MkT t3
3905 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3906 variable that is not already in scope. Indeed, it cannot already be in scope,
3907 because it is bound by the pattern match. GHC's rule is that in this situation
3908 (and only then), a pattern type signature can mention a type variable that is
3909 not already in scope; the effect is to bring it into scope, standing for the
3910 existentially-bound type variable.
3913 If this seems a little odd, we think so too. But we must have
3914 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3915 could not name existentially-bound type variables in subequent type signatures.
3918 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3919 signature is allowed to mention a lexical variable that is not already in
3921 For example, both <literal>f</literal> and <literal>g</literal> would be
3922 illegal if <literal>a</literal> was not already in scope.
3928 <!-- ==================== Commented out part about result type signatures
3930 <sect3 id="result-type-sigs">
3931 <title>Result type signatures</title>
3934 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3937 {- f assumes that 'a' is already in scope -}
3938 f x y :: [a] = [x,y,x]
3940 g = \ x :: [Int] -> [3,4]
3942 h :: forall a. [a] -> a
3946 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3947 the result of the function. Similarly, the body of the lambda in the RHS of
3948 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3949 alternative in <literal>h</literal> is <literal>a</literal>.
3951 <para> A result type signature never brings new type variables into scope.</para>
3953 There are a couple of syntactic wrinkles. First, notice that all three
3954 examples would parse quite differently with parentheses:
3956 {- f assumes that 'a' is already in scope -}
3957 f x (y :: [a]) = [x,y,x]
3959 g = \ (x :: [Int]) -> [3,4]
3961 h :: forall a. [a] -> a
3965 Now the signature is on the <emphasis>pattern</emphasis>; and
3966 <literal>h</literal> would certainly be ill-typed (since the pattern
3967 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3969 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3970 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3971 token or a parenthesised type of some sort). To see why,
3972 consider how one would parse this:
3981 <sect3 id="cls-inst-scoped-tyvars">
3982 <title>Class and instance declarations</title>
3985 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3986 scope over the methods defined in the <literal>where</literal> part. For example:
4004 <sect2 id="typing-binds">
4005 <title>Generalised typing of mutually recursive bindings</title>
4008 The Haskell Report specifies that a group of bindings (at top level, or in a
4009 <literal>let</literal> or <literal>where</literal>) should be sorted into
4010 strongly-connected components, and then type-checked in dependency order
4011 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4012 Report, Section 4.5.1</ulink>).
4013 As each group is type-checked, any binders of the group that
4015 an explicit type signature are put in the type environment with the specified
4017 and all others are monomorphic until the group is generalised
4018 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4021 <para>Following a suggestion of Mark Jones, in his paper
4022 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4024 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4026 <emphasis>the dependency analysis ignores references to variables that have an explicit
4027 type signature</emphasis>.
4028 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4029 typecheck. For example, consider:
4031 f :: Eq a => a -> Bool
4032 f x = (x == x) || g True || g "Yes"
4034 g y = (y <= y) || f True
4036 This is rejected by Haskell 98, but under Jones's scheme the definition for
4037 <literal>g</literal> is typechecked first, separately from that for
4038 <literal>f</literal>,
4039 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4040 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4041 type is generalised, to get
4043 g :: Ord a => a -> Bool
4045 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4046 <literal>g</literal> in the type environment.
4050 The same refined dependency analysis also allows the type signatures of
4051 mutually-recursive functions to have different contexts, something that is illegal in
4052 Haskell 98 (Section 4.5.2, last sentence). With
4053 <option>-fglasgow-exts</option>
4054 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4055 type signatures; in practice this means that only variables bound by the same
4056 pattern binding must have the same context. For example, this is fine:
4058 f :: Eq a => a -> Bool
4059 f x = (x == x) || g True
4061 g :: Ord a => a -> Bool
4062 g y = (y <= y) || f True
4067 <sect2 id="overloaded-strings">
4068 <title>Overloaded string literals
4072 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4073 string literal has type <literal>String</literal>, but with overloaded string
4074 literals enabled (with <literal>-foverloaded-strings</literal>)
4075 a string literal has type <literal>(IsString a) => a</literal>.
4078 This means that the usual string syntax can be used, e.g., for packed strings
4079 and other variations of string like types. String literals behave very much
4080 like integer literals, i.e., they can be used in both expressions and patterns.
4081 If used in a pattern the literal with be replaced by an equality test, in the same
4082 way as an integer literal is.
4085 The class <literal>IsString</literal> is defined as:
4087 class IsString a where
4088 fromString :: String -> a
4090 The only predefined instance is the obvious one to make strings work as usual:
4092 instance IsString [Char] where
4095 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4096 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4097 from module <literal>GHC.Exts</literal>.
4100 Haskell's defaulting mechanism is extended to cover string literals, when <option>-foverloaded-strings</option> is specified.
4104 Each type in a default declaration must be an
4105 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4109 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4110 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4111 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4112 <emphasis>or</emphasis> <literal>IsString</literal>.
4121 import GHC.Exts( IsString(..) )
4123 newtype MyString = MyString String deriving (Eq, Show)
4124 instance IsString MyString where
4125 fromString = MyString
4127 greet :: MyString -> MyString
4128 greet "hello" = "world"
4132 print $ greet "hello"
4133 print $ greet "fool"
4137 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4138 to work since it gets translated into an equality comparison.
4142 <sect2 id="type-families">
4143 <title>Type families
4147 GHC supports the definition of type families indexed by types. They may be
4148 seen as an extension of Haskell 98's class-based overloading of values to
4149 types. When type families are declared in classes, they are also known as
4153 There are two forms of type families: data families and type synonym families.
4154 Currently, only the former are fully implemented, while we are still working
4155 on the latter. As a result, the specification of the language extension is
4156 also still to some degree in flux. Hence, a more detailed description of
4157 the language extension and its use is currently available
4158 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4159 wiki page on type families</ulink>. The material will be moved to this user's
4160 guide when it has stabilised.
4163 Type families are enabled by the flag <option>-ftype-families</option>.
4170 <!-- ==================== End of type system extensions ================= -->
4172 <!-- ====================== TEMPLATE HASKELL ======================= -->
4174 <sect1 id="template-haskell">
4175 <title>Template Haskell</title>
4177 <para>Template Haskell allows you to do compile-time meta-programming in
4180 the main technical innovations is discussed in "<ulink
4181 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4182 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4185 There is a Wiki page about
4186 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4187 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4191 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4192 Haskell library reference material</ulink>
4193 (search for the type ExpQ).
4194 [Temporary: many changes to the original design are described in
4195 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4196 Not all of these changes are in GHC 6.6.]
4199 <para> The first example from that paper is set out below as a worked example to help get you started.
4203 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4204 Tim Sheard is going to expand it.)
4208 <title>Syntax</title>
4210 <para> Template Haskell has the following new syntactic
4211 constructions. You need to use the flag
4212 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4213 </indexterm>to switch these syntactic extensions on
4214 (<option>-fth</option> is no longer implied by
4215 <option>-fglasgow-exts</option>).</para>
4219 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4220 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4221 There must be no space between the "$" and the identifier or parenthesis. This use
4222 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4223 of "." as an infix operator. If you want the infix operator, put spaces around it.
4225 <para> A splice can occur in place of
4227 <listitem><para> an expression; the spliced expression must
4228 have type <literal>Q Exp</literal></para></listitem>
4229 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4230 <listitem><para> [Planned, but not implemented yet.] a
4231 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4233 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4234 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4240 A expression quotation is written in Oxford brackets, thus:
4242 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4243 the quotation has type <literal>Expr</literal>.</para></listitem>
4244 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4245 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4246 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4247 the quotation has type <literal>Type</literal>.</para></listitem>
4248 </itemizedlist></para></listitem>
4251 Reification is written thus:
4253 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4254 has type <literal>Dec</literal>. </para></listitem>
4255 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4256 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4257 <listitem><para> Still to come: fixities </para></listitem>
4259 </itemizedlist></para>
4266 <sect2> <title> Using Template Haskell </title>
4270 The data types and monadic constructor functions for Template Haskell are in the library
4271 <literal>Language.Haskell.THSyntax</literal>.
4275 You can only run a function at compile time if it is imported from another module. That is,
4276 you can't define a function in a module, and call it from within a splice in the same module.
4277 (It would make sense to do so, but it's hard to implement.)
4281 Furthermore, you can only run a function at compile time if it is imported
4282 from another module <emphasis>that is not part of a mutually-recursive group of modules
4283 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4284 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4285 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4289 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4292 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4293 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4294 compiles and runs a program, and then looks at the result. So it's important that
4295 the program it compiles produces results whose representations are identical to
4296 those of the compiler itself.
4300 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4301 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4306 <sect2> <title> A Template Haskell Worked Example </title>
4307 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4308 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4315 -- Import our template "pr"
4316 import Printf ( pr )
4318 -- The splice operator $ takes the Haskell source code
4319 -- generated at compile time by "pr" and splices it into
4320 -- the argument of "putStrLn".
4321 main = putStrLn ( $(pr "Hello") )
4327 -- Skeletal printf from the paper.
4328 -- It needs to be in a separate module to the one where
4329 -- you intend to use it.
4331 -- Import some Template Haskell syntax
4332 import Language.Haskell.TH
4334 -- Describe a format string
4335 data Format = D | S | L String
4337 -- Parse a format string. This is left largely to you
4338 -- as we are here interested in building our first ever
4339 -- Template Haskell program and not in building printf.
4340 parse :: String -> [Format]
4343 -- Generate Haskell source code from a parsed representation
4344 -- of the format string. This code will be spliced into
4345 -- the module which calls "pr", at compile time.
4346 gen :: [Format] -> ExpQ
4347 gen [D] = [| \n -> show n |]
4348 gen [S] = [| \s -> s |]
4349 gen [L s] = stringE s
4351 -- Here we generate the Haskell code for the splice
4352 -- from an input format string.
4353 pr :: String -> ExpQ
4354 pr s = gen (parse s)
4357 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4360 $ ghc --make -fth main.hs -o main.exe
4363 <para>Run "main.exe" and here is your output:</para>
4373 <title>Using Template Haskell with Profiling</title>
4374 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4376 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4377 interpreter to run the splice expressions. The bytecode interpreter
4378 runs the compiled expression on top of the same runtime on which GHC
4379 itself is running; this means that the compiled code referred to by
4380 the interpreted expression must be compatible with this runtime, and
4381 in particular this means that object code that is compiled for
4382 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4383 expression, because profiled object code is only compatible with the
4384 profiling version of the runtime.</para>
4386 <para>This causes difficulties if you have a multi-module program
4387 containing Template Haskell code and you need to compile it for
4388 profiling, because GHC cannot load the profiled object code and use it
4389 when executing the splices. Fortunately GHC provides a workaround.
4390 The basic idea is to compile the program twice:</para>
4394 <para>Compile the program or library first the normal way, without
4395 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4398 <para>Then compile it again with <option>-prof</option>, and
4399 additionally use <option>-osuf
4400 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4401 to name the object files differentliy (you can choose any suffix
4402 that isn't the normal object suffix here). GHC will automatically
4403 load the object files built in the first step when executing splice
4404 expressions. If you omit the <option>-osuf</option> flag when
4405 building with <option>-prof</option> and Template Haskell is used,
4406 GHC will emit an error message. </para>
4413 <!-- ===================== Arrow notation =================== -->
4415 <sect1 id="arrow-notation">
4416 <title>Arrow notation
4419 <para>Arrows are a generalization of monads introduced by John Hughes.
4420 For more details, see
4425 “Generalising Monads to Arrows”,
4426 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4427 pp67–111, May 2000.
4433 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4434 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4440 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4441 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4447 and the arrows web page at
4448 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4449 With the <option>-farrows</option> flag, GHC supports the arrow
4450 notation described in the second of these papers.
4451 What follows is a brief introduction to the notation;
4452 it won't make much sense unless you've read Hughes's paper.
4453 This notation is translated to ordinary Haskell,
4454 using combinators from the
4455 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4459 <para>The extension adds a new kind of expression for defining arrows:
4461 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4462 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4464 where <literal>proc</literal> is a new keyword.
4465 The variables of the pattern are bound in the body of the
4466 <literal>proc</literal>-expression,
4467 which is a new sort of thing called a <firstterm>command</firstterm>.
4468 The syntax of commands is as follows:
4470 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4471 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4472 | <replaceable>cmd</replaceable><superscript>0</superscript>
4474 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4475 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4476 infix operators as for expressions, and
4478 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4479 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4480 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4481 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4482 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4483 | <replaceable>fcmd</replaceable>
4485 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4486 | ( <replaceable>cmd</replaceable> )
4487 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4489 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4490 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4491 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4492 | <replaceable>cmd</replaceable>
4494 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4495 except that the bodies are commands instead of expressions.
4499 Commands produce values, but (like monadic computations)
4500 may yield more than one value,
4501 or none, and may do other things as well.
4502 For the most part, familiarity with monadic notation is a good guide to
4504 However the values of expressions, even monadic ones,
4505 are determined by the values of the variables they contain;
4506 this is not necessarily the case for commands.
4510 A simple example of the new notation is the expression
4512 proc x -> f -< x+1
4514 We call this a <firstterm>procedure</firstterm> or
4515 <firstterm>arrow abstraction</firstterm>.
4516 As with a lambda expression, the variable <literal>x</literal>
4517 is a new variable bound within the <literal>proc</literal>-expression.
4518 It refers to the input to the arrow.
4519 In the above example, <literal>-<</literal> is not an identifier but an
4520 new reserved symbol used for building commands from an expression of arrow
4521 type and an expression to be fed as input to that arrow.
4522 (The weird look will make more sense later.)
4523 It may be read as analogue of application for arrows.
4524 The above example is equivalent to the Haskell expression
4526 arr (\ x -> x+1) >>> f
4528 That would make no sense if the expression to the left of
4529 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4530 More generally, the expression to the left of <literal>-<</literal>
4531 may not involve any <firstterm>local variable</firstterm>,
4532 i.e. a variable bound in the current arrow abstraction.
4533 For such a situation there is a variant <literal>-<<</literal>, as in
4535 proc x -> f x -<< x+1
4537 which is equivalent to
4539 arr (\ x -> (f x, x+1)) >>> app
4541 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4543 Such an arrow is equivalent to a monad, so if you're using this form
4544 you may find a monadic formulation more convenient.
4548 <title>do-notation for commands</title>
4551 Another form of command is a form of <literal>do</literal>-notation.
4552 For example, you can write
4561 You can read this much like ordinary <literal>do</literal>-notation,
4562 but with commands in place of monadic expressions.
4563 The first line sends the value of <literal>x+1</literal> as an input to
4564 the arrow <literal>f</literal>, and matches its output against
4565 <literal>y</literal>.
4566 In the next line, the output is discarded.
4567 The arrow <function>returnA</function> is defined in the
4568 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4569 module as <literal>arr id</literal>.
4570 The above example is treated as an abbreviation for
4572 arr (\ x -> (x, x)) >>>
4573 first (arr (\ x -> x+1) >>> f) >>>
4574 arr (\ (y, x) -> (y, (x, y))) >>>
4575 first (arr (\ y -> 2*y) >>> g) >>>
4577 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4578 first (arr (\ (x, z) -> x*z) >>> h) >>>
4579 arr (\ (t, z) -> t+z) >>>
4582 Note that variables not used later in the composition are projected out.
4583 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4585 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4586 module, this reduces to
4588 arr (\ x -> (x+1, x)) >>>
4590 arr (\ (y, x) -> (2*y, (x, y))) >>>
4592 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4594 arr (\ (t, z) -> t+z)
4596 which is what you might have written by hand.
4597 With arrow notation, GHC keeps track of all those tuples of variables for you.
4601 Note that although the above translation suggests that
4602 <literal>let</literal>-bound variables like <literal>z</literal> must be
4603 monomorphic, the actual translation produces Core,
4604 so polymorphic variables are allowed.
4608 It's also possible to have mutually recursive bindings,
4609 using the new <literal>rec</literal> keyword, as in the following example:
4611 counter :: ArrowCircuit a => a Bool Int
4612 counter = proc reset -> do
4613 rec output <- returnA -< if reset then 0 else next
4614 next <- delay 0 -< output+1
4615 returnA -< output
4617 The translation of such forms uses the <function>loop</function> combinator,
4618 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4624 <title>Conditional commands</title>
4627 In the previous example, we used a conditional expression to construct the
4629 Sometimes we want to conditionally execute different commands, as in
4636 which is translated to
4638 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4639 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4641 Since the translation uses <function>|||</function>,
4642 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4646 There are also <literal>case</literal> commands, like
4652 y <- h -< (x1, x2)
4656 The syntax is the same as for <literal>case</literal> expressions,
4657 except that the bodies of the alternatives are commands rather than expressions.
4658 The translation is similar to that of <literal>if</literal> commands.
4664 <title>Defining your own control structures</title>
4667 As we're seen, arrow notation provides constructs,
4668 modelled on those for expressions,
4669 for sequencing, value recursion and conditionals.
4670 But suitable combinators,
4671 which you can define in ordinary Haskell,
4672 may also be used to build new commands out of existing ones.
4673 The basic idea is that a command defines an arrow from environments to values.
4674 These environments assign values to the free local variables of the command.
4675 Thus combinators that produce arrows from arrows
4676 may also be used to build commands from commands.
4677 For example, the <literal>ArrowChoice</literal> class includes a combinator
4679 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4681 so we can use it to build commands:
4683 expr' = proc x -> do
4686 symbol Plus -< ()
4687 y <- term -< ()
4690 symbol Minus -< ()
4691 y <- term -< ()
4694 (The <literal>do</literal> on the first line is needed to prevent the first
4695 <literal><+> ...</literal> from being interpreted as part of the
4696 expression on the previous line.)
4697 This is equivalent to
4699 expr' = (proc x -> returnA -< x)
4700 <+> (proc x -> do
4701 symbol Plus -< ()
4702 y <- term -< ()
4704 <+> (proc x -> do
4705 symbol Minus -< ()
4706 y <- term -< ()
4709 It is essential that this operator be polymorphic in <literal>e</literal>
4710 (representing the environment input to the command
4711 and thence to its subcommands)
4712 and satisfy the corresponding naturality property
4714 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4716 at least for strict <literal>k</literal>.
4717 (This should be automatic if you're not using <function>seq</function>.)
4718 This ensures that environments seen by the subcommands are environments
4719 of the whole command,
4720 and also allows the translation to safely trim these environments.
4721 The operator must also not use any variable defined within the current
4726 We could define our own operator
4728 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4729 untilA body cond = proc x ->
4730 if cond x then returnA -< ()
4733 untilA body cond -< x
4735 and use it in the same way.
4736 Of course this infix syntax only makes sense for binary operators;
4737 there is also a more general syntax involving special brackets:
4741 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4748 <title>Primitive constructs</title>
4751 Some operators will need to pass additional inputs to their subcommands.
4752 For example, in an arrow type supporting exceptions,
4753 the operator that attaches an exception handler will wish to pass the
4754 exception that occurred to the handler.
4755 Such an operator might have a type
4757 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4759 where <literal>Ex</literal> is the type of exceptions handled.
4760 You could then use this with arrow notation by writing a command
4762 body `handleA` \ ex -> handler
4764 so that if an exception is raised in the command <literal>body</literal>,
4765 the variable <literal>ex</literal> is bound to the value of the exception
4766 and the command <literal>handler</literal>,
4767 which typically refers to <literal>ex</literal>, is entered.
4768 Though the syntax here looks like a functional lambda,
4769 we are talking about commands, and something different is going on.
4770 The input to the arrow represented by a command consists of values for
4771 the free local variables in the command, plus a stack of anonymous values.
4772 In all the prior examples, this stack was empty.
4773 In the second argument to <function>handleA</function>,
4774 this stack consists of one value, the value of the exception.
4775 The command form of lambda merely gives this value a name.
4780 the values on the stack are paired to the right of the environment.
4781 So operators like <function>handleA</function> that pass
4782 extra inputs to their subcommands can be designed for use with the notation
4783 by pairing the values with the environment in this way.
4784 More precisely, the type of each argument of the operator (and its result)
4785 should have the form
4787 a (...(e,t1), ... tn) t
4789 where <replaceable>e</replaceable> is a polymorphic variable
4790 (representing the environment)
4791 and <replaceable>ti</replaceable> are the types of the values on the stack,
4792 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4793 The polymorphic variable <replaceable>e</replaceable> must not occur in
4794 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4795 <replaceable>t</replaceable>.
4796 However the arrows involved need not be the same.
4797 Here are some more examples of suitable operators:
4799 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4800 runReader :: ... => a e c -> a' (e,State) c
4801 runState :: ... => a e c -> a' (e,State) (c,State)
4803 We can supply the extra input required by commands built with the last two
4804 by applying them to ordinary expressions, as in
4808 (|runReader (do { ... })|) s
4810 which adds <literal>s</literal> to the stack of inputs to the command
4811 built using <function>runReader</function>.
4815 The command versions of lambda abstraction and application are analogous to
4816 the expression versions.
4817 In particular, the beta and eta rules describe equivalences of commands.
4818 These three features (operators, lambda abstraction and application)
4819 are the core of the notation; everything else can be built using them,
4820 though the results would be somewhat clumsy.
4821 For example, we could simulate <literal>do</literal>-notation by defining
4823 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4824 u `bind` f = returnA &&& u >>> f
4826 bind_ :: Arrow a => a e b -> a e c -> a e c
4827 u `bind_` f = u `bind` (arr fst >>> f)
4829 We could simulate <literal>if</literal> by defining
4831 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4832 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4839 <title>Differences with the paper</title>
4844 <para>Instead of a single form of arrow application (arrow tail) with two
4845 translations, the implementation provides two forms
4846 <quote><literal>-<</literal></quote> (first-order)
4847 and <quote><literal>-<<</literal></quote> (higher-order).
4852 <para>User-defined operators are flagged with banana brackets instead of
4853 a new <literal>form</literal> keyword.
4862 <title>Portability</title>
4865 Although only GHC implements arrow notation directly,
4866 there is also a preprocessor
4868 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4869 that translates arrow notation into Haskell 98
4870 for use with other Haskell systems.
4871 You would still want to check arrow programs with GHC;
4872 tracing type errors in the preprocessor output is not easy.
4873 Modules intended for both GHC and the preprocessor must observe some
4874 additional restrictions:
4879 The module must import
4880 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4886 The preprocessor cannot cope with other Haskell extensions.
4887 These would have to go in separate modules.
4893 Because the preprocessor targets Haskell (rather than Core),
4894 <literal>let</literal>-bound variables are monomorphic.
4905 <!-- ==================== BANG PATTERNS ================= -->
4907 <sect1 id="bang-patterns">
4908 <title>Bang patterns
4909 <indexterm><primary>Bang patterns</primary></indexterm>
4911 <para>GHC supports an extension of pattern matching called <emphasis>bang
4912 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4914 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4915 prime feature description</ulink> contains more discussion and examples
4916 than the material below.
4919 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4922 <sect2 id="bang-patterns-informal">
4923 <title>Informal description of bang patterns
4926 The main idea is to add a single new production to the syntax of patterns:
4930 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4931 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4936 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4937 whereas without the bang it would be lazy.
4938 Bang patterns can be nested of course:
4942 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4943 <literal>y</literal>.
4944 A bang only really has an effect if it precedes a variable or wild-card pattern:
4949 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4950 forces evaluation anyway does nothing.
4952 Bang patterns work in <literal>case</literal> expressions too, of course:
4954 g5 x = let y = f x in body
4955 g6 x = case f x of { y -> body }
4956 g7 x = case f x of { !y -> body }
4958 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4959 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4960 result, and then evaluates <literal>body</literal>.
4962 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4963 definitions too. For example:
4967 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4968 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4969 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4970 in a function argument <literal>![x,y]</literal> means the
4971 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4972 is part of the syntax of <literal>let</literal> bindings.
4977 <sect2 id="bang-patterns-sem">
4978 <title>Syntax and semantics
4982 We add a single new production to the syntax of patterns:
4986 There is one problem with syntactic ambiguity. Consider:
4990 Is this a definition of the infix function "<literal>(!)</literal>",
4991 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4992 ambiguity in favour of the latter. If you want to define
4993 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4998 The semantics of Haskell pattern matching is described in <ulink
4999 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
5000 Section 3.17.2</ulink> of the Haskell Report. To this description add
5001 one extra item 10, saying:
5002 <itemizedlist><listitem><para>Matching
5003 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
5004 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
5005 <listitem><para>otherwise, <literal>pat</literal> is matched against
5006 <literal>v</literal></para></listitem>
5008 </para></listitem></itemizedlist>
5009 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5010 Section 3.17.3</ulink>, add a new case (t):
5012 case v of { !pat -> e; _ -> e' }
5013 = v `seq` case v of { pat -> e; _ -> e' }
5016 That leaves let expressions, whose translation is given in
5017 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5019 of the Haskell Report.
5020 In the translation box, first apply
5021 the following transformation: for each pattern <literal>pi</literal> that is of
5022 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5023 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5024 have a bang at the top, apply the rules in the existing box.
5026 <para>The effect of the let rule is to force complete matching of the pattern
5027 <literal>qi</literal> before evaluation of the body is begun. The bang is
5028 retained in the translated form in case <literal>qi</literal> is a variable,
5036 The let-binding can be recursive. However, it is much more common for
5037 the let-binding to be non-recursive, in which case the following law holds:
5038 <literal>(let !p = rhs in body)</literal>
5040 <literal>(case rhs of !p -> body)</literal>
5043 A pattern with a bang at the outermost level is not allowed at the top level of
5049 <!-- ==================== ASSERTIONS ================= -->
5051 <sect1 id="assertions">
5053 <indexterm><primary>Assertions</primary></indexterm>
5057 If you want to make use of assertions in your standard Haskell code, you
5058 could define a function like the following:
5064 assert :: Bool -> a -> a
5065 assert False x = error "assertion failed!"
5072 which works, but gives you back a less than useful error message --
5073 an assertion failed, but which and where?
5077 One way out is to define an extended <function>assert</function> function which also
5078 takes a descriptive string to include in the error message and
5079 perhaps combine this with the use of a pre-processor which inserts
5080 the source location where <function>assert</function> was used.
5084 Ghc offers a helping hand here, doing all of this for you. For every
5085 use of <function>assert</function> in the user's source:
5091 kelvinToC :: Double -> Double
5092 kelvinToC k = assert (k >= 0.0) (k+273.15)
5098 Ghc will rewrite this to also include the source location where the
5105 assert pred val ==> assertError "Main.hs|15" pred val
5111 The rewrite is only performed by the compiler when it spots
5112 applications of <function>Control.Exception.assert</function>, so you
5113 can still define and use your own versions of
5114 <function>assert</function>, should you so wish. If not, import
5115 <literal>Control.Exception</literal> to make use
5116 <function>assert</function> in your code.
5120 GHC ignores assertions when optimisation is turned on with the
5121 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5122 <literal>assert pred e</literal> will be rewritten to
5123 <literal>e</literal>. You can also disable assertions using the
5124 <option>-fignore-asserts</option>
5125 option<indexterm><primary><option>-fignore-asserts</option></primary>
5126 </indexterm>.</para>
5129 Assertion failures can be caught, see the documentation for the
5130 <literal>Control.Exception</literal> library for the details.
5136 <!-- =============================== PRAGMAS =========================== -->
5138 <sect1 id="pragmas">
5139 <title>Pragmas</title>
5141 <indexterm><primary>pragma</primary></indexterm>
5143 <para>GHC supports several pragmas, or instructions to the
5144 compiler placed in the source code. Pragmas don't normally affect
5145 the meaning of the program, but they might affect the efficiency
5146 of the generated code.</para>
5148 <para>Pragmas all take the form
5150 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5152 where <replaceable>word</replaceable> indicates the type of
5153 pragma, and is followed optionally by information specific to that
5154 type of pragma. Case is ignored in
5155 <replaceable>word</replaceable>. The various values for
5156 <replaceable>word</replaceable> that GHC understands are described
5157 in the following sections; any pragma encountered with an
5158 unrecognised <replaceable>word</replaceable> is (silently)
5161 <sect2 id="deprecated-pragma">
5162 <title>DEPRECATED pragma</title>
5163 <indexterm><primary>DEPRECATED</primary>
5166 <para>The DEPRECATED pragma lets you specify that a particular
5167 function, class, or type, is deprecated. There are two
5172 <para>You can deprecate an entire module thus:</para>
5174 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5177 <para>When you compile any module that import
5178 <literal>Wibble</literal>, GHC will print the specified
5183 <para>You can deprecate a function, class, type, or data constructor, with the
5184 following top-level declaration:</para>
5186 {-# DEPRECATED f, C, T "Don't use these" #-}
5188 <para>When you compile any module that imports and uses any
5189 of the specified entities, GHC will print the specified
5191 <para> You can only depecate entities declared at top level in the module
5192 being compiled, and you can only use unqualified names in the list of
5193 entities being deprecated. A capitalised name, such as <literal>T</literal>
5194 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5195 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5196 both are in scope. If both are in scope, there is currently no way to deprecate
5197 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5200 Any use of the deprecated item, or of anything from a deprecated
5201 module, will be flagged with an appropriate message. However,
5202 deprecations are not reported for
5203 (a) uses of a deprecated function within its defining module, and
5204 (b) uses of a deprecated function in an export list.
5205 The latter reduces spurious complaints within a library
5206 in which one module gathers together and re-exports
5207 the exports of several others.
5209 <para>You can suppress the warnings with the flag
5210 <option>-fno-warn-deprecations</option>.</para>
5213 <sect2 id="include-pragma">
5214 <title>INCLUDE pragma</title>
5216 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5217 of C header files that should be <literal>#include</literal>'d into
5218 the C source code generated by the compiler for the current module (if
5219 compiling via C). For example:</para>
5222 {-# INCLUDE "foo.h" #-}
5223 {-# INCLUDE <stdio.h> #-}</programlisting>
5225 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5226 your source file with any <literal>OPTIONS_GHC</literal>
5229 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5230 to the <option>-#include</option> option (<xref
5231 linkend="options-C-compiler" />), because the
5232 <literal>INCLUDE</literal> pragma is understood by other
5233 compilers. Yet another alternative is to add the include file to each
5234 <literal>foreign import</literal> declaration in your code, but we
5235 don't recommend using this approach with GHC.</para>
5238 <sect2 id="inline-noinline-pragma">
5239 <title>INLINE and NOINLINE pragmas</title>
5241 <para>These pragmas control the inlining of function
5244 <sect3 id="inline-pragma">
5245 <title>INLINE pragma</title>
5246 <indexterm><primary>INLINE</primary></indexterm>
5248 <para>GHC (with <option>-O</option>, as always) tries to
5249 inline (or “unfold”) functions/values that are
5250 “small enough,” thus avoiding the call overhead
5251 and possibly exposing other more-wonderful optimisations.
5252 Normally, if GHC decides a function is “too
5253 expensive” to inline, it will not do so, nor will it
5254 export that unfolding for other modules to use.</para>
5256 <para>The sledgehammer you can bring to bear is the
5257 <literal>INLINE</literal><indexterm><primary>INLINE
5258 pragma</primary></indexterm> pragma, used thusly:</para>
5261 key_function :: Int -> String -> (Bool, Double)
5263 #ifdef __GLASGOW_HASKELL__
5264 {-# INLINE key_function #-}
5268 <para>(You don't need to do the C pre-processor carry-on
5269 unless you're going to stick the code through HBC—it
5270 doesn't like <literal>INLINE</literal> pragmas.)</para>
5272 <para>The major effect of an <literal>INLINE</literal> pragma
5273 is to declare a function's “cost” to be very low.
5274 The normal unfolding machinery will then be very keen to
5277 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5278 function can be put anywhere its type signature could be
5281 <para><literal>INLINE</literal> pragmas are a particularly
5283 <literal>then</literal>/<literal>return</literal> (or
5284 <literal>bind</literal>/<literal>unit</literal>) functions in
5285 a monad. For example, in GHC's own
5286 <literal>UniqueSupply</literal> monad code, we have:</para>
5289 #ifdef __GLASGOW_HASKELL__
5290 {-# INLINE thenUs #-}
5291 {-# INLINE returnUs #-}
5295 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5296 linkend="noinline-pragma"/>).</para>
5299 <sect3 id="noinline-pragma">
5300 <title>NOINLINE pragma</title>
5302 <indexterm><primary>NOINLINE</primary></indexterm>
5303 <indexterm><primary>NOTINLINE</primary></indexterm>
5305 <para>The <literal>NOINLINE</literal> pragma does exactly what
5306 you'd expect: it stops the named function from being inlined
5307 by the compiler. You shouldn't ever need to do this, unless
5308 you're very cautious about code size.</para>
5310 <para><literal>NOTINLINE</literal> is a synonym for
5311 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5312 specified by Haskell 98 as the standard way to disable
5313 inlining, so it should be used if you want your code to be
5317 <sect3 id="phase-control">
5318 <title>Phase control</title>
5320 <para> Sometimes you want to control exactly when in GHC's
5321 pipeline the INLINE pragma is switched on. Inlining happens
5322 only during runs of the <emphasis>simplifier</emphasis>. Each
5323 run of the simplifier has a different <emphasis>phase
5324 number</emphasis>; the phase number decreases towards zero.
5325 If you use <option>-dverbose-core2core</option> you'll see the
5326 sequence of phase numbers for successive runs of the
5327 simplifier. In an INLINE pragma you can optionally specify a
5331 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5332 <literal>f</literal>
5333 until phase <literal>k</literal>, but from phase
5334 <literal>k</literal> onwards be very keen to inline it.
5337 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5338 <literal>f</literal>
5339 until phase <literal>k</literal>, but from phase
5340 <literal>k</literal> onwards do not inline it.
5343 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5344 <literal>f</literal>
5345 until phase <literal>k</literal>, but from phase
5346 <literal>k</literal> onwards be willing to inline it (as if
5347 there was no pragma).
5350 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5351 <literal>f</literal>
5352 until phase <literal>k</literal>, but from phase
5353 <literal>k</literal> onwards do not inline it.
5356 The same information is summarised here:
5358 -- Before phase 2 Phase 2 and later
5359 {-# INLINE [2] f #-} -- No Yes
5360 {-# INLINE [~2] f #-} -- Yes No
5361 {-# NOINLINE [2] f #-} -- No Maybe
5362 {-# NOINLINE [~2] f #-} -- Maybe No
5364 {-# INLINE f #-} -- Yes Yes
5365 {-# NOINLINE f #-} -- No No
5367 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5368 function body is small, or it is applied to interesting-looking arguments etc).
5369 Another way to understand the semantics is this:
5371 <listitem><para>For both INLINE and NOINLINE, the phase number says
5372 when inlining is allowed at all.</para></listitem>
5373 <listitem><para>The INLINE pragma has the additional effect of making the
5374 function body look small, so that when inlining is allowed it is very likely to
5379 <para>The same phase-numbering control is available for RULES
5380 (<xref linkend="rewrite-rules"/>).</para>
5384 <sect2 id="language-pragma">
5385 <title>LANGUAGE pragma</title>
5387 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5388 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5390 <para>This allows language extensions to be enabled in a portable way.
5391 It is the intention that all Haskell compilers support the
5392 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5393 all extensions are supported by all compilers, of
5394 course. The <literal>LANGUAGE</literal> pragma should be used instead
5395 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5397 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5399 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5401 <para>Any extension from the <literal>Extension</literal> type defined in
5403 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>
5407 <sect2 id="line-pragma">
5408 <title>LINE pragma</title>
5410 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5411 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5412 <para>This pragma is similar to C's <literal>#line</literal>
5413 pragma, and is mainly for use in automatically generated Haskell
5414 code. It lets you specify the line number and filename of the
5415 original code; for example</para>
5417 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5419 <para>if you'd generated the current file from something called
5420 <filename>Foo.vhs</filename> and this line corresponds to line
5421 42 in the original. GHC will adjust its error messages to refer
5422 to the line/file named in the <literal>LINE</literal>
5426 <sect2 id="options-pragma">
5427 <title>OPTIONS_GHC pragma</title>
5428 <indexterm><primary>OPTIONS_GHC</primary>
5430 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5433 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5434 additional options that are given to the compiler when compiling
5435 this source file. See <xref linkend="source-file-options"/> for
5438 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5439 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5443 <title>RULES pragma</title>
5445 <para>The RULES pragma lets you specify rewrite rules. It is
5446 described in <xref linkend="rewrite-rules"/>.</para>
5449 <sect2 id="specialize-pragma">
5450 <title>SPECIALIZE pragma</title>
5452 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5453 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5454 <indexterm><primary>overloading, death to</primary></indexterm>
5456 <para>(UK spelling also accepted.) For key overloaded
5457 functions, you can create extra versions (NB: more code space)
5458 specialised to particular types. Thus, if you have an
5459 overloaded function:</para>
5462 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5465 <para>If it is heavily used on lists with
5466 <literal>Widget</literal> keys, you could specialise it as
5470 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5473 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5474 be put anywhere its type signature could be put.</para>
5476 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5477 (a) a specialised version of the function and (b) a rewrite rule
5478 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5479 un-specialised function into a call to the specialised one.</para>
5481 <para>The type in a SPECIALIZE pragma can be any type that is less
5482 polymorphic than the type of the original function. In concrete terms,
5483 if the original function is <literal>f</literal> then the pragma
5485 {-# SPECIALIZE f :: <type> #-}
5487 is valid if and only if the defintion
5489 f_spec :: <type>
5492 is valid. Here are some examples (where we only give the type signature
5493 for the original function, not its code):
5495 f :: Eq a => a -> b -> b
5496 {-# SPECIALISE f :: Int -> b -> b #-}
5498 g :: (Eq a, Ix b) => a -> b -> b
5499 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5501 h :: Eq a => a -> a -> a
5502 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5504 The last of these examples will generate a
5505 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5506 well. If you use this kind of specialisation, let us know how well it works.
5509 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5510 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5511 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5512 The <literal>INLINE</literal> pragma affects the specialised verison of the
5513 function (only), and applies even if the function is recursive. The motivating
5516 -- A GADT for arrays with type-indexed representation
5518 ArrInt :: !Int -> ByteArray# -> Arr Int
5519 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5521 (!:) :: Arr e -> Int -> e
5522 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5523 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5524 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5525 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5527 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5528 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5529 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5530 the specialised function will be inlined. It has two calls to
5531 <literal>(!:)</literal>,
5532 both at type <literal>Int</literal>. Both these calls fire the first
5533 specialisation, whose body is also inlined. The result is a type-based
5534 unrolling of the indexing function.</para>
5535 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5536 on an ordinarily-recursive function.</para>
5538 <para>Note: In earlier versions of GHC, it was possible to provide your own
5539 specialised function for a given type:
5542 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5545 This feature has been removed, as it is now subsumed by the
5546 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5550 <sect2 id="specialize-instance-pragma">
5551 <title>SPECIALIZE instance pragma
5555 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5556 <indexterm><primary>overloading, death to</primary></indexterm>
5557 Same idea, except for instance declarations. For example:
5560 instance (Eq a) => Eq (Foo a) where {
5561 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5565 The pragma must occur inside the <literal>where</literal> part
5566 of the instance declaration.
5569 Compatible with HBC, by the way, except perhaps in the placement
5575 <sect2 id="unpack-pragma">
5576 <title>UNPACK pragma</title>
5578 <indexterm><primary>UNPACK</primary></indexterm>
5580 <para>The <literal>UNPACK</literal> indicates to the compiler
5581 that it should unpack the contents of a constructor field into
5582 the constructor itself, removing a level of indirection. For
5586 data T = T {-# UNPACK #-} !Float
5587 {-# UNPACK #-} !Float
5590 <para>will create a constructor <literal>T</literal> containing
5591 two unboxed floats. This may not always be an optimisation: if
5592 the <function>T</function> constructor is scrutinised and the
5593 floats passed to a non-strict function for example, they will
5594 have to be reboxed (this is done automatically by the
5597 <para>Unpacking constructor fields should only be used in
5598 conjunction with <option>-O</option>, in order to expose
5599 unfoldings to the compiler so the reboxing can be removed as
5600 often as possible. For example:</para>
5604 f (T f1 f2) = f1 + f2
5607 <para>The compiler will avoid reboxing <function>f1</function>
5608 and <function>f2</function> by inlining <function>+</function>
5609 on floats, but only when <option>-O</option> is on.</para>
5611 <para>Any single-constructor data is eligible for unpacking; for
5615 data T = T {-# UNPACK #-} !(Int,Int)
5618 <para>will store the two <literal>Int</literal>s directly in the
5619 <function>T</function> constructor, by flattening the pair.
5620 Multi-level unpacking is also supported:</para>
5623 data T = T {-# UNPACK #-} !S
5624 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5627 <para>will store two unboxed <literal>Int#</literal>s
5628 directly in the <function>T</function> constructor. The
5629 unpacker can see through newtypes, too.</para>
5631 <para>If a field cannot be unpacked, you will not get a warning,
5632 so it might be an idea to check the generated code with
5633 <option>-ddump-simpl</option>.</para>
5635 <para>See also the <option>-funbox-strict-fields</option> flag,
5636 which essentially has the effect of adding
5637 <literal>{-# UNPACK #-}</literal> to every strict
5638 constructor field.</para>
5643 <!-- ======================= REWRITE RULES ======================== -->
5645 <sect1 id="rewrite-rules">
5646 <title>Rewrite rules
5648 <indexterm><primary>RULES pragma</primary></indexterm>
5649 <indexterm><primary>pragma, RULES</primary></indexterm>
5650 <indexterm><primary>rewrite rules</primary></indexterm></title>
5653 The programmer can specify rewrite rules as part of the source program
5654 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5655 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5656 and (b) the <option>-frules-off</option> flag
5657 (<xref linkend="options-f"/>) is not specified, and (c) the
5658 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5667 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5674 <title>Syntax</title>
5677 From a syntactic point of view:
5683 There may be zero or more rules in a <literal>RULES</literal> pragma.
5690 Each rule has a name, enclosed in double quotes. The name itself has
5691 no significance at all. It is only used when reporting how many times the rule fired.
5697 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5698 immediately after the name of the rule. Thus:
5701 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5704 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5705 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5714 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5715 is set, so you must lay out your rules starting in the same column as the
5716 enclosing definitions.
5723 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5724 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5725 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5726 by spaces, just like in a type <literal>forall</literal>.
5732 A pattern variable may optionally have a type signature.
5733 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5734 For example, here is the <literal>foldr/build</literal> rule:
5737 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5738 foldr k z (build g) = g k z
5741 Since <function>g</function> has a polymorphic type, it must have a type signature.
5748 The left hand side of a rule must consist of a top-level variable applied
5749 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5752 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5753 "wrong2" forall f. f True = True
5756 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5763 A rule does not need to be in the same module as (any of) the
5764 variables it mentions, though of course they need to be in scope.
5770 Rules are automatically exported from a module, just as instance declarations are.
5781 <title>Semantics</title>
5784 From a semantic point of view:
5790 Rules are only applied if you use the <option>-O</option> flag.
5796 Rules are regarded as left-to-right rewrite rules.
5797 When GHC finds an expression that is a substitution instance of the LHS
5798 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5799 By "a substitution instance" we mean that the LHS can be made equal to the
5800 expression by substituting for the pattern variables.
5807 The LHS and RHS of a rule are typechecked, and must have the
5815 GHC makes absolutely no attempt to verify that the LHS and RHS
5816 of a rule have the same meaning. That is undecidable in general, and
5817 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5824 GHC makes no attempt to make sure that the rules are confluent or
5825 terminating. For example:
5828 "loop" forall x,y. f x y = f y x
5831 This rule will cause the compiler to go into an infinite loop.
5838 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5844 GHC currently uses a very simple, syntactic, matching algorithm
5845 for matching a rule LHS with an expression. It seeks a substitution
5846 which makes the LHS and expression syntactically equal modulo alpha
5847 conversion. The pattern (rule), but not the expression, is eta-expanded if
5848 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5849 But not beta conversion (that's called higher-order matching).
5853 Matching is carried out on GHC's intermediate language, which includes
5854 type abstractions and applications. So a rule only matches if the
5855 types match too. See <xref linkend="rule-spec"/> below.
5861 GHC keeps trying to apply the rules as it optimises the program.
5862 For example, consider:
5871 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5872 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5873 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5874 not be substituted, and the rule would not fire.
5881 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5882 that appears on the LHS of a rule</emphasis>, because once you have substituted
5883 for something you can't match against it (given the simple minded
5884 matching). So if you write the rule
5887 "map/map" forall f,g. map f . map g = map (f.g)
5890 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5891 It will only match something written with explicit use of ".".
5892 Well, not quite. It <emphasis>will</emphasis> match the expression
5898 where <function>wibble</function> is defined:
5901 wibble f g = map f . map g
5904 because <function>wibble</function> will be inlined (it's small).
5906 Later on in compilation, GHC starts inlining even things on the
5907 LHS of rules, but still leaves the rules enabled. This inlining
5908 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5915 All rules are implicitly exported from the module, and are therefore
5916 in force in any module that imports the module that defined the rule, directly
5917 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5918 in force when compiling A.) The situation is very similar to that for instance
5930 <title>List fusion</title>
5933 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5934 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5935 intermediate list should be eliminated entirely.
5939 The following are good producers:
5951 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5957 Explicit lists (e.g. <literal>[True, False]</literal>)
5963 The cons constructor (e.g <literal>3:4:[]</literal>)
5969 <function>++</function>
5975 <function>map</function>
5981 <function>take</function>, <function>filter</function>
5987 <function>iterate</function>, <function>repeat</function>
5993 <function>zip</function>, <function>zipWith</function>
6002 The following are good consumers:
6014 <function>array</function> (on its second argument)
6020 <function>++</function> (on its first argument)
6026 <function>foldr</function>
6032 <function>map</function>
6038 <function>take</function>, <function>filter</function>
6044 <function>concat</function>
6050 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6056 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6057 will fuse with one but not the other)
6063 <function>partition</function>
6069 <function>head</function>
6075 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6081 <function>sequence_</function>
6087 <function>msum</function>
6093 <function>sortBy</function>
6102 So, for example, the following should generate no intermediate lists:
6105 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6111 This list could readily be extended; if there are Prelude functions that you use
6112 a lot which are not included, please tell us.
6116 If you want to write your own good consumers or producers, look at the
6117 Prelude definitions of the above functions to see how to do so.
6122 <sect2 id="rule-spec">
6123 <title>Specialisation
6127 Rewrite rules can be used to get the same effect as a feature
6128 present in earlier versions of GHC.
6129 For example, suppose that:
6132 genericLookup :: Ord a => Table a b -> a -> b
6133 intLookup :: Table Int b -> Int -> b
6136 where <function>intLookup</function> is an implementation of
6137 <function>genericLookup</function> that works very fast for
6138 keys of type <literal>Int</literal>. You might wish
6139 to tell GHC to use <function>intLookup</function> instead of
6140 <function>genericLookup</function> whenever the latter was called with
6141 type <literal>Table Int b -> Int -> b</literal>.
6142 It used to be possible to write
6145 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6148 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6151 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6154 This slightly odd-looking rule instructs GHC to replace
6155 <function>genericLookup</function> by <function>intLookup</function>
6156 <emphasis>whenever the types match</emphasis>.
6157 What is more, this rule does not need to be in the same
6158 file as <function>genericLookup</function>, unlike the
6159 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6160 have an original definition available to specialise).
6163 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6164 <function>intLookup</function> really behaves as a specialised version
6165 of <function>genericLookup</function>!!!</para>
6167 <para>An example in which using <literal>RULES</literal> for
6168 specialisation will Win Big:
6171 toDouble :: Real a => a -> Double
6172 toDouble = fromRational . toRational
6174 {-# RULES "toDouble/Int" toDouble = i2d #-}
6175 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6178 The <function>i2d</function> function is virtually one machine
6179 instruction; the default conversion—via an intermediate
6180 <literal>Rational</literal>—is obscenely expensive by
6187 <title>Controlling what's going on</title>
6195 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6201 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6202 If you add <option>-dppr-debug</option> you get a more detailed listing.
6208 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6211 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6212 {-# INLINE build #-}
6216 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6217 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6218 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6219 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6226 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6227 see how to write rules that will do fusion and yet give an efficient
6228 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6238 <sect2 id="core-pragma">
6239 <title>CORE pragma</title>
6241 <indexterm><primary>CORE pragma</primary></indexterm>
6242 <indexterm><primary>pragma, CORE</primary></indexterm>
6243 <indexterm><primary>core, annotation</primary></indexterm>
6246 The external core format supports <quote>Note</quote> annotations;
6247 the <literal>CORE</literal> pragma gives a way to specify what these
6248 should be in your Haskell source code. Syntactically, core
6249 annotations are attached to expressions and take a Haskell string
6250 literal as an argument. The following function definition shows an
6254 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6257 Semantically, this is equivalent to:
6265 However, when external for is generated (via
6266 <option>-fext-core</option>), there will be Notes attached to the
6267 expressions <function>show</function> and <varname>x</varname>.
6268 The core function declaration for <function>f</function> is:
6272 f :: %forall a . GHCziShow.ZCTShow a ->
6273 a -> GHCziBase.ZMZN GHCziBase.Char =
6274 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6276 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6278 (tpl1::GHCziBase.Int ->
6280 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6282 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6283 (tpl3::GHCziBase.ZMZN a ->
6284 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6292 Here, we can see that the function <function>show</function> (which
6293 has been expanded out to a case expression over the Show dictionary)
6294 has a <literal>%note</literal> attached to it, as does the
6295 expression <varname>eta</varname> (which used to be called
6296 <varname>x</varname>).
6303 <sect1 id="special-ids">
6304 <title>Special built-in functions</title>
6305 <para>GHC has a few built-in funcions with special behaviour,
6306 described in this section. All are exported by
6307 <literal>GHC.Exts</literal>.</para>
6309 <sect2> <title>The <literal>seq</literal> function </title>
6311 The function <literal>seq</literal> is as described in the Haskell98 Report.
6315 It evaluates its first argument to head normal form, and then returns its
6316 second argument as the result. The reason that it is documented here is
6317 that, despite <literal>seq</literal>'s polymorphism, its
6318 second argument can have an unboxed type, or
6319 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6320 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6321 to be instantiated to an unboxed type, which is not usually allowed.
6325 <sect2> <title>The <literal>inline</literal> function </title>
6327 The <literal>inline</literal> function is somewhat experimental.
6331 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6332 is inlined, regardless of its size. More precisely, the call
6333 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6335 This allows the programmer to control inlining from
6336 a particular <emphasis>call site</emphasis>
6337 rather than the <emphasis>definition site</emphasis> of the function
6338 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6341 This inlining occurs regardless of the argument to the call
6342 or the size of <literal>f</literal>'s definition; it is unconditional.
6343 The main caveat is that <literal>f</literal>'s definition must be
6344 visible to the compiler. That is, <literal>f</literal> must be
6345 let-bound in the current scope.
6346 If no inlining takes place, the <literal>inline</literal> function
6347 expands to the identity function in Phase zero; so its use imposes
6350 <para> If the function is defined in another
6351 module, GHC only exposes its inlining in the interface file if the
6352 function is sufficiently small that it <emphasis>might</emphasis> be
6353 inlined by the automatic mechanism. There is currently no way to tell
6354 GHC to expose arbitrarily-large functions in the interface file. (This
6355 shortcoming is something that could be fixed, with some kind of pragma.)
6359 <sect2> <title>The <literal>lazy</literal> function </title>
6361 The <literal>lazy</literal> function restrains strictness analysis a little:
6365 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6366 but <literal>lazy</literal> has a magical property so far as strictness
6367 analysis is concerned: it is lazy in its first argument,
6368 even though its semantics is strict. After strictness analysis has run,
6369 calls to <literal>lazy</literal> are inlined to be the identity function.
6372 This behaviour is occasionally useful when controlling evaluation order.
6373 Notably, <literal>lazy</literal> is used in the library definition of
6374 <literal>Control.Parallel.par</literal>:
6377 par x y = case (par# x) of { _ -> lazy y }
6379 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6380 look strict in <literal>y</literal> which would defeat the whole
6381 purpose of <literal>par</literal>.
6384 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6390 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6392 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6393 typechecker entirely. It has type
6395 unsafeCoerce# :: a -> b
6397 That is, it allows you to coerce any type into any other type. If you use this
6398 function, you had better get it right, otherwise segmentation faults await.
6399 It is generally used when you want to write a program that you know is
6400 well-typed, but where Haskell's type system is not expressive enough to prove
6401 that it is well typed.
6404 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6405 although extremely bad things will happen if you coerce a boxed type
6414 <sect1 id="generic-classes">
6415 <title>Generic classes</title>
6418 The ideas behind this extension are described in detail in "Derivable type classes",
6419 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6420 An example will give the idea:
6428 fromBin :: [Int] -> (a, [Int])
6430 toBin {| Unit |} Unit = []
6431 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6432 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6433 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6435 fromBin {| Unit |} bs = (Unit, bs)
6436 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6437 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6438 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6439 (y,bs'') = fromBin bs'
6442 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6443 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6444 which are defined thus in the library module <literal>Generics</literal>:
6448 data a :+: b = Inl a | Inr b
6449 data a :*: b = a :*: b
6452 Now you can make a data type into an instance of Bin like this:
6454 instance (Bin a, Bin b) => Bin (a,b)
6455 instance Bin a => Bin [a]
6457 That is, just leave off the "where" clause. Of course, you can put in the
6458 where clause and over-ride whichever methods you please.
6462 <title> Using generics </title>
6463 <para>To use generics you need to</para>
6466 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6467 <option>-fgenerics</option> (to generate extra per-data-type code),
6468 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6472 <para>Import the module <literal>Generics</literal> from the
6473 <literal>lang</literal> package. This import brings into
6474 scope the data types <literal>Unit</literal>,
6475 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6476 don't need this import if you don't mention these types
6477 explicitly; for example, if you are simply giving instance
6478 declarations.)</para>
6483 <sect2> <title> Changes wrt the paper </title>
6485 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6486 can be written infix (indeed, you can now use
6487 any operator starting in a colon as an infix type constructor). Also note that
6488 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6489 Finally, note that the syntax of the type patterns in the class declaration
6490 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6491 alone would ambiguous when they appear on right hand sides (an extension we
6492 anticipate wanting).
6496 <sect2> <title>Terminology and restrictions</title>
6498 Terminology. A "generic default method" in a class declaration
6499 is one that is defined using type patterns as above.
6500 A "polymorphic default method" is a default method defined as in Haskell 98.
6501 A "generic class declaration" is a class declaration with at least one
6502 generic default method.
6510 Alas, we do not yet implement the stuff about constructor names and
6517 A generic class can have only one parameter; you can't have a generic
6518 multi-parameter class.
6524 A default method must be defined entirely using type patterns, or entirely
6525 without. So this is illegal:
6528 op :: a -> (a, Bool)
6529 op {| Unit |} Unit = (Unit, True)
6532 However it is perfectly OK for some methods of a generic class to have
6533 generic default methods and others to have polymorphic default methods.
6539 The type variable(s) in the type pattern for a generic method declaration
6540 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:
6544 op {| p :*: q |} (x :*: y) = op (x :: p)
6552 The type patterns in a generic default method must take one of the forms:
6558 where "a" and "b" are type variables. Furthermore, all the type patterns for
6559 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6560 must use the same type variables. So this is illegal:
6564 op {| a :+: b |} (Inl x) = True
6565 op {| p :+: q |} (Inr y) = False
6567 The type patterns must be identical, even in equations for different methods of the class.
6568 So this too is illegal:
6572 op1 {| a :*: b |} (x :*: y) = True
6575 op2 {| p :*: q |} (x :*: y) = False
6577 (The reason for this restriction is that we gather all the equations for a particular type consructor
6578 into a single generic instance declaration.)
6584 A generic method declaration must give a case for each of the three type constructors.
6590 The type for a generic method can be built only from:
6592 <listitem> <para> Function arrows </para> </listitem>
6593 <listitem> <para> Type variables </para> </listitem>
6594 <listitem> <para> Tuples </para> </listitem>
6595 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6597 Here are some example type signatures for generic methods:
6600 op2 :: Bool -> (a,Bool)
6601 op3 :: [Int] -> a -> a
6604 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6608 This restriction is an implementation restriction: we just havn't got around to
6609 implementing the necessary bidirectional maps over arbitrary type constructors.
6610 It would be relatively easy to add specific type constructors, such as Maybe and list,
6611 to the ones that are allowed.</para>
6616 In an instance declaration for a generic class, the idea is that the compiler
6617 will fill in the methods for you, based on the generic templates. However it can only
6622 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6627 No constructor of the instance type has unboxed fields.
6631 (Of course, these things can only arise if you are already using GHC extensions.)
6632 However, you can still give an instance declarations for types which break these rules,
6633 provided you give explicit code to override any generic default methods.
6641 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6642 what the compiler does with generic declarations.
6647 <sect2> <title> Another example </title>
6649 Just to finish with, here's another example I rather like:
6653 nCons {| Unit |} _ = 1
6654 nCons {| a :*: b |} _ = 1
6655 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6658 tag {| Unit |} _ = 1
6659 tag {| a :*: b |} _ = 1
6660 tag {| a :+: b |} (Inl x) = tag x
6661 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6667 <sect1 id="monomorphism">
6668 <title>Control over monomorphism</title>
6670 <para>GHC supports two flags that control the way in which generalisation is
6671 carried out at let and where bindings.
6675 <title>Switching off the dreaded Monomorphism Restriction</title>
6676 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6678 <para>Haskell's monomorphism restriction (see
6679 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6681 of the Haskell Report)
6682 can be completely switched off by
6683 <option>-fno-monomorphism-restriction</option>.
6688 <title>Monomorphic pattern bindings</title>
6689 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6690 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6692 <para> As an experimental change, we are exploring the possibility of
6693 making pattern bindings monomorphic; that is, not generalised at all.
6694 A pattern binding is a binding whose LHS has no function arguments,
6695 and is not a simple variable. For example:
6697 f x = x -- Not a pattern binding
6698 f = \x -> x -- Not a pattern binding
6699 f :: Int -> Int = \x -> x -- Not a pattern binding
6701 (g,h) = e -- A pattern binding
6702 (f) = e -- A pattern binding
6703 [x] = e -- A pattern binding
6705 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6706 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6715 ;;; Local Variables: ***
6717 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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