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 <!-- included from primitives.sgml -->
281 <!-- &primitives; -->
282 <sect1 id="primitives">
283 <title>Unboxed types and primitive operations</title>
285 <para>GHC is built on a raft of primitive data types and operations.
286 While you really can use this stuff to write fast code,
287 we generally find it a lot less painful, and more satisfying in the
288 long run, to use higher-level language features and libraries. With
289 any luck, the code you write will be optimised to the efficient
290 unboxed version in any case. And if it isn't, we'd like to know
293 <para>We do not currently have good, up-to-date documentation about the
294 primitives, perhaps because they are mainly intended for internal use.
295 There used to be a long section about them here in the User Guide, but it
296 became out of date, and wrong information is worse than none.</para>
298 <para>The Real Truth about what primitive types there are, and what operations
299 work over those types, is held in the file
300 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
301 This file is used directly to generate GHC's primitive-operation definitions, so
302 it is always correct! It is also intended for processing into text.</para>
305 the result of such processing is part of the description of the
307 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
308 Core language</ulink>.
309 So that document is a good place to look for a type-set version.
310 We would be very happy if someone wanted to volunteer to produce an SGML
311 back end to the program that processes <filename>primops.txt</filename> so that
312 we could include the results here in the User Guide.</para>
314 <para>What follows here is a brief summary of some main points.</para>
316 <sect2 id="glasgow-unboxed">
321 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
324 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
325 that values of that type are represented by a pointer to a heap
326 object. The representation of a Haskell <literal>Int</literal>, for
327 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
328 type, however, is represented by the value itself, no pointers or heap
329 allocation are involved.
333 Unboxed types correspond to the “raw machine” types you
334 would use in C: <literal>Int#</literal> (long int),
335 <literal>Double#</literal> (double), <literal>Addr#</literal>
336 (void *), etc. The <emphasis>primitive operations</emphasis>
337 (PrimOps) on these types are what you might expect; e.g.,
338 <literal>(+#)</literal> is addition on
339 <literal>Int#</literal>s, and is the machine-addition that we all
340 know and love—usually one instruction.
344 Primitive (unboxed) types cannot be defined in Haskell, and are
345 therefore built into the language and compiler. Primitive types are
346 always unlifted; that is, a value of a primitive type cannot be
347 bottom. We use the convention that primitive types, values, and
348 operations have a <literal>#</literal> suffix.
352 Primitive values are often represented by a simple bit-pattern, such
353 as <literal>Int#</literal>, <literal>Float#</literal>,
354 <literal>Double#</literal>. But this is not necessarily the case:
355 a primitive value might be represented by a pointer to a
356 heap-allocated object. Examples include
357 <literal>Array#</literal>, the type of primitive arrays. A
358 primitive array is heap-allocated because it is too big a value to fit
359 in a register, and would be too expensive to copy around; in a sense,
360 it is accidental that it is represented by a pointer. If a pointer
361 represents a primitive value, then it really does point to that value:
362 no unevaluated thunks, no indirections…nothing can be at the
363 other end of the pointer than the primitive value.
364 A numerically-intensive program using unboxed types can
365 go a <emphasis>lot</emphasis> faster than its “standard”
366 counterpart—we saw a threefold speedup on one example.
370 There are some restrictions on the use of primitive types:
372 <listitem><para>The main restriction
373 is that you can't pass a primitive value to a polymorphic
374 function or store one in a polymorphic data type. This rules out
375 things like <literal>[Int#]</literal> (i.e. lists of primitive
376 integers). The reason for this restriction is that polymorphic
377 arguments and constructor fields are assumed to be pointers: if an
378 unboxed integer is stored in one of these, the garbage collector would
379 attempt to follow it, leading to unpredictable space leaks. Or a
380 <function>seq</function> operation on the polymorphic component may
381 attempt to dereference the pointer, with disastrous results. Even
382 worse, the unboxed value might be larger than a pointer
383 (<literal>Double#</literal> for instance).
386 <listitem><para> You cannot bind a variable with an unboxed type
387 in a <emphasis>top-level</emphasis> binding.
389 <listitem><para> You cannot bind a variable with an unboxed type
390 in a <emphasis>recursive</emphasis> binding.
392 <listitem><para> You may bind unboxed variables in a (non-recursive,
393 non-top-level) pattern binding, but any such variable causes the entire
395 to become strict. For example:
397 data Foo = Foo Int Int#
399 f x = let (Foo a b, w) = ..rhs.. in ..body..
401 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
403 is strict, and the program behaves as if you had written
405 data Foo = Foo Int Int#
407 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
416 <sect2 id="unboxed-tuples">
417 <title>Unboxed Tuples
421 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
422 they're available by default with <option>-fglasgow-exts</option>. An
423 unboxed tuple looks like this:
435 where <literal>e_1..e_n</literal> are expressions of any
436 type (primitive or non-primitive). The type of an unboxed tuple looks
441 Unboxed tuples are used for functions that need to return multiple
442 values, but they avoid the heap allocation normally associated with
443 using fully-fledged tuples. When an unboxed tuple is returned, the
444 components are put directly into registers or on the stack; the
445 unboxed tuple itself does not have a composite representation. Many
446 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
448 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
449 tuples to avoid unnecessary allocation during sequences of operations.
453 There are some pretty stringent restrictions on the use of unboxed tuples:
458 Values of unboxed tuple types are subject to the same restrictions as
459 other unboxed types; i.e. they may not be stored in polymorphic data
460 structures or passed to polymorphic functions.
467 No variable can have an unboxed tuple type, nor may a constructor or function
468 argument have an unboxed tuple type. The following are all illegal:
472 data Foo = Foo (# Int, Int #)
474 f :: (# Int, Int #) -> (# Int, Int #)
477 g :: (# Int, Int #) -> Int
480 h x = let y = (# x,x #) in ...
487 The typical use of unboxed tuples is simply to return multiple values,
488 binding those multiple results with a <literal>case</literal> expression, thus:
490 f x y = (# x+1, y-1 #)
491 g x = case f x x of { (# a, b #) -> a + b }
493 You can have an unboxed tuple in a pattern binding, thus
495 f x = let (# p,q #) = h x in ..body..
497 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
498 the resulting binding is lazy like any other Haskell pattern binding. The
499 above example desugars like this:
501 f x = let t = case h x o f{ (# p,q #) -> (p,q)
506 Indeed, the bindings can even be recursive.
513 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
515 <sect1 id="syntax-extns">
516 <title>Syntactic extensions</title>
518 <!-- ====================== HIERARCHICAL MODULES ======================= -->
520 <sect2 id="hierarchical-modules">
521 <title>Hierarchical Modules</title>
523 <para>GHC supports a small extension to the syntax of module
524 names: a module name is allowed to contain a dot
525 <literal>‘.’</literal>. This is also known as the
526 “hierarchical module namespace” extension, because
527 it extends the normally flat Haskell module namespace into a
528 more flexible hierarchy of modules.</para>
530 <para>This extension has very little impact on the language
531 itself; modules names are <emphasis>always</emphasis> fully
532 qualified, so you can just think of the fully qualified module
533 name as <quote>the module name</quote>. In particular, this
534 means that the full module name must be given after the
535 <literal>module</literal> keyword at the beginning of the
536 module; for example, the module <literal>A.B.C</literal> must
539 <programlisting>module A.B.C</programlisting>
542 <para>It is a common strategy to use the <literal>as</literal>
543 keyword to save some typing when using qualified names with
544 hierarchical modules. For example:</para>
547 import qualified Control.Monad.ST.Strict as ST
550 <para>For details on how GHC searches for source and interface
551 files in the presence of hierarchical modules, see <xref
552 linkend="search-path"/>.</para>
554 <para>GHC comes with a large collection of libraries arranged
555 hierarchically; see the accompanying library documentation.
556 There is an ongoing project to create and maintain a stable set
557 of <quote>core</quote> libraries used by several Haskell
558 compilers, and the libraries that GHC comes with represent the
559 current status of that project. For more details, see <ulink
560 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
561 Libraries</ulink>.</para>
565 <!-- ====================== PATTERN GUARDS ======================= -->
567 <sect2 id="pattern-guards">
568 <title>Pattern guards</title>
571 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
572 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.)
576 Suppose we have an abstract data type of finite maps, with a
580 lookup :: FiniteMap -> Int -> Maybe Int
583 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
584 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
588 clunky env var1 var2 | ok1 && ok2 = val1 + val2
589 | otherwise = var1 + var2
600 The auxiliary functions are
604 maybeToBool :: Maybe a -> Bool
605 maybeToBool (Just x) = True
606 maybeToBool Nothing = False
608 expectJust :: Maybe a -> a
609 expectJust (Just x) = x
610 expectJust Nothing = error "Unexpected Nothing"
614 What is <function>clunky</function> doing? The guard <literal>ok1 &&
615 ok2</literal> checks that both lookups succeed, using
616 <function>maybeToBool</function> to convert the <function>Maybe</function>
617 types to booleans. The (lazily evaluated) <function>expectJust</function>
618 calls extract the values from the results of the lookups, and binds the
619 returned values to <varname>val1</varname> and <varname>val2</varname>
620 respectively. If either lookup fails, then clunky takes the
621 <literal>otherwise</literal> case and returns the sum of its arguments.
625 This is certainly legal Haskell, but it is a tremendously verbose and
626 un-obvious way to achieve the desired effect. Arguably, a more direct way
627 to write clunky would be to use case expressions:
631 clunky env var1 var2 = case lookup env var1 of
633 Just val1 -> case lookup env var2 of
635 Just val2 -> val1 + val2
641 This is a bit shorter, but hardly better. Of course, we can rewrite any set
642 of pattern-matching, guarded equations as case expressions; that is
643 precisely what the compiler does when compiling equations! The reason that
644 Haskell provides guarded equations is because they allow us to write down
645 the cases we want to consider, one at a time, independently of each other.
646 This structure is hidden in the case version. Two of the right-hand sides
647 are really the same (<function>fail</function>), and the whole expression
648 tends to become more and more indented.
652 Here is how I would write clunky:
657 | Just val1 <- lookup env var1
658 , Just val2 <- lookup env var2
660 ...other equations for clunky...
664 The semantics should be clear enough. The qualifiers are matched in order.
665 For a <literal><-</literal> qualifier, which I call a pattern guard, the
666 right hand side is evaluated and matched against the pattern on the left.
667 If the match fails then the whole guard fails and the next equation is
668 tried. If it succeeds, then the appropriate binding takes place, and the
669 next qualifier is matched, in the augmented environment. Unlike list
670 comprehensions, however, the type of the expression to the right of the
671 <literal><-</literal> is the same as the type of the pattern to its
672 left. The bindings introduced by pattern guards scope over all the
673 remaining guard qualifiers, and over the right hand side of the equation.
677 Just as with list comprehensions, boolean expressions can be freely mixed
678 with among the pattern guards. For example:
689 Haskell's current guards therefore emerge as a special case, in which the
690 qualifier list has just one element, a boolean expression.
694 <!-- ===================== Recursive do-notation =================== -->
696 <sect2 id="mdo-notation">
697 <title>The recursive do-notation
700 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
701 "A recursive do for Haskell",
702 Levent Erkok, John Launchbury",
703 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
706 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
707 that is, the variables bound in a do-expression are visible only in the textually following
708 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
709 group. It turns out that several applications can benefit from recursive bindings in
710 the do-notation, and this extension provides the necessary syntactic support.
713 Here is a simple (yet contrived) example:
716 import Control.Monad.Fix
718 justOnes = mdo xs <- Just (1:xs)
722 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
726 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
729 class Monad m => MonadFix m where
730 mfix :: (a -> m a) -> m a
733 The function <literal>mfix</literal>
734 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
735 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
736 For details, see the above mentioned reference.
739 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
740 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
741 for Haskell's internal state monad (strict and lazy, respectively).
744 There are three important points in using the recursive-do notation:
747 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
748 than <literal>do</literal>).
752 You should <literal>import Control.Monad.Fix</literal>.
753 (Note: Strictly speaking, this import is required only when you need to refer to the name
754 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
755 are encouraged to always import this module when using the mdo-notation.)
759 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
765 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
766 contains up to date information on recursive monadic bindings.
770 Historical note: The old implementation of the mdo-notation (and most
771 of the existing documents) used the name
772 <literal>MonadRec</literal> for the class and the corresponding library.
773 This name is not supported by GHC.
779 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
781 <sect2 id="parallel-list-comprehensions">
782 <title>Parallel List Comprehensions</title>
783 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
785 <indexterm><primary>parallel list comprehensions</primary>
788 <para>Parallel list comprehensions are a natural extension to list
789 comprehensions. List comprehensions can be thought of as a nice
790 syntax for writing maps and filters. Parallel comprehensions
791 extend this to include the zipWith family.</para>
793 <para>A parallel list comprehension has multiple independent
794 branches of qualifier lists, each separated by a `|' symbol. For
795 example, the following zips together two lists:</para>
798 [ (x, y) | x <- xs | y <- ys ]
801 <para>The behavior of parallel list comprehensions follows that of
802 zip, in that the resulting list will have the same length as the
803 shortest branch.</para>
805 <para>We can define parallel list comprehensions by translation to
806 regular comprehensions. Here's the basic idea:</para>
808 <para>Given a parallel comprehension of the form: </para>
811 [ e | p1 <- e11, p2 <- e12, ...
812 | q1 <- e21, q2 <- e22, ...
817 <para>This will be translated to: </para>
820 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
821 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
826 <para>where `zipN' is the appropriate zip for the given number of
831 <sect2 id="rebindable-syntax">
832 <title>Rebindable syntax</title>
835 <para>GHC allows most kinds of built-in syntax to be rebound by
836 the user, to facilitate replacing the <literal>Prelude</literal>
837 with a home-grown version, for example.</para>
839 <para>You may want to define your own numeric class
840 hierarchy. It completely defeats that purpose if the
841 literal "1" means "<literal>Prelude.fromInteger
842 1</literal>", which is what the Haskell Report specifies.
843 So the <option>-fno-implicit-prelude</option> flag causes
844 the following pieces of built-in syntax to refer to
845 <emphasis>whatever is in scope</emphasis>, not the Prelude
850 <para>An integer literal <literal>368</literal> means
851 "<literal>fromInteger (368::Integer)</literal>", rather than
852 "<literal>Prelude.fromInteger (368::Integer)</literal>".
855 <listitem><para>Fractional literals are handed in just the same way,
856 except that the translation is
857 <literal>fromRational (3.68::Rational)</literal>.
860 <listitem><para>The equality test in an overloaded numeric pattern
861 uses whatever <literal>(==)</literal> is in scope.
864 <listitem><para>The subtraction operation, and the
865 greater-than-or-equal test, in <literal>n+k</literal> patterns
866 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
870 <para>Negation (e.g. "<literal>- (f x)</literal>")
871 means "<literal>negate (f x)</literal>", both in numeric
872 patterns, and expressions.
876 <para>"Do" notation is translated using whatever
877 functions <literal>(>>=)</literal>,
878 <literal>(>>)</literal>, and <literal>fail</literal>,
879 are in scope (not the Prelude
880 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
881 comprehensions, are unaffected. </para></listitem>
885 notation (see <xref linkend="arrow-notation"/>)
886 uses whatever <literal>arr</literal>,
887 <literal>(>>>)</literal>, <literal>first</literal>,
888 <literal>app</literal>, <literal>(|||)</literal> and
889 <literal>loop</literal> functions are in scope. But unlike the
890 other constructs, the types of these functions must match the
891 Prelude types very closely. Details are in flux; if you want
895 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
896 even if that is a little unexpected. For emample, the
897 static semantics of the literal <literal>368</literal>
898 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
899 <literal>fromInteger</literal> to have any of the types:
901 fromInteger :: Integer -> Integer
902 fromInteger :: forall a. Foo a => Integer -> a
903 fromInteger :: Num a => a -> Integer
904 fromInteger :: Integer -> Bool -> Bool
908 <para>Be warned: this is an experimental facility, with
909 fewer checks than usual. Use <literal>-dcore-lint</literal>
910 to typecheck the desugared program. If Core Lint is happy
911 you should be all right.</para>
915 <sect2 id="postfix-operators">
916 <title>Postfix operators</title>
919 GHC allows a small extension to the syntax of left operator sections, which
920 allows you to define postfix operators. The extension is this: the left section
924 is equivalent (from the point of view of both type checking and execution) to the expression
928 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
929 The strict Haskell 98 interpretation is that the section is equivalent to
933 That is, the operator must be a function of two arguments. GHC allows it to
934 take only one argument, and that in turn allows you to write the function
937 <para>Since this extension goes beyond Haskell 98, it should really be enabled
938 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
939 change their behaviour, of course.)
941 <para>The extension does not extend to the left-hand side of function
942 definitions; you must define such a function in prefix form.</para>
949 <!-- TYPE SYSTEM EXTENSIONS -->
950 <sect1 id="data-type-extensions">
951 <title>Extensions to data types and type synonyms</title>
953 <sect2 id="nullary-types">
954 <title>Data types with no constructors</title>
956 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
957 a data type with no constructors. For example:</para>
961 data T a -- T :: * -> *
964 <para>Syntactically, the declaration lacks the "= constrs" part. The
965 type can be parameterised over types of any kind, but if the kind is
966 not <literal>*</literal> then an explicit kind annotation must be used
967 (see <xref linkend="kinding"/>).</para>
969 <para>Such data types have only one value, namely bottom.
970 Nevertheless, they can be useful when defining "phantom types".</para>
973 <sect2 id="infix-tycons">
974 <title>Infix type constructors, classes, and type variables</title>
977 GHC allows type constructors, classes, and type variables to be operators, and
978 to be written infix, very much like expressions. More specifically:
981 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
982 The lexical syntax is the same as that for data constructors.
985 Data type and type-synonym declarations can be written infix, parenthesised
986 if you want further arguments. E.g.
988 data a :*: b = Foo a b
989 type a :+: b = Either a b
990 class a :=: b where ...
992 data (a :**: b) x = Baz a b x
993 type (a :++: b) y = Either (a,b) y
997 Types, and class constraints, can be written infix. For example
1000 f :: (a :=: b) => a -> b
1004 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1005 The lexical syntax is the same as that for variable operators, excluding "(.)",
1006 "(!)", and "(*)". In a binding position, the operator must be
1007 parenthesised. For example:
1009 type T (+) = Int + Int
1013 liftA2 :: Arrow (~>)
1014 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1020 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1021 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1024 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1025 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1026 sets the fixity for a data constructor and the corresponding type constructor. For example:
1030 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1031 and similarly for <literal>:*:</literal>.
1032 <literal>Int `a` Bool</literal>.
1035 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1042 <sect2 id="type-synonyms">
1043 <title>Liberalised type synonyms</title>
1046 Type synonyms are like macros at the type level, and
1047 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1048 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1050 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1051 in a type synonym, thus:
1053 type Discard a = forall b. Show b => a -> b -> (a, String)
1058 g :: Discard Int -> (Int,String) -- A rank-2 type
1065 You can write an unboxed tuple in a type synonym:
1067 type Pr = (# Int, Int #)
1075 You can apply a type synonym to a forall type:
1077 type Foo a = a -> a -> Bool
1079 f :: Foo (forall b. b->b)
1081 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1083 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1088 You can apply a type synonym to a partially applied type synonym:
1090 type Generic i o = forall x. i x -> o x
1093 foo :: Generic Id []
1095 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1097 foo :: forall x. x -> [x]
1105 GHC currently does kind checking before expanding synonyms (though even that
1109 After expanding type synonyms, GHC does validity checking on types, looking for
1110 the following mal-formedness which isn't detected simply by kind checking:
1113 Type constructor applied to a type involving for-alls.
1116 Unboxed tuple on left of an arrow.
1119 Partially-applied type synonym.
1123 this will be rejected:
1125 type Pr = (# Int, Int #)
1130 because GHC does not allow unboxed tuples on the left of a function arrow.
1135 <sect2 id="existential-quantification">
1136 <title>Existentially quantified data constructors
1140 The idea of using existential quantification in data type declarations
1141 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1142 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1143 London, 1991). It was later formalised by Laufer and Odersky
1144 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1145 TOPLAS, 16(5), pp1411-1430, 1994).
1146 It's been in Lennart
1147 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1148 proved very useful. Here's the idea. Consider the declaration:
1154 data Foo = forall a. MkFoo a (a -> Bool)
1161 The data type <literal>Foo</literal> has two constructors with types:
1167 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1174 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1175 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1176 For example, the following expression is fine:
1182 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1188 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1189 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1190 isUpper</function> packages a character with a compatible function. These
1191 two things are each of type <literal>Foo</literal> and can be put in a list.
1195 What can we do with a value of type <literal>Foo</literal>?. In particular,
1196 what happens when we pattern-match on <function>MkFoo</function>?
1202 f (MkFoo val fn) = ???
1208 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1209 are compatible, the only (useful) thing we can do with them is to
1210 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1217 f (MkFoo val fn) = fn val
1223 What this allows us to do is to package heterogenous values
1224 together with a bunch of functions that manipulate them, and then treat
1225 that collection of packages in a uniform manner. You can express
1226 quite a bit of object-oriented-like programming this way.
1229 <sect3 id="existential">
1230 <title>Why existential?
1234 What has this to do with <emphasis>existential</emphasis> quantification?
1235 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1241 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1247 But Haskell programmers can safely think of the ordinary
1248 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1249 adding a new existential quantification construct.
1255 <title>Type classes</title>
1258 An easy extension is to allow
1259 arbitrary contexts before the constructor. For example:
1265 data Baz = forall a. Eq a => Baz1 a a
1266 | forall b. Show b => Baz2 b (b -> b)
1272 The two constructors have the types you'd expect:
1278 Baz1 :: forall a. Eq a => a -> a -> Baz
1279 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1285 But when pattern matching on <function>Baz1</function> the matched values can be compared
1286 for equality, and when pattern matching on <function>Baz2</function> the first matched
1287 value can be converted to a string (as well as applying the function to it).
1288 So this program is legal:
1295 f (Baz1 p q) | p == q = "Yes"
1297 f (Baz2 v fn) = show (fn v)
1303 Operationally, in a dictionary-passing implementation, the
1304 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1305 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1306 extract it on pattern matching.
1310 Notice the way that the syntax fits smoothly with that used for
1311 universal quantification earlier.
1316 <sect3 id="existential-records">
1317 <title>Record Constructors</title>
1320 GHC allows existentials to be used with records syntax as well. For example:
1323 data Counter a = forall self. NewCounter
1325 , _inc :: self -> self
1326 , _display :: self -> IO ()
1330 Here <literal>tag</literal> is a public field, with a well-typed selector
1331 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1332 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1333 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1334 compile-time error. In other words, <emphasis>GHC defines a record selector function
1335 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1336 (This example used an underscore in the fields for which record selectors
1337 will not be defined, but that is only programming style; GHC ignores them.)
1341 To make use of these hidden fields, we need to create some helper functions:
1344 inc :: Counter a -> Counter a
1345 inc (NewCounter x i d t) = NewCounter
1346 { _this = i x, _inc = i, _display = d, tag = t }
1348 display :: Counter a -> IO ()
1349 display NewCounter{ _this = x, _display = d } = d x
1352 Now we can define counters with different underlying implementations:
1355 counterA :: Counter String
1356 counterA = NewCounter
1357 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1359 counterB :: Counter String
1360 counterB = NewCounter
1361 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1364 display (inc counterA) -- prints "1"
1365 display (inc (inc counterB)) -- prints "##"
1368 At the moment, record update syntax is only supported for Haskell 98 data types,
1369 so the following function does <emphasis>not</emphasis> work:
1372 -- This is invalid; use explicit NewCounter instead for now
1373 setTag :: Counter a -> a -> Counter a
1374 setTag obj t = obj{ tag = t }
1383 <title>Restrictions</title>
1386 There are several restrictions on the ways in which existentially-quantified
1387 constructors can be use.
1396 When pattern matching, each pattern match introduces a new,
1397 distinct, type for each existential type variable. These types cannot
1398 be unified with any other type, nor can they escape from the scope of
1399 the pattern match. For example, these fragments are incorrect:
1407 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1408 is the result of <function>f1</function>. One way to see why this is wrong is to
1409 ask what type <function>f1</function> has:
1413 f1 :: Foo -> a -- Weird!
1417 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1422 f1 :: forall a. Foo -> a -- Wrong!
1426 The original program is just plain wrong. Here's another sort of error
1430 f2 (Baz1 a b) (Baz1 p q) = a==q
1434 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1435 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1436 from the two <function>Baz1</function> constructors.
1444 You can't pattern-match on an existentially quantified
1445 constructor in a <literal>let</literal> or <literal>where</literal> group of
1446 bindings. So this is illegal:
1450 f3 x = a==b where { Baz1 a b = x }
1453 Instead, use a <literal>case</literal> expression:
1456 f3 x = case x of Baz1 a b -> a==b
1459 In general, you can only pattern-match
1460 on an existentially-quantified constructor in a <literal>case</literal> expression or
1461 in the patterns of a function definition.
1463 The reason for this restriction is really an implementation one.
1464 Type-checking binding groups is already a nightmare without
1465 existentials complicating the picture. Also an existential pattern
1466 binding at the top level of a module doesn't make sense, because it's
1467 not clear how to prevent the existentially-quantified type "escaping".
1468 So for now, there's a simple-to-state restriction. We'll see how
1476 You can't use existential quantification for <literal>newtype</literal>
1477 declarations. So this is illegal:
1481 newtype T = forall a. Ord a => MkT a
1485 Reason: a value of type <literal>T</literal> must be represented as a
1486 pair of a dictionary for <literal>Ord t</literal> and a value of type
1487 <literal>t</literal>. That contradicts the idea that
1488 <literal>newtype</literal> should have no concrete representation.
1489 You can get just the same efficiency and effect by using
1490 <literal>data</literal> instead of <literal>newtype</literal>. If
1491 there is no overloading involved, then there is more of a case for
1492 allowing an existentially-quantified <literal>newtype</literal>,
1493 because the <literal>data</literal> version does carry an
1494 implementation cost, but single-field existentially quantified
1495 constructors aren't much use. So the simple restriction (no
1496 existential stuff on <literal>newtype</literal>) stands, unless there
1497 are convincing reasons to change it.
1505 You can't use <literal>deriving</literal> to define instances of a
1506 data type with existentially quantified data constructors.
1508 Reason: in most cases it would not make sense. For example:;
1511 data T = forall a. MkT [a] deriving( Eq )
1514 To derive <literal>Eq</literal> in the standard way we would need to have equality
1515 between the single component of two <function>MkT</function> constructors:
1519 (MkT a) == (MkT b) = ???
1522 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1523 It's just about possible to imagine examples in which the derived instance
1524 would make sense, but it seems altogether simpler simply to prohibit such
1525 declarations. Define your own instances!
1536 <!-- ====================== Generalised algebraic data types ======================= -->
1538 <sect2 id="gadt-style">
1539 <title>Declaring data types with explicit constructor signatures</title>
1541 <para>GHC allows you to declare an algebraic data type by
1542 giving the type signatures of constructors explicitly. For example:
1546 Just :: a -> Maybe a
1548 The form is called a "GADT-style declaration"
1549 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1550 can only be declared using this form.</para>
1551 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1552 For example, these two declarations are equivalent:
1554 data Foo = forall a. MkFoo a (a -> Bool)
1555 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1558 <para>Any data type that can be declared in standard Haskell-98 syntax
1559 can also be declared using GADT-style syntax.
1560 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1561 they treat class constraints on the data constructors differently.
1562 Specifically, if the constructor is given a type-class context, that
1563 context is made available by pattern matching. For example:
1566 MkSet :: Eq a => [a] -> Set a
1568 makeSet :: Eq a => [a] -> Set a
1569 makeSet xs = MkSet (nub xs)
1571 insert :: a -> Set a -> Set a
1572 insert a (MkSet as) | a `elem` as = MkSet as
1573 | otherwise = MkSet (a:as)
1575 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1576 gives rise to a <literal>(Eq a)</literal>
1577 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1578 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1579 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1580 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1581 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1582 In the example, the equality dictionary is used to satisfy the equality constraint
1583 generated by the call to <literal>elem</literal>, so that the type of
1584 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1586 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1587 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1588 In Haskell 98 the defintion
1590 data Eq a => Set' a = MkSet' [a]
1592 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1593 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1594 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1595 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1596 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1598 For example, a possible application of GHC's behaviour is to reify dictionaries:
1600 data NumInst a where
1601 MkNumInst :: Num a => NumInst a
1603 intInst :: NumInst Int
1606 plus :: NumInst a -> a -> a -> a
1607 plus MkNumInst p q = p + q
1609 Here, a value of type <literal>NumInst a</literal> is equivalent
1610 to an explicit <literal>(Num a)</literal> dictionary.
1614 The rest of this section gives further details about GADT-style data
1619 The result type of each data constructor must begin with the type constructor being defined.
1620 If the result type of all constructors
1621 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1622 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1623 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1627 The type signature of
1628 each constructor is independent, and is implicitly universally quantified as usual.
1629 Different constructors may have different universally-quantified type variables
1630 and different type-class constraints.
1631 For example, this is fine:
1634 T1 :: Eq b => b -> T b
1635 T2 :: (Show c, Ix c) => c -> [c] -> T c
1640 Unlike a Haskell-98-style
1641 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1642 have no scope. Indeed, one can write a kind signature instead:
1644 data Set :: * -> * where ...
1646 or even a mixture of the two:
1648 data Foo a :: (* -> *) -> * where ...
1650 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1653 data Foo a (b :: * -> *) where ...
1659 You can use strictness annotations, in the obvious places
1660 in the constructor type:
1663 Lit :: !Int -> Term Int
1664 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1665 Pair :: Term a -> Term b -> Term (a,b)
1670 You can use a <literal>deriving</literal> clause on a GADT-style data type
1671 declaration. For example, these two declarations are equivalent
1673 data Maybe1 a where {
1674 Nothing1 :: Maybe1 a ;
1675 Just1 :: a -> Maybe1 a
1676 } deriving( Eq, Ord )
1678 data Maybe2 a = Nothing2 | Just2 a
1684 You can use record syntax on a GADT-style data type declaration:
1688 Adult { name :: String, children :: [Person] } :: Person
1689 Child { name :: String } :: Person
1691 As usual, for every constructor that has a field <literal>f</literal>, the type of
1692 field <literal>f</literal> must be the same (modulo alpha conversion).
1695 At the moment, record updates are not yet possible with GADT-style declarations,
1696 so support is limited to record construction, selection and pattern matching.
1699 aPerson = Adult { name = "Fred", children = [] }
1701 shortName :: Person -> Bool
1702 hasChildren (Adult { children = kids }) = not (null kids)
1703 hasChildren (Child {}) = False
1708 As in the case of existentials declared using the Haskell-98-like record syntax
1709 (<xref linkend="existential-records"/>),
1710 record-selector functions are generated only for those fields that have well-typed
1712 Here is the example of that section, in GADT-style syntax:
1714 data Counter a where
1715 NewCounter { _this :: self
1716 , _inc :: self -> self
1717 , _display :: self -> IO ()
1722 As before, only one selector function is generated here, that for <literal>tag</literal>.
1723 Nevertheless, you can still use all the field names in pattern matching and record construction.
1725 </itemizedlist></para>
1729 <title>Generalised Algebraic Data Types (GADTs)</title>
1731 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1732 by allowing constructors to have richer return types. Here is an example:
1735 Lit :: Int -> Term Int
1736 Succ :: Term Int -> Term Int
1737 IsZero :: Term Int -> Term Bool
1738 If :: Term Bool -> Term a -> Term a -> Term a
1739 Pair :: Term a -> Term b -> Term (a,b)
1741 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1742 case with ordinary data types. This generality allows us to
1743 write a well-typed <literal>eval</literal> function
1744 for these <literal>Terms</literal>:
1748 eval (Succ t) = 1 + eval t
1749 eval (IsZero t) = eval t == 0
1750 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1751 eval (Pair e1 e2) = (eval e1, eval e2)
1753 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1754 For example, in the right hand side of the equation
1759 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1760 A precise specification of the type rules is beyond what this user manual aspires to,
1761 but the design closely follows that described in
1763 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1764 unification-based type inference for GADTs</ulink>,
1766 The general principle is this: <emphasis>type refinement is only carried out
1767 based on user-supplied type annotations</emphasis>.
1768 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1769 and lots of obscure error messages will
1770 occur. However, the refinement is quite general. For example, if we had:
1772 eval :: Term a -> a -> a
1773 eval (Lit i) j = i+j
1775 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1776 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1777 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1780 These and many other examples are given in papers by Hongwei Xi, and
1781 Tim Sheard. There is a longer introduction
1782 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1784 <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
1785 may use different notation to that implemented in GHC.
1788 The rest of this section outlines the extensions to GHC that support GADTs.
1791 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1792 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1793 The result type of each constructor must begin with the type constructor being defined,
1794 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1795 For example, in the <literal>Term</literal> data
1796 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1797 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1802 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1803 an ordianary data type.
1807 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1811 Lit { val :: Int } :: Term Int
1812 Succ { num :: Term Int } :: Term Int
1813 Pred { num :: Term Int } :: Term Int
1814 IsZero { arg :: Term Int } :: Term Bool
1815 Pair { arg1 :: Term a
1818 If { cnd :: Term Bool
1823 However, for GADTs there is the following additional constraint:
1824 every constructor that has a field <literal>f</literal> must have
1825 the same result type (modulo alpha conversion)
1826 Hence, in the above example, we cannot merge the <literal>num</literal>
1827 and <literal>arg</literal> fields above into a
1828 single name. Although their field types are both <literal>Term Int</literal>,
1829 their selector functions actually have different types:
1832 num :: Term Int -> Term Int
1833 arg :: Term Bool -> Term Int
1842 <!-- ====================== End of Generalised algebraic data types ======================= -->
1845 <sect2 id="deriving-typeable">
1846 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1849 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1850 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1851 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1852 classes <literal>Eq</literal>, <literal>Ord</literal>,
1853 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1856 GHC extends this list with two more classes that may be automatically derived
1857 (provided the <option>-fglasgow-exts</option> flag is specified):
1858 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1859 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1860 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1862 <para>An instance of <literal>Typeable</literal> can only be derived if the
1863 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1864 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1866 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1867 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1869 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1870 are used, and only <literal>Typeable1</literal> up to
1871 <literal>Typeable7</literal> are provided in the library.)
1872 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1873 class, whose kind suits that of the data type constructor, and
1874 then writing the data type instance by hand.
1878 <sect2 id="newtype-deriving">
1879 <title>Generalised derived instances for newtypes</title>
1882 When you define an abstract type using <literal>newtype</literal>, you may want
1883 the new type to inherit some instances from its representation. In
1884 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1885 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1886 other classes you have to write an explicit instance declaration. For
1887 example, if you define
1890 newtype Dollars = Dollars Int
1893 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1894 explicitly define an instance of <literal>Num</literal>:
1897 instance Num Dollars where
1898 Dollars a + Dollars b = Dollars (a+b)
1901 All the instance does is apply and remove the <literal>newtype</literal>
1902 constructor. It is particularly galling that, since the constructor
1903 doesn't appear at run-time, this instance declaration defines a
1904 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1905 dictionary, only slower!
1909 <sect3> <title> Generalising the deriving clause </title>
1911 GHC now permits such instances to be derived instead, so one can write
1913 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1916 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1917 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1918 derives an instance declaration of the form
1921 instance Num Int => Num Dollars
1924 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1928 We can also derive instances of constructor classes in a similar
1929 way. For example, suppose we have implemented state and failure monad
1930 transformers, such that
1933 instance Monad m => Monad (State s m)
1934 instance Monad m => Monad (Failure m)
1936 In Haskell 98, we can define a parsing monad by
1938 type Parser tok m a = State [tok] (Failure m) a
1941 which is automatically a monad thanks to the instance declarations
1942 above. With the extension, we can make the parser type abstract,
1943 without needing to write an instance of class <literal>Monad</literal>, via
1946 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1949 In this case the derived instance declaration is of the form
1951 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1954 Notice that, since <literal>Monad</literal> is a constructor class, the
1955 instance is a <emphasis>partial application</emphasis> of the new type, not the
1956 entire left hand side. We can imagine that the type declaration is
1957 ``eta-converted'' to generate the context of the instance
1962 We can even derive instances of multi-parameter classes, provided the
1963 newtype is the last class parameter. In this case, a ``partial
1964 application'' of the class appears in the <literal>deriving</literal>
1965 clause. For example, given the class
1968 class StateMonad s m | m -> s where ...
1969 instance Monad m => StateMonad s (State s m) where ...
1971 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1973 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1974 deriving (Monad, StateMonad [tok])
1977 The derived instance is obtained by completing the application of the
1978 class to the new type:
1981 instance StateMonad [tok] (State [tok] (Failure m)) =>
1982 StateMonad [tok] (Parser tok m)
1987 As a result of this extension, all derived instances in newtype
1988 declarations are treated uniformly (and implemented just by reusing
1989 the dictionary for the representation type), <emphasis>except</emphasis>
1990 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
1991 the newtype and its representation.
1995 <sect3> <title> A more precise specification </title>
1997 Derived instance declarations are constructed as follows. Consider the
1998 declaration (after expansion of any type synonyms)
2001 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2007 The <literal>ci</literal> are partial applications of
2008 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2009 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2012 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2015 The type <literal>t</literal> is an arbitrary type.
2018 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2019 nor in the <literal>ci</literal>, and
2022 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2023 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2024 should not "look through" the type or its constructor. You can still
2025 derive these classes for a newtype, but it happens in the usual way, not
2026 via this new mechanism.
2029 Then, for each <literal>ci</literal>, the derived instance
2032 instance ci t => ci (T v1...vk)
2034 As an example which does <emphasis>not</emphasis> work, consider
2036 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2038 Here we cannot derive the instance
2040 instance Monad (State s m) => Monad (NonMonad m)
2043 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2044 and so cannot be "eta-converted" away. It is a good thing that this
2045 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2046 not, in fact, a monad --- for the same reason. Try defining
2047 <literal>>>=</literal> with the correct type: you won't be able to.
2051 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2052 important, since we can only derive instances for the last one. If the
2053 <literal>StateMonad</literal> class above were instead defined as
2056 class StateMonad m s | m -> s where ...
2059 then we would not have been able to derive an instance for the
2060 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2061 classes usually have one "main" parameter for which deriving new
2062 instances is most interesting.
2064 <para>Lastly, all of this applies only for classes other than
2065 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2066 and <literal>Data</literal>, for which the built-in derivation applies (section
2067 4.3.3. of the Haskell Report).
2068 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2069 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2070 the standard method is used or the one described here.)
2076 <sect2 id="stand-alone-deriving">
2077 <title>Stand-alone deriving declarations</title>
2080 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2082 data Foo a = Bar a | Baz String
2084 derive instance Eq (Foo a)
2086 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2087 you can use it as a variable name elsewhere.</para>
2088 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2089 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2092 newtype Foo a = MkFoo (State Int a)
2094 derive instance MonadState Int Foo
2096 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2097 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2105 <!-- TYPE SYSTEM EXTENSIONS -->
2106 <sect1 id="other-type-extensions">
2107 <title>Other type system extensions</title>
2109 <sect2 id="multi-param-type-classes">
2110 <title>Class declarations</title>
2113 This section, and the next one, documents GHC's type-class extensions.
2114 There's lots of background in the paper <ulink
2115 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2116 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2117 Jones, Erik Meijer).
2120 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2124 <title>Multi-parameter type classes</title>
2126 Multi-parameter type classes are permitted. For example:
2130 class Collection c a where
2131 union :: c a -> c a -> c a
2139 <title>The superclasses of a class declaration</title>
2142 There are no restrictions on the context in a class declaration
2143 (which introduces superclasses), except that the class hierarchy must
2144 be acyclic. So these class declarations are OK:
2148 class Functor (m k) => FiniteMap m k where
2151 class (Monad m, Monad (t m)) => Transform t m where
2152 lift :: m a -> (t m) a
2158 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2159 of "acyclic" involves only the superclass relationships. For example,
2165 op :: D b => a -> b -> b
2168 class C a => D a where { ... }
2172 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2173 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2174 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2181 <sect3 id="class-method-types">
2182 <title>Class method types</title>
2185 Haskell 98 prohibits class method types to mention constraints on the
2186 class type variable, thus:
2189 fromList :: [a] -> s a
2190 elem :: Eq a => a -> s a -> Bool
2192 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2193 contains the constraint <literal>Eq a</literal>, constrains only the
2194 class type variable (in this case <literal>a</literal>).
2195 GHC lifts this restriction.
2202 <sect2 id="functional-dependencies">
2203 <title>Functional dependencies
2206 <para> Functional dependencies are implemented as described by Mark Jones
2207 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2208 In Proceedings of the 9th European Symposium on Programming,
2209 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2213 Functional dependencies are introduced by a vertical bar in the syntax of a
2214 class declaration; e.g.
2216 class (Monad m) => MonadState s m | m -> s where ...
2218 class Foo a b c | a b -> c where ...
2220 There should be more documentation, but there isn't (yet). Yell if you need it.
2223 <sect3><title>Rules for functional dependencies </title>
2225 In a class declaration, all of the class type variables must be reachable (in the sense
2226 mentioned in <xref linkend="type-restrictions"/>)
2227 from the free variables of each method type.
2231 class Coll s a where
2233 insert :: s -> a -> s
2236 is not OK, because the type of <literal>empty</literal> doesn't mention
2237 <literal>a</literal>. Functional dependencies can make the type variable
2240 class Coll s a | s -> a where
2242 insert :: s -> a -> s
2245 Alternatively <literal>Coll</literal> might be rewritten
2248 class Coll s a where
2250 insert :: s a -> a -> s a
2254 which makes the connection between the type of a collection of
2255 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2256 Occasionally this really doesn't work, in which case you can split the
2264 class CollE s => Coll s a where
2265 insert :: s -> a -> s
2272 <title>Background on functional dependencies</title>
2274 <para>The following description of the motivation and use of functional dependencies is taken
2275 from the Hugs user manual, reproduced here (with minor changes) by kind
2276 permission of Mark Jones.
2279 Consider the following class, intended as part of a
2280 library for collection types:
2282 class Collects e ce where
2284 insert :: e -> ce -> ce
2285 member :: e -> ce -> Bool
2287 The type variable e used here represents the element type, while ce is the type
2288 of the container itself. Within this framework, we might want to define
2289 instances of this class for lists or characteristic functions (both of which
2290 can be used to represent collections of any equality type), bit sets (which can
2291 be used to represent collections of characters), or hash tables (which can be
2292 used to represent any collection whose elements have a hash function). Omitting
2293 standard implementation details, this would lead to the following declarations:
2295 instance Eq e => Collects e [e] where ...
2296 instance Eq e => Collects e (e -> Bool) where ...
2297 instance Collects Char BitSet where ...
2298 instance (Hashable e, Collects a ce)
2299 => Collects e (Array Int ce) where ...
2301 All this looks quite promising; we have a class and a range of interesting
2302 implementations. Unfortunately, there are some serious problems with the class
2303 declaration. First, the empty function has an ambiguous type:
2305 empty :: Collects e ce => ce
2307 By "ambiguous" we mean that there is a type variable e that appears on the left
2308 of the <literal>=></literal> symbol, but not on the right. The problem with
2309 this is that, according to the theoretical foundations of Haskell overloading,
2310 we cannot guarantee a well-defined semantics for any term with an ambiguous
2314 We can sidestep this specific problem by removing the empty member from the
2315 class declaration. However, although the remaining members, insert and member,
2316 do not have ambiguous types, we still run into problems when we try to use
2317 them. For example, consider the following two functions:
2319 f x y = insert x . insert y
2322 for which GHC infers the following types:
2324 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2325 g :: (Collects Bool c, Collects Char c) => c -> c
2327 Notice that the type for f allows the two parameters x and y to be assigned
2328 different types, even though it attempts to insert each of the two values, one
2329 after the other, into the same collection. If we're trying to model collections
2330 that contain only one type of value, then this is clearly an inaccurate
2331 type. Worse still, the definition for g is accepted, without causing a type
2332 error. As a result, the error in this code will not be flagged at the point
2333 where it appears. Instead, it will show up only when we try to use g, which
2334 might even be in a different module.
2337 <sect4><title>An attempt to use constructor classes</title>
2340 Faced with the problems described above, some Haskell programmers might be
2341 tempted to use something like the following version of the class declaration:
2343 class Collects e c where
2345 insert :: e -> c e -> c e
2346 member :: e -> c e -> Bool
2348 The key difference here is that we abstract over the type constructor c that is
2349 used to form the collection type c e, and not over that collection type itself,
2350 represented by ce in the original class declaration. This avoids the immediate
2351 problems that we mentioned above: empty has type <literal>Collects e c => c
2352 e</literal>, which is not ambiguous.
2355 The function f from the previous section has a more accurate type:
2357 f :: (Collects e c) => e -> e -> c e -> c e
2359 The function g from the previous section is now rejected with a type error as
2360 we would hope because the type of f does not allow the two arguments to have
2362 This, then, is an example of a multiple parameter class that does actually work
2363 quite well in practice, without ambiguity problems.
2364 There is, however, a catch. This version of the Collects class is nowhere near
2365 as general as the original class seemed to be: only one of the four instances
2366 for <literal>Collects</literal>
2367 given above can be used with this version of Collects because only one of
2368 them---the instance for lists---has a collection type that can be written in
2369 the form c e, for some type constructor c, and element type e.
2373 <sect4><title>Adding functional dependencies</title>
2376 To get a more useful version of the Collects class, Hugs provides a mechanism
2377 that allows programmers to specify dependencies between the parameters of a
2378 multiple parameter class (For readers with an interest in theoretical
2379 foundations and previous work: The use of dependency information can be seen
2380 both as a generalization of the proposal for `parametric type classes' that was
2381 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2382 later framework for "improvement" of qualified types. The
2383 underlying ideas are also discussed in a more theoretical and abstract setting
2384 in a manuscript [implparam], where they are identified as one point in a
2385 general design space for systems of implicit parameterization.).
2387 To start with an abstract example, consider a declaration such as:
2389 class C a b where ...
2391 which tells us simply that C can be thought of as a binary relation on types
2392 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2393 included in the definition of classes to add information about dependencies
2394 between parameters, as in the following examples:
2396 class D a b | a -> b where ...
2397 class E a b | a -> b, b -> a where ...
2399 The notation <literal>a -> b</literal> used here between the | and where
2400 symbols --- not to be
2401 confused with a function type --- indicates that the a parameter uniquely
2402 determines the b parameter, and might be read as "a determines b." Thus D is
2403 not just a relation, but actually a (partial) function. Similarly, from the two
2404 dependencies that are included in the definition of E, we can see that E
2405 represents a (partial) one-one mapping between types.
2408 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2409 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2410 m>=0, meaning that the y parameters are uniquely determined by the x
2411 parameters. Spaces can be used as separators if more than one variable appears
2412 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2413 annotated with multiple dependencies using commas as separators, as in the
2414 definition of E above. Some dependencies that we can write in this notation are
2415 redundant, and will be rejected because they don't serve any useful
2416 purpose, and may instead indicate an error in the program. Examples of
2417 dependencies like this include <literal>a -> a </literal>,
2418 <literal>a -> a a </literal>,
2419 <literal>a -> </literal>, etc. There can also be
2420 some redundancy if multiple dependencies are given, as in
2421 <literal>a->b</literal>,
2422 <literal>b->c </literal>, <literal>a->c </literal>, and
2423 in which some subset implies the remaining dependencies. Examples like this are
2424 not treated as errors. Note that dependencies appear only in class
2425 declarations, and not in any other part of the language. In particular, the
2426 syntax for instance declarations, class constraints, and types is completely
2430 By including dependencies in a class declaration, we provide a mechanism for
2431 the programmer to specify each multiple parameter class more precisely. The
2432 compiler, on the other hand, is responsible for ensuring that the set of
2433 instances that are in scope at any given point in the program is consistent
2434 with any declared dependencies. For example, the following pair of instance
2435 declarations cannot appear together in the same scope because they violate the
2436 dependency for D, even though either one on its own would be acceptable:
2438 instance D Bool Int where ...
2439 instance D Bool Char where ...
2441 Note also that the following declaration is not allowed, even by itself:
2443 instance D [a] b where ...
2445 The problem here is that this instance would allow one particular choice of [a]
2446 to be associated with more than one choice for b, which contradicts the
2447 dependency specified in the definition of D. More generally, this means that,
2448 in any instance of the form:
2450 instance D t s where ...
2452 for some particular types t and s, the only variables that can appear in s are
2453 the ones that appear in t, and hence, if the type t is known, then s will be
2454 uniquely determined.
2457 The benefit of including dependency information is that it allows us to define
2458 more general multiple parameter classes, without ambiguity problems, and with
2459 the benefit of more accurate types. To illustrate this, we return to the
2460 collection class example, and annotate the original definition of <literal>Collects</literal>
2461 with a simple dependency:
2463 class Collects e ce | ce -> e where
2465 insert :: e -> ce -> ce
2466 member :: e -> ce -> Bool
2468 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2469 determined by the type of the collection ce. Note that both parameters of
2470 Collects are of kind *; there are no constructor classes here. Note too that
2471 all of the instances of Collects that we gave earlier can be used
2472 together with this new definition.
2475 What about the ambiguity problems that we encountered with the original
2476 definition? The empty function still has type Collects e ce => ce, but it is no
2477 longer necessary to regard that as an ambiguous type: Although the variable e
2478 does not appear on the right of the => symbol, the dependency for class
2479 Collects tells us that it is uniquely determined by ce, which does appear on
2480 the right of the => symbol. Hence the context in which empty is used can still
2481 give enough information to determine types for both ce and e, without
2482 ambiguity. More generally, we need only regard a type as ambiguous if it
2483 contains a variable on the left of the => that is not uniquely determined
2484 (either directly or indirectly) by the variables on the right.
2487 Dependencies also help to produce more accurate types for user defined
2488 functions, and hence to provide earlier detection of errors, and less cluttered
2489 types for programmers to work with. Recall the previous definition for a
2492 f x y = insert x y = insert x . insert y
2494 for which we originally obtained a type:
2496 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2498 Given the dependency information that we have for Collects, however, we can
2499 deduce that a and b must be equal because they both appear as the second
2500 parameter in a Collects constraint with the same first parameter c. Hence we
2501 can infer a shorter and more accurate type for f:
2503 f :: (Collects a c) => a -> a -> c -> c
2505 In a similar way, the earlier definition of g will now be flagged as a type error.
2508 Although we have given only a few examples here, it should be clear that the
2509 addition of dependency information can help to make multiple parameter classes
2510 more useful in practice, avoiding ambiguity problems, and allowing more general
2511 sets of instance declarations.
2517 <sect2 id="instance-decls">
2518 <title>Instance declarations</title>
2520 <sect3 id="instance-rules">
2521 <title>Relaxed rules for instance declarations</title>
2523 <para>An instance declaration has the form
2525 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 ...
2527 The part before the "<literal>=></literal>" is the
2528 <emphasis>context</emphasis>, while the part after the
2529 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2533 In Haskell 98 the head of an instance declaration
2534 must be of the form <literal>C (T a1 ... an)</literal>, where
2535 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2536 and the <literal>a1 ... an</literal> are distinct type variables.
2537 Furthermore, the assertions in the context of the instance declaration
2538 must be of the form <literal>C a</literal> where <literal>a</literal>
2539 is a type variable that occurs in the head.
2542 The <option>-fglasgow-exts</option> flag loosens these restrictions
2543 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2544 the context and head of the instance declaration can each consist of arbitrary
2545 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2549 The Paterson Conditions: for each assertion in the context
2551 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2552 <listitem><para>The assertion has fewer constructors and variables (taken together
2553 and counting repetitions) than the head</para></listitem>
2557 <listitem><para>The Coverage Condition. For each functional dependency,
2558 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2559 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2560 every type variable in
2561 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2562 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2563 substitution mapping each type variable in the class declaration to the
2564 corresponding type in the instance declaration.
2567 These restrictions ensure that context reduction terminates: each reduction
2568 step makes the problem smaller by at least one
2569 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2570 if you give the <option>-fallow-undecidable-instances</option>
2571 flag (<xref linkend="undecidable-instances"/>).
2572 You can find lots of background material about the reason for these
2573 restrictions in the paper <ulink
2574 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2575 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2578 For example, these are OK:
2580 instance C Int [a] -- Multiple parameters
2581 instance Eq (S [a]) -- Structured type in head
2583 -- Repeated type variable in head
2584 instance C4 a a => C4 [a] [a]
2585 instance Stateful (ST s) (MutVar s)
2587 -- Head can consist of type variables only
2589 instance (Eq a, Show b) => C2 a b
2591 -- Non-type variables in context
2592 instance Show (s a) => Show (Sized s a)
2593 instance C2 Int a => C3 Bool [a]
2594 instance C2 Int a => C3 [a] b
2598 -- Context assertion no smaller than head
2599 instance C a => C a where ...
2600 -- (C b b) has more more occurrences of b than the head
2601 instance C b b => Foo [b] where ...
2606 The same restrictions apply to instances generated by
2607 <literal>deriving</literal> clauses. Thus the following is accepted:
2609 data MinHeap h a = H a (h a)
2612 because the derived instance
2614 instance (Show a, Show (h a)) => Show (MinHeap h a)
2616 conforms to the above rules.
2620 A useful idiom permitted by the above rules is as follows.
2621 If one allows overlapping instance declarations then it's quite
2622 convenient to have a "default instance" declaration that applies if
2623 something more specific does not:
2631 <sect3 id="undecidable-instances">
2632 <title>Undecidable instances</title>
2635 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2636 For example, sometimes you might want to use the following to get the
2637 effect of a "class synonym":
2639 class (C1 a, C2 a, C3 a) => C a where { }
2641 instance (C1 a, C2 a, C3 a) => C a where { }
2643 This allows you to write shorter signatures:
2649 f :: (C1 a, C2 a, C3 a) => ...
2651 The restrictions on functional dependencies (<xref
2652 linkend="functional-dependencies"/>) are particularly troublesome.
2653 It is tempting to introduce type variables in the context that do not appear in
2654 the head, something that is excluded by the normal rules. For example:
2656 class HasConverter a b | a -> b where
2659 data Foo a = MkFoo a
2661 instance (HasConverter a b,Show b) => Show (Foo a) where
2662 show (MkFoo value) = show (convert value)
2664 This is dangerous territory, however. Here, for example, is a program that would make the
2669 instance F [a] [[a]]
2670 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2672 Similarly, it can be tempting to lift the coverage condition:
2674 class Mul a b c | a b -> c where
2675 (.*.) :: a -> b -> c
2677 instance Mul Int Int Int where (.*.) = (*)
2678 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2679 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2681 The third instance declaration does not obey the coverage condition;
2682 and indeed the (somewhat strange) definition:
2684 f = \ b x y -> if b then x .*. [y] else y
2686 makes instance inference go into a loop, because it requires the constraint
2687 <literal>(Mul a [b] b)</literal>.
2690 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2691 the experimental flag <option>-fallow-undecidable-instances</option>
2692 <indexterm><primary>-fallow-undecidable-instances
2693 option</primary></indexterm>, both the Paterson Conditions and the Coverage Condition
2694 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2695 fixed-depth recursion stack. If you exceed the stack depth you get a
2696 sort of backtrace, and the opportunity to increase the stack depth
2697 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2703 <sect3 id="instance-overlap">
2704 <title>Overlapping instances</title>
2706 In general, <emphasis>GHC requires that that it be unambiguous which instance
2708 should be used to resolve a type-class constraint</emphasis>. This behaviour
2709 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2710 <indexterm><primary>-fallow-overlapping-instances
2711 </primary></indexterm>
2712 and <option>-fallow-incoherent-instances</option>
2713 <indexterm><primary>-fallow-incoherent-instances
2714 </primary></indexterm>, as this section discusses. Both these
2715 flags are dynamic flags, and can be set on a per-module basis, using
2716 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2718 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2719 it tries to match every instance declaration against the
2721 by instantiating the head of the instance declaration. For example, consider
2724 instance context1 => C Int a where ... -- (A)
2725 instance context2 => C a Bool where ... -- (B)
2726 instance context3 => C Int [a] where ... -- (C)
2727 instance context4 => C Int [Int] where ... -- (D)
2729 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2730 but (C) and (D) do not. When matching, GHC takes
2731 no account of the context of the instance declaration
2732 (<literal>context1</literal> etc).
2733 GHC's default behaviour is that <emphasis>exactly one instance must match the
2734 constraint it is trying to resolve</emphasis>.
2735 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2736 including both declarations (A) and (B), say); an error is only reported if a
2737 particular constraint matches more than one.
2741 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2742 more than one instance to match, provided there is a most specific one. For
2743 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2744 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2745 most-specific match, the program is rejected.
2748 However, GHC is conservative about committing to an overlapping instance. For example:
2753 Suppose that from the RHS of <literal>f</literal> we get the constraint
2754 <literal>C Int [b]</literal>. But
2755 GHC does not commit to instance (C), because in a particular
2756 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2757 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2758 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2759 GHC will instead pick (C), without complaining about
2760 the problem of subsequent instantiations.
2763 The willingness to be overlapped or incoherent is a property of
2764 the <emphasis>instance declaration</emphasis> itself, controlled by the
2765 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2766 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2767 being defined. Neither flag is required in a module that imports and uses the
2768 instance declaration. Specifically, during the lookup process:
2771 An instance declaration is ignored during the lookup process if (a) a more specific
2772 match is found, and (b) the instance declaration was compiled with
2773 <option>-fallow-overlapping-instances</option>. The flag setting for the
2774 more-specific instance does not matter.
2777 Suppose an instance declaration does not matche the constraint being looked up, but
2778 does unify with it, so that it might match when the constraint is further
2779 instantiated. Usually GHC will regard this as a reason for not committing to
2780 some other constraint. But if the instance declaration was compiled with
2781 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2782 check for that declaration.
2785 These rules make it possible for a library author to design a library that relies on
2786 overlapping instances without the library client having to know.
2789 If an instance declaration is compiled without
2790 <option>-fallow-overlapping-instances</option>,
2791 then that instance can never be overlapped. This could perhaps be
2792 inconvenient. Perhaps the rule should instead say that the
2793 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2794 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2795 at a usage site should be permitted regardless of how the instance declarations
2796 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2797 used at the usage site. (Mind you, the exact usage site can occasionally be
2798 hard to pin down.) We are interested to receive feedback on these points.
2800 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2801 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2806 <title>Type synonyms in the instance head</title>
2809 <emphasis>Unlike Haskell 98, instance heads may use type
2810 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2811 As always, using a type synonym is just shorthand for
2812 writing the RHS of the type synonym definition. For example:
2816 type Point = (Int,Int)
2817 instance C Point where ...
2818 instance C [Point] where ...
2822 is legal. However, if you added
2826 instance C (Int,Int) where ...
2830 as well, then the compiler will complain about the overlapping
2831 (actually, identical) instance declarations. As always, type synonyms
2832 must be fully applied. You cannot, for example, write:
2837 instance Monad P where ...
2841 This design decision is independent of all the others, and easily
2842 reversed, but it makes sense to me.
2850 <sect2 id="type-restrictions">
2851 <title>Type signatures</title>
2853 <sect3><title>The context of a type signature</title>
2855 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2856 the form <emphasis>(class type-variable)</emphasis> or
2857 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2858 these type signatures are perfectly OK
2861 g :: Ord (T a ()) => ...
2865 GHC imposes the following restrictions on the constraints in a type signature.
2869 forall tv1..tvn (c1, ...,cn) => type
2872 (Here, we write the "foralls" explicitly, although the Haskell source
2873 language omits them; in Haskell 98, all the free type variables of an
2874 explicit source-language type signature are universally quantified,
2875 except for the class type variables in a class declaration. However,
2876 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2885 <emphasis>Each universally quantified type variable
2886 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2888 A type variable <literal>a</literal> is "reachable" if it it appears
2889 in the same constraint as either a type variable free in in
2890 <literal>type</literal>, or another reachable type variable.
2891 A value with a type that does not obey
2892 this reachability restriction cannot be used without introducing
2893 ambiguity; that is why the type is rejected.
2894 Here, for example, is an illegal type:
2898 forall a. Eq a => Int
2902 When a value with this type was used, the constraint <literal>Eq tv</literal>
2903 would be introduced where <literal>tv</literal> is a fresh type variable, and
2904 (in the dictionary-translation implementation) the value would be
2905 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2906 can never know which instance of <literal>Eq</literal> to use because we never
2907 get any more information about <literal>tv</literal>.
2911 that the reachability condition is weaker than saying that <literal>a</literal> is
2912 functionally dependent on a type variable free in
2913 <literal>type</literal> (see <xref
2914 linkend="functional-dependencies"/>). The reason for this is there
2915 might be a "hidden" dependency, in a superclass perhaps. So
2916 "reachable" is a conservative approximation to "functionally dependent".
2917 For example, consider:
2919 class C a b | a -> b where ...
2920 class C a b => D a b where ...
2921 f :: forall a b. D a b => a -> a
2923 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2924 but that is not immediately apparent from <literal>f</literal>'s type.
2930 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2931 universally quantified type variables <literal>tvi</literal></emphasis>.
2933 For example, this type is OK because <literal>C a b</literal> mentions the
2934 universally quantified type variable <literal>b</literal>:
2938 forall a. C a b => burble
2942 The next type is illegal because the constraint <literal>Eq b</literal> does not
2943 mention <literal>a</literal>:
2947 forall a. Eq b => burble
2951 The reason for this restriction is milder than the other one. The
2952 excluded types are never useful or necessary (because the offending
2953 context doesn't need to be witnessed at this point; it can be floated
2954 out). Furthermore, floating them out increases sharing. Lastly,
2955 excluding them is a conservative choice; it leaves a patch of
2956 territory free in case we need it later.
2970 <sect2 id="implicit-parameters">
2971 <title>Implicit parameters</title>
2973 <para> Implicit parameters are implemented as described in
2974 "Implicit parameters: dynamic scoping with static types",
2975 J Lewis, MB Shields, E Meijer, J Launchbury,
2976 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2980 <para>(Most of the following, stil rather incomplete, documentation is
2981 due to Jeff Lewis.)</para>
2983 <para>Implicit parameter support is enabled with the option
2984 <option>-fimplicit-params</option>.</para>
2987 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2988 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2989 context. In Haskell, all variables are statically bound. Dynamic
2990 binding of variables is a notion that goes back to Lisp, but was later
2991 discarded in more modern incarnations, such as Scheme. Dynamic binding
2992 can be very confusing in an untyped language, and unfortunately, typed
2993 languages, in particular Hindley-Milner typed languages like Haskell,
2994 only support static scoping of variables.
2997 However, by a simple extension to the type class system of Haskell, we
2998 can support dynamic binding. Basically, we express the use of a
2999 dynamically bound variable as a constraint on the type. These
3000 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
3001 function uses a dynamically-bound variable <literal>?x</literal>
3002 of type <literal>t'</literal>". For
3003 example, the following expresses the type of a sort function,
3004 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3006 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3008 The dynamic binding constraints are just a new form of predicate in the type class system.
3011 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3012 where <literal>x</literal> is
3013 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3014 Use of this construct also introduces a new
3015 dynamic-binding constraint in the type of the expression.
3016 For example, the following definition
3017 shows how we can define an implicitly parameterized sort function in
3018 terms of an explicitly parameterized <literal>sortBy</literal> function:
3020 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3022 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3028 <title>Implicit-parameter type constraints</title>
3030 Dynamic binding constraints behave just like other type class
3031 constraints in that they are automatically propagated. Thus, when a
3032 function is used, its implicit parameters are inherited by the
3033 function that called it. For example, our <literal>sort</literal> function might be used
3034 to pick out the least value in a list:
3036 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3037 least xs = head (sort xs)
3039 Without lifting a finger, the <literal>?cmp</literal> parameter is
3040 propagated to become a parameter of <literal>least</literal> as well. With explicit
3041 parameters, the default is that parameters must always be explicit
3042 propagated. With implicit parameters, the default is to always
3046 An implicit-parameter type constraint differs from other type class constraints in the
3047 following way: All uses of a particular implicit parameter must have
3048 the same type. This means that the type of <literal>(?x, ?x)</literal>
3049 is <literal>(?x::a) => (a,a)</literal>, and not
3050 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3054 <para> You can't have an implicit parameter in the context of a class or instance
3055 declaration. For example, both these declarations are illegal:
3057 class (?x::Int) => C a where ...
3058 instance (?x::a) => Foo [a] where ...
3060 Reason: exactly which implicit parameter you pick up depends on exactly where
3061 you invoke a function. But the ``invocation'' of instance declarations is done
3062 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3063 Easiest thing is to outlaw the offending types.</para>
3065 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3067 f :: (?x :: [a]) => Int -> Int
3070 g :: (Read a, Show a) => String -> String
3073 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3074 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3075 quite unambiguous, and fixes the type <literal>a</literal>.
3080 <title>Implicit-parameter bindings</title>
3083 An implicit parameter is <emphasis>bound</emphasis> using the standard
3084 <literal>let</literal> or <literal>where</literal> binding forms.
3085 For example, we define the <literal>min</literal> function by binding
3086 <literal>cmp</literal>.
3089 min = let ?cmp = (<=) in least
3093 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3094 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3095 (including in a list comprehension, or do-notation, or pattern guards),
3096 or a <literal>where</literal> clause.
3097 Note the following points:
3100 An implicit-parameter binding group must be a
3101 collection of simple bindings to implicit-style variables (no
3102 function-style bindings, and no type signatures); these bindings are
3103 neither polymorphic or recursive.
3106 You may not mix implicit-parameter bindings with ordinary bindings in a
3107 single <literal>let</literal>
3108 expression; use two nested <literal>let</literal>s instead.
3109 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3113 You may put multiple implicit-parameter bindings in a
3114 single binding group; but they are <emphasis>not</emphasis> treated
3115 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3116 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3117 parameter. The bindings are not nested, and may be re-ordered without changing
3118 the meaning of the program.
3119 For example, consider:
3121 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3123 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3124 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3126 f :: (?x::Int) => Int -> Int
3134 <sect3><title>Implicit parameters and polymorphic recursion</title>
3137 Consider these two definitions:
3140 len1 xs = let ?acc = 0 in len_acc1 xs
3143 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3148 len2 xs = let ?acc = 0 in len_acc2 xs
3150 len_acc2 :: (?acc :: Int) => [a] -> Int
3152 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3154 The only difference between the two groups is that in the second group
3155 <literal>len_acc</literal> is given a type signature.
3156 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3157 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3158 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3159 has a type signature, the recursive call is made to the
3160 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3161 as an implicit parameter. So we get the following results in GHCi:
3168 Adding a type signature dramatically changes the result! This is a rather
3169 counter-intuitive phenomenon, worth watching out for.
3173 <sect3><title>Implicit parameters and monomorphism</title>
3175 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3176 Haskell Report) to implicit parameters. For example, consider:
3184 Since the binding for <literal>y</literal> falls under the Monomorphism
3185 Restriction it is not generalised, so the type of <literal>y</literal> is
3186 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3187 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3188 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3189 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3190 <literal>y</literal> in the body of the <literal>let</literal> will see the
3191 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3192 <literal>14</literal>.
3197 <!-- ======================= COMMENTED OUT ========================
3199 We intend to remove linear implicit parameters, so I'm at least removing
3200 them from the 6.6 user manual
3202 <sect2 id="linear-implicit-parameters">
3203 <title>Linear implicit parameters</title>
3205 Linear implicit parameters are an idea developed by Koen Claessen,
3206 Mark Shields, and Simon PJ. They address the long-standing
3207 problem that monads seem over-kill for certain sorts of problem, notably:
3210 <listitem> <para> distributing a supply of unique names </para> </listitem>
3211 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3212 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3216 Linear implicit parameters are just like ordinary implicit parameters,
3217 except that they are "linear"; that is, they cannot be copied, and
3218 must be explicitly "split" instead. Linear implicit parameters are
3219 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3220 (The '/' in the '%' suggests the split!)
3225 import GHC.Exts( Splittable )
3227 data NameSupply = ...
3229 splitNS :: NameSupply -> (NameSupply, NameSupply)
3230 newName :: NameSupply -> Name
3232 instance Splittable NameSupply where
3236 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3237 f env (Lam x e) = Lam x' (f env e)
3240 env' = extend env x x'
3241 ...more equations for f...
3243 Notice that the implicit parameter %ns is consumed
3245 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3246 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3250 So the translation done by the type checker makes
3251 the parameter explicit:
3253 f :: NameSupply -> Env -> Expr -> Expr
3254 f ns env (Lam x e) = Lam x' (f ns1 env e)
3256 (ns1,ns2) = splitNS ns
3258 env = extend env x x'
3260 Notice the call to 'split' introduced by the type checker.
3261 How did it know to use 'splitNS'? Because what it really did
3262 was to introduce a call to the overloaded function 'split',
3263 defined by the class <literal>Splittable</literal>:
3265 class Splittable a where
3268 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3269 split for name supplies. But we can simply write
3275 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3277 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3278 <literal>GHC.Exts</literal>.
3283 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3284 are entirely distinct implicit parameters: you
3285 can use them together and they won't intefere with each other. </para>
3288 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3290 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3291 in the context of a class or instance declaration. </para></listitem>
3295 <sect3><title>Warnings</title>
3298 The monomorphism restriction is even more important than usual.
3299 Consider the example above:
3301 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3302 f env (Lam x e) = Lam x' (f env e)
3305 env' = extend env x x'
3307 If we replaced the two occurrences of x' by (newName %ns), which is
3308 usually a harmless thing to do, we get:
3310 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3311 f env (Lam x e) = Lam (newName %ns) (f env e)
3313 env' = extend env x (newName %ns)
3315 But now the name supply is consumed in <emphasis>three</emphasis> places
3316 (the two calls to newName,and the recursive call to f), so
3317 the result is utterly different. Urk! We don't even have
3321 Well, this is an experimental change. With implicit
3322 parameters we have already lost beta reduction anyway, and
3323 (as John Launchbury puts it) we can't sensibly reason about
3324 Haskell programs without knowing their typing.
3329 <sect3><title>Recursive functions</title>
3330 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3333 foo :: %x::T => Int -> [Int]
3335 foo n = %x : foo (n-1)
3337 where T is some type in class Splittable.</para>
3339 Do you get a list of all the same T's or all different T's
3340 (assuming that split gives two distinct T's back)?
3342 If you supply the type signature, taking advantage of polymorphic
3343 recursion, you get what you'd probably expect. Here's the
3344 translated term, where the implicit param is made explicit:
3347 foo x n = let (x1,x2) = split x
3348 in x1 : foo x2 (n-1)
3350 But if you don't supply a type signature, GHC uses the Hindley
3351 Milner trick of using a single monomorphic instance of the function
3352 for the recursive calls. That is what makes Hindley Milner type inference
3353 work. So the translation becomes
3357 foom n = x : foom (n-1)
3361 Result: 'x' is not split, and you get a list of identical T's. So the
3362 semantics of the program depends on whether or not foo has a type signature.
3365 You may say that this is a good reason to dislike linear implicit parameters
3366 and you'd be right. That is why they are an experimental feature.
3372 ================ END OF Linear Implicit Parameters commented out -->
3374 <sect2 id="kinding">
3375 <title>Explicitly-kinded quantification</title>
3378 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3379 to give the kind explicitly as (machine-checked) documentation,
3380 just as it is nice to give a type signature for a function. On some occasions,
3381 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3382 John Hughes had to define the data type:
3384 data Set cxt a = Set [a]
3385 | Unused (cxt a -> ())
3387 The only use for the <literal>Unused</literal> constructor was to force the correct
3388 kind for the type variable <literal>cxt</literal>.
3391 GHC now instead allows you to specify the kind of a type variable directly, wherever
3392 a type variable is explicitly bound. Namely:
3394 <listitem><para><literal>data</literal> declarations:
3396 data Set (cxt :: * -> *) a = Set [a]
3397 </screen></para></listitem>
3398 <listitem><para><literal>type</literal> declarations:
3400 type T (f :: * -> *) = f Int
3401 </screen></para></listitem>
3402 <listitem><para><literal>class</literal> declarations:
3404 class (Eq a) => C (f :: * -> *) a where ...
3405 </screen></para></listitem>
3406 <listitem><para><literal>forall</literal>'s in type signatures:
3408 f :: forall (cxt :: * -> *). Set cxt Int
3409 </screen></para></listitem>
3414 The parentheses are required. Some of the spaces are required too, to
3415 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3416 will get a parse error, because "<literal>::*->*</literal>" is a
3417 single lexeme in Haskell.
3421 As part of the same extension, you can put kind annotations in types
3424 f :: (Int :: *) -> Int
3425 g :: forall a. a -> (a :: *)
3429 atype ::= '(' ctype '::' kind ')
3431 The parentheses are required.
3436 <sect2 id="universal-quantification">
3437 <title>Arbitrary-rank polymorphism
3441 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3442 allows us to say exactly what this means. For example:
3450 g :: forall b. (b -> b)
3452 The two are treated identically.
3456 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3457 explicit universal quantification in
3459 For example, all the following types are legal:
3461 f1 :: forall a b. a -> b -> a
3462 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3464 f2 :: (forall a. a->a) -> Int -> Int
3465 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3467 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3469 f4 :: Int -> (forall a. a -> a)
3471 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3472 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3473 The <literal>forall</literal> makes explicit the universal quantification that
3474 is implicitly added by Haskell.
3477 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3478 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3479 shows, the polymorphic type on the left of the function arrow can be overloaded.
3482 The function <literal>f3</literal> has a rank-3 type;
3483 it has rank-2 types on the left of a function arrow.
3486 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3487 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3488 that restriction has now been lifted.)
3489 In particular, a forall-type (also called a "type scheme"),
3490 including an operational type class context, is legal:
3492 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3493 of a function arrow </para> </listitem>
3494 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3495 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3496 field type signatures.</para> </listitem>
3497 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3498 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3500 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3501 a type variable any more!
3510 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3511 the types of the constructor arguments. Here are several examples:
3517 data T a = T1 (forall b. b -> b -> b) a
3519 data MonadT m = MkMonad { return :: forall a. a -> m a,
3520 bind :: forall a b. m a -> (a -> m b) -> m b
3523 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3529 The constructors have rank-2 types:
3535 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3536 MkMonad :: forall m. (forall a. a -> m a)
3537 -> (forall a b. m a -> (a -> m b) -> m b)
3539 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3545 Notice that you don't need to use a <literal>forall</literal> if there's an
3546 explicit context. For example in the first argument of the
3547 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3548 prefixed to the argument type. The implicit <literal>forall</literal>
3549 quantifies all type variables that are not already in scope, and are
3550 mentioned in the type quantified over.
3554 As for type signatures, implicit quantification happens for non-overloaded
3555 types too. So if you write this:
3558 data T a = MkT (Either a b) (b -> b)
3561 it's just as if you had written this:
3564 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3567 That is, since the type variable <literal>b</literal> isn't in scope, it's
3568 implicitly universally quantified. (Arguably, it would be better
3569 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3570 where that is what is wanted. Feedback welcomed.)
3574 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3575 the constructor to suitable values, just as usual. For example,
3586 a3 = MkSwizzle reverse
3589 a4 = let r x = Just x
3596 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3597 mkTs f x y = [T1 f x, T1 f y]
3603 The type of the argument can, as usual, be more general than the type
3604 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3605 does not need the <literal>Ord</literal> constraint.)
3609 When you use pattern matching, the bound variables may now have
3610 polymorphic types. For example:
3616 f :: T a -> a -> (a, Char)
3617 f (T1 w k) x = (w k x, w 'c' 'd')
3619 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3620 g (MkSwizzle s) xs f = s (map f (s xs))
3622 h :: MonadT m -> [m a] -> m [a]
3623 h m [] = return m []
3624 h m (x:xs) = bind m x $ \y ->
3625 bind m (h m xs) $ \ys ->
3632 In the function <function>h</function> we use the record selectors <literal>return</literal>
3633 and <literal>bind</literal> to extract the polymorphic bind and return functions
3634 from the <literal>MonadT</literal> data structure, rather than using pattern
3640 <title>Type inference</title>
3643 In general, type inference for arbitrary-rank types is undecidable.
3644 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3645 to get a decidable algorithm by requiring some help from the programmer.
3646 We do not yet have a formal specification of "some help" but the rule is this:
3649 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3650 provides an explicit polymorphic type for x, or GHC's type inference will assume
3651 that x's type has no foralls in it</emphasis>.
3654 What does it mean to "provide" an explicit type for x? You can do that by
3655 giving a type signature for x directly, using a pattern type signature
3656 (<xref linkend="scoped-type-variables"/>), thus:
3658 \ f :: (forall a. a->a) -> (f True, f 'c')
3660 Alternatively, you can give a type signature to the enclosing
3661 context, which GHC can "push down" to find the type for the variable:
3663 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3665 Here the type signature on the expression can be pushed inwards
3666 to give a type signature for f. Similarly, and more commonly,
3667 one can give a type signature for the function itself:
3669 h :: (forall a. a->a) -> (Bool,Char)
3670 h f = (f True, f 'c')
3672 You don't need to give a type signature if the lambda bound variable
3673 is a constructor argument. Here is an example we saw earlier:
3675 f :: T a -> a -> (a, Char)
3676 f (T1 w k) x = (w k x, w 'c' 'd')
3678 Here we do not need to give a type signature to <literal>w</literal>, because
3679 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3686 <sect3 id="implicit-quant">
3687 <title>Implicit quantification</title>
3690 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3691 user-written types, if and only if there is no explicit <literal>forall</literal>,
3692 GHC finds all the type variables mentioned in the type that are not already
3693 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3697 f :: forall a. a -> a
3704 h :: forall b. a -> b -> b
3710 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3713 f :: (a -> a) -> Int
3715 f :: forall a. (a -> a) -> Int
3717 f :: (forall a. a -> a) -> Int
3720 g :: (Ord a => a -> a) -> Int
3721 -- MEANS the illegal type
3722 g :: forall a. (Ord a => a -> a) -> Int
3724 g :: (forall a. Ord a => a -> a) -> Int
3726 The latter produces an illegal type, which you might think is silly,
3727 but at least the rule is simple. If you want the latter type, you
3728 can write your for-alls explicitly. Indeed, doing so is strongly advised
3735 <sect2 id="impredicative-polymorphism">
3736 <title>Impredicative polymorphism
3738 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3739 that you can call a polymorphic function at a polymorphic type, and
3740 parameterise data structures over polymorphic types. For example:
3742 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3743 f (Just g) = Just (g [3], g "hello")
3746 Notice here that the <literal>Maybe</literal> type is parameterised by the
3747 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3750 <para>The technical details of this extension are described in the paper
3751 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3752 type inference for higher-rank types and impredicativity</ulink>,
3753 which appeared at ICFP 2006.
3757 <sect2 id="scoped-type-variables">
3758 <title>Lexically scoped type variables
3762 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3763 which some type signatures are simply impossible to write. For example:
3765 f :: forall a. [a] -> [a]
3771 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3772 the entire definition of <literal>f</literal>.
3773 In particular, it is in scope at the type signature for <varname>ys</varname>.
3774 In Haskell 98 it is not possible to declare
3775 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3776 it becomes possible to do so.
3778 <para>Lexically-scoped type variables are enabled by
3779 <option>-fglasgow-exts</option>.
3781 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3782 variables work, compared to earlier releases. Read this section
3786 <title>Overview</title>
3788 <para>The design follows the following principles
3790 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3791 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3792 design.)</para></listitem>
3793 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3794 type variables. This means that every programmer-written type signature
3795 (includin one that contains free scoped type variables) denotes a
3796 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3797 checker, and no inference is involved.</para></listitem>
3798 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3799 changing the program.</para></listitem>
3803 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3805 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3806 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3807 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3808 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3812 In Haskell, a programmer-written type signature is implicitly quantifed over
3813 its free type variables (<ulink
3814 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3816 of the Haskel Report).
3817 Lexically scoped type variables affect this implicit quantification rules
3818 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3819 quantified. For example, if type variable <literal>a</literal> is in scope,
3822 (e :: a -> a) means (e :: a -> a)
3823 (e :: b -> b) means (e :: forall b. b->b)
3824 (e :: a -> b) means (e :: forall b. a->b)
3832 <sect3 id="decl-type-sigs">
3833 <title>Declaration type signatures</title>
3834 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3835 quantification (using <literal>forall</literal>) brings into scope the
3836 explicitly-quantified
3837 type variables, in the definition of the named function(s). For example:
3839 f :: forall a. [a] -> [a]
3840 f (x:xs) = xs ++ [ x :: a ]
3842 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3843 the definition of "<literal>f</literal>".
3845 <para>This only happens if the quantification in <literal>f</literal>'s type
3846 signature is explicit. For example:
3849 g (x:xs) = xs ++ [ x :: a ]
3851 This program will be rejected, because "<literal>a</literal>" does not scope
3852 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3853 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3854 quantification rules.
3858 <sect3 id="exp-type-sigs">
3859 <title>Expression type signatures</title>
3861 <para>An expression type signature that has <emphasis>explicit</emphasis>
3862 quantification (using <literal>forall</literal>) brings into scope the
3863 explicitly-quantified
3864 type variables, in the annotated expression. For example:
3866 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3868 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3869 type variable <literal>s</literal> into scope, in the annotated expression
3870 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3875 <sect3 id="pattern-type-sigs">
3876 <title>Pattern type signatures</title>
3878 A type signature may occur in any pattern; this is a <emphasis>pattern type
3879 signature</emphasis>.
3882 -- f and g assume that 'a' is already in scope
3883 f = \(x::Int, y::a) -> x
3885 h ((x,y) :: (Int,Bool)) = (y,x)
3887 In the case where all the type variables in the pattern type sigature are
3888 already in scope (i.e. bound by the enclosing context), matters are simple: the
3889 signature simply constrains the type of the pattern in the obvious way.
3892 There is only one situation in which you can write a pattern type signature that
3893 mentions a type variable that is not already in scope, namely in pattern match
3894 of an existential data constructor. For example:
3896 data T = forall a. MkT [a]
3899 k (MkT [t::a]) = MkT t3
3903 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3904 variable that is not already in scope. Indeed, it cannot already be in scope,
3905 because it is bound by the pattern match. GHC's rule is that in this situation
3906 (and only then), a pattern type signature can mention a type variable that is
3907 not already in scope; the effect is to bring it into scope, standing for the
3908 existentially-bound type variable.
3911 If this seems a little odd, we think so too. But we must have
3912 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3913 could not name existentially-bound type variables in subequent type signatures.
3916 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3917 signature is allowed to mention a lexical variable that is not already in
3919 For example, both <literal>f</literal> and <literal>g</literal> would be
3920 illegal if <literal>a</literal> was not already in scope.
3926 <!-- ==================== Commented out part about result type signatures
3928 <sect3 id="result-type-sigs">
3929 <title>Result type signatures</title>
3932 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3935 {- f assumes that 'a' is already in scope -}
3936 f x y :: [a] = [x,y,x]
3938 g = \ x :: [Int] -> [3,4]
3940 h :: forall a. [a] -> a
3944 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3945 the result of the function. Similarly, the body of the lambda in the RHS of
3946 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3947 alternative in <literal>h</literal> is <literal>a</literal>.
3949 <para> A result type signature never brings new type variables into scope.</para>
3951 There are a couple of syntactic wrinkles. First, notice that all three
3952 examples would parse quite differently with parentheses:
3954 {- f assumes that 'a' is already in scope -}
3955 f x (y :: [a]) = [x,y,x]
3957 g = \ (x :: [Int]) -> [3,4]
3959 h :: forall a. [a] -> a
3963 Now the signature is on the <emphasis>pattern</emphasis>; and
3964 <literal>h</literal> would certainly be ill-typed (since the pattern
3965 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3967 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3968 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3969 token or a parenthesised type of some sort). To see why,
3970 consider how one would parse this:
3979 <sect3 id="cls-inst-scoped-tyvars">
3980 <title>Class and instance declarations</title>
3983 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3984 scope over the methods defined in the <literal>where</literal> part. For example:
4002 <sect2 id="typing-binds">
4003 <title>Generalised typing of mutually recursive bindings</title>
4006 The Haskell Report specifies that a group of bindings (at top level, or in a
4007 <literal>let</literal> or <literal>where</literal>) should be sorted into
4008 strongly-connected components, and then type-checked in dependency order
4009 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4010 Report, Section 4.5.1</ulink>).
4011 As each group is type-checked, any binders of the group that
4013 an explicit type signature are put in the type environment with the specified
4015 and all others are monomorphic until the group is generalised
4016 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4019 <para>Following a suggestion of Mark Jones, in his paper
4020 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4022 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4024 <emphasis>the dependency analysis ignores references to variables that have an explicit
4025 type signature</emphasis>.
4026 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4027 typecheck. For example, consider:
4029 f :: Eq a => a -> Bool
4030 f x = (x == x) || g True || g "Yes"
4032 g y = (y <= y) || f True
4034 This is rejected by Haskell 98, but under Jones's scheme the definition for
4035 <literal>g</literal> is typechecked first, separately from that for
4036 <literal>f</literal>,
4037 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4038 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4039 type is generalised, to get
4041 g :: Ord a => a -> Bool
4043 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4044 <literal>g</literal> in the type environment.
4048 The same refined dependency analysis also allows the type signatures of
4049 mutually-recursive functions to have different contexts, something that is illegal in
4050 Haskell 98 (Section 4.5.2, last sentence). With
4051 <option>-fglasgow-exts</option>
4052 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4053 type signatures; in practice this means that only variables bound by the same
4054 pattern binding must have the same context. For example, this is fine:
4056 f :: Eq a => a -> Bool
4057 f x = (x == x) || g True
4059 g :: Ord a => a -> Bool
4060 g y = (y <= y) || f True
4065 <sect2 id="overloaded-strings">
4066 <title>Overloaded string literals
4070 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4071 string literal has type <literal>String</literal>, but with overloaded string
4072 literals enabled (with <literal>-foverloaded-strings</literal>)
4073 a string literal has type <literal>(IsString a) => a</literal>.
4076 This means that the usual string syntax can be used, e.g., for packed strings
4077 and other variations of string like types. String literals behave very much
4078 like integer literals, i.e., they can be used in both expressions and patterns.
4079 If used in a pattern the literal with be replaced by an equality test, in the same
4080 way as an integer literal is.
4083 The class <literal>IsString</literal> is defined as:
4085 class IsString a where
4086 fromString :: String -> a
4088 The only predefined instance is the obvious one to make strings work as usual:
4090 instance IsString [Char] where
4093 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4094 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4095 from module <literal>GHC.Exts</literal>.
4098 Haskell's defaulting mechanism is extended to cover string literals, when <option>-foverloaded-strings</option> is specified.
4102 Each type in a default declaration must be an
4103 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4107 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4108 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4109 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4110 <emphasis>or</emphasis> <literal>IsString</literal>.
4119 import GHC.Exts( IsString(..) )
4121 newtype MyString = MyString String deriving (Eq, Show)
4122 instance IsString MyString where
4123 fromString = MyString
4125 greet :: MyString -> MyString
4126 greet "hello" = "world"
4130 print $ greet "hello"
4131 print $ greet "fool"
4135 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4136 to work since it gets translated into an equality comparison.
4141 <!-- ==================== End of type system extensions ================= -->
4143 <!-- ====================== TEMPLATE HASKELL ======================= -->
4145 <sect1 id="template-haskell">
4146 <title>Template Haskell</title>
4148 <para>Template Haskell allows you to do compile-time meta-programming in
4151 the main technical innovations is discussed in "<ulink
4152 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4153 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4156 There is a Wiki page about
4157 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4158 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4162 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4163 Haskell library reference material</ulink>
4164 (search for the type ExpQ).
4165 [Temporary: many changes to the original design are described in
4166 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4167 Not all of these changes are in GHC 6.6.]
4170 <para> The first example from that paper is set out below as a worked example to help get you started.
4174 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4175 Tim Sheard is going to expand it.)
4179 <title>Syntax</title>
4181 <para> Template Haskell has the following new syntactic
4182 constructions. You need to use the flag
4183 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4184 </indexterm>to switch these syntactic extensions on
4185 (<option>-fth</option> is no longer implied by
4186 <option>-fglasgow-exts</option>).</para>
4190 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4191 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4192 There must be no space between the "$" and the identifier or parenthesis. This use
4193 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4194 of "." as an infix operator. If you want the infix operator, put spaces around it.
4196 <para> A splice can occur in place of
4198 <listitem><para> an expression; the spliced expression must
4199 have type <literal>Q Exp</literal></para></listitem>
4200 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4201 <listitem><para> [Planned, but not implemented yet.] a
4202 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4204 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4205 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4211 A expression quotation is written in Oxford brackets, thus:
4213 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4214 the quotation has type <literal>Expr</literal>.</para></listitem>
4215 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4216 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4217 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4218 the quotation has type <literal>Type</literal>.</para></listitem>
4219 </itemizedlist></para></listitem>
4222 Reification is written thus:
4224 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4225 has type <literal>Dec</literal>. </para></listitem>
4226 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4227 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4228 <listitem><para> Still to come: fixities </para></listitem>
4230 </itemizedlist></para>
4237 <sect2> <title> Using Template Haskell </title>
4241 The data types and monadic constructor functions for Template Haskell are in the library
4242 <literal>Language.Haskell.THSyntax</literal>.
4246 You can only run a function at compile time if it is imported from another module. That is,
4247 you can't define a function in a module, and call it from within a splice in the same module.
4248 (It would make sense to do so, but it's hard to implement.)
4252 Furthermore, you can only run a function at compile time if it is imported
4253 from another module <emphasis>that is not part of a mutually-recursive group of modules
4254 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4255 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4256 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4260 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4263 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4264 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4265 compiles and runs a program, and then looks at the result. So it's important that
4266 the program it compiles produces results whose representations are identical to
4267 those of the compiler itself.
4271 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4272 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4277 <sect2> <title> A Template Haskell Worked Example </title>
4278 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4279 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4286 -- Import our template "pr"
4287 import Printf ( pr )
4289 -- The splice operator $ takes the Haskell source code
4290 -- generated at compile time by "pr" and splices it into
4291 -- the argument of "putStrLn".
4292 main = putStrLn ( $(pr "Hello") )
4298 -- Skeletal printf from the paper.
4299 -- It needs to be in a separate module to the one where
4300 -- you intend to use it.
4302 -- Import some Template Haskell syntax
4303 import Language.Haskell.TH
4305 -- Describe a format string
4306 data Format = D | S | L String
4308 -- Parse a format string. This is left largely to you
4309 -- as we are here interested in building our first ever
4310 -- Template Haskell program and not in building printf.
4311 parse :: String -> [Format]
4314 -- Generate Haskell source code from a parsed representation
4315 -- of the format string. This code will be spliced into
4316 -- the module which calls "pr", at compile time.
4317 gen :: [Format] -> ExpQ
4318 gen [D] = [| \n -> show n |]
4319 gen [S] = [| \s -> s |]
4320 gen [L s] = stringE s
4322 -- Here we generate the Haskell code for the splice
4323 -- from an input format string.
4324 pr :: String -> ExpQ
4325 pr s = gen (parse s)
4328 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4331 $ ghc --make -fth main.hs -o main.exe
4334 <para>Run "main.exe" and here is your output:</para>
4344 <title>Using Template Haskell with Profiling</title>
4345 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4347 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4348 interpreter to run the splice expressions. The bytecode interpreter
4349 runs the compiled expression on top of the same runtime on which GHC
4350 itself is running; this means that the compiled code referred to by
4351 the interpreted expression must be compatible with this runtime, and
4352 in particular this means that object code that is compiled for
4353 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4354 expression, because profiled object code is only compatible with the
4355 profiling version of the runtime.</para>
4357 <para>This causes difficulties if you have a multi-module program
4358 containing Template Haskell code and you need to compile it for
4359 profiling, because GHC cannot load the profiled object code and use it
4360 when executing the splices. Fortunately GHC provides a workaround.
4361 The basic idea is to compile the program twice:</para>
4365 <para>Compile the program or library first the normal way, without
4366 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4369 <para>Then compile it again with <option>-prof</option>, and
4370 additionally use <option>-osuf
4371 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4372 to name the object files differentliy (you can choose any suffix
4373 that isn't the normal object suffix here). GHC will automatically
4374 load the object files built in the first step when executing splice
4375 expressions. If you omit the <option>-osuf</option> flag when
4376 building with <option>-prof</option> and Template Haskell is used,
4377 GHC will emit an error message. </para>
4384 <!-- ===================== Arrow notation =================== -->
4386 <sect1 id="arrow-notation">
4387 <title>Arrow notation
4390 <para>Arrows are a generalization of monads introduced by John Hughes.
4391 For more details, see
4396 “Generalising Monads to Arrows”,
4397 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4398 pp67–111, May 2000.
4404 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4405 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4411 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4412 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4418 and the arrows web page at
4419 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4420 With the <option>-farrows</option> flag, GHC supports the arrow
4421 notation described in the second of these papers.
4422 What follows is a brief introduction to the notation;
4423 it won't make much sense unless you've read Hughes's paper.
4424 This notation is translated to ordinary Haskell,
4425 using combinators from the
4426 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4430 <para>The extension adds a new kind of expression for defining arrows:
4432 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4433 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4435 where <literal>proc</literal> is a new keyword.
4436 The variables of the pattern are bound in the body of the
4437 <literal>proc</literal>-expression,
4438 which is a new sort of thing called a <firstterm>command</firstterm>.
4439 The syntax of commands is as follows:
4441 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4442 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4443 | <replaceable>cmd</replaceable><superscript>0</superscript>
4445 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4446 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4447 infix operators as for expressions, and
4449 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4450 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4451 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4452 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4453 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4454 | <replaceable>fcmd</replaceable>
4456 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4457 | ( <replaceable>cmd</replaceable> )
4458 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4460 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4461 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4462 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4463 | <replaceable>cmd</replaceable>
4465 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4466 except that the bodies are commands instead of expressions.
4470 Commands produce values, but (like monadic computations)
4471 may yield more than one value,
4472 or none, and may do other things as well.
4473 For the most part, familiarity with monadic notation is a good guide to
4475 However the values of expressions, even monadic ones,
4476 are determined by the values of the variables they contain;
4477 this is not necessarily the case for commands.
4481 A simple example of the new notation is the expression
4483 proc x -> f -< x+1
4485 We call this a <firstterm>procedure</firstterm> or
4486 <firstterm>arrow abstraction</firstterm>.
4487 As with a lambda expression, the variable <literal>x</literal>
4488 is a new variable bound within the <literal>proc</literal>-expression.
4489 It refers to the input to the arrow.
4490 In the above example, <literal>-<</literal> is not an identifier but an
4491 new reserved symbol used for building commands from an expression of arrow
4492 type and an expression to be fed as input to that arrow.
4493 (The weird look will make more sense later.)
4494 It may be read as analogue of application for arrows.
4495 The above example is equivalent to the Haskell expression
4497 arr (\ x -> x+1) >>> f
4499 That would make no sense if the expression to the left of
4500 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4501 More generally, the expression to the left of <literal>-<</literal>
4502 may not involve any <firstterm>local variable</firstterm>,
4503 i.e. a variable bound in the current arrow abstraction.
4504 For such a situation there is a variant <literal>-<<</literal>, as in
4506 proc x -> f x -<< x+1
4508 which is equivalent to
4510 arr (\ x -> (f x, x+1)) >>> app
4512 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4514 Such an arrow is equivalent to a monad, so if you're using this form
4515 you may find a monadic formulation more convenient.
4519 <title>do-notation for commands</title>
4522 Another form of command is a form of <literal>do</literal>-notation.
4523 For example, you can write
4532 You can read this much like ordinary <literal>do</literal>-notation,
4533 but with commands in place of monadic expressions.
4534 The first line sends the value of <literal>x+1</literal> as an input to
4535 the arrow <literal>f</literal>, and matches its output against
4536 <literal>y</literal>.
4537 In the next line, the output is discarded.
4538 The arrow <function>returnA</function> is defined in the
4539 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4540 module as <literal>arr id</literal>.
4541 The above example is treated as an abbreviation for
4543 arr (\ x -> (x, x)) >>>
4544 first (arr (\ x -> x+1) >>> f) >>>
4545 arr (\ (y, x) -> (y, (x, y))) >>>
4546 first (arr (\ y -> 2*y) >>> g) >>>
4548 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4549 first (arr (\ (x, z) -> x*z) >>> h) >>>
4550 arr (\ (t, z) -> t+z) >>>
4553 Note that variables not used later in the composition are projected out.
4554 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4556 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4557 module, this reduces to
4559 arr (\ x -> (x+1, x)) >>>
4561 arr (\ (y, x) -> (2*y, (x, y))) >>>
4563 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4565 arr (\ (t, z) -> t+z)
4567 which is what you might have written by hand.
4568 With arrow notation, GHC keeps track of all those tuples of variables for you.
4572 Note that although the above translation suggests that
4573 <literal>let</literal>-bound variables like <literal>z</literal> must be
4574 monomorphic, the actual translation produces Core,
4575 so polymorphic variables are allowed.
4579 It's also possible to have mutually recursive bindings,
4580 using the new <literal>rec</literal> keyword, as in the following example:
4582 counter :: ArrowCircuit a => a Bool Int
4583 counter = proc reset -> do
4584 rec output <- returnA -< if reset then 0 else next
4585 next <- delay 0 -< output+1
4586 returnA -< output
4588 The translation of such forms uses the <function>loop</function> combinator,
4589 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4595 <title>Conditional commands</title>
4598 In the previous example, we used a conditional expression to construct the
4600 Sometimes we want to conditionally execute different commands, as in
4607 which is translated to
4609 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4610 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4612 Since the translation uses <function>|||</function>,
4613 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4617 There are also <literal>case</literal> commands, like
4623 y <- h -< (x1, x2)
4627 The syntax is the same as for <literal>case</literal> expressions,
4628 except that the bodies of the alternatives are commands rather than expressions.
4629 The translation is similar to that of <literal>if</literal> commands.
4635 <title>Defining your own control structures</title>
4638 As we're seen, arrow notation provides constructs,
4639 modelled on those for expressions,
4640 for sequencing, value recursion and conditionals.
4641 But suitable combinators,
4642 which you can define in ordinary Haskell,
4643 may also be used to build new commands out of existing ones.
4644 The basic idea is that a command defines an arrow from environments to values.
4645 These environments assign values to the free local variables of the command.
4646 Thus combinators that produce arrows from arrows
4647 may also be used to build commands from commands.
4648 For example, the <literal>ArrowChoice</literal> class includes a combinator
4650 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4652 so we can use it to build commands:
4654 expr' = proc x -> do
4657 symbol Plus -< ()
4658 y <- term -< ()
4661 symbol Minus -< ()
4662 y <- term -< ()
4665 (The <literal>do</literal> on the first line is needed to prevent the first
4666 <literal><+> ...</literal> from being interpreted as part of the
4667 expression on the previous line.)
4668 This is equivalent to
4670 expr' = (proc x -> returnA -< x)
4671 <+> (proc x -> do
4672 symbol Plus -< ()
4673 y <- term -< ()
4675 <+> (proc x -> do
4676 symbol Minus -< ()
4677 y <- term -< ()
4680 It is essential that this operator be polymorphic in <literal>e</literal>
4681 (representing the environment input to the command
4682 and thence to its subcommands)
4683 and satisfy the corresponding naturality property
4685 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4687 at least for strict <literal>k</literal>.
4688 (This should be automatic if you're not using <function>seq</function>.)
4689 This ensures that environments seen by the subcommands are environments
4690 of the whole command,
4691 and also allows the translation to safely trim these environments.
4692 The operator must also not use any variable defined within the current
4697 We could define our own operator
4699 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4700 untilA body cond = proc x ->
4701 if cond x then returnA -< ()
4704 untilA body cond -< x
4706 and use it in the same way.
4707 Of course this infix syntax only makes sense for binary operators;
4708 there is also a more general syntax involving special brackets:
4712 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4719 <title>Primitive constructs</title>
4722 Some operators will need to pass additional inputs to their subcommands.
4723 For example, in an arrow type supporting exceptions,
4724 the operator that attaches an exception handler will wish to pass the
4725 exception that occurred to the handler.
4726 Such an operator might have a type
4728 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4730 where <literal>Ex</literal> is the type of exceptions handled.
4731 You could then use this with arrow notation by writing a command
4733 body `handleA` \ ex -> handler
4735 so that if an exception is raised in the command <literal>body</literal>,
4736 the variable <literal>ex</literal> is bound to the value of the exception
4737 and the command <literal>handler</literal>,
4738 which typically refers to <literal>ex</literal>, is entered.
4739 Though the syntax here looks like a functional lambda,
4740 we are talking about commands, and something different is going on.
4741 The input to the arrow represented by a command consists of values for
4742 the free local variables in the command, plus a stack of anonymous values.
4743 In all the prior examples, this stack was empty.
4744 In the second argument to <function>handleA</function>,
4745 this stack consists of one value, the value of the exception.
4746 The command form of lambda merely gives this value a name.
4751 the values on the stack are paired to the right of the environment.
4752 So operators like <function>handleA</function> that pass
4753 extra inputs to their subcommands can be designed for use with the notation
4754 by pairing the values with the environment in this way.
4755 More precisely, the type of each argument of the operator (and its result)
4756 should have the form
4758 a (...(e,t1), ... tn) t
4760 where <replaceable>e</replaceable> is a polymorphic variable
4761 (representing the environment)
4762 and <replaceable>ti</replaceable> are the types of the values on the stack,
4763 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4764 The polymorphic variable <replaceable>e</replaceable> must not occur in
4765 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4766 <replaceable>t</replaceable>.
4767 However the arrows involved need not be the same.
4768 Here are some more examples of suitable operators:
4770 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4771 runReader :: ... => a e c -> a' (e,State) c
4772 runState :: ... => a e c -> a' (e,State) (c,State)
4774 We can supply the extra input required by commands built with the last two
4775 by applying them to ordinary expressions, as in
4779 (|runReader (do { ... })|) s
4781 which adds <literal>s</literal> to the stack of inputs to the command
4782 built using <function>runReader</function>.
4786 The command versions of lambda abstraction and application are analogous to
4787 the expression versions.
4788 In particular, the beta and eta rules describe equivalences of commands.
4789 These three features (operators, lambda abstraction and application)
4790 are the core of the notation; everything else can be built using them,
4791 though the results would be somewhat clumsy.
4792 For example, we could simulate <literal>do</literal>-notation by defining
4794 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4795 u `bind` f = returnA &&& u >>> f
4797 bind_ :: Arrow a => a e b -> a e c -> a e c
4798 u `bind_` f = u `bind` (arr fst >>> f)
4800 We could simulate <literal>if</literal> by defining
4802 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4803 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4810 <title>Differences with the paper</title>
4815 <para>Instead of a single form of arrow application (arrow tail) with two
4816 translations, the implementation provides two forms
4817 <quote><literal>-<</literal></quote> (first-order)
4818 and <quote><literal>-<<</literal></quote> (higher-order).
4823 <para>User-defined operators are flagged with banana brackets instead of
4824 a new <literal>form</literal> keyword.
4833 <title>Portability</title>
4836 Although only GHC implements arrow notation directly,
4837 there is also a preprocessor
4839 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4840 that translates arrow notation into Haskell 98
4841 for use with other Haskell systems.
4842 You would still want to check arrow programs with GHC;
4843 tracing type errors in the preprocessor output is not easy.
4844 Modules intended for both GHC and the preprocessor must observe some
4845 additional restrictions:
4850 The module must import
4851 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4857 The preprocessor cannot cope with other Haskell extensions.
4858 These would have to go in separate modules.
4864 Because the preprocessor targets Haskell (rather than Core),
4865 <literal>let</literal>-bound variables are monomorphic.
4876 <!-- ==================== BANG PATTERNS ================= -->
4878 <sect1 id="bang-patterns">
4879 <title>Bang patterns
4880 <indexterm><primary>Bang patterns</primary></indexterm>
4882 <para>GHC supports an extension of pattern matching called <emphasis>bang
4883 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4885 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4886 prime feature description</ulink> contains more discussion and examples
4887 than the material below.
4890 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4893 <sect2 id="bang-patterns-informal">
4894 <title>Informal description of bang patterns
4897 The main idea is to add a single new production to the syntax of patterns:
4901 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4902 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4907 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4908 whereas without the bang it would be lazy.
4909 Bang patterns can be nested of course:
4913 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4914 <literal>y</literal>.
4915 A bang only really has an effect if it precedes a variable or wild-card pattern:
4920 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4921 forces evaluation anyway does nothing.
4923 Bang patterns work in <literal>case</literal> expressions too, of course:
4925 g5 x = let y = f x in body
4926 g6 x = case f x of { y -> body }
4927 g7 x = case f x of { !y -> body }
4929 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4930 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4931 result, and then evaluates <literal>body</literal>.
4933 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4934 definitions too. For example:
4938 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4939 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4940 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4941 in a function argument <literal>![x,y]</literal> means the
4942 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4943 is part of the syntax of <literal>let</literal> bindings.
4948 <sect2 id="bang-patterns-sem">
4949 <title>Syntax and semantics
4953 We add a single new production to the syntax of patterns:
4957 There is one problem with syntactic ambiguity. Consider:
4961 Is this a definition of the infix function "<literal>(!)</literal>",
4962 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4963 ambiguity in favour of the latter. If you want to define
4964 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4969 The semantics of Haskell pattern matching is described in <ulink
4970 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4971 Section 3.17.2</ulink> of the Haskell Report. To this description add
4972 one extra item 10, saying:
4973 <itemizedlist><listitem><para>Matching
4974 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4975 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4976 <listitem><para>otherwise, <literal>pat</literal> is matched against
4977 <literal>v</literal></para></listitem>
4979 </para></listitem></itemizedlist>
4980 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4981 Section 3.17.3</ulink>, add a new case (t):
4983 case v of { !pat -> e; _ -> e' }
4984 = v `seq` case v of { pat -> e; _ -> e' }
4987 That leaves let expressions, whose translation is given in
4988 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4990 of the Haskell Report.
4991 In the translation box, first apply
4992 the following transformation: for each pattern <literal>pi</literal> that is of
4993 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4994 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4995 have a bang at the top, apply the rules in the existing box.
4997 <para>The effect of the let rule is to force complete matching of the pattern
4998 <literal>qi</literal> before evaluation of the body is begun. The bang is
4999 retained in the translated form in case <literal>qi</literal> is a variable,
5007 The let-binding can be recursive. However, it is much more common for
5008 the let-binding to be non-recursive, in which case the following law holds:
5009 <literal>(let !p = rhs in body)</literal>
5011 <literal>(case rhs of !p -> body)</literal>
5014 A pattern with a bang at the outermost level is not allowed at the top level of
5020 <!-- ==================== ASSERTIONS ================= -->
5022 <sect1 id="assertions">
5024 <indexterm><primary>Assertions</primary></indexterm>
5028 If you want to make use of assertions in your standard Haskell code, you
5029 could define a function like the following:
5035 assert :: Bool -> a -> a
5036 assert False x = error "assertion failed!"
5043 which works, but gives you back a less than useful error message --
5044 an assertion failed, but which and where?
5048 One way out is to define an extended <function>assert</function> function which also
5049 takes a descriptive string to include in the error message and
5050 perhaps combine this with the use of a pre-processor which inserts
5051 the source location where <function>assert</function> was used.
5055 Ghc offers a helping hand here, doing all of this for you. For every
5056 use of <function>assert</function> in the user's source:
5062 kelvinToC :: Double -> Double
5063 kelvinToC k = assert (k >= 0.0) (k+273.15)
5069 Ghc will rewrite this to also include the source location where the
5076 assert pred val ==> assertError "Main.hs|15" pred val
5082 The rewrite is only performed by the compiler when it spots
5083 applications of <function>Control.Exception.assert</function>, so you
5084 can still define and use your own versions of
5085 <function>assert</function>, should you so wish. If not, import
5086 <literal>Control.Exception</literal> to make use
5087 <function>assert</function> in your code.
5091 GHC ignores assertions when optimisation is turned on with the
5092 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5093 <literal>assert pred e</literal> will be rewritten to
5094 <literal>e</literal>. You can also disable assertions using the
5095 <option>-fignore-asserts</option>
5096 option<indexterm><primary><option>-fignore-asserts</option></primary>
5097 </indexterm>.</para>
5100 Assertion failures can be caught, see the documentation for the
5101 <literal>Control.Exception</literal> library for the details.
5107 <!-- =============================== PRAGMAS =========================== -->
5109 <sect1 id="pragmas">
5110 <title>Pragmas</title>
5112 <indexterm><primary>pragma</primary></indexterm>
5114 <para>GHC supports several pragmas, or instructions to the
5115 compiler placed in the source code. Pragmas don't normally affect
5116 the meaning of the program, but they might affect the efficiency
5117 of the generated code.</para>
5119 <para>Pragmas all take the form
5121 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5123 where <replaceable>word</replaceable> indicates the type of
5124 pragma, and is followed optionally by information specific to that
5125 type of pragma. Case is ignored in
5126 <replaceable>word</replaceable>. The various values for
5127 <replaceable>word</replaceable> that GHC understands are described
5128 in the following sections; any pragma encountered with an
5129 unrecognised <replaceable>word</replaceable> is (silently)
5132 <sect2 id="deprecated-pragma">
5133 <title>DEPRECATED pragma</title>
5134 <indexterm><primary>DEPRECATED</primary>
5137 <para>The DEPRECATED pragma lets you specify that a particular
5138 function, class, or type, is deprecated. There are two
5143 <para>You can deprecate an entire module thus:</para>
5145 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5148 <para>When you compile any module that import
5149 <literal>Wibble</literal>, GHC will print the specified
5154 <para>You can deprecate a function, class, type, or data constructor, with the
5155 following top-level declaration:</para>
5157 {-# DEPRECATED f, C, T "Don't use these" #-}
5159 <para>When you compile any module that imports and uses any
5160 of the specified entities, GHC will print the specified
5162 <para> You can only depecate entities declared at top level in the module
5163 being compiled, and you can only use unqualified names in the list of
5164 entities being deprecated. A capitalised name, such as <literal>T</literal>
5165 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5166 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5167 both are in scope. If both are in scope, there is currently no way to deprecate
5168 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5171 Any use of the deprecated item, or of anything from a deprecated
5172 module, will be flagged with an appropriate message. However,
5173 deprecations are not reported for
5174 (a) uses of a deprecated function within its defining module, and
5175 (b) uses of a deprecated function in an export list.
5176 The latter reduces spurious complaints within a library
5177 in which one module gathers together and re-exports
5178 the exports of several others.
5180 <para>You can suppress the warnings with the flag
5181 <option>-fno-warn-deprecations</option>.</para>
5184 <sect2 id="include-pragma">
5185 <title>INCLUDE pragma</title>
5187 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5188 of C header files that should be <literal>#include</literal>'d into
5189 the C source code generated by the compiler for the current module (if
5190 compiling via C). For example:</para>
5193 {-# INCLUDE "foo.h" #-}
5194 {-# INCLUDE <stdio.h> #-}</programlisting>
5196 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5197 your source file with any <literal>OPTIONS_GHC</literal>
5200 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5201 to the <option>-#include</option> option (<xref
5202 linkend="options-C-compiler" />), because the
5203 <literal>INCLUDE</literal> pragma is understood by other
5204 compilers. Yet another alternative is to add the include file to each
5205 <literal>foreign import</literal> declaration in your code, but we
5206 don't recommend using this approach with GHC.</para>
5209 <sect2 id="inline-noinline-pragma">
5210 <title>INLINE and NOINLINE pragmas</title>
5212 <para>These pragmas control the inlining of function
5215 <sect3 id="inline-pragma">
5216 <title>INLINE pragma</title>
5217 <indexterm><primary>INLINE</primary></indexterm>
5219 <para>GHC (with <option>-O</option>, as always) tries to
5220 inline (or “unfold”) functions/values that are
5221 “small enough,” thus avoiding the call overhead
5222 and possibly exposing other more-wonderful optimisations.
5223 Normally, if GHC decides a function is “too
5224 expensive” to inline, it will not do so, nor will it
5225 export that unfolding for other modules to use.</para>
5227 <para>The sledgehammer you can bring to bear is the
5228 <literal>INLINE</literal><indexterm><primary>INLINE
5229 pragma</primary></indexterm> pragma, used thusly:</para>
5232 key_function :: Int -> String -> (Bool, Double)
5234 #ifdef __GLASGOW_HASKELL__
5235 {-# INLINE key_function #-}
5239 <para>(You don't need to do the C pre-processor carry-on
5240 unless you're going to stick the code through HBC—it
5241 doesn't like <literal>INLINE</literal> pragmas.)</para>
5243 <para>The major effect of an <literal>INLINE</literal> pragma
5244 is to declare a function's “cost” to be very low.
5245 The normal unfolding machinery will then be very keen to
5248 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5249 function can be put anywhere its type signature could be
5252 <para><literal>INLINE</literal> pragmas are a particularly
5254 <literal>then</literal>/<literal>return</literal> (or
5255 <literal>bind</literal>/<literal>unit</literal>) functions in
5256 a monad. For example, in GHC's own
5257 <literal>UniqueSupply</literal> monad code, we have:</para>
5260 #ifdef __GLASGOW_HASKELL__
5261 {-# INLINE thenUs #-}
5262 {-# INLINE returnUs #-}
5266 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5267 linkend="noinline-pragma"/>).</para>
5270 <sect3 id="noinline-pragma">
5271 <title>NOINLINE pragma</title>
5273 <indexterm><primary>NOINLINE</primary></indexterm>
5274 <indexterm><primary>NOTINLINE</primary></indexterm>
5276 <para>The <literal>NOINLINE</literal> pragma does exactly what
5277 you'd expect: it stops the named function from being inlined
5278 by the compiler. You shouldn't ever need to do this, unless
5279 you're very cautious about code size.</para>
5281 <para><literal>NOTINLINE</literal> is a synonym for
5282 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5283 specified by Haskell 98 as the standard way to disable
5284 inlining, so it should be used if you want your code to be
5288 <sect3 id="phase-control">
5289 <title>Phase control</title>
5291 <para> Sometimes you want to control exactly when in GHC's
5292 pipeline the INLINE pragma is switched on. Inlining happens
5293 only during runs of the <emphasis>simplifier</emphasis>. Each
5294 run of the simplifier has a different <emphasis>phase
5295 number</emphasis>; the phase number decreases towards zero.
5296 If you use <option>-dverbose-core2core</option> you'll see the
5297 sequence of phase numbers for successive runs of the
5298 simplifier. In an INLINE pragma you can optionally specify a
5302 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5303 <literal>f</literal>
5304 until phase <literal>k</literal>, but from phase
5305 <literal>k</literal> onwards be very keen to inline it.
5308 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5309 <literal>f</literal>
5310 until phase <literal>k</literal>, but from phase
5311 <literal>k</literal> onwards do not inline it.
5314 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5315 <literal>f</literal>
5316 until phase <literal>k</literal>, but from phase
5317 <literal>k</literal> onwards be willing to inline it (as if
5318 there was no pragma).
5321 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5322 <literal>f</literal>
5323 until phase <literal>k</literal>, but from phase
5324 <literal>k</literal> onwards do not inline it.
5327 The same information is summarised here:
5329 -- Before phase 2 Phase 2 and later
5330 {-# INLINE [2] f #-} -- No Yes
5331 {-# INLINE [~2] f #-} -- Yes No
5332 {-# NOINLINE [2] f #-} -- No Maybe
5333 {-# NOINLINE [~2] f #-} -- Maybe No
5335 {-# INLINE f #-} -- Yes Yes
5336 {-# NOINLINE f #-} -- No No
5338 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5339 function body is small, or it is applied to interesting-looking arguments etc).
5340 Another way to understand the semantics is this:
5342 <listitem><para>For both INLINE and NOINLINE, the phase number says
5343 when inlining is allowed at all.</para></listitem>
5344 <listitem><para>The INLINE pragma has the additional effect of making the
5345 function body look small, so that when inlining is allowed it is very likely to
5350 <para>The same phase-numbering control is available for RULES
5351 (<xref linkend="rewrite-rules"/>).</para>
5355 <sect2 id="language-pragma">
5356 <title>LANGUAGE pragma</title>
5358 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5359 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5361 <para>This allows language extensions to be enabled in a portable way.
5362 It is the intention that all Haskell compilers support the
5363 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5364 all extensions are supported by all compilers, of
5365 course. The <literal>LANGUAGE</literal> pragma should be used instead
5366 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5368 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5370 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5372 <para>Any extension from the <literal>Extension</literal> type defined in
5374 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>
5378 <sect2 id="line-pragma">
5379 <title>LINE pragma</title>
5381 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5382 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5383 <para>This pragma is similar to C's <literal>#line</literal>
5384 pragma, and is mainly for use in automatically generated Haskell
5385 code. It lets you specify the line number and filename of the
5386 original code; for example</para>
5388 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5390 <para>if you'd generated the current file from something called
5391 <filename>Foo.vhs</filename> and this line corresponds to line
5392 42 in the original. GHC will adjust its error messages to refer
5393 to the line/file named in the <literal>LINE</literal>
5397 <sect2 id="options-pragma">
5398 <title>OPTIONS_GHC pragma</title>
5399 <indexterm><primary>OPTIONS_GHC</primary>
5401 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5404 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5405 additional options that are given to the compiler when compiling
5406 this source file. See <xref linkend="source-file-options"/> for
5409 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5410 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5414 <title>RULES pragma</title>
5416 <para>The RULES pragma lets you specify rewrite rules. It is
5417 described in <xref linkend="rewrite-rules"/>.</para>
5420 <sect2 id="specialize-pragma">
5421 <title>SPECIALIZE pragma</title>
5423 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5424 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5425 <indexterm><primary>overloading, death to</primary></indexterm>
5427 <para>(UK spelling also accepted.) For key overloaded
5428 functions, you can create extra versions (NB: more code space)
5429 specialised to particular types. Thus, if you have an
5430 overloaded function:</para>
5433 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5436 <para>If it is heavily used on lists with
5437 <literal>Widget</literal> keys, you could specialise it as
5441 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5444 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5445 be put anywhere its type signature could be put.</para>
5447 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5448 (a) a specialised version of the function and (b) a rewrite rule
5449 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5450 un-specialised function into a call to the specialised one.</para>
5452 <para>The type in a SPECIALIZE pragma can be any type that is less
5453 polymorphic than the type of the original function. In concrete terms,
5454 if the original function is <literal>f</literal> then the pragma
5456 {-# SPECIALIZE f :: <type> #-}
5458 is valid if and only if the defintion
5460 f_spec :: <type>
5463 is valid. Here are some examples (where we only give the type signature
5464 for the original function, not its code):
5466 f :: Eq a => a -> b -> b
5467 {-# SPECIALISE f :: Int -> b -> b #-}
5469 g :: (Eq a, Ix b) => a -> b -> b
5470 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5472 h :: Eq a => a -> a -> a
5473 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5475 The last of these examples will generate a
5476 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5477 well. If you use this kind of specialisation, let us know how well it works.
5480 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5481 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5482 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5483 The <literal>INLINE</literal> pragma affects the specialised verison of the
5484 function (only), and applies even if the function is recursive. The motivating
5487 -- A GADT for arrays with type-indexed representation
5489 ArrInt :: !Int -> ByteArray# -> Arr Int
5490 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5492 (!:) :: Arr e -> Int -> e
5493 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5494 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5495 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5496 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5498 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5499 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5500 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5501 the specialised function will be inlined. It has two calls to
5502 <literal>(!:)</literal>,
5503 both at type <literal>Int</literal>. Both these calls fire the first
5504 specialisation, whose body is also inlined. The result is a type-based
5505 unrolling of the indexing function.</para>
5506 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5507 on an ordinarily-recursive function.</para>
5509 <para>Note: In earlier versions of GHC, it was possible to provide your own
5510 specialised function for a given type:
5513 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5516 This feature has been removed, as it is now subsumed by the
5517 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5521 <sect2 id="specialize-instance-pragma">
5522 <title>SPECIALIZE instance pragma
5526 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5527 <indexterm><primary>overloading, death to</primary></indexterm>
5528 Same idea, except for instance declarations. For example:
5531 instance (Eq a) => Eq (Foo a) where {
5532 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5536 The pragma must occur inside the <literal>where</literal> part
5537 of the instance declaration.
5540 Compatible with HBC, by the way, except perhaps in the placement
5546 <sect2 id="unpack-pragma">
5547 <title>UNPACK pragma</title>
5549 <indexterm><primary>UNPACK</primary></indexterm>
5551 <para>The <literal>UNPACK</literal> indicates to the compiler
5552 that it should unpack the contents of a constructor field into
5553 the constructor itself, removing a level of indirection. For
5557 data T = T {-# UNPACK #-} !Float
5558 {-# UNPACK #-} !Float
5561 <para>will create a constructor <literal>T</literal> containing
5562 two unboxed floats. This may not always be an optimisation: if
5563 the <function>T</function> constructor is scrutinised and the
5564 floats passed to a non-strict function for example, they will
5565 have to be reboxed (this is done automatically by the
5568 <para>Unpacking constructor fields should only be used in
5569 conjunction with <option>-O</option>, in order to expose
5570 unfoldings to the compiler so the reboxing can be removed as
5571 often as possible. For example:</para>
5575 f (T f1 f2) = f1 + f2
5578 <para>The compiler will avoid reboxing <function>f1</function>
5579 and <function>f2</function> by inlining <function>+</function>
5580 on floats, but only when <option>-O</option> is on.</para>
5582 <para>Any single-constructor data is eligible for unpacking; for
5586 data T = T {-# UNPACK #-} !(Int,Int)
5589 <para>will store the two <literal>Int</literal>s directly in the
5590 <function>T</function> constructor, by flattening the pair.
5591 Multi-level unpacking is also supported:</para>
5594 data T = T {-# UNPACK #-} !S
5595 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5598 <para>will store two unboxed <literal>Int#</literal>s
5599 directly in the <function>T</function> constructor. The
5600 unpacker can see through newtypes, too.</para>
5602 <para>If a field cannot be unpacked, you will not get a warning,
5603 so it might be an idea to check the generated code with
5604 <option>-ddump-simpl</option>.</para>
5606 <para>See also the <option>-funbox-strict-fields</option> flag,
5607 which essentially has the effect of adding
5608 <literal>{-# UNPACK #-}</literal> to every strict
5609 constructor field.</para>
5614 <!-- ======================= REWRITE RULES ======================== -->
5616 <sect1 id="rewrite-rules">
5617 <title>Rewrite rules
5619 <indexterm><primary>RULES pragma</primary></indexterm>
5620 <indexterm><primary>pragma, RULES</primary></indexterm>
5621 <indexterm><primary>rewrite rules</primary></indexterm></title>
5624 The programmer can specify rewrite rules as part of the source program
5625 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5626 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5627 and (b) the <option>-frules-off</option> flag
5628 (<xref linkend="options-f"/>) is not specified, and (c) the
5629 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5638 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5645 <title>Syntax</title>
5648 From a syntactic point of view:
5654 There may be zero or more rules in a <literal>RULES</literal> pragma.
5661 Each rule has a name, enclosed in double quotes. The name itself has
5662 no significance at all. It is only used when reporting how many times the rule fired.
5668 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5669 immediately after the name of the rule. Thus:
5672 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5675 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5676 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5685 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5686 is set, so you must lay out your rules starting in the same column as the
5687 enclosing definitions.
5694 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5695 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5696 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5697 by spaces, just like in a type <literal>forall</literal>.
5703 A pattern variable may optionally have a type signature.
5704 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5705 For example, here is the <literal>foldr/build</literal> rule:
5708 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5709 foldr k z (build g) = g k z
5712 Since <function>g</function> has a polymorphic type, it must have a type signature.
5719 The left hand side of a rule must consist of a top-level variable applied
5720 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5723 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5724 "wrong2" forall f. f True = True
5727 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5734 A rule does not need to be in the same module as (any of) the
5735 variables it mentions, though of course they need to be in scope.
5741 Rules are automatically exported from a module, just as instance declarations are.
5752 <title>Semantics</title>
5755 From a semantic point of view:
5761 Rules are only applied if you use the <option>-O</option> flag.
5767 Rules are regarded as left-to-right rewrite rules.
5768 When GHC finds an expression that is a substitution instance of the LHS
5769 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5770 By "a substitution instance" we mean that the LHS can be made equal to the
5771 expression by substituting for the pattern variables.
5778 The LHS and RHS of a rule are typechecked, and must have the
5786 GHC makes absolutely no attempt to verify that the LHS and RHS
5787 of a rule have the same meaning. That is undecidable in general, and
5788 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5795 GHC makes no attempt to make sure that the rules are confluent or
5796 terminating. For example:
5799 "loop" forall x,y. f x y = f y x
5802 This rule will cause the compiler to go into an infinite loop.
5809 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5815 GHC currently uses a very simple, syntactic, matching algorithm
5816 for matching a rule LHS with an expression. It seeks a substitution
5817 which makes the LHS and expression syntactically equal modulo alpha
5818 conversion. The pattern (rule), but not the expression, is eta-expanded if
5819 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5820 But not beta conversion (that's called higher-order matching).
5824 Matching is carried out on GHC's intermediate language, which includes
5825 type abstractions and applications. So a rule only matches if the
5826 types match too. See <xref linkend="rule-spec"/> below.
5832 GHC keeps trying to apply the rules as it optimises the program.
5833 For example, consider:
5842 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5843 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5844 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5845 not be substituted, and the rule would not fire.
5852 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5853 that appears on the LHS of a rule</emphasis>, because once you have substituted
5854 for something you can't match against it (given the simple minded
5855 matching). So if you write the rule
5858 "map/map" forall f,g. map f . map g = map (f.g)
5861 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5862 It will only match something written with explicit use of ".".
5863 Well, not quite. It <emphasis>will</emphasis> match the expression
5869 where <function>wibble</function> is defined:
5872 wibble f g = map f . map g
5875 because <function>wibble</function> will be inlined (it's small).
5877 Later on in compilation, GHC starts inlining even things on the
5878 LHS of rules, but still leaves the rules enabled. This inlining
5879 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5886 All rules are implicitly exported from the module, and are therefore
5887 in force in any module that imports the module that defined the rule, directly
5888 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5889 in force when compiling A.) The situation is very similar to that for instance
5901 <title>List fusion</title>
5904 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5905 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5906 intermediate list should be eliminated entirely.
5910 The following are good producers:
5922 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5928 Explicit lists (e.g. <literal>[True, False]</literal>)
5934 The cons constructor (e.g <literal>3:4:[]</literal>)
5940 <function>++</function>
5946 <function>map</function>
5952 <function>take</function>, <function>filter</function>
5958 <function>iterate</function>, <function>repeat</function>
5964 <function>zip</function>, <function>zipWith</function>
5973 The following are good consumers:
5985 <function>array</function> (on its second argument)
5991 <function>++</function> (on its first argument)
5997 <function>foldr</function>
6003 <function>map</function>
6009 <function>take</function>, <function>filter</function>
6015 <function>concat</function>
6021 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6027 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6028 will fuse with one but not the other)
6034 <function>partition</function>
6040 <function>head</function>
6046 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6052 <function>sequence_</function>
6058 <function>msum</function>
6064 <function>sortBy</function>
6073 So, for example, the following should generate no intermediate lists:
6076 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6082 This list could readily be extended; if there are Prelude functions that you use
6083 a lot which are not included, please tell us.
6087 If you want to write your own good consumers or producers, look at the
6088 Prelude definitions of the above functions to see how to do so.
6093 <sect2 id="rule-spec">
6094 <title>Specialisation
6098 Rewrite rules can be used to get the same effect as a feature
6099 present in earlier versions of GHC.
6100 For example, suppose that:
6103 genericLookup :: Ord a => Table a b -> a -> b
6104 intLookup :: Table Int b -> Int -> b
6107 where <function>intLookup</function> is an implementation of
6108 <function>genericLookup</function> that works very fast for
6109 keys of type <literal>Int</literal>. You might wish
6110 to tell GHC to use <function>intLookup</function> instead of
6111 <function>genericLookup</function> whenever the latter was called with
6112 type <literal>Table Int b -> Int -> b</literal>.
6113 It used to be possible to write
6116 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6119 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6122 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6125 This slightly odd-looking rule instructs GHC to replace
6126 <function>genericLookup</function> by <function>intLookup</function>
6127 <emphasis>whenever the types match</emphasis>.
6128 What is more, this rule does not need to be in the same
6129 file as <function>genericLookup</function>, unlike the
6130 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6131 have an original definition available to specialise).
6134 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6135 <function>intLookup</function> really behaves as a specialised version
6136 of <function>genericLookup</function>!!!</para>
6138 <para>An example in which using <literal>RULES</literal> for
6139 specialisation will Win Big:
6142 toDouble :: Real a => a -> Double
6143 toDouble = fromRational . toRational
6145 {-# RULES "toDouble/Int" toDouble = i2d #-}
6146 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6149 The <function>i2d</function> function is virtually one machine
6150 instruction; the default conversion—via an intermediate
6151 <literal>Rational</literal>—is obscenely expensive by
6158 <title>Controlling what's going on</title>
6166 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6172 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6173 If you add <option>-dppr-debug</option> you get a more detailed listing.
6179 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6182 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6183 {-# INLINE build #-}
6187 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6188 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6189 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6190 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6197 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6198 see how to write rules that will do fusion and yet give an efficient
6199 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6209 <sect2 id="core-pragma">
6210 <title>CORE pragma</title>
6212 <indexterm><primary>CORE pragma</primary></indexterm>
6213 <indexterm><primary>pragma, CORE</primary></indexterm>
6214 <indexterm><primary>core, annotation</primary></indexterm>
6217 The external core format supports <quote>Note</quote> annotations;
6218 the <literal>CORE</literal> pragma gives a way to specify what these
6219 should be in your Haskell source code. Syntactically, core
6220 annotations are attached to expressions and take a Haskell string
6221 literal as an argument. The following function definition shows an
6225 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6228 Semantically, this is equivalent to:
6236 However, when external for is generated (via
6237 <option>-fext-core</option>), there will be Notes attached to the
6238 expressions <function>show</function> and <varname>x</varname>.
6239 The core function declaration for <function>f</function> is:
6243 f :: %forall a . GHCziShow.ZCTShow a ->
6244 a -> GHCziBase.ZMZN GHCziBase.Char =
6245 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6247 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6249 (tpl1::GHCziBase.Int ->
6251 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6253 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6254 (tpl3::GHCziBase.ZMZN a ->
6255 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6263 Here, we can see that the function <function>show</function> (which
6264 has been expanded out to a case expression over the Show dictionary)
6265 has a <literal>%note</literal> attached to it, as does the
6266 expression <varname>eta</varname> (which used to be called
6267 <varname>x</varname>).
6274 <sect1 id="special-ids">
6275 <title>Special built-in functions</title>
6276 <para>GHC has a few built-in funcions with special behaviour,
6277 described in this section. All are exported by
6278 <literal>GHC.Exts</literal>.</para>
6280 <sect2> <title>The <literal>seq</literal> function </title>
6282 The function <literal>seq</literal> is as described in the Haskell98 Report.
6286 It evaluates its first argument to head normal form, and then returns its
6287 second argument as the result. The reason that it is documented here is
6288 that, despite <literal>seq</literal>'s polymorphism, its
6289 second argument can have an unboxed type, or
6290 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6291 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6292 to be instantiated to an unboxed type, which is not usually allowed.
6296 <sect2> <title>The <literal>inline</literal> function </title>
6298 The <literal>inline</literal> function is somewhat experimental.
6302 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6303 is inlined, regardless of its size. More precisely, the call
6304 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6306 This allows the programmer to control inlining from
6307 a particular <emphasis>call site</emphasis>
6308 rather than the <emphasis>definition site</emphasis> of the function
6309 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6312 This inlining occurs regardless of the argument to the call
6313 or the size of <literal>f</literal>'s definition; it is unconditional.
6314 The main caveat is that <literal>f</literal>'s definition must be
6315 visible to the compiler. That is, <literal>f</literal> must be
6316 let-bound in the current scope.
6317 If no inlining takes place, the <literal>inline</literal> function
6318 expands to the identity function in Phase zero; so its use imposes
6321 <para> If the function is defined in another
6322 module, GHC only exposes its inlining in the interface file if the
6323 function is sufficiently small that it <emphasis>might</emphasis> be
6324 inlined by the automatic mechanism. There is currently no way to tell
6325 GHC to expose arbitrarily-large functions in the interface file. (This
6326 shortcoming is something that could be fixed, with some kind of pragma.)
6330 <sect2> <title>The <literal>lazy</literal> function </title>
6332 The <literal>lazy</literal> function restrains strictness analysis a little:
6336 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6337 but <literal>lazy</literal> has a magical property so far as strictness
6338 analysis is concerned: it is lazy in its first argument,
6339 even though its semantics is strict. After strictness analysis has run,
6340 calls to <literal>lazy</literal> are inlined to be the identity function.
6343 This behaviour is occasionally useful when controlling evaluation order.
6344 Notably, <literal>lazy</literal> is used in the library definition of
6345 <literal>Control.Parallel.par</literal>:
6348 par x y = case (par# x) of { _ -> lazy y }
6350 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6351 look strict in <literal>y</literal> which would defeat the whole
6352 purpose of <literal>par</literal>.
6355 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6361 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6363 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6364 typechecker entirely. It has type
6366 unsafeCoerce# :: a -> b
6368 That is, it allows you to coerce any type into any other type. If you use this
6369 function, you had better get it right, otherwise segmentation faults await.
6370 It is generally used when you want to write a program that you know is
6371 well-typed, but where Haskell's type system is not expressive enough to prove
6372 that it is well typed.
6375 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6376 although extremely bad things will happen if you coerce a boxed type
6385 <sect1 id="generic-classes">
6386 <title>Generic classes</title>
6389 The ideas behind this extension are described in detail in "Derivable type classes",
6390 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6391 An example will give the idea:
6399 fromBin :: [Int] -> (a, [Int])
6401 toBin {| Unit |} Unit = []
6402 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6403 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6404 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6406 fromBin {| Unit |} bs = (Unit, bs)
6407 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6408 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6409 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6410 (y,bs'') = fromBin bs'
6413 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6414 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6415 which are defined thus in the library module <literal>Generics</literal>:
6419 data a :+: b = Inl a | Inr b
6420 data a :*: b = a :*: b
6423 Now you can make a data type into an instance of Bin like this:
6425 instance (Bin a, Bin b) => Bin (a,b)
6426 instance Bin a => Bin [a]
6428 That is, just leave off the "where" clause. Of course, you can put in the
6429 where clause and over-ride whichever methods you please.
6433 <title> Using generics </title>
6434 <para>To use generics you need to</para>
6437 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6438 <option>-fgenerics</option> (to generate extra per-data-type code),
6439 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6443 <para>Import the module <literal>Generics</literal> from the
6444 <literal>lang</literal> package. This import brings into
6445 scope the data types <literal>Unit</literal>,
6446 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6447 don't need this import if you don't mention these types
6448 explicitly; for example, if you are simply giving instance
6449 declarations.)</para>
6454 <sect2> <title> Changes wrt the paper </title>
6456 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6457 can be written infix (indeed, you can now use
6458 any operator starting in a colon as an infix type constructor). Also note that
6459 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6460 Finally, note that the syntax of the type patterns in the class declaration
6461 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6462 alone would ambiguous when they appear on right hand sides (an extension we
6463 anticipate wanting).
6467 <sect2> <title>Terminology and restrictions</title>
6469 Terminology. A "generic default method" in a class declaration
6470 is one that is defined using type patterns as above.
6471 A "polymorphic default method" is a default method defined as in Haskell 98.
6472 A "generic class declaration" is a class declaration with at least one
6473 generic default method.
6481 Alas, we do not yet implement the stuff about constructor names and
6488 A generic class can have only one parameter; you can't have a generic
6489 multi-parameter class.
6495 A default method must be defined entirely using type patterns, or entirely
6496 without. So this is illegal:
6499 op :: a -> (a, Bool)
6500 op {| Unit |} Unit = (Unit, True)
6503 However it is perfectly OK for some methods of a generic class to have
6504 generic default methods and others to have polymorphic default methods.
6510 The type variable(s) in the type pattern for a generic method declaration
6511 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:
6515 op {| p :*: q |} (x :*: y) = op (x :: p)
6523 The type patterns in a generic default method must take one of the forms:
6529 where "a" and "b" are type variables. Furthermore, all the type patterns for
6530 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6531 must use the same type variables. So this is illegal:
6535 op {| a :+: b |} (Inl x) = True
6536 op {| p :+: q |} (Inr y) = False
6538 The type patterns must be identical, even in equations for different methods of the class.
6539 So this too is illegal:
6543 op1 {| a :*: b |} (x :*: y) = True
6546 op2 {| p :*: q |} (x :*: y) = False
6548 (The reason for this restriction is that we gather all the equations for a particular type consructor
6549 into a single generic instance declaration.)
6555 A generic method declaration must give a case for each of the three type constructors.
6561 The type for a generic method can be built only from:
6563 <listitem> <para> Function arrows </para> </listitem>
6564 <listitem> <para> Type variables </para> </listitem>
6565 <listitem> <para> Tuples </para> </listitem>
6566 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6568 Here are some example type signatures for generic methods:
6571 op2 :: Bool -> (a,Bool)
6572 op3 :: [Int] -> a -> a
6575 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6579 This restriction is an implementation restriction: we just havn't got around to
6580 implementing the necessary bidirectional maps over arbitrary type constructors.
6581 It would be relatively easy to add specific type constructors, such as Maybe and list,
6582 to the ones that are allowed.</para>
6587 In an instance declaration for a generic class, the idea is that the compiler
6588 will fill in the methods for you, based on the generic templates. However it can only
6593 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6598 No constructor of the instance type has unboxed fields.
6602 (Of course, these things can only arise if you are already using GHC extensions.)
6603 However, you can still give an instance declarations for types which break these rules,
6604 provided you give explicit code to override any generic default methods.
6612 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6613 what the compiler does with generic declarations.
6618 <sect2> <title> Another example </title>
6620 Just to finish with, here's another example I rather like:
6624 nCons {| Unit |} _ = 1
6625 nCons {| a :*: b |} _ = 1
6626 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6629 tag {| Unit |} _ = 1
6630 tag {| a :*: b |} _ = 1
6631 tag {| a :+: b |} (Inl x) = tag x
6632 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6638 <sect1 id="monomorphism">
6639 <title>Control over monomorphism</title>
6641 <para>GHC supports two flags that control the way in which generalisation is
6642 carried out at let and where bindings.
6646 <title>Switching off the dreaded Monomorphism Restriction</title>
6647 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6649 <para>Haskell's monomorphism restriction (see
6650 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6652 of the Haskell Report)
6653 can be completely switched off by
6654 <option>-fno-monomorphism-restriction</option>.
6659 <title>Monomorphic pattern bindings</title>
6660 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6661 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6663 <para> As an experimental change, we are exploring the possibility of
6664 making pattern bindings monomorphic; that is, not generalised at all.
6665 A pattern binding is a binding whose LHS has no function arguments,
6666 and is not a simple variable. For example:
6668 f x = x -- Not a pattern binding
6669 f = \x -> x -- Not a pattern binding
6670 f :: Int -> Int = \x -> x -- Not a pattern binding
6672 (g,h) = e -- A pattern binding
6673 (f) = e -- A pattern binding
6674 [x] = e -- A pattern binding
6676 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6677 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6686 ;;; Local Variables: ***
6688 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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