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 <ulink
556 url="../libraries/index.html">library
557 documentation</ulink>. More libraries to install are available
559 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
562 <!-- ====================== PATTERN GUARDS ======================= -->
564 <sect2 id="pattern-guards">
565 <title>Pattern guards</title>
568 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
569 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.)
573 Suppose we have an abstract data type of finite maps, with a
577 lookup :: FiniteMap -> Int -> Maybe Int
580 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
581 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
585 clunky env var1 var2 | ok1 && ok2 = val1 + val2
586 | otherwise = var1 + var2
597 The auxiliary functions are
601 maybeToBool :: Maybe a -> Bool
602 maybeToBool (Just x) = True
603 maybeToBool Nothing = False
605 expectJust :: Maybe a -> a
606 expectJust (Just x) = x
607 expectJust Nothing = error "Unexpected Nothing"
611 What is <function>clunky</function> doing? The guard <literal>ok1 &&
612 ok2</literal> checks that both lookups succeed, using
613 <function>maybeToBool</function> to convert the <function>Maybe</function>
614 types to booleans. The (lazily evaluated) <function>expectJust</function>
615 calls extract the values from the results of the lookups, and binds the
616 returned values to <varname>val1</varname> and <varname>val2</varname>
617 respectively. If either lookup fails, then clunky takes the
618 <literal>otherwise</literal> case and returns the sum of its arguments.
622 This is certainly legal Haskell, but it is a tremendously verbose and
623 un-obvious way to achieve the desired effect. Arguably, a more direct way
624 to write clunky would be to use case expressions:
628 clunky env var1 var2 = case lookup env var1 of
630 Just val1 -> case lookup env var2 of
632 Just val2 -> val1 + val2
638 This is a bit shorter, but hardly better. Of course, we can rewrite any set
639 of pattern-matching, guarded equations as case expressions; that is
640 precisely what the compiler does when compiling equations! The reason that
641 Haskell provides guarded equations is because they allow us to write down
642 the cases we want to consider, one at a time, independently of each other.
643 This structure is hidden in the case version. Two of the right-hand sides
644 are really the same (<function>fail</function>), and the whole expression
645 tends to become more and more indented.
649 Here is how I would write clunky:
654 | Just val1 <- lookup env var1
655 , Just val2 <- lookup env var2
657 ...other equations for clunky...
661 The semantics should be clear enough. The qualifiers are matched in order.
662 For a <literal><-</literal> qualifier, which I call a pattern guard, the
663 right hand side is evaluated and matched against the pattern on the left.
664 If the match fails then the whole guard fails and the next equation is
665 tried. If it succeeds, then the appropriate binding takes place, and the
666 next qualifier is matched, in the augmented environment. Unlike list
667 comprehensions, however, the type of the expression to the right of the
668 <literal><-</literal> is the same as the type of the pattern to its
669 left. The bindings introduced by pattern guards scope over all the
670 remaining guard qualifiers, and over the right hand side of the equation.
674 Just as with list comprehensions, boolean expressions can be freely mixed
675 with among the pattern guards. For example:
686 Haskell's current guards therefore emerge as a special case, in which the
687 qualifier list has just one element, a boolean expression.
691 <!-- ===================== Recursive do-notation =================== -->
693 <sect2 id="mdo-notation">
694 <title>The recursive do-notation
697 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
698 "A recursive do for Haskell",
699 Levent Erkok, John Launchbury",
700 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
703 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
704 that is, the variables bound in a do-expression are visible only in the textually following
705 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
706 group. It turns out that several applications can benefit from recursive bindings in
707 the do-notation, and this extension provides the necessary syntactic support.
710 Here is a simple (yet contrived) example:
713 import Control.Monad.Fix
715 justOnes = mdo xs <- Just (1:xs)
719 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
723 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
726 class Monad m => MonadFix m where
727 mfix :: (a -> m a) -> m a
730 The function <literal>mfix</literal>
731 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
732 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
733 For details, see the above mentioned reference.
736 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
737 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
738 for Haskell's internal state monad (strict and lazy, respectively).
741 There are three important points in using the recursive-do notation:
744 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
745 than <literal>do</literal>).
749 You should <literal>import Control.Monad.Fix</literal>.
750 (Note: Strictly speaking, this import is required only when you need to refer to the name
751 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
752 are encouraged to always import this module when using the mdo-notation.)
756 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
762 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
763 contains up to date information on recursive monadic bindings.
767 Historical note: The old implementation of the mdo-notation (and most
768 of the existing documents) used the name
769 <literal>MonadRec</literal> for the class and the corresponding library.
770 This name is not supported by GHC.
776 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
778 <sect2 id="parallel-list-comprehensions">
779 <title>Parallel List Comprehensions</title>
780 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
782 <indexterm><primary>parallel list comprehensions</primary>
785 <para>Parallel list comprehensions are a natural extension to list
786 comprehensions. List comprehensions can be thought of as a nice
787 syntax for writing maps and filters. Parallel comprehensions
788 extend this to include the zipWith family.</para>
790 <para>A parallel list comprehension has multiple independent
791 branches of qualifier lists, each separated by a `|' symbol. For
792 example, the following zips together two lists:</para>
795 [ (x, y) | x <- xs | y <- ys ]
798 <para>The behavior of parallel list comprehensions follows that of
799 zip, in that the resulting list will have the same length as the
800 shortest branch.</para>
802 <para>We can define parallel list comprehensions by translation to
803 regular comprehensions. Here's the basic idea:</para>
805 <para>Given a parallel comprehension of the form: </para>
808 [ e | p1 <- e11, p2 <- e12, ...
809 | q1 <- e21, q2 <- e22, ...
814 <para>This will be translated to: </para>
817 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
818 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
823 <para>where `zipN' is the appropriate zip for the given number of
828 <sect2 id="rebindable-syntax">
829 <title>Rebindable syntax</title>
832 <para>GHC allows most kinds of built-in syntax to be rebound by
833 the user, to facilitate replacing the <literal>Prelude</literal>
834 with a home-grown version, for example.</para>
836 <para>You may want to define your own numeric class
837 hierarchy. It completely defeats that purpose if the
838 literal "1" means "<literal>Prelude.fromInteger
839 1</literal>", which is what the Haskell Report specifies.
840 So the <option>-fno-implicit-prelude</option> flag causes
841 the following pieces of built-in syntax to refer to
842 <emphasis>whatever is in scope</emphasis>, not the Prelude
847 <para>An integer literal <literal>368</literal> means
848 "<literal>fromInteger (368::Integer)</literal>", rather than
849 "<literal>Prelude.fromInteger (368::Integer)</literal>".
852 <listitem><para>Fractional literals are handed in just the same way,
853 except that the translation is
854 <literal>fromRational (3.68::Rational)</literal>.
857 <listitem><para>The equality test in an overloaded numeric pattern
858 uses whatever <literal>(==)</literal> is in scope.
861 <listitem><para>The subtraction operation, and the
862 greater-than-or-equal test, in <literal>n+k</literal> patterns
863 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
867 <para>Negation (e.g. "<literal>- (f x)</literal>")
868 means "<literal>negate (f x)</literal>", both in numeric
869 patterns, and expressions.
873 <para>"Do" notation is translated using whatever
874 functions <literal>(>>=)</literal>,
875 <literal>(>>)</literal>, and <literal>fail</literal>,
876 are in scope (not the Prelude
877 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
878 comprehensions, are unaffected. </para></listitem>
882 notation (see <xref linkend="arrow-notation"/>)
883 uses whatever <literal>arr</literal>,
884 <literal>(>>>)</literal>, <literal>first</literal>,
885 <literal>app</literal>, <literal>(|||)</literal> and
886 <literal>loop</literal> functions are in scope. But unlike the
887 other constructs, the types of these functions must match the
888 Prelude types very closely. Details are in flux; if you want
892 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
893 even if that is a little unexpected. For emample, the
894 static semantics of the literal <literal>368</literal>
895 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
896 <literal>fromInteger</literal> to have any of the types:
898 fromInteger :: Integer -> Integer
899 fromInteger :: forall a. Foo a => Integer -> a
900 fromInteger :: Num a => a -> Integer
901 fromInteger :: Integer -> Bool -> Bool
905 <para>Be warned: this is an experimental facility, with
906 fewer checks than usual. Use <literal>-dcore-lint</literal>
907 to typecheck the desugared program. If Core Lint is happy
908 you should be all right.</para>
912 <sect2 id="postfix-operators">
913 <title>Postfix operators</title>
916 GHC allows a small extension to the syntax of left operator sections, which
917 allows you to define postfix operators. The extension is this: the left section
921 is equivalent (from the point of view of both type checking and execution) to the expression
925 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
926 The strict Haskell 98 interpretation is that the section is equivalent to
930 That is, the operator must be a function of two arguments. GHC allows it to
931 take only one argument, and that in turn allows you to write the function
934 <para>Since this extension goes beyond Haskell 98, it should really be enabled
935 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
936 change their behaviour, of course.)
938 <para>The extension does not extend to the left-hand side of function
939 definitions; you must define such a function in prefix form.</para>
946 <!-- TYPE SYSTEM EXTENSIONS -->
947 <sect1 id="data-type-extensions">
948 <title>Extensions to data types and type synonyms</title>
950 <sect2 id="nullary-types">
951 <title>Data types with no constructors</title>
953 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
954 a data type with no constructors. For example:</para>
958 data T a -- T :: * -> *
961 <para>Syntactically, the declaration lacks the "= constrs" part. The
962 type can be parameterised over types of any kind, but if the kind is
963 not <literal>*</literal> then an explicit kind annotation must be used
964 (see <xref linkend="kinding"/>).</para>
966 <para>Such data types have only one value, namely bottom.
967 Nevertheless, they can be useful when defining "phantom types".</para>
970 <sect2 id="infix-tycons">
971 <title>Infix type constructors, classes, and type variables</title>
974 GHC allows type constructors, classes, and type variables to be operators, and
975 to be written infix, very much like expressions. More specifically:
978 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
979 The lexical syntax is the same as that for data constructors.
982 Data type and type-synonym declarations can be written infix, parenthesised
983 if you want further arguments. E.g.
985 data a :*: b = Foo a b
986 type a :+: b = Either a b
987 class a :=: b where ...
989 data (a :**: b) x = Baz a b x
990 type (a :++: b) y = Either (a,b) y
994 Types, and class constraints, can be written infix. For example
997 f :: (a :=: b) => a -> b
1001 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1002 The lexical syntax is the same as that for variable operators, excluding "(.)",
1003 "(!)", and "(*)". In a binding position, the operator must be
1004 parenthesised. For example:
1006 type T (+) = Int + Int
1010 liftA2 :: Arrow (~>)
1011 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1017 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1018 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1021 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1022 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1023 sets the fixity for a data constructor and the corresponding type constructor. For example:
1027 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1028 and similarly for <literal>:*:</literal>.
1029 <literal>Int `a` Bool</literal>.
1032 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1039 <sect2 id="type-synonyms">
1040 <title>Liberalised type synonyms</title>
1043 Type synonyms are like macros at the type level, and
1044 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1045 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1047 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1048 in a type synonym, thus:
1050 type Discard a = forall b. Show b => a -> b -> (a, String)
1055 g :: Discard Int -> (Int,String) -- A rank-2 type
1062 You can write an unboxed tuple in a type synonym:
1064 type Pr = (# Int, Int #)
1072 You can apply a type synonym to a forall type:
1074 type Foo a = a -> a -> Bool
1076 f :: Foo (forall b. b->b)
1078 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1080 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1085 You can apply a type synonym to a partially applied type synonym:
1087 type Generic i o = forall x. i x -> o x
1090 foo :: Generic Id []
1092 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1094 foo :: forall x. x -> [x]
1102 GHC currently does kind checking before expanding synonyms (though even that
1106 After expanding type synonyms, GHC does validity checking on types, looking for
1107 the following mal-formedness which isn't detected simply by kind checking:
1110 Type constructor applied to a type involving for-alls.
1113 Unboxed tuple on left of an arrow.
1116 Partially-applied type synonym.
1120 this will be rejected:
1122 type Pr = (# Int, Int #)
1127 because GHC does not allow unboxed tuples on the left of a function arrow.
1132 <sect2 id="existential-quantification">
1133 <title>Existentially quantified data constructors
1137 The idea of using existential quantification in data type declarations
1138 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1139 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1140 London, 1991). It was later formalised by Laufer and Odersky
1141 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1142 TOPLAS, 16(5), pp1411-1430, 1994).
1143 It's been in Lennart
1144 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1145 proved very useful. Here's the idea. Consider the declaration:
1151 data Foo = forall a. MkFoo a (a -> Bool)
1158 The data type <literal>Foo</literal> has two constructors with types:
1164 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1171 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1172 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1173 For example, the following expression is fine:
1179 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1185 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1186 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1187 isUpper</function> packages a character with a compatible function. These
1188 two things are each of type <literal>Foo</literal> and can be put in a list.
1192 What can we do with a value of type <literal>Foo</literal>?. In particular,
1193 what happens when we pattern-match on <function>MkFoo</function>?
1199 f (MkFoo val fn) = ???
1205 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1206 are compatible, the only (useful) thing we can do with them is to
1207 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1214 f (MkFoo val fn) = fn val
1220 What this allows us to do is to package heterogenous values
1221 together with a bunch of functions that manipulate them, and then treat
1222 that collection of packages in a uniform manner. You can express
1223 quite a bit of object-oriented-like programming this way.
1226 <sect3 id="existential">
1227 <title>Why existential?
1231 What has this to do with <emphasis>existential</emphasis> quantification?
1232 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1238 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1244 But Haskell programmers can safely think of the ordinary
1245 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1246 adding a new existential quantification construct.
1252 <title>Type classes</title>
1255 An easy extension is to allow
1256 arbitrary contexts before the constructor. For example:
1262 data Baz = forall a. Eq a => Baz1 a a
1263 | forall b. Show b => Baz2 b (b -> b)
1269 The two constructors have the types you'd expect:
1275 Baz1 :: forall a. Eq a => a -> a -> Baz
1276 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1282 But when pattern matching on <function>Baz1</function> the matched values can be compared
1283 for equality, and when pattern matching on <function>Baz2</function> the first matched
1284 value can be converted to a string (as well as applying the function to it).
1285 So this program is legal:
1292 f (Baz1 p q) | p == q = "Yes"
1294 f (Baz2 v fn) = show (fn v)
1300 Operationally, in a dictionary-passing implementation, the
1301 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1302 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1303 extract it on pattern matching.
1307 Notice the way that the syntax fits smoothly with that used for
1308 universal quantification earlier.
1313 <sect3 id="existential-records">
1314 <title>Record Constructors</title>
1317 GHC allows existentials to be used with records syntax as well. For example:
1320 data Counter a = forall self. NewCounter
1322 , _inc :: self -> self
1323 , _display :: self -> IO ()
1327 Here <literal>tag</literal> is a public field, with a well-typed selector
1328 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1329 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1330 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1331 compile-time error. In other words, <emphasis>GHC defines a record selector function
1332 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1333 (This example used an underscore in the fields for which record selectors
1334 will not be defined, but that is only programming style; GHC ignores them.)
1338 To make use of these hidden fields, we need to create some helper functions:
1341 inc :: Counter a -> Counter a
1342 inc (NewCounter x i d t) = NewCounter
1343 { _this = i x, _inc = i, _display = d, tag = t }
1345 display :: Counter a -> IO ()
1346 display NewCounter{ _this = x, _display = d } = d x
1349 Now we can define counters with different underlying implementations:
1352 counterA :: Counter String
1353 counterA = NewCounter
1354 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1356 counterB :: Counter String
1357 counterB = NewCounter
1358 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1361 display (inc counterA) -- prints "1"
1362 display (inc (inc counterB)) -- prints "##"
1365 At the moment, record update syntax is only supported for Haskell 98 data types,
1366 so the following function does <emphasis>not</emphasis> work:
1369 -- This is invalid; use explicit NewCounter instead for now
1370 setTag :: Counter a -> a -> Counter a
1371 setTag obj t = obj{ tag = t }
1380 <title>Restrictions</title>
1383 There are several restrictions on the ways in which existentially-quantified
1384 constructors can be use.
1393 When pattern matching, each pattern match introduces a new,
1394 distinct, type for each existential type variable. These types cannot
1395 be unified with any other type, nor can they escape from the scope of
1396 the pattern match. For example, these fragments are incorrect:
1404 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1405 is the result of <function>f1</function>. One way to see why this is wrong is to
1406 ask what type <function>f1</function> has:
1410 f1 :: Foo -> a -- Weird!
1414 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1419 f1 :: forall a. Foo -> a -- Wrong!
1423 The original program is just plain wrong. Here's another sort of error
1427 f2 (Baz1 a b) (Baz1 p q) = a==q
1431 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1432 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1433 from the two <function>Baz1</function> constructors.
1441 You can't pattern-match on an existentially quantified
1442 constructor in a <literal>let</literal> or <literal>where</literal> group of
1443 bindings. So this is illegal:
1447 f3 x = a==b where { Baz1 a b = x }
1450 Instead, use a <literal>case</literal> expression:
1453 f3 x = case x of Baz1 a b -> a==b
1456 In general, you can only pattern-match
1457 on an existentially-quantified constructor in a <literal>case</literal> expression or
1458 in the patterns of a function definition.
1460 The reason for this restriction is really an implementation one.
1461 Type-checking binding groups is already a nightmare without
1462 existentials complicating the picture. Also an existential pattern
1463 binding at the top level of a module doesn't make sense, because it's
1464 not clear how to prevent the existentially-quantified type "escaping".
1465 So for now, there's a simple-to-state restriction. We'll see how
1473 You can't use existential quantification for <literal>newtype</literal>
1474 declarations. So this is illegal:
1478 newtype T = forall a. Ord a => MkT a
1482 Reason: a value of type <literal>T</literal> must be represented as a
1483 pair of a dictionary for <literal>Ord t</literal> and a value of type
1484 <literal>t</literal>. That contradicts the idea that
1485 <literal>newtype</literal> should have no concrete representation.
1486 You can get just the same efficiency and effect by using
1487 <literal>data</literal> instead of <literal>newtype</literal>. If
1488 there is no overloading involved, then there is more of a case for
1489 allowing an existentially-quantified <literal>newtype</literal>,
1490 because the <literal>data</literal> version does carry an
1491 implementation cost, but single-field existentially quantified
1492 constructors aren't much use. So the simple restriction (no
1493 existential stuff on <literal>newtype</literal>) stands, unless there
1494 are convincing reasons to change it.
1502 You can't use <literal>deriving</literal> to define instances of a
1503 data type with existentially quantified data constructors.
1505 Reason: in most cases it would not make sense. For example:;
1508 data T = forall a. MkT [a] deriving( Eq )
1511 To derive <literal>Eq</literal> in the standard way we would need to have equality
1512 between the single component of two <function>MkT</function> constructors:
1516 (MkT a) == (MkT b) = ???
1519 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1520 It's just about possible to imagine examples in which the derived instance
1521 would make sense, but it seems altogether simpler simply to prohibit such
1522 declarations. Define your own instances!
1533 <!-- ====================== Generalised algebraic data types ======================= -->
1535 <sect2 id="gadt-style">
1536 <title>Declaring data types with explicit constructor signatures</title>
1538 <para>GHC allows you to declare an algebraic data type by
1539 giving the type signatures of constructors explicitly. For example:
1543 Just :: a -> Maybe a
1545 The form is called a "GADT-style declaration"
1546 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1547 can only be declared using this form.</para>
1548 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1549 For example, these two declarations are equivalent:
1551 data Foo = forall a. MkFoo a (a -> Bool)
1552 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1555 <para>Any data type that can be declared in standard Haskell-98 syntax
1556 can also be declared using GADT-style syntax.
1557 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1558 they treat class constraints on the data constructors differently.
1559 Specifically, if the constructor is given a type-class context, that
1560 context is made available by pattern matching. For example:
1563 MkSet :: Eq a => [a] -> Set a
1565 makeSet :: Eq a => [a] -> Set a
1566 makeSet xs = MkSet (nub xs)
1568 insert :: a -> Set a -> Set a
1569 insert a (MkSet as) | a `elem` as = MkSet as
1570 | otherwise = MkSet (a:as)
1572 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1573 gives rise to a <literal>(Eq a)</literal>
1574 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1575 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1576 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1577 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1578 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1579 In the example, the equality dictionary is used to satisfy the equality constraint
1580 generated by the call to <literal>elem</literal>, so that the type of
1581 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1583 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1584 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1585 In Haskell 98 the defintion
1587 data Eq a => Set' a = MkSet' [a]
1589 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1590 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1591 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1592 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1593 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1595 For example, a possible application of GHC's behaviour is to reify dictionaries:
1597 data NumInst a where
1598 MkNumInst :: Num a => NumInst a
1600 intInst :: NumInst Int
1603 plus :: NumInst a -> a -> a -> a
1604 plus MkNumInst p q = p + q
1606 Here, a value of type <literal>NumInst a</literal> is equivalent
1607 to an explicit <literal>(Num a)</literal> dictionary.
1611 The rest of this section gives further details about GADT-style data
1616 The result type of each data constructor must begin with the type constructor being defined.
1617 If the result type of all constructors
1618 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1619 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1620 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1624 The type signature of
1625 each constructor is independent, and is implicitly universally quantified as usual.
1626 Different constructors may have different universally-quantified type variables
1627 and different type-class constraints.
1628 For example, this is fine:
1631 T1 :: Eq b => b -> T b
1632 T2 :: (Show c, Ix c) => c -> [c] -> T c
1637 Unlike a Haskell-98-style
1638 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1639 have no scope. Indeed, one can write a kind signature instead:
1641 data Set :: * -> * where ...
1643 or even a mixture of the two:
1645 data Foo a :: (* -> *) -> * where ...
1647 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1650 data Foo a (b :: * -> *) where ...
1656 You can use strictness annotations, in the obvious places
1657 in the constructor type:
1660 Lit :: !Int -> Term Int
1661 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1662 Pair :: Term a -> Term b -> Term (a,b)
1667 You can use a <literal>deriving</literal> clause on a GADT-style data type
1668 declaration. For example, these two declarations are equivalent
1670 data Maybe1 a where {
1671 Nothing1 :: Maybe1 a ;
1672 Just1 :: a -> Maybe1 a
1673 } deriving( Eq, Ord )
1675 data Maybe2 a = Nothing2 | Just2 a
1681 You can use record syntax on a GADT-style data type declaration:
1685 Adult { name :: String, children :: [Person] } :: Person
1686 Child { name :: String } :: Person
1688 As usual, for every constructor that has a field <literal>f</literal>, the type of
1689 field <literal>f</literal> must be the same (modulo alpha conversion).
1692 At the moment, record updates are not yet possible with GADT-style declarations,
1693 so support is limited to record construction, selection and pattern matching.
1696 aPerson = Adult { name = "Fred", children = [] }
1698 shortName :: Person -> Bool
1699 hasChildren (Adult { children = kids }) = not (null kids)
1700 hasChildren (Child {}) = False
1705 As in the case of existentials declared using the Haskell-98-like record syntax
1706 (<xref linkend="existential-records"/>),
1707 record-selector functions are generated only for those fields that have well-typed
1709 Here is the example of that section, in GADT-style syntax:
1711 data Counter a where
1712 NewCounter { _this :: self
1713 , _inc :: self -> self
1714 , _display :: self -> IO ()
1719 As before, only one selector function is generated here, that for <literal>tag</literal>.
1720 Nevertheless, you can still use all the field names in pattern matching and record construction.
1722 </itemizedlist></para>
1726 <title>Generalised Algebraic Data Types (GADTs)</title>
1728 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1729 by allowing constructors to have richer return types. Here is an example:
1732 Lit :: Int -> Term Int
1733 Succ :: Term Int -> Term Int
1734 IsZero :: Term Int -> Term Bool
1735 If :: Term Bool -> Term a -> Term a -> Term a
1736 Pair :: Term a -> Term b -> Term (a,b)
1738 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1739 case with ordinary data types. This generality allows us to
1740 write a well-typed <literal>eval</literal> function
1741 for these <literal>Terms</literal>:
1745 eval (Succ t) = 1 + eval t
1746 eval (IsZero t) = eval t == 0
1747 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1748 eval (Pair e1 e2) = (eval e1, eval e2)
1750 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1751 For example, in the right hand side of the equation
1756 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1757 A precise specification of the type rules is beyond what this user manual aspires to,
1758 but the design closely follows that described in
1760 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1761 unification-based type inference for GADTs</ulink>,
1763 The general principle is this: <emphasis>type refinement is only carried out
1764 based on user-supplied type annotations</emphasis>.
1765 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1766 and lots of obscure error messages will
1767 occur. However, the refinement is quite general. For example, if we had:
1769 eval :: Term a -> a -> a
1770 eval (Lit i) j = i+j
1772 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1773 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1774 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1777 These and many other examples are given in papers by Hongwei Xi, and
1778 Tim Sheard. There is a longer introduction
1779 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1781 <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
1782 may use different notation to that implemented in GHC.
1785 The rest of this section outlines the extensions to GHC that support GADTs.
1788 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1789 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1790 The result type of each constructor must begin with the type constructor being defined,
1791 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1792 For example, in the <literal>Term</literal> data
1793 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1794 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1799 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1800 an ordianary data type.
1804 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1808 Lit { val :: Int } :: Term Int
1809 Succ { num :: Term Int } :: Term Int
1810 Pred { num :: Term Int } :: Term Int
1811 IsZero { arg :: Term Int } :: Term Bool
1812 Pair { arg1 :: Term a
1815 If { cnd :: Term Bool
1820 However, for GADTs there is the following additional constraint:
1821 every constructor that has a field <literal>f</literal> must have
1822 the same result type (modulo alpha conversion)
1823 Hence, in the above example, we cannot merge the <literal>num</literal>
1824 and <literal>arg</literal> fields above into a
1825 single name. Although their field types are both <literal>Term Int</literal>,
1826 their selector functions actually have different types:
1829 num :: Term Int -> Term Int
1830 arg :: Term Bool -> Term Int
1839 <!-- ====================== End of Generalised algebraic data types ======================= -->
1842 <sect2 id="deriving-typeable">
1843 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1846 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1847 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1848 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1849 classes <literal>Eq</literal>, <literal>Ord</literal>,
1850 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1853 GHC extends this list with two more classes that may be automatically derived
1854 (provided the <option>-fglasgow-exts</option> flag is specified):
1855 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1856 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1857 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1859 <para>An instance of <literal>Typeable</literal> can only be derived if the
1860 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1861 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1863 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1864 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1866 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1867 are used, and only <literal>Typeable1</literal> up to
1868 <literal>Typeable7</literal> are provided in the library.)
1869 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1870 class, whose kind suits that of the data type constructor, and
1871 then writing the data type instance by hand.
1875 <sect2 id="newtype-deriving">
1876 <title>Generalised derived instances for newtypes</title>
1879 When you define an abstract type using <literal>newtype</literal>, you may want
1880 the new type to inherit some instances from its representation. In
1881 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1882 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1883 other classes you have to write an explicit instance declaration. For
1884 example, if you define
1887 newtype Dollars = Dollars Int
1890 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1891 explicitly define an instance of <literal>Num</literal>:
1894 instance Num Dollars where
1895 Dollars a + Dollars b = Dollars (a+b)
1898 All the instance does is apply and remove the <literal>newtype</literal>
1899 constructor. It is particularly galling that, since the constructor
1900 doesn't appear at run-time, this instance declaration defines a
1901 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1902 dictionary, only slower!
1906 <sect3> <title> Generalising the deriving clause </title>
1908 GHC now permits such instances to be derived instead, so one can write
1910 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1913 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1914 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1915 derives an instance declaration of the form
1918 instance Num Int => Num Dollars
1921 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1925 We can also derive instances of constructor classes in a similar
1926 way. For example, suppose we have implemented state and failure monad
1927 transformers, such that
1930 instance Monad m => Monad (State s m)
1931 instance Monad m => Monad (Failure m)
1933 In Haskell 98, we can define a parsing monad by
1935 type Parser tok m a = State [tok] (Failure m) a
1938 which is automatically a monad thanks to the instance declarations
1939 above. With the extension, we can make the parser type abstract,
1940 without needing to write an instance of class <literal>Monad</literal>, via
1943 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1946 In this case the derived instance declaration is of the form
1948 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1951 Notice that, since <literal>Monad</literal> is a constructor class, the
1952 instance is a <emphasis>partial application</emphasis> of the new type, not the
1953 entire left hand side. We can imagine that the type declaration is
1954 ``eta-converted'' to generate the context of the instance
1959 We can even derive instances of multi-parameter classes, provided the
1960 newtype is the last class parameter. In this case, a ``partial
1961 application'' of the class appears in the <literal>deriving</literal>
1962 clause. For example, given the class
1965 class StateMonad s m | m -> s where ...
1966 instance Monad m => StateMonad s (State s m) where ...
1968 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1970 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1971 deriving (Monad, StateMonad [tok])
1974 The derived instance is obtained by completing the application of the
1975 class to the new type:
1978 instance StateMonad [tok] (State [tok] (Failure m)) =>
1979 StateMonad [tok] (Parser tok m)
1984 As a result of this extension, all derived instances in newtype
1985 declarations are treated uniformly (and implemented just by reusing
1986 the dictionary for the representation type), <emphasis>except</emphasis>
1987 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
1988 the newtype and its representation.
1992 <sect3> <title> A more precise specification </title>
1994 Derived instance declarations are constructed as follows. Consider the
1995 declaration (after expansion of any type synonyms)
1998 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2004 The <literal>ci</literal> are partial applications of
2005 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2006 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2009 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2012 The type <literal>t</literal> is an arbitrary type.
2015 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2016 nor in the <literal>ci</literal>, and
2019 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2020 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2021 should not "look through" the type or its constructor. You can still
2022 derive these classes for a newtype, but it happens in the usual way, not
2023 via this new mechanism.
2026 Then, for each <literal>ci</literal>, the derived instance
2029 instance ci t => ci (T v1...vk)
2031 As an example which does <emphasis>not</emphasis> work, consider
2033 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2035 Here we cannot derive the instance
2037 instance Monad (State s m) => Monad (NonMonad m)
2040 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2041 and so cannot be "eta-converted" away. It is a good thing that this
2042 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2043 not, in fact, a monad --- for the same reason. Try defining
2044 <literal>>>=</literal> with the correct type: you won't be able to.
2048 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2049 important, since we can only derive instances for the last one. If the
2050 <literal>StateMonad</literal> class above were instead defined as
2053 class StateMonad m s | m -> s where ...
2056 then we would not have been able to derive an instance for the
2057 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2058 classes usually have one "main" parameter for which deriving new
2059 instances is most interesting.
2061 <para>Lastly, all of this applies only for classes other than
2062 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2063 and <literal>Data</literal>, for which the built-in derivation applies (section
2064 4.3.3. of the Haskell Report).
2065 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2066 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2067 the standard method is used or the one described here.)
2073 <sect2 id="stand-alone-deriving">
2074 <title>Stand-alone deriving declarations</title>
2077 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2079 data Foo a = Bar a | Baz String
2081 derive instance Eq (Foo a)
2083 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2084 you can use it as a variable name elsewhere.</para>
2085 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2086 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2089 newtype Foo a = MkFoo (State Int a)
2091 derive instance MonadState Int Foo
2093 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2094 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2102 <!-- TYPE SYSTEM EXTENSIONS -->
2103 <sect1 id="other-type-extensions">
2104 <title>Other type system extensions</title>
2106 <sect2 id="multi-param-type-classes">
2107 <title>Class declarations</title>
2110 This section, and the next one, documents GHC's type-class extensions.
2111 There's lots of background in the paper <ulink
2112 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2113 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2114 Jones, Erik Meijer).
2117 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2121 <title>Multi-parameter type classes</title>
2123 Multi-parameter type classes are permitted. For example:
2127 class Collection c a where
2128 union :: c a -> c a -> c a
2136 <title>The superclasses of a class declaration</title>
2139 There are no restrictions on the context in a class declaration
2140 (which introduces superclasses), except that the class hierarchy must
2141 be acyclic. So these class declarations are OK:
2145 class Functor (m k) => FiniteMap m k where
2148 class (Monad m, Monad (t m)) => Transform t m where
2149 lift :: m a -> (t m) a
2155 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2156 of "acyclic" involves only the superclass relationships. For example,
2162 op :: D b => a -> b -> b
2165 class C a => D a where { ... }
2169 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2170 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2171 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2178 <sect3 id="class-method-types">
2179 <title>Class method types</title>
2182 Haskell 98 prohibits class method types to mention constraints on the
2183 class type variable, thus:
2186 fromList :: [a] -> s a
2187 elem :: Eq a => a -> s a -> Bool
2189 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2190 contains the constraint <literal>Eq a</literal>, constrains only the
2191 class type variable (in this case <literal>a</literal>).
2192 GHC lifts this restriction.
2199 <sect2 id="functional-dependencies">
2200 <title>Functional dependencies
2203 <para> Functional dependencies are implemented as described by Mark Jones
2204 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2205 In Proceedings of the 9th European Symposium on Programming,
2206 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2210 Functional dependencies are introduced by a vertical bar in the syntax of a
2211 class declaration; e.g.
2213 class (Monad m) => MonadState s m | m -> s where ...
2215 class Foo a b c | a b -> c where ...
2217 There should be more documentation, but there isn't (yet). Yell if you need it.
2220 <sect3><title>Rules for functional dependencies </title>
2222 In a class declaration, all of the class type variables must be reachable (in the sense
2223 mentioned in <xref linkend="type-restrictions"/>)
2224 from the free variables of each method type.
2228 class Coll s a where
2230 insert :: s -> a -> s
2233 is not OK, because the type of <literal>empty</literal> doesn't mention
2234 <literal>a</literal>. Functional dependencies can make the type variable
2237 class Coll s a | s -> a where
2239 insert :: s -> a -> s
2242 Alternatively <literal>Coll</literal> might be rewritten
2245 class Coll s a where
2247 insert :: s a -> a -> s a
2251 which makes the connection between the type of a collection of
2252 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2253 Occasionally this really doesn't work, in which case you can split the
2261 class CollE s => Coll s a where
2262 insert :: s -> a -> s
2269 <title>Background on functional dependencies</title>
2271 <para>The following description of the motivation and use of functional dependencies is taken
2272 from the Hugs user manual, reproduced here (with minor changes) by kind
2273 permission of Mark Jones.
2276 Consider the following class, intended as part of a
2277 library for collection types:
2279 class Collects e ce where
2281 insert :: e -> ce -> ce
2282 member :: e -> ce -> Bool
2284 The type variable e used here represents the element type, while ce is the type
2285 of the container itself. Within this framework, we might want to define
2286 instances of this class for lists or characteristic functions (both of which
2287 can be used to represent collections of any equality type), bit sets (which can
2288 be used to represent collections of characters), or hash tables (which can be
2289 used to represent any collection whose elements have a hash function). Omitting
2290 standard implementation details, this would lead to the following declarations:
2292 instance Eq e => Collects e [e] where ...
2293 instance Eq e => Collects e (e -> Bool) where ...
2294 instance Collects Char BitSet where ...
2295 instance (Hashable e, Collects a ce)
2296 => Collects e (Array Int ce) where ...
2298 All this looks quite promising; we have a class and a range of interesting
2299 implementations. Unfortunately, there are some serious problems with the class
2300 declaration. First, the empty function has an ambiguous type:
2302 empty :: Collects e ce => ce
2304 By "ambiguous" we mean that there is a type variable e that appears on the left
2305 of the <literal>=></literal> symbol, but not on the right. The problem with
2306 this is that, according to the theoretical foundations of Haskell overloading,
2307 we cannot guarantee a well-defined semantics for any term with an ambiguous
2311 We can sidestep this specific problem by removing the empty member from the
2312 class declaration. However, although the remaining members, insert and member,
2313 do not have ambiguous types, we still run into problems when we try to use
2314 them. For example, consider the following two functions:
2316 f x y = insert x . insert y
2319 for which GHC infers the following types:
2321 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2322 g :: (Collects Bool c, Collects Char c) => c -> c
2324 Notice that the type for f allows the two parameters x and y to be assigned
2325 different types, even though it attempts to insert each of the two values, one
2326 after the other, into the same collection. If we're trying to model collections
2327 that contain only one type of value, then this is clearly an inaccurate
2328 type. Worse still, the definition for g is accepted, without causing a type
2329 error. As a result, the error in this code will not be flagged at the point
2330 where it appears. Instead, it will show up only when we try to use g, which
2331 might even be in a different module.
2334 <sect4><title>An attempt to use constructor classes</title>
2337 Faced with the problems described above, some Haskell programmers might be
2338 tempted to use something like the following version of the class declaration:
2340 class Collects e c where
2342 insert :: e -> c e -> c e
2343 member :: e -> c e -> Bool
2345 The key difference here is that we abstract over the type constructor c that is
2346 used to form the collection type c e, and not over that collection type itself,
2347 represented by ce in the original class declaration. This avoids the immediate
2348 problems that we mentioned above: empty has type <literal>Collects e c => c
2349 e</literal>, which is not ambiguous.
2352 The function f from the previous section has a more accurate type:
2354 f :: (Collects e c) => e -> e -> c e -> c e
2356 The function g from the previous section is now rejected with a type error as
2357 we would hope because the type of f does not allow the two arguments to have
2359 This, then, is an example of a multiple parameter class that does actually work
2360 quite well in practice, without ambiguity problems.
2361 There is, however, a catch. This version of the Collects class is nowhere near
2362 as general as the original class seemed to be: only one of the four instances
2363 for <literal>Collects</literal>
2364 given above can be used with this version of Collects because only one of
2365 them---the instance for lists---has a collection type that can be written in
2366 the form c e, for some type constructor c, and element type e.
2370 <sect4><title>Adding functional dependencies</title>
2373 To get a more useful version of the Collects class, Hugs provides a mechanism
2374 that allows programmers to specify dependencies between the parameters of a
2375 multiple parameter class (For readers with an interest in theoretical
2376 foundations and previous work: The use of dependency information can be seen
2377 both as a generalization of the proposal for `parametric type classes' that was
2378 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2379 later framework for "improvement" of qualified types. The
2380 underlying ideas are also discussed in a more theoretical and abstract setting
2381 in a manuscript [implparam], where they are identified as one point in a
2382 general design space for systems of implicit parameterization.).
2384 To start with an abstract example, consider a declaration such as:
2386 class C a b where ...
2388 which tells us simply that C can be thought of as a binary relation on types
2389 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2390 included in the definition of classes to add information about dependencies
2391 between parameters, as in the following examples:
2393 class D a b | a -> b where ...
2394 class E a b | a -> b, b -> a where ...
2396 The notation <literal>a -> b</literal> used here between the | and where
2397 symbols --- not to be
2398 confused with a function type --- indicates that the a parameter uniquely
2399 determines the b parameter, and might be read as "a determines b." Thus D is
2400 not just a relation, but actually a (partial) function. Similarly, from the two
2401 dependencies that are included in the definition of E, we can see that E
2402 represents a (partial) one-one mapping between types.
2405 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2406 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2407 m>=0, meaning that the y parameters are uniquely determined by the x
2408 parameters. Spaces can be used as separators if more than one variable appears
2409 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2410 annotated with multiple dependencies using commas as separators, as in the
2411 definition of E above. Some dependencies that we can write in this notation are
2412 redundant, and will be rejected because they don't serve any useful
2413 purpose, and may instead indicate an error in the program. Examples of
2414 dependencies like this include <literal>a -> a </literal>,
2415 <literal>a -> a a </literal>,
2416 <literal>a -> </literal>, etc. There can also be
2417 some redundancy if multiple dependencies are given, as in
2418 <literal>a->b</literal>,
2419 <literal>b->c </literal>, <literal>a->c </literal>, and
2420 in which some subset implies the remaining dependencies. Examples like this are
2421 not treated as errors. Note that dependencies appear only in class
2422 declarations, and not in any other part of the language. In particular, the
2423 syntax for instance declarations, class constraints, and types is completely
2427 By including dependencies in a class declaration, we provide a mechanism for
2428 the programmer to specify each multiple parameter class more precisely. The
2429 compiler, on the other hand, is responsible for ensuring that the set of
2430 instances that are in scope at any given point in the program is consistent
2431 with any declared dependencies. For example, the following pair of instance
2432 declarations cannot appear together in the same scope because they violate the
2433 dependency for D, even though either one on its own would be acceptable:
2435 instance D Bool Int where ...
2436 instance D Bool Char where ...
2438 Note also that the following declaration is not allowed, even by itself:
2440 instance D [a] b where ...
2442 The problem here is that this instance would allow one particular choice of [a]
2443 to be associated with more than one choice for b, which contradicts the
2444 dependency specified in the definition of D. More generally, this means that,
2445 in any instance of the form:
2447 instance D t s where ...
2449 for some particular types t and s, the only variables that can appear in s are
2450 the ones that appear in t, and hence, if the type t is known, then s will be
2451 uniquely determined.
2454 The benefit of including dependency information is that it allows us to define
2455 more general multiple parameter classes, without ambiguity problems, and with
2456 the benefit of more accurate types. To illustrate this, we return to the
2457 collection class example, and annotate the original definition of <literal>Collects</literal>
2458 with a simple dependency:
2460 class Collects e ce | ce -> e where
2462 insert :: e -> ce -> ce
2463 member :: e -> ce -> Bool
2465 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2466 determined by the type of the collection ce. Note that both parameters of
2467 Collects are of kind *; there are no constructor classes here. Note too that
2468 all of the instances of Collects that we gave earlier can be used
2469 together with this new definition.
2472 What about the ambiguity problems that we encountered with the original
2473 definition? The empty function still has type Collects e ce => ce, but it is no
2474 longer necessary to regard that as an ambiguous type: Although the variable e
2475 does not appear on the right of the => symbol, the dependency for class
2476 Collects tells us that it is uniquely determined by ce, which does appear on
2477 the right of the => symbol. Hence the context in which empty is used can still
2478 give enough information to determine types for both ce and e, without
2479 ambiguity. More generally, we need only regard a type as ambiguous if it
2480 contains a variable on the left of the => that is not uniquely determined
2481 (either directly or indirectly) by the variables on the right.
2484 Dependencies also help to produce more accurate types for user defined
2485 functions, and hence to provide earlier detection of errors, and less cluttered
2486 types for programmers to work with. Recall the previous definition for a
2489 f x y = insert x y = insert x . insert y
2491 for which we originally obtained a type:
2493 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2495 Given the dependency information that we have for Collects, however, we can
2496 deduce that a and b must be equal because they both appear as the second
2497 parameter in a Collects constraint with the same first parameter c. Hence we
2498 can infer a shorter and more accurate type for f:
2500 f :: (Collects a c) => a -> a -> c -> c
2502 In a similar way, the earlier definition of g will now be flagged as a type error.
2505 Although we have given only a few examples here, it should be clear that the
2506 addition of dependency information can help to make multiple parameter classes
2507 more useful in practice, avoiding ambiguity problems, and allowing more general
2508 sets of instance declarations.
2514 <sect2 id="instance-decls">
2515 <title>Instance declarations</title>
2517 <sect3 id="instance-rules">
2518 <title>Relaxed rules for instance declarations</title>
2520 <para>An instance declaration has the form
2522 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 ...
2524 The part before the "<literal>=></literal>" is the
2525 <emphasis>context</emphasis>, while the part after the
2526 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2530 In Haskell 98 the head of an instance declaration
2531 must be of the form <literal>C (T a1 ... an)</literal>, where
2532 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2533 and the <literal>a1 ... an</literal> are distinct type variables.
2534 Furthermore, the assertions in the context of the instance declaration
2535 must be of the form <literal>C a</literal> where <literal>a</literal>
2536 is a type variable that occurs in the head.
2539 The <option>-fglasgow-exts</option> flag loosens these restrictions
2540 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2541 the context and head of the instance declaration can each consist of arbitrary
2542 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2546 The Paterson Conditions: for each assertion in the context
2548 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2549 <listitem><para>The assertion has fewer constructors and variables (taken together
2550 and counting repetitions) than the head</para></listitem>
2554 <listitem><para>The Coverage Condition. For each functional dependency,
2555 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2556 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2557 every type variable in
2558 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2559 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2560 substitution mapping each type variable in the class declaration to the
2561 corresponding type in the instance declaration.
2564 These restrictions ensure that context reduction terminates: each reduction
2565 step makes the problem smaller by at least one
2566 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2567 if you give the <option>-fallow-undecidable-instances</option>
2568 flag (<xref linkend="undecidable-instances"/>).
2569 You can find lots of background material about the reason for these
2570 restrictions in the paper <ulink
2571 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2572 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2575 For example, these are OK:
2577 instance C Int [a] -- Multiple parameters
2578 instance Eq (S [a]) -- Structured type in head
2580 -- Repeated type variable in head
2581 instance C4 a a => C4 [a] [a]
2582 instance Stateful (ST s) (MutVar s)
2584 -- Head can consist of type variables only
2586 instance (Eq a, Show b) => C2 a b
2588 -- Non-type variables in context
2589 instance Show (s a) => Show (Sized s a)
2590 instance C2 Int a => C3 Bool [a]
2591 instance C2 Int a => C3 [a] b
2595 -- Context assertion no smaller than head
2596 instance C a => C a where ...
2597 -- (C b b) has more more occurrences of b than the head
2598 instance C b b => Foo [b] where ...
2603 The same restrictions apply to instances generated by
2604 <literal>deriving</literal> clauses. Thus the following is accepted:
2606 data MinHeap h a = H a (h a)
2609 because the derived instance
2611 instance (Show a, Show (h a)) => Show (MinHeap h a)
2613 conforms to the above rules.
2617 A useful idiom permitted by the above rules is as follows.
2618 If one allows overlapping instance declarations then it's quite
2619 convenient to have a "default instance" declaration that applies if
2620 something more specific does not:
2628 <sect3 id="undecidable-instances">
2629 <title>Undecidable instances</title>
2632 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2633 For example, sometimes you might want to use the following to get the
2634 effect of a "class synonym":
2636 class (C1 a, C2 a, C3 a) => C a where { }
2638 instance (C1 a, C2 a, C3 a) => C a where { }
2640 This allows you to write shorter signatures:
2646 f :: (C1 a, C2 a, C3 a) => ...
2648 The restrictions on functional dependencies (<xref
2649 linkend="functional-dependencies"/>) are particularly troublesome.
2650 It is tempting to introduce type variables in the context that do not appear in
2651 the head, something that is excluded by the normal rules. For example:
2653 class HasConverter a b | a -> b where
2656 data Foo a = MkFoo a
2658 instance (HasConverter a b,Show b) => Show (Foo a) where
2659 show (MkFoo value) = show (convert value)
2661 This is dangerous territory, however. Here, for example, is a program that would make the
2666 instance F [a] [[a]]
2667 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2669 Similarly, it can be tempting to lift the coverage condition:
2671 class Mul a b c | a b -> c where
2672 (.*.) :: a -> b -> c
2674 instance Mul Int Int Int where (.*.) = (*)
2675 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2676 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2678 The third instance declaration does not obey the coverage condition;
2679 and indeed the (somewhat strange) definition:
2681 f = \ b x y -> if b then x .*. [y] else y
2683 makes instance inference go into a loop, because it requires the constraint
2684 <literal>(Mul a [b] b)</literal>.
2687 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2688 the experimental flag <option>-fallow-undecidable-instances</option>
2689 <indexterm><primary>-fallow-undecidable-instances
2690 option</primary></indexterm>, both the Paterson Conditions and the Coverage Condition
2691 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2692 fixed-depth recursion stack. If you exceed the stack depth you get a
2693 sort of backtrace, and the opportunity to increase the stack depth
2694 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2700 <sect3 id="instance-overlap">
2701 <title>Overlapping instances</title>
2703 In general, <emphasis>GHC requires that that it be unambiguous which instance
2705 should be used to resolve a type-class constraint</emphasis>. This behaviour
2706 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2707 <indexterm><primary>-fallow-overlapping-instances
2708 </primary></indexterm>
2709 and <option>-fallow-incoherent-instances</option>
2710 <indexterm><primary>-fallow-incoherent-instances
2711 </primary></indexterm>, as this section discusses. Both these
2712 flags are dynamic flags, and can be set on a per-module basis, using
2713 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2715 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2716 it tries to match every instance declaration against the
2718 by instantiating the head of the instance declaration. For example, consider
2721 instance context1 => C Int a where ... -- (A)
2722 instance context2 => C a Bool where ... -- (B)
2723 instance context3 => C Int [a] where ... -- (C)
2724 instance context4 => C Int [Int] where ... -- (D)
2726 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2727 but (C) and (D) do not. When matching, GHC takes
2728 no account of the context of the instance declaration
2729 (<literal>context1</literal> etc).
2730 GHC's default behaviour is that <emphasis>exactly one instance must match the
2731 constraint it is trying to resolve</emphasis>.
2732 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2733 including both declarations (A) and (B), say); an error is only reported if a
2734 particular constraint matches more than one.
2738 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2739 more than one instance to match, provided there is a most specific one. For
2740 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2741 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2742 most-specific match, the program is rejected.
2745 However, GHC is conservative about committing to an overlapping instance. For example:
2750 Suppose that from the RHS of <literal>f</literal> we get the constraint
2751 <literal>C Int [b]</literal>. But
2752 GHC does not commit to instance (C), because in a particular
2753 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2754 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2755 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2756 GHC will instead pick (C), without complaining about
2757 the problem of subsequent instantiations.
2760 The willingness to be overlapped or incoherent is a property of
2761 the <emphasis>instance declaration</emphasis> itself, controlled by the
2762 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2763 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2764 being defined. Neither flag is required in a module that imports and uses the
2765 instance declaration. Specifically, during the lookup process:
2768 An instance declaration is ignored during the lookup process if (a) a more specific
2769 match is found, and (b) the instance declaration was compiled with
2770 <option>-fallow-overlapping-instances</option>. The flag setting for the
2771 more-specific instance does not matter.
2774 Suppose an instance declaration does not matche the constraint being looked up, but
2775 does unify with it, so that it might match when the constraint is further
2776 instantiated. Usually GHC will regard this as a reason for not committing to
2777 some other constraint. But if the instance declaration was compiled with
2778 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2779 check for that declaration.
2782 These rules make it possible for a library author to design a library that relies on
2783 overlapping instances without the library client having to know.
2786 If an instance declaration is compiled without
2787 <option>-fallow-overlapping-instances</option>,
2788 then that instance can never be overlapped. This could perhaps be
2789 inconvenient. Perhaps the rule should instead say that the
2790 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2791 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2792 at a usage site should be permitted regardless of how the instance declarations
2793 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2794 used at the usage site. (Mind you, the exact usage site can occasionally be
2795 hard to pin down.) We are interested to receive feedback on these points.
2797 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2798 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2803 <title>Type synonyms in the instance head</title>
2806 <emphasis>Unlike Haskell 98, instance heads may use type
2807 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2808 As always, using a type synonym is just shorthand for
2809 writing the RHS of the type synonym definition. For example:
2813 type Point = (Int,Int)
2814 instance C Point where ...
2815 instance C [Point] where ...
2819 is legal. However, if you added
2823 instance C (Int,Int) where ...
2827 as well, then the compiler will complain about the overlapping
2828 (actually, identical) instance declarations. As always, type synonyms
2829 must be fully applied. You cannot, for example, write:
2834 instance Monad P where ...
2838 This design decision is independent of all the others, and easily
2839 reversed, but it makes sense to me.
2847 <sect2 id="type-restrictions">
2848 <title>Type signatures</title>
2850 <sect3><title>The context of a type signature</title>
2852 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2853 the form <emphasis>(class type-variable)</emphasis> or
2854 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2855 these type signatures are perfectly OK
2858 g :: Ord (T a ()) => ...
2862 GHC imposes the following restrictions on the constraints in a type signature.
2866 forall tv1..tvn (c1, ...,cn) => type
2869 (Here, we write the "foralls" explicitly, although the Haskell source
2870 language omits them; in Haskell 98, all the free type variables of an
2871 explicit source-language type signature are universally quantified,
2872 except for the class type variables in a class declaration. However,
2873 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2882 <emphasis>Each universally quantified type variable
2883 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2885 A type variable <literal>a</literal> is "reachable" if it it appears
2886 in the same constraint as either a type variable free in in
2887 <literal>type</literal>, or another reachable type variable.
2888 A value with a type that does not obey
2889 this reachability restriction cannot be used without introducing
2890 ambiguity; that is why the type is rejected.
2891 Here, for example, is an illegal type:
2895 forall a. Eq a => Int
2899 When a value with this type was used, the constraint <literal>Eq tv</literal>
2900 would be introduced where <literal>tv</literal> is a fresh type variable, and
2901 (in the dictionary-translation implementation) the value would be
2902 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2903 can never know which instance of <literal>Eq</literal> to use because we never
2904 get any more information about <literal>tv</literal>.
2908 that the reachability condition is weaker than saying that <literal>a</literal> is
2909 functionally dependent on a type variable free in
2910 <literal>type</literal> (see <xref
2911 linkend="functional-dependencies"/>). The reason for this is there
2912 might be a "hidden" dependency, in a superclass perhaps. So
2913 "reachable" is a conservative approximation to "functionally dependent".
2914 For example, consider:
2916 class C a b | a -> b where ...
2917 class C a b => D a b where ...
2918 f :: forall a b. D a b => a -> a
2920 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2921 but that is not immediately apparent from <literal>f</literal>'s type.
2927 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2928 universally quantified type variables <literal>tvi</literal></emphasis>.
2930 For example, this type is OK because <literal>C a b</literal> mentions the
2931 universally quantified type variable <literal>b</literal>:
2935 forall a. C a b => burble
2939 The next type is illegal because the constraint <literal>Eq b</literal> does not
2940 mention <literal>a</literal>:
2944 forall a. Eq b => burble
2948 The reason for this restriction is milder than the other one. The
2949 excluded types are never useful or necessary (because the offending
2950 context doesn't need to be witnessed at this point; it can be floated
2951 out). Furthermore, floating them out increases sharing. Lastly,
2952 excluding them is a conservative choice; it leaves a patch of
2953 territory free in case we need it later.
2967 <sect2 id="implicit-parameters">
2968 <title>Implicit parameters</title>
2970 <para> Implicit parameters are implemented as described in
2971 "Implicit parameters: dynamic scoping with static types",
2972 J Lewis, MB Shields, E Meijer, J Launchbury,
2973 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2977 <para>(Most of the following, stil rather incomplete, documentation is
2978 due to Jeff Lewis.)</para>
2980 <para>Implicit parameter support is enabled with the option
2981 <option>-fimplicit-params</option>.</para>
2984 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2985 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2986 context. In Haskell, all variables are statically bound. Dynamic
2987 binding of variables is a notion that goes back to Lisp, but was later
2988 discarded in more modern incarnations, such as Scheme. Dynamic binding
2989 can be very confusing in an untyped language, and unfortunately, typed
2990 languages, in particular Hindley-Milner typed languages like Haskell,
2991 only support static scoping of variables.
2994 However, by a simple extension to the type class system of Haskell, we
2995 can support dynamic binding. Basically, we express the use of a
2996 dynamically bound variable as a constraint on the type. These
2997 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2998 function uses a dynamically-bound variable <literal>?x</literal>
2999 of type <literal>t'</literal>". For
3000 example, the following expresses the type of a sort function,
3001 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3003 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3005 The dynamic binding constraints are just a new form of predicate in the type class system.
3008 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3009 where <literal>x</literal> is
3010 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3011 Use of this construct also introduces a new
3012 dynamic-binding constraint in the type of the expression.
3013 For example, the following definition
3014 shows how we can define an implicitly parameterized sort function in
3015 terms of an explicitly parameterized <literal>sortBy</literal> function:
3017 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3019 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3025 <title>Implicit-parameter type constraints</title>
3027 Dynamic binding constraints behave just like other type class
3028 constraints in that they are automatically propagated. Thus, when a
3029 function is used, its implicit parameters are inherited by the
3030 function that called it. For example, our <literal>sort</literal> function might be used
3031 to pick out the least value in a list:
3033 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3034 least xs = head (sort xs)
3036 Without lifting a finger, the <literal>?cmp</literal> parameter is
3037 propagated to become a parameter of <literal>least</literal> as well. With explicit
3038 parameters, the default is that parameters must always be explicit
3039 propagated. With implicit parameters, the default is to always
3043 An implicit-parameter type constraint differs from other type class constraints in the
3044 following way: All uses of a particular implicit parameter must have
3045 the same type. This means that the type of <literal>(?x, ?x)</literal>
3046 is <literal>(?x::a) => (a,a)</literal>, and not
3047 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3051 <para> You can't have an implicit parameter in the context of a class or instance
3052 declaration. For example, both these declarations are illegal:
3054 class (?x::Int) => C a where ...
3055 instance (?x::a) => Foo [a] where ...
3057 Reason: exactly which implicit parameter you pick up depends on exactly where
3058 you invoke a function. But the ``invocation'' of instance declarations is done
3059 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3060 Easiest thing is to outlaw the offending types.</para>
3062 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3064 f :: (?x :: [a]) => Int -> Int
3067 g :: (Read a, Show a) => String -> String
3070 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3071 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3072 quite unambiguous, and fixes the type <literal>a</literal>.
3077 <title>Implicit-parameter bindings</title>
3080 An implicit parameter is <emphasis>bound</emphasis> using the standard
3081 <literal>let</literal> or <literal>where</literal> binding forms.
3082 For example, we define the <literal>min</literal> function by binding
3083 <literal>cmp</literal>.
3086 min = let ?cmp = (<=) in least
3090 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3091 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3092 (including in a list comprehension, or do-notation, or pattern guards),
3093 or a <literal>where</literal> clause.
3094 Note the following points:
3097 An implicit-parameter binding group must be a
3098 collection of simple bindings to implicit-style variables (no
3099 function-style bindings, and no type signatures); these bindings are
3100 neither polymorphic or recursive.
3103 You may not mix implicit-parameter bindings with ordinary bindings in a
3104 single <literal>let</literal>
3105 expression; use two nested <literal>let</literal>s instead.
3106 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3110 You may put multiple implicit-parameter bindings in a
3111 single binding group; but they are <emphasis>not</emphasis> treated
3112 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3113 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3114 parameter. The bindings are not nested, and may be re-ordered without changing
3115 the meaning of the program.
3116 For example, consider:
3118 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3120 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3121 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3123 f :: (?x::Int) => Int -> Int
3131 <sect3><title>Implicit parameters and polymorphic recursion</title>
3134 Consider these two definitions:
3137 len1 xs = let ?acc = 0 in len_acc1 xs
3140 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3145 len2 xs = let ?acc = 0 in len_acc2 xs
3147 len_acc2 :: (?acc :: Int) => [a] -> Int
3149 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3151 The only difference between the two groups is that in the second group
3152 <literal>len_acc</literal> is given a type signature.
3153 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3154 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3155 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3156 has a type signature, the recursive call is made to the
3157 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3158 as an implicit parameter. So we get the following results in GHCi:
3165 Adding a type signature dramatically changes the result! This is a rather
3166 counter-intuitive phenomenon, worth watching out for.
3170 <sect3><title>Implicit parameters and monomorphism</title>
3172 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3173 Haskell Report) to implicit parameters. For example, consider:
3181 Since the binding for <literal>y</literal> falls under the Monomorphism
3182 Restriction it is not generalised, so the type of <literal>y</literal> is
3183 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3184 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3185 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3186 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3187 <literal>y</literal> in the body of the <literal>let</literal> will see the
3188 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3189 <literal>14</literal>.
3194 <!-- ======================= COMMENTED OUT ========================
3196 We intend to remove linear implicit parameters, so I'm at least removing
3197 them from the 6.6 user manual
3199 <sect2 id="linear-implicit-parameters">
3200 <title>Linear implicit parameters</title>
3202 Linear implicit parameters are an idea developed by Koen Claessen,
3203 Mark Shields, and Simon PJ. They address the long-standing
3204 problem that monads seem over-kill for certain sorts of problem, notably:
3207 <listitem> <para> distributing a supply of unique names </para> </listitem>
3208 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3209 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3213 Linear implicit parameters are just like ordinary implicit parameters,
3214 except that they are "linear"; that is, they cannot be copied, and
3215 must be explicitly "split" instead. Linear implicit parameters are
3216 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3217 (The '/' in the '%' suggests the split!)
3222 import GHC.Exts( Splittable )
3224 data NameSupply = ...
3226 splitNS :: NameSupply -> (NameSupply, NameSupply)
3227 newName :: NameSupply -> Name
3229 instance Splittable NameSupply where
3233 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3234 f env (Lam x e) = Lam x' (f env e)
3237 env' = extend env x x'
3238 ...more equations for f...
3240 Notice that the implicit parameter %ns is consumed
3242 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3243 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3247 So the translation done by the type checker makes
3248 the parameter explicit:
3250 f :: NameSupply -> Env -> Expr -> Expr
3251 f ns env (Lam x e) = Lam x' (f ns1 env e)
3253 (ns1,ns2) = splitNS ns
3255 env = extend env x x'
3257 Notice the call to 'split' introduced by the type checker.
3258 How did it know to use 'splitNS'? Because what it really did
3259 was to introduce a call to the overloaded function 'split',
3260 defined by the class <literal>Splittable</literal>:
3262 class Splittable a where
3265 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3266 split for name supplies. But we can simply write
3272 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3274 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3275 <literal>GHC.Exts</literal>.
3280 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3281 are entirely distinct implicit parameters: you
3282 can use them together and they won't intefere with each other. </para>
3285 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3287 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3288 in the context of a class or instance declaration. </para></listitem>
3292 <sect3><title>Warnings</title>
3295 The monomorphism restriction is even more important than usual.
3296 Consider the example above:
3298 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3299 f env (Lam x e) = Lam x' (f env e)
3302 env' = extend env x x'
3304 If we replaced the two occurrences of x' by (newName %ns), which is
3305 usually a harmless thing to do, we get:
3307 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3308 f env (Lam x e) = Lam (newName %ns) (f env e)
3310 env' = extend env x (newName %ns)
3312 But now the name supply is consumed in <emphasis>three</emphasis> places
3313 (the two calls to newName,and the recursive call to f), so
3314 the result is utterly different. Urk! We don't even have
3318 Well, this is an experimental change. With implicit
3319 parameters we have already lost beta reduction anyway, and
3320 (as John Launchbury puts it) we can't sensibly reason about
3321 Haskell programs without knowing their typing.
3326 <sect3><title>Recursive functions</title>
3327 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3330 foo :: %x::T => Int -> [Int]
3332 foo n = %x : foo (n-1)
3334 where T is some type in class Splittable.</para>
3336 Do you get a list of all the same T's or all different T's
3337 (assuming that split gives two distinct T's back)?
3339 If you supply the type signature, taking advantage of polymorphic
3340 recursion, you get what you'd probably expect. Here's the
3341 translated term, where the implicit param is made explicit:
3344 foo x n = let (x1,x2) = split x
3345 in x1 : foo x2 (n-1)
3347 But if you don't supply a type signature, GHC uses the Hindley
3348 Milner trick of using a single monomorphic instance of the function
3349 for the recursive calls. That is what makes Hindley Milner type inference
3350 work. So the translation becomes
3354 foom n = x : foom (n-1)
3358 Result: 'x' is not split, and you get a list of identical T's. So the
3359 semantics of the program depends on whether or not foo has a type signature.
3362 You may say that this is a good reason to dislike linear implicit parameters
3363 and you'd be right. That is why they are an experimental feature.
3369 ================ END OF Linear Implicit Parameters commented out -->
3371 <sect2 id="kinding">
3372 <title>Explicitly-kinded quantification</title>
3375 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3376 to give the kind explicitly as (machine-checked) documentation,
3377 just as it is nice to give a type signature for a function. On some occasions,
3378 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3379 John Hughes had to define the data type:
3381 data Set cxt a = Set [a]
3382 | Unused (cxt a -> ())
3384 The only use for the <literal>Unused</literal> constructor was to force the correct
3385 kind for the type variable <literal>cxt</literal>.
3388 GHC now instead allows you to specify the kind of a type variable directly, wherever
3389 a type variable is explicitly bound. Namely:
3391 <listitem><para><literal>data</literal> declarations:
3393 data Set (cxt :: * -> *) a = Set [a]
3394 </screen></para></listitem>
3395 <listitem><para><literal>type</literal> declarations:
3397 type T (f :: * -> *) = f Int
3398 </screen></para></listitem>
3399 <listitem><para><literal>class</literal> declarations:
3401 class (Eq a) => C (f :: * -> *) a where ...
3402 </screen></para></listitem>
3403 <listitem><para><literal>forall</literal>'s in type signatures:
3405 f :: forall (cxt :: * -> *). Set cxt Int
3406 </screen></para></listitem>
3411 The parentheses are required. Some of the spaces are required too, to
3412 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3413 will get a parse error, because "<literal>::*->*</literal>" is a
3414 single lexeme in Haskell.
3418 As part of the same extension, you can put kind annotations in types
3421 f :: (Int :: *) -> Int
3422 g :: forall a. a -> (a :: *)
3426 atype ::= '(' ctype '::' kind ')
3428 The parentheses are required.
3433 <sect2 id="universal-quantification">
3434 <title>Arbitrary-rank polymorphism
3438 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3439 allows us to say exactly what this means. For example:
3447 g :: forall b. (b -> b)
3449 The two are treated identically.
3453 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3454 explicit universal quantification in
3456 For example, all the following types are legal:
3458 f1 :: forall a b. a -> b -> a
3459 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3461 f2 :: (forall a. a->a) -> Int -> Int
3462 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3464 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3466 f4 :: Int -> (forall a. a -> a)
3468 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3469 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3470 The <literal>forall</literal> makes explicit the universal quantification that
3471 is implicitly added by Haskell.
3474 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3475 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3476 shows, the polymorphic type on the left of the function arrow can be overloaded.
3479 The function <literal>f3</literal> has a rank-3 type;
3480 it has rank-2 types on the left of a function arrow.
3483 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3484 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3485 that restriction has now been lifted.)
3486 In particular, a forall-type (also called a "type scheme"),
3487 including an operational type class context, is legal:
3489 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3490 of a function arrow </para> </listitem>
3491 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3492 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3493 field type signatures.</para> </listitem>
3494 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3495 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3497 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3498 a type variable any more!
3507 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3508 the types of the constructor arguments. Here are several examples:
3514 data T a = T1 (forall b. b -> b -> b) a
3516 data MonadT m = MkMonad { return :: forall a. a -> m a,
3517 bind :: forall a b. m a -> (a -> m b) -> m b
3520 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3526 The constructors have rank-2 types:
3532 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3533 MkMonad :: forall m. (forall a. a -> m a)
3534 -> (forall a b. m a -> (a -> m b) -> m b)
3536 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3542 Notice that you don't need to use a <literal>forall</literal> if there's an
3543 explicit context. For example in the first argument of the
3544 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3545 prefixed to the argument type. The implicit <literal>forall</literal>
3546 quantifies all type variables that are not already in scope, and are
3547 mentioned in the type quantified over.
3551 As for type signatures, implicit quantification happens for non-overloaded
3552 types too. So if you write this:
3555 data T a = MkT (Either a b) (b -> b)
3558 it's just as if you had written this:
3561 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3564 That is, since the type variable <literal>b</literal> isn't in scope, it's
3565 implicitly universally quantified. (Arguably, it would be better
3566 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3567 where that is what is wanted. Feedback welcomed.)
3571 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3572 the constructor to suitable values, just as usual. For example,
3583 a3 = MkSwizzle reverse
3586 a4 = let r x = Just x
3593 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3594 mkTs f x y = [T1 f x, T1 f y]
3600 The type of the argument can, as usual, be more general than the type
3601 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3602 does not need the <literal>Ord</literal> constraint.)
3606 When you use pattern matching, the bound variables may now have
3607 polymorphic types. For example:
3613 f :: T a -> a -> (a, Char)
3614 f (T1 w k) x = (w k x, w 'c' 'd')
3616 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3617 g (MkSwizzle s) xs f = s (map f (s xs))
3619 h :: MonadT m -> [m a] -> m [a]
3620 h m [] = return m []
3621 h m (x:xs) = bind m x $ \y ->
3622 bind m (h m xs) $ \ys ->
3629 In the function <function>h</function> we use the record selectors <literal>return</literal>
3630 and <literal>bind</literal> to extract the polymorphic bind and return functions
3631 from the <literal>MonadT</literal> data structure, rather than using pattern
3637 <title>Type inference</title>
3640 In general, type inference for arbitrary-rank types is undecidable.
3641 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3642 to get a decidable algorithm by requiring some help from the programmer.
3643 We do not yet have a formal specification of "some help" but the rule is this:
3646 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3647 provides an explicit polymorphic type for x, or GHC's type inference will assume
3648 that x's type has no foralls in it</emphasis>.
3651 What does it mean to "provide" an explicit type for x? You can do that by
3652 giving a type signature for x directly, using a pattern type signature
3653 (<xref linkend="scoped-type-variables"/>), thus:
3655 \ f :: (forall a. a->a) -> (f True, f 'c')
3657 Alternatively, you can give a type signature to the enclosing
3658 context, which GHC can "push down" to find the type for the variable:
3660 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3662 Here the type signature on the expression can be pushed inwards
3663 to give a type signature for f. Similarly, and more commonly,
3664 one can give a type signature for the function itself:
3666 h :: (forall a. a->a) -> (Bool,Char)
3667 h f = (f True, f 'c')
3669 You don't need to give a type signature if the lambda bound variable
3670 is a constructor argument. Here is an example we saw earlier:
3672 f :: T a -> a -> (a, Char)
3673 f (T1 w k) x = (w k x, w 'c' 'd')
3675 Here we do not need to give a type signature to <literal>w</literal>, because
3676 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3683 <sect3 id="implicit-quant">
3684 <title>Implicit quantification</title>
3687 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3688 user-written types, if and only if there is no explicit <literal>forall</literal>,
3689 GHC finds all the type variables mentioned in the type that are not already
3690 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3694 f :: forall a. a -> a
3701 h :: forall b. a -> b -> b
3707 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3710 f :: (a -> a) -> Int
3712 f :: forall a. (a -> a) -> Int
3714 f :: (forall a. a -> a) -> Int
3717 g :: (Ord a => a -> a) -> Int
3718 -- MEANS the illegal type
3719 g :: forall a. (Ord a => a -> a) -> Int
3721 g :: (forall a. Ord a => a -> a) -> Int
3723 The latter produces an illegal type, which you might think is silly,
3724 but at least the rule is simple. If you want the latter type, you
3725 can write your for-alls explicitly. Indeed, doing so is strongly advised
3732 <sect2 id="impredicative-polymorphism">
3733 <title>Impredicative polymorphism
3735 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3736 that you can call a polymorphic function at a polymorphic type, and
3737 parameterise data structures over polymorphic types. For example:
3739 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3740 f (Just g) = Just (g [3], g "hello")
3743 Notice here that the <literal>Maybe</literal> type is parameterised by the
3744 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3747 <para>The technical details of this extension are described in the paper
3748 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3749 type inference for higher-rank types and impredicativity</ulink>,
3750 which appeared at ICFP 2006.
3754 <sect2 id="scoped-type-variables">
3755 <title>Lexically scoped type variables
3759 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3760 which some type signatures are simply impossible to write. For example:
3762 f :: forall a. [a] -> [a]
3768 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3769 the entire definition of <literal>f</literal>.
3770 In particular, it is in scope at the type signature for <varname>ys</varname>.
3771 In Haskell 98 it is not possible to declare
3772 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3773 it becomes possible to do so.
3775 <para>Lexically-scoped type variables are enabled by
3776 <option>-fglasgow-exts</option>.
3778 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3779 variables work, compared to earlier releases. Read this section
3783 <title>Overview</title>
3785 <para>The design follows the following principles
3787 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3788 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3789 design.)</para></listitem>
3790 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3791 type variables. This means that every programmer-written type signature
3792 (includin one that contains free scoped type variables) denotes a
3793 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3794 checker, and no inference is involved.</para></listitem>
3795 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3796 changing the program.</para></listitem>
3800 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3802 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3803 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3804 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3805 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3809 In Haskell, a programmer-written type signature is implicitly quantifed over
3810 its free type variables (<ulink
3811 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3813 of the Haskel Report).
3814 Lexically scoped type variables affect this implicit quantification rules
3815 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3816 quantified. For example, if type variable <literal>a</literal> is in scope,
3819 (e :: a -> a) means (e :: a -> a)
3820 (e :: b -> b) means (e :: forall b. b->b)
3821 (e :: a -> b) means (e :: forall b. a->b)
3829 <sect3 id="decl-type-sigs">
3830 <title>Declaration type signatures</title>
3831 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3832 quantification (using <literal>forall</literal>) brings into scope the
3833 explicitly-quantified
3834 type variables, in the definition of the named function(s). For example:
3836 f :: forall a. [a] -> [a]
3837 f (x:xs) = xs ++ [ x :: a ]
3839 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3840 the definition of "<literal>f</literal>".
3842 <para>This only happens if the quantification in <literal>f</literal>'s type
3843 signature is explicit. For example:
3846 g (x:xs) = xs ++ [ x :: a ]
3848 This program will be rejected, because "<literal>a</literal>" does not scope
3849 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3850 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3851 quantification rules.
3855 <sect3 id="exp-type-sigs">
3856 <title>Expression type signatures</title>
3858 <para>An expression type signature that has <emphasis>explicit</emphasis>
3859 quantification (using <literal>forall</literal>) brings into scope the
3860 explicitly-quantified
3861 type variables, in the annotated expression. For example:
3863 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3865 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3866 type variable <literal>s</literal> into scope, in the annotated expression
3867 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3872 <sect3 id="pattern-type-sigs">
3873 <title>Pattern type signatures</title>
3875 A type signature may occur in any pattern; this is a <emphasis>pattern type
3876 signature</emphasis>.
3879 -- f and g assume that 'a' is already in scope
3880 f = \(x::Int, y::a) -> x
3882 h ((x,y) :: (Int,Bool)) = (y,x)
3884 In the case where all the type variables in the pattern type sigature are
3885 already in scope (i.e. bound by the enclosing context), matters are simple: the
3886 signature simply constrains the type of the pattern in the obvious way.
3889 There is only one situation in which you can write a pattern type signature that
3890 mentions a type variable that is not already in scope, namely in pattern match
3891 of an existential data constructor. For example:
3893 data T = forall a. MkT [a]
3896 k (MkT [t::a]) = MkT t3
3900 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3901 variable that is not already in scope. Indeed, it cannot already be in scope,
3902 because it is bound by the pattern match. GHC's rule is that in this situation
3903 (and only then), a pattern type signature can mention a type variable that is
3904 not already in scope; the effect is to bring it into scope, standing for the
3905 existentially-bound type variable.
3908 If this seems a little odd, we think so too. But we must have
3909 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3910 could not name existentially-bound type variables in subequent type signatures.
3913 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3914 signature is allowed to mention a lexical variable that is not already in
3916 For example, both <literal>f</literal> and <literal>g</literal> would be
3917 illegal if <literal>a</literal> was not already in scope.
3923 <!-- ==================== Commented out part about result type signatures
3925 <sect3 id="result-type-sigs">
3926 <title>Result type signatures</title>
3929 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3932 {- f assumes that 'a' is already in scope -}
3933 f x y :: [a] = [x,y,x]
3935 g = \ x :: [Int] -> [3,4]
3937 h :: forall a. [a] -> a
3941 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3942 the result of the function. Similarly, the body of the lambda in the RHS of
3943 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3944 alternative in <literal>h</literal> is <literal>a</literal>.
3946 <para> A result type signature never brings new type variables into scope.</para>
3948 There are a couple of syntactic wrinkles. First, notice that all three
3949 examples would parse quite differently with parentheses:
3951 {- f assumes that 'a' is already in scope -}
3952 f x (y :: [a]) = [x,y,x]
3954 g = \ (x :: [Int]) -> [3,4]
3956 h :: forall a. [a] -> a
3960 Now the signature is on the <emphasis>pattern</emphasis>; and
3961 <literal>h</literal> would certainly be ill-typed (since the pattern
3962 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3964 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3965 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3966 token or a parenthesised type of some sort). To see why,
3967 consider how one would parse this:
3976 <sect3 id="cls-inst-scoped-tyvars">
3977 <title>Class and instance declarations</title>
3980 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3981 scope over the methods defined in the <literal>where</literal> part. For example:
3999 <sect2 id="typing-binds">
4000 <title>Generalised typing of mutually recursive bindings</title>
4003 The Haskell Report specifies that a group of bindings (at top level, or in a
4004 <literal>let</literal> or <literal>where</literal>) should be sorted into
4005 strongly-connected components, and then type-checked in dependency order
4006 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4007 Report, Section 4.5.1</ulink>).
4008 As each group is type-checked, any binders of the group that
4010 an explicit type signature are put in the type environment with the specified
4012 and all others are monomorphic until the group is generalised
4013 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4016 <para>Following a suggestion of Mark Jones, in his paper
4017 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4019 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4021 <emphasis>the dependency analysis ignores references to variables that have an explicit
4022 type signature</emphasis>.
4023 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4024 typecheck. For example, consider:
4026 f :: Eq a => a -> Bool
4027 f x = (x == x) || g True || g "Yes"
4029 g y = (y <= y) || f True
4031 This is rejected by Haskell 98, but under Jones's scheme the definition for
4032 <literal>g</literal> is typechecked first, separately from that for
4033 <literal>f</literal>,
4034 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4035 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4036 type is generalised, to get
4038 g :: Ord a => a -> Bool
4040 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4041 <literal>g</literal> in the type environment.
4045 The same refined dependency analysis also allows the type signatures of
4046 mutually-recursive functions to have different contexts, something that is illegal in
4047 Haskell 98 (Section 4.5.2, last sentence). With
4048 <option>-fglasgow-exts</option>
4049 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4050 type signatures; in practice this means that only variables bound by the same
4051 pattern binding must have the same context. For example, this is fine:
4053 f :: Eq a => a -> Bool
4054 f x = (x == x) || g True
4056 g :: Ord a => a -> Bool
4057 g y = (y <= y) || f True
4062 <sect2 id="overloaded-strings">
4063 <title>Overloaded string literals
4067 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4068 string literal has type <literal>String</literal>, but with overloaded string
4069 literals enabled (with <literal>-foverloaded-strings</literal>)
4070 a string literal has type <literal>(IsString a) => a</literal>.
4073 This means that the usual string syntax can be used, e.g., for packed strings
4074 and other variations of string like types. String literals behave very much
4075 like integer literals, i.e., they can be used in both expressions and patterns.
4076 If used in a pattern the literal with be replaced by an equality test, in the same
4077 way as an integer literal is.
4080 The class <literal>IsString</literal> is defined as:
4082 class IsString a where
4083 fromString :: String -> a
4085 The only predefined instance is the obvious one to make strings work as usual:
4087 instance IsString [Char] where
4090 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4091 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4092 from module <literal>GHC.Exts</literal>.
4095 Haskell's defaulting mechanism is extended to cover string literals, when <option>-foverloaded-strings</option> is specified.
4099 Each type in a default declaration must be an
4100 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4104 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4105 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4106 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4107 <emphasis>or</emphasis> <literal>IsString</literal>.
4116 import GHC.Exts( IsString(..) )
4118 newtype MyString = MyString String deriving (Eq, Show)
4119 instance IsString MyString where
4120 fromString = MyString
4122 greet :: MyString -> MyString
4123 greet "hello" = "world"
4127 print $ greet "hello"
4128 print $ greet "fool"
4132 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4133 to work since it gets translated into an equality comparison.
4138 <!-- ==================== End of type system extensions ================= -->
4140 <!-- ====================== TEMPLATE HASKELL ======================= -->
4142 <sect1 id="template-haskell">
4143 <title>Template Haskell</title>
4145 <para>Template Haskell allows you to do compile-time meta-programming in
4148 the main technical innovations is discussed in "<ulink
4149 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4150 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4153 There is a Wiki page about
4154 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4155 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4159 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4160 Haskell library reference material</ulink>
4161 (search for the type ExpQ).
4162 [Temporary: many changes to the original design are described in
4163 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4164 Not all of these changes are in GHC 6.6.]
4167 <para> The first example from that paper is set out below as a worked example to help get you started.
4171 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4172 Tim Sheard is going to expand it.)
4176 <title>Syntax</title>
4178 <para> Template Haskell has the following new syntactic
4179 constructions. You need to use the flag
4180 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4181 </indexterm>to switch these syntactic extensions on
4182 (<option>-fth</option> is no longer implied by
4183 <option>-fglasgow-exts</option>).</para>
4187 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4188 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4189 There must be no space between the "$" and the identifier or parenthesis. This use
4190 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4191 of "." as an infix operator. If you want the infix operator, put spaces around it.
4193 <para> A splice can occur in place of
4195 <listitem><para> an expression; the spliced expression must
4196 have type <literal>Q Exp</literal></para></listitem>
4197 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4198 <listitem><para> [Planned, but not implemented yet.] a
4199 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4201 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4202 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4208 A expression quotation is written in Oxford brackets, thus:
4210 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4211 the quotation has type <literal>Expr</literal>.</para></listitem>
4212 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4213 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4214 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4215 the quotation has type <literal>Type</literal>.</para></listitem>
4216 </itemizedlist></para></listitem>
4219 Reification is written thus:
4221 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4222 has type <literal>Dec</literal>. </para></listitem>
4223 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4224 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4225 <listitem><para> Still to come: fixities </para></listitem>
4227 </itemizedlist></para>
4234 <sect2> <title> Using Template Haskell </title>
4238 The data types and monadic constructor functions for Template Haskell are in the library
4239 <literal>Language.Haskell.THSyntax</literal>.
4243 You can only run a function at compile time if it is imported from another module. That is,
4244 you can't define a function in a module, and call it from within a splice in the same module.
4245 (It would make sense to do so, but it's hard to implement.)
4249 Furthermore, you can only run a function at compile time if it is imported
4250 from another module <emphasis>that is not part of a mutually-recursive group of modules
4251 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4252 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4253 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4257 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4260 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4261 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4262 compiles and runs a program, and then looks at the result. So it's important that
4263 the program it compiles produces results whose representations are identical to
4264 those of the compiler itself.
4268 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4269 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4274 <sect2> <title> A Template Haskell Worked Example </title>
4275 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4276 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4283 -- Import our template "pr"
4284 import Printf ( pr )
4286 -- The splice operator $ takes the Haskell source code
4287 -- generated at compile time by "pr" and splices it into
4288 -- the argument of "putStrLn".
4289 main = putStrLn ( $(pr "Hello") )
4295 -- Skeletal printf from the paper.
4296 -- It needs to be in a separate module to the one where
4297 -- you intend to use it.
4299 -- Import some Template Haskell syntax
4300 import Language.Haskell.TH
4302 -- Describe a format string
4303 data Format = D | S | L String
4305 -- Parse a format string. This is left largely to you
4306 -- as we are here interested in building our first ever
4307 -- Template Haskell program and not in building printf.
4308 parse :: String -> [Format]
4311 -- Generate Haskell source code from a parsed representation
4312 -- of the format string. This code will be spliced into
4313 -- the module which calls "pr", at compile time.
4314 gen :: [Format] -> ExpQ
4315 gen [D] = [| \n -> show n |]
4316 gen [S] = [| \s -> s |]
4317 gen [L s] = stringE s
4319 -- Here we generate the Haskell code for the splice
4320 -- from an input format string.
4321 pr :: String -> ExpQ
4322 pr s = gen (parse s)
4325 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4328 $ ghc --make -fth main.hs -o main.exe
4331 <para>Run "main.exe" and here is your output:</para>
4341 <title>Using Template Haskell with Profiling</title>
4342 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4344 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4345 interpreter to run the splice expressions. The bytecode interpreter
4346 runs the compiled expression on top of the same runtime on which GHC
4347 itself is running; this means that the compiled code referred to by
4348 the interpreted expression must be compatible with this runtime, and
4349 in particular this means that object code that is compiled for
4350 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4351 expression, because profiled object code is only compatible with the
4352 profiling version of the runtime.</para>
4354 <para>This causes difficulties if you have a multi-module program
4355 containing Template Haskell code and you need to compile it for
4356 profiling, because GHC cannot load the profiled object code and use it
4357 when executing the splices. Fortunately GHC provides a workaround.
4358 The basic idea is to compile the program twice:</para>
4362 <para>Compile the program or library first the normal way, without
4363 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4366 <para>Then compile it again with <option>-prof</option>, and
4367 additionally use <option>-osuf
4368 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4369 to name the object files differentliy (you can choose any suffix
4370 that isn't the normal object suffix here). GHC will automatically
4371 load the object files built in the first step when executing splice
4372 expressions. If you omit the <option>-osuf</option> flag when
4373 building with <option>-prof</option> and Template Haskell is used,
4374 GHC will emit an error message. </para>
4381 <!-- ===================== Arrow notation =================== -->
4383 <sect1 id="arrow-notation">
4384 <title>Arrow notation
4387 <para>Arrows are a generalization of monads introduced by John Hughes.
4388 For more details, see
4393 “Generalising Monads to Arrows”,
4394 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4395 pp67–111, May 2000.
4401 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4402 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4408 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4409 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4415 and the arrows web page at
4416 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4417 With the <option>-farrows</option> flag, GHC supports the arrow
4418 notation described in the second of these papers.
4419 What follows is a brief introduction to the notation;
4420 it won't make much sense unless you've read Hughes's paper.
4421 This notation is translated to ordinary Haskell,
4422 using combinators from the
4423 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4427 <para>The extension adds a new kind of expression for defining arrows:
4429 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4430 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4432 where <literal>proc</literal> is a new keyword.
4433 The variables of the pattern are bound in the body of the
4434 <literal>proc</literal>-expression,
4435 which is a new sort of thing called a <firstterm>command</firstterm>.
4436 The syntax of commands is as follows:
4438 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4439 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4440 | <replaceable>cmd</replaceable><superscript>0</superscript>
4442 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4443 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4444 infix operators as for expressions, and
4446 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4447 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4448 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4449 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4450 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4451 | <replaceable>fcmd</replaceable>
4453 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4454 | ( <replaceable>cmd</replaceable> )
4455 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4457 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4458 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4459 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4460 | <replaceable>cmd</replaceable>
4462 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4463 except that the bodies are commands instead of expressions.
4467 Commands produce values, but (like monadic computations)
4468 may yield more than one value,
4469 or none, and may do other things as well.
4470 For the most part, familiarity with monadic notation is a good guide to
4472 However the values of expressions, even monadic ones,
4473 are determined by the values of the variables they contain;
4474 this is not necessarily the case for commands.
4478 A simple example of the new notation is the expression
4480 proc x -> f -< x+1
4482 We call this a <firstterm>procedure</firstterm> or
4483 <firstterm>arrow abstraction</firstterm>.
4484 As with a lambda expression, the variable <literal>x</literal>
4485 is a new variable bound within the <literal>proc</literal>-expression.
4486 It refers to the input to the arrow.
4487 In the above example, <literal>-<</literal> is not an identifier but an
4488 new reserved symbol used for building commands from an expression of arrow
4489 type and an expression to be fed as input to that arrow.
4490 (The weird look will make more sense later.)
4491 It may be read as analogue of application for arrows.
4492 The above example is equivalent to the Haskell expression
4494 arr (\ x -> x+1) >>> f
4496 That would make no sense if the expression to the left of
4497 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4498 More generally, the expression to the left of <literal>-<</literal>
4499 may not involve any <firstterm>local variable</firstterm>,
4500 i.e. a variable bound in the current arrow abstraction.
4501 For such a situation there is a variant <literal>-<<</literal>, as in
4503 proc x -> f x -<< x+1
4505 which is equivalent to
4507 arr (\ x -> (f x, x+1)) >>> app
4509 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4511 Such an arrow is equivalent to a monad, so if you're using this form
4512 you may find a monadic formulation more convenient.
4516 <title>do-notation for commands</title>
4519 Another form of command is a form of <literal>do</literal>-notation.
4520 For example, you can write
4529 You can read this much like ordinary <literal>do</literal>-notation,
4530 but with commands in place of monadic expressions.
4531 The first line sends the value of <literal>x+1</literal> as an input to
4532 the arrow <literal>f</literal>, and matches its output against
4533 <literal>y</literal>.
4534 In the next line, the output is discarded.
4535 The arrow <function>returnA</function> is defined in the
4536 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4537 module as <literal>arr id</literal>.
4538 The above example is treated as an abbreviation for
4540 arr (\ x -> (x, x)) >>>
4541 first (arr (\ x -> x+1) >>> f) >>>
4542 arr (\ (y, x) -> (y, (x, y))) >>>
4543 first (arr (\ y -> 2*y) >>> g) >>>
4545 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4546 first (arr (\ (x, z) -> x*z) >>> h) >>>
4547 arr (\ (t, z) -> t+z) >>>
4550 Note that variables not used later in the composition are projected out.
4551 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4553 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4554 module, this reduces to
4556 arr (\ x -> (x+1, x)) >>>
4558 arr (\ (y, x) -> (2*y, (x, y))) >>>
4560 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4562 arr (\ (t, z) -> t+z)
4564 which is what you might have written by hand.
4565 With arrow notation, GHC keeps track of all those tuples of variables for you.
4569 Note that although the above translation suggests that
4570 <literal>let</literal>-bound variables like <literal>z</literal> must be
4571 monomorphic, the actual translation produces Core,
4572 so polymorphic variables are allowed.
4576 It's also possible to have mutually recursive bindings,
4577 using the new <literal>rec</literal> keyword, as in the following example:
4579 counter :: ArrowCircuit a => a Bool Int
4580 counter = proc reset -> do
4581 rec output <- returnA -< if reset then 0 else next
4582 next <- delay 0 -< output+1
4583 returnA -< output
4585 The translation of such forms uses the <function>loop</function> combinator,
4586 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4592 <title>Conditional commands</title>
4595 In the previous example, we used a conditional expression to construct the
4597 Sometimes we want to conditionally execute different commands, as in
4604 which is translated to
4606 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4607 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4609 Since the translation uses <function>|||</function>,
4610 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4614 There are also <literal>case</literal> commands, like
4620 y <- h -< (x1, x2)
4624 The syntax is the same as for <literal>case</literal> expressions,
4625 except that the bodies of the alternatives are commands rather than expressions.
4626 The translation is similar to that of <literal>if</literal> commands.
4632 <title>Defining your own control structures</title>
4635 As we're seen, arrow notation provides constructs,
4636 modelled on those for expressions,
4637 for sequencing, value recursion and conditionals.
4638 But suitable combinators,
4639 which you can define in ordinary Haskell,
4640 may also be used to build new commands out of existing ones.
4641 The basic idea is that a command defines an arrow from environments to values.
4642 These environments assign values to the free local variables of the command.
4643 Thus combinators that produce arrows from arrows
4644 may also be used to build commands from commands.
4645 For example, the <literal>ArrowChoice</literal> class includes a combinator
4647 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4649 so we can use it to build commands:
4651 expr' = proc x -> do
4654 symbol Plus -< ()
4655 y <- term -< ()
4658 symbol Minus -< ()
4659 y <- term -< ()
4662 (The <literal>do</literal> on the first line is needed to prevent the first
4663 <literal><+> ...</literal> from being interpreted as part of the
4664 expression on the previous line.)
4665 This is equivalent to
4667 expr' = (proc x -> returnA -< x)
4668 <+> (proc x -> do
4669 symbol Plus -< ()
4670 y <- term -< ()
4672 <+> (proc x -> do
4673 symbol Minus -< ()
4674 y <- term -< ()
4677 It is essential that this operator be polymorphic in <literal>e</literal>
4678 (representing the environment input to the command
4679 and thence to its subcommands)
4680 and satisfy the corresponding naturality property
4682 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4684 at least for strict <literal>k</literal>.
4685 (This should be automatic if you're not using <function>seq</function>.)
4686 This ensures that environments seen by the subcommands are environments
4687 of the whole command,
4688 and also allows the translation to safely trim these environments.
4689 The operator must also not use any variable defined within the current
4694 We could define our own operator
4696 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4697 untilA body cond = proc x ->
4698 if cond x then returnA -< ()
4701 untilA body cond -< x
4703 and use it in the same way.
4704 Of course this infix syntax only makes sense for binary operators;
4705 there is also a more general syntax involving special brackets:
4709 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4716 <title>Primitive constructs</title>
4719 Some operators will need to pass additional inputs to their subcommands.
4720 For example, in an arrow type supporting exceptions,
4721 the operator that attaches an exception handler will wish to pass the
4722 exception that occurred to the handler.
4723 Such an operator might have a type
4725 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4727 where <literal>Ex</literal> is the type of exceptions handled.
4728 You could then use this with arrow notation by writing a command
4730 body `handleA` \ ex -> handler
4732 so that if an exception is raised in the command <literal>body</literal>,
4733 the variable <literal>ex</literal> is bound to the value of the exception
4734 and the command <literal>handler</literal>,
4735 which typically refers to <literal>ex</literal>, is entered.
4736 Though the syntax here looks like a functional lambda,
4737 we are talking about commands, and something different is going on.
4738 The input to the arrow represented by a command consists of values for
4739 the free local variables in the command, plus a stack of anonymous values.
4740 In all the prior examples, this stack was empty.
4741 In the second argument to <function>handleA</function>,
4742 this stack consists of one value, the value of the exception.
4743 The command form of lambda merely gives this value a name.
4748 the values on the stack are paired to the right of the environment.
4749 So operators like <function>handleA</function> that pass
4750 extra inputs to their subcommands can be designed for use with the notation
4751 by pairing the values with the environment in this way.
4752 More precisely, the type of each argument of the operator (and its result)
4753 should have the form
4755 a (...(e,t1), ... tn) t
4757 where <replaceable>e</replaceable> is a polymorphic variable
4758 (representing the environment)
4759 and <replaceable>ti</replaceable> are the types of the values on the stack,
4760 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4761 The polymorphic variable <replaceable>e</replaceable> must not occur in
4762 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4763 <replaceable>t</replaceable>.
4764 However the arrows involved need not be the same.
4765 Here are some more examples of suitable operators:
4767 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4768 runReader :: ... => a e c -> a' (e,State) c
4769 runState :: ... => a e c -> a' (e,State) (c,State)
4771 We can supply the extra input required by commands built with the last two
4772 by applying them to ordinary expressions, as in
4776 (|runReader (do { ... })|) s
4778 which adds <literal>s</literal> to the stack of inputs to the command
4779 built using <function>runReader</function>.
4783 The command versions of lambda abstraction and application are analogous to
4784 the expression versions.
4785 In particular, the beta and eta rules describe equivalences of commands.
4786 These three features (operators, lambda abstraction and application)
4787 are the core of the notation; everything else can be built using them,
4788 though the results would be somewhat clumsy.
4789 For example, we could simulate <literal>do</literal>-notation by defining
4791 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4792 u `bind` f = returnA &&& u >>> f
4794 bind_ :: Arrow a => a e b -> a e c -> a e c
4795 u `bind_` f = u `bind` (arr fst >>> f)
4797 We could simulate <literal>if</literal> by defining
4799 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4800 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4807 <title>Differences with the paper</title>
4812 <para>Instead of a single form of arrow application (arrow tail) with two
4813 translations, the implementation provides two forms
4814 <quote><literal>-<</literal></quote> (first-order)
4815 and <quote><literal>-<<</literal></quote> (higher-order).
4820 <para>User-defined operators are flagged with banana brackets instead of
4821 a new <literal>form</literal> keyword.
4830 <title>Portability</title>
4833 Although only GHC implements arrow notation directly,
4834 there is also a preprocessor
4836 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4837 that translates arrow notation into Haskell 98
4838 for use with other Haskell systems.
4839 You would still want to check arrow programs with GHC;
4840 tracing type errors in the preprocessor output is not easy.
4841 Modules intended for both GHC and the preprocessor must observe some
4842 additional restrictions:
4847 The module must import
4848 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4854 The preprocessor cannot cope with other Haskell extensions.
4855 These would have to go in separate modules.
4861 Because the preprocessor targets Haskell (rather than Core),
4862 <literal>let</literal>-bound variables are monomorphic.
4873 <!-- ==================== BANG PATTERNS ================= -->
4875 <sect1 id="bang-patterns">
4876 <title>Bang patterns
4877 <indexterm><primary>Bang patterns</primary></indexterm>
4879 <para>GHC supports an extension of pattern matching called <emphasis>bang
4880 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4882 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4883 prime feature description</ulink> contains more discussion and examples
4884 than the material below.
4887 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4890 <sect2 id="bang-patterns-informal">
4891 <title>Informal description of bang patterns
4894 The main idea is to add a single new production to the syntax of patterns:
4898 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4899 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4904 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4905 whereas without the bang it would be lazy.
4906 Bang patterns can be nested of course:
4910 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4911 <literal>y</literal>.
4912 A bang only really has an effect if it precedes a variable or wild-card pattern:
4917 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4918 forces evaluation anyway does nothing.
4920 Bang patterns work in <literal>case</literal> expressions too, of course:
4922 g5 x = let y = f x in body
4923 g6 x = case f x of { y -> body }
4924 g7 x = case f x of { !y -> body }
4926 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4927 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4928 result, and then evaluates <literal>body</literal>.
4930 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4931 definitions too. For example:
4935 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4936 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4937 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4938 in a function argument <literal>![x,y]</literal> means the
4939 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4940 is part of the syntax of <literal>let</literal> bindings.
4945 <sect2 id="bang-patterns-sem">
4946 <title>Syntax and semantics
4950 We add a single new production to the syntax of patterns:
4954 There is one problem with syntactic ambiguity. Consider:
4958 Is this a definition of the infix function "<literal>(!)</literal>",
4959 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4960 ambiguity in favour of the latter. If you want to define
4961 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4966 The semantics of Haskell pattern matching is described in <ulink
4967 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4968 Section 3.17.2</ulink> of the Haskell Report. To this description add
4969 one extra item 10, saying:
4970 <itemizedlist><listitem><para>Matching
4971 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4972 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4973 <listitem><para>otherwise, <literal>pat</literal> is matched against
4974 <literal>v</literal></para></listitem>
4976 </para></listitem></itemizedlist>
4977 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4978 Section 3.17.3</ulink>, add a new case (t):
4980 case v of { !pat -> e; _ -> e' }
4981 = v `seq` case v of { pat -> e; _ -> e' }
4984 That leaves let expressions, whose translation is given in
4985 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4987 of the Haskell Report.
4988 In the translation box, first apply
4989 the following transformation: for each pattern <literal>pi</literal> that is of
4990 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4991 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4992 have a bang at the top, apply the rules in the existing box.
4994 <para>The effect of the let rule is to force complete matching of the pattern
4995 <literal>qi</literal> before evaluation of the body is begun. The bang is
4996 retained in the translated form in case <literal>qi</literal> is a variable,
5004 The let-binding can be recursive. However, it is much more common for
5005 the let-binding to be non-recursive, in which case the following law holds:
5006 <literal>(let !p = rhs in body)</literal>
5008 <literal>(case rhs of !p -> body)</literal>
5011 A pattern with a bang at the outermost level is not allowed at the top level of
5017 <!-- ==================== ASSERTIONS ================= -->
5019 <sect1 id="assertions">
5021 <indexterm><primary>Assertions</primary></indexterm>
5025 If you want to make use of assertions in your standard Haskell code, you
5026 could define a function like the following:
5032 assert :: Bool -> a -> a
5033 assert False x = error "assertion failed!"
5040 which works, but gives you back a less than useful error message --
5041 an assertion failed, but which and where?
5045 One way out is to define an extended <function>assert</function> function which also
5046 takes a descriptive string to include in the error message and
5047 perhaps combine this with the use of a pre-processor which inserts
5048 the source location where <function>assert</function> was used.
5052 Ghc offers a helping hand here, doing all of this for you. For every
5053 use of <function>assert</function> in the user's source:
5059 kelvinToC :: Double -> Double
5060 kelvinToC k = assert (k >= 0.0) (k+273.15)
5066 Ghc will rewrite this to also include the source location where the
5073 assert pred val ==> assertError "Main.hs|15" pred val
5079 The rewrite is only performed by the compiler when it spots
5080 applications of <function>Control.Exception.assert</function>, so you
5081 can still define and use your own versions of
5082 <function>assert</function>, should you so wish. If not, import
5083 <literal>Control.Exception</literal> to make use
5084 <function>assert</function> in your code.
5088 GHC ignores assertions when optimisation is turned on with the
5089 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5090 <literal>assert pred e</literal> will be rewritten to
5091 <literal>e</literal>. You can also disable assertions using the
5092 <option>-fignore-asserts</option>
5093 option<indexterm><primary><option>-fignore-asserts</option></primary>
5094 </indexterm>.</para>
5097 Assertion failures can be caught, see the documentation for the
5098 <literal>Control.Exception</literal> library for the details.
5104 <!-- =============================== PRAGMAS =========================== -->
5106 <sect1 id="pragmas">
5107 <title>Pragmas</title>
5109 <indexterm><primary>pragma</primary></indexterm>
5111 <para>GHC supports several pragmas, or instructions to the
5112 compiler placed in the source code. Pragmas don't normally affect
5113 the meaning of the program, but they might affect the efficiency
5114 of the generated code.</para>
5116 <para>Pragmas all take the form
5118 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5120 where <replaceable>word</replaceable> indicates the type of
5121 pragma, and is followed optionally by information specific to that
5122 type of pragma. Case is ignored in
5123 <replaceable>word</replaceable>. The various values for
5124 <replaceable>word</replaceable> that GHC understands are described
5125 in the following sections; any pragma encountered with an
5126 unrecognised <replaceable>word</replaceable> is (silently)
5129 <sect2 id="deprecated-pragma">
5130 <title>DEPRECATED pragma</title>
5131 <indexterm><primary>DEPRECATED</primary>
5134 <para>The DEPRECATED pragma lets you specify that a particular
5135 function, class, or type, is deprecated. There are two
5140 <para>You can deprecate an entire module thus:</para>
5142 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5145 <para>When you compile any module that import
5146 <literal>Wibble</literal>, GHC will print the specified
5151 <para>You can deprecate a function, class, type, or data constructor, with the
5152 following top-level declaration:</para>
5154 {-# DEPRECATED f, C, T "Don't use these" #-}
5156 <para>When you compile any module that imports and uses any
5157 of the specified entities, GHC will print the specified
5159 <para> You can only depecate entities declared at top level in the module
5160 being compiled, and you can only use unqualified names in the list of
5161 entities being deprecated. A capitalised name, such as <literal>T</literal>
5162 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5163 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5164 both are in scope. If both are in scope, there is currently no way to deprecate
5165 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5168 Any use of the deprecated item, or of anything from a deprecated
5169 module, will be flagged with an appropriate message. However,
5170 deprecations are not reported for
5171 (a) uses of a deprecated function within its defining module, and
5172 (b) uses of a deprecated function in an export list.
5173 The latter reduces spurious complaints within a library
5174 in which one module gathers together and re-exports
5175 the exports of several others.
5177 <para>You can suppress the warnings with the flag
5178 <option>-fno-warn-deprecations</option>.</para>
5181 <sect2 id="include-pragma">
5182 <title>INCLUDE pragma</title>
5184 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5185 of C header files that should be <literal>#include</literal>'d into
5186 the C source code generated by the compiler for the current module (if
5187 compiling via C). For example:</para>
5190 {-# INCLUDE "foo.h" #-}
5191 {-# INCLUDE <stdio.h> #-}</programlisting>
5193 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5194 your source file with any <literal>OPTIONS_GHC</literal>
5197 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5198 to the <option>-#include</option> option (<xref
5199 linkend="options-C-compiler" />), because the
5200 <literal>INCLUDE</literal> pragma is understood by other
5201 compilers. Yet another alternative is to add the include file to each
5202 <literal>foreign import</literal> declaration in your code, but we
5203 don't recommend using this approach with GHC.</para>
5206 <sect2 id="inline-noinline-pragma">
5207 <title>INLINE and NOINLINE pragmas</title>
5209 <para>These pragmas control the inlining of function
5212 <sect3 id="inline-pragma">
5213 <title>INLINE pragma</title>
5214 <indexterm><primary>INLINE</primary></indexterm>
5216 <para>GHC (with <option>-O</option>, as always) tries to
5217 inline (or “unfold”) functions/values that are
5218 “small enough,” thus avoiding the call overhead
5219 and possibly exposing other more-wonderful optimisations.
5220 Normally, if GHC decides a function is “too
5221 expensive” to inline, it will not do so, nor will it
5222 export that unfolding for other modules to use.</para>
5224 <para>The sledgehammer you can bring to bear is the
5225 <literal>INLINE</literal><indexterm><primary>INLINE
5226 pragma</primary></indexterm> pragma, used thusly:</para>
5229 key_function :: Int -> String -> (Bool, Double)
5231 #ifdef __GLASGOW_HASKELL__
5232 {-# INLINE key_function #-}
5236 <para>(You don't need to do the C pre-processor carry-on
5237 unless you're going to stick the code through HBC—it
5238 doesn't like <literal>INLINE</literal> pragmas.)</para>
5240 <para>The major effect of an <literal>INLINE</literal> pragma
5241 is to declare a function's “cost” to be very low.
5242 The normal unfolding machinery will then be very keen to
5245 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5246 function can be put anywhere its type signature could be
5249 <para><literal>INLINE</literal> pragmas are a particularly
5251 <literal>then</literal>/<literal>return</literal> (or
5252 <literal>bind</literal>/<literal>unit</literal>) functions in
5253 a monad. For example, in GHC's own
5254 <literal>UniqueSupply</literal> monad code, we have:</para>
5257 #ifdef __GLASGOW_HASKELL__
5258 {-# INLINE thenUs #-}
5259 {-# INLINE returnUs #-}
5263 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5264 linkend="noinline-pragma"/>).</para>
5267 <sect3 id="noinline-pragma">
5268 <title>NOINLINE pragma</title>
5270 <indexterm><primary>NOINLINE</primary></indexterm>
5271 <indexterm><primary>NOTINLINE</primary></indexterm>
5273 <para>The <literal>NOINLINE</literal> pragma does exactly what
5274 you'd expect: it stops the named function from being inlined
5275 by the compiler. You shouldn't ever need to do this, unless
5276 you're very cautious about code size.</para>
5278 <para><literal>NOTINLINE</literal> is a synonym for
5279 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5280 specified by Haskell 98 as the standard way to disable
5281 inlining, so it should be used if you want your code to be
5285 <sect3 id="phase-control">
5286 <title>Phase control</title>
5288 <para> Sometimes you want to control exactly when in GHC's
5289 pipeline the INLINE pragma is switched on. Inlining happens
5290 only during runs of the <emphasis>simplifier</emphasis>. Each
5291 run of the simplifier has a different <emphasis>phase
5292 number</emphasis>; the phase number decreases towards zero.
5293 If you use <option>-dverbose-core2core</option> you'll see the
5294 sequence of phase numbers for successive runs of the
5295 simplifier. In an INLINE pragma you can optionally specify a
5299 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5300 <literal>f</literal>
5301 until phase <literal>k</literal>, but from phase
5302 <literal>k</literal> onwards be very keen to inline it.
5305 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5306 <literal>f</literal>
5307 until phase <literal>k</literal>, but from phase
5308 <literal>k</literal> onwards do not inline it.
5311 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5312 <literal>f</literal>
5313 until phase <literal>k</literal>, but from phase
5314 <literal>k</literal> onwards be willing to inline it (as if
5315 there was no pragma).
5318 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5319 <literal>f</literal>
5320 until phase <literal>k</literal>, but from phase
5321 <literal>k</literal> onwards do not inline it.
5324 The same information is summarised here:
5326 -- Before phase 2 Phase 2 and later
5327 {-# INLINE [2] f #-} -- No Yes
5328 {-# INLINE [~2] f #-} -- Yes No
5329 {-# NOINLINE [2] f #-} -- No Maybe
5330 {-# NOINLINE [~2] f #-} -- Maybe No
5332 {-# INLINE f #-} -- Yes Yes
5333 {-# NOINLINE f #-} -- No No
5335 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5336 function body is small, or it is applied to interesting-looking arguments etc).
5337 Another way to understand the semantics is this:
5339 <listitem><para>For both INLINE and NOINLINE, the phase number says
5340 when inlining is allowed at all.</para></listitem>
5341 <listitem><para>The INLINE pragma has the additional effect of making the
5342 function body look small, so that when inlining is allowed it is very likely to
5347 <para>The same phase-numbering control is available for RULES
5348 (<xref linkend="rewrite-rules"/>).</para>
5352 <sect2 id="language-pragma">
5353 <title>LANGUAGE pragma</title>
5355 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5356 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5358 <para>This allows language extensions to be enabled in a portable way.
5359 It is the intention that all Haskell compilers support the
5360 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5361 all extensions are supported by all compilers, of
5362 course. The <literal>LANGUAGE</literal> pragma should be used instead
5363 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5365 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5367 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5369 <para>Any extension from the <literal>Extension</literal> type defined in
5371 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>
5375 <sect2 id="line-pragma">
5376 <title>LINE pragma</title>
5378 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5379 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5380 <para>This pragma is similar to C's <literal>#line</literal>
5381 pragma, and is mainly for use in automatically generated Haskell
5382 code. It lets you specify the line number and filename of the
5383 original code; for example</para>
5385 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5387 <para>if you'd generated the current file from something called
5388 <filename>Foo.vhs</filename> and this line corresponds to line
5389 42 in the original. GHC will adjust its error messages to refer
5390 to the line/file named in the <literal>LINE</literal>
5394 <sect2 id="options-pragma">
5395 <title>OPTIONS_GHC pragma</title>
5396 <indexterm><primary>OPTIONS_GHC</primary>
5398 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5401 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5402 additional options that are given to the compiler when compiling
5403 this source file. See <xref linkend="source-file-options"/> for
5406 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5407 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5411 <title>RULES pragma</title>
5413 <para>The RULES pragma lets you specify rewrite rules. It is
5414 described in <xref linkend="rewrite-rules"/>.</para>
5417 <sect2 id="specialize-pragma">
5418 <title>SPECIALIZE pragma</title>
5420 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5421 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5422 <indexterm><primary>overloading, death to</primary></indexterm>
5424 <para>(UK spelling also accepted.) For key overloaded
5425 functions, you can create extra versions (NB: more code space)
5426 specialised to particular types. Thus, if you have an
5427 overloaded function:</para>
5430 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5433 <para>If it is heavily used on lists with
5434 <literal>Widget</literal> keys, you could specialise it as
5438 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5441 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5442 be put anywhere its type signature could be put.</para>
5444 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5445 (a) a specialised version of the function and (b) a rewrite rule
5446 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5447 un-specialised function into a call to the specialised one.</para>
5449 <para>The type in a SPECIALIZE pragma can be any type that is less
5450 polymorphic than the type of the original function. In concrete terms,
5451 if the original function is <literal>f</literal> then the pragma
5453 {-# SPECIALIZE f :: <type> #-}
5455 is valid if and only if the defintion
5457 f_spec :: <type>
5460 is valid. Here are some examples (where we only give the type signature
5461 for the original function, not its code):
5463 f :: Eq a => a -> b -> b
5464 {-# SPECIALISE f :: Int -> b -> b #-}
5466 g :: (Eq a, Ix b) => a -> b -> b
5467 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5469 h :: Eq a => a -> a -> a
5470 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5472 The last of these examples will generate a
5473 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5474 well. If you use this kind of specialisation, let us know how well it works.
5477 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5478 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5479 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5480 The <literal>INLINE</literal> pragma affects the specialised verison of the
5481 function (only), and applies even if the function is recursive. The motivating
5484 -- A GADT for arrays with type-indexed representation
5486 ArrInt :: !Int -> ByteArray# -> Arr Int
5487 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5489 (!:) :: Arr e -> Int -> e
5490 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5491 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5492 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5493 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5495 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5496 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5497 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5498 the specialised function will be inlined. It has two calls to
5499 <literal>(!:)</literal>,
5500 both at type <literal>Int</literal>. Both these calls fire the first
5501 specialisation, whose body is also inlined. The result is a type-based
5502 unrolling of the indexing function.</para>
5503 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5504 on an ordinarily-recursive function.</para>
5506 <para>Note: In earlier versions of GHC, it was possible to provide your own
5507 specialised function for a given type:
5510 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5513 This feature has been removed, as it is now subsumed by the
5514 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5518 <sect2 id="specialize-instance-pragma">
5519 <title>SPECIALIZE instance pragma
5523 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5524 <indexterm><primary>overloading, death to</primary></indexterm>
5525 Same idea, except for instance declarations. For example:
5528 instance (Eq a) => Eq (Foo a) where {
5529 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5533 The pragma must occur inside the <literal>where</literal> part
5534 of the instance declaration.
5537 Compatible with HBC, by the way, except perhaps in the placement
5543 <sect2 id="unpack-pragma">
5544 <title>UNPACK pragma</title>
5546 <indexterm><primary>UNPACK</primary></indexterm>
5548 <para>The <literal>UNPACK</literal> indicates to the compiler
5549 that it should unpack the contents of a constructor field into
5550 the constructor itself, removing a level of indirection. For
5554 data T = T {-# UNPACK #-} !Float
5555 {-# UNPACK #-} !Float
5558 <para>will create a constructor <literal>T</literal> containing
5559 two unboxed floats. This may not always be an optimisation: if
5560 the <function>T</function> constructor is scrutinised and the
5561 floats passed to a non-strict function for example, they will
5562 have to be reboxed (this is done automatically by the
5565 <para>Unpacking constructor fields should only be used in
5566 conjunction with <option>-O</option>, in order to expose
5567 unfoldings to the compiler so the reboxing can be removed as
5568 often as possible. For example:</para>
5572 f (T f1 f2) = f1 + f2
5575 <para>The compiler will avoid reboxing <function>f1</function>
5576 and <function>f2</function> by inlining <function>+</function>
5577 on floats, but only when <option>-O</option> is on.</para>
5579 <para>Any single-constructor data is eligible for unpacking; for
5583 data T = T {-# UNPACK #-} !(Int,Int)
5586 <para>will store the two <literal>Int</literal>s directly in the
5587 <function>T</function> constructor, by flattening the pair.
5588 Multi-level unpacking is also supported:</para>
5591 data T = T {-# UNPACK #-} !S
5592 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5595 <para>will store two unboxed <literal>Int#</literal>s
5596 directly in the <function>T</function> constructor. The
5597 unpacker can see through newtypes, too.</para>
5599 <para>If a field cannot be unpacked, you will not get a warning,
5600 so it might be an idea to check the generated code with
5601 <option>-ddump-simpl</option>.</para>
5603 <para>See also the <option>-funbox-strict-fields</option> flag,
5604 which essentially has the effect of adding
5605 <literal>{-# UNPACK #-}</literal> to every strict
5606 constructor field.</para>
5611 <!-- ======================= REWRITE RULES ======================== -->
5613 <sect1 id="rewrite-rules">
5614 <title>Rewrite rules
5616 <indexterm><primary>RULES pragma</primary></indexterm>
5617 <indexterm><primary>pragma, RULES</primary></indexterm>
5618 <indexterm><primary>rewrite rules</primary></indexterm></title>
5621 The programmer can specify rewrite rules as part of the source program
5622 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5623 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5624 and (b) the <option>-frules-off</option> flag
5625 (<xref linkend="options-f"/>) is not specified, and (c) the
5626 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5635 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5642 <title>Syntax</title>
5645 From a syntactic point of view:
5651 There may be zero or more rules in a <literal>RULES</literal> pragma.
5658 Each rule has a name, enclosed in double quotes. The name itself has
5659 no significance at all. It is only used when reporting how many times the rule fired.
5665 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5666 immediately after the name of the rule. Thus:
5669 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5672 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5673 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5682 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5683 is set, so you must lay out your rules starting in the same column as the
5684 enclosing definitions.
5691 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5692 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5693 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5694 by spaces, just like in a type <literal>forall</literal>.
5700 A pattern variable may optionally have a type signature.
5701 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5702 For example, here is the <literal>foldr/build</literal> rule:
5705 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5706 foldr k z (build g) = g k z
5709 Since <function>g</function> has a polymorphic type, it must have a type signature.
5716 The left hand side of a rule must consist of a top-level variable applied
5717 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5720 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5721 "wrong2" forall f. f True = True
5724 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5731 A rule does not need to be in the same module as (any of) the
5732 variables it mentions, though of course they need to be in scope.
5738 Rules are automatically exported from a module, just as instance declarations are.
5749 <title>Semantics</title>
5752 From a semantic point of view:
5758 Rules are only applied if you use the <option>-O</option> flag.
5764 Rules are regarded as left-to-right rewrite rules.
5765 When GHC finds an expression that is a substitution instance of the LHS
5766 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5767 By "a substitution instance" we mean that the LHS can be made equal to the
5768 expression by substituting for the pattern variables.
5775 The LHS and RHS of a rule are typechecked, and must have the
5783 GHC makes absolutely no attempt to verify that the LHS and RHS
5784 of a rule have the same meaning. That is undecidable in general, and
5785 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5792 GHC makes no attempt to make sure that the rules are confluent or
5793 terminating. For example:
5796 "loop" forall x,y. f x y = f y x
5799 This rule will cause the compiler to go into an infinite loop.
5806 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5812 GHC currently uses a very simple, syntactic, matching algorithm
5813 for matching a rule LHS with an expression. It seeks a substitution
5814 which makes the LHS and expression syntactically equal modulo alpha
5815 conversion. The pattern (rule), but not the expression, is eta-expanded if
5816 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5817 But not beta conversion (that's called higher-order matching).
5821 Matching is carried out on GHC's intermediate language, which includes
5822 type abstractions and applications. So a rule only matches if the
5823 types match too. See <xref linkend="rule-spec"/> below.
5829 GHC keeps trying to apply the rules as it optimises the program.
5830 For example, consider:
5839 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5840 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5841 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5842 not be substituted, and the rule would not fire.
5849 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5850 that appears on the LHS of a rule</emphasis>, because once you have substituted
5851 for something you can't match against it (given the simple minded
5852 matching). So if you write the rule
5855 "map/map" forall f,g. map f . map g = map (f.g)
5858 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5859 It will only match something written with explicit use of ".".
5860 Well, not quite. It <emphasis>will</emphasis> match the expression
5866 where <function>wibble</function> is defined:
5869 wibble f g = map f . map g
5872 because <function>wibble</function> will be inlined (it's small).
5874 Later on in compilation, GHC starts inlining even things on the
5875 LHS of rules, but still leaves the rules enabled. This inlining
5876 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5883 All rules are implicitly exported from the module, and are therefore
5884 in force in any module that imports the module that defined the rule, directly
5885 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5886 in force when compiling A.) The situation is very similar to that for instance
5898 <title>List fusion</title>
5901 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5902 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5903 intermediate list should be eliminated entirely.
5907 The following are good producers:
5919 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5925 Explicit lists (e.g. <literal>[True, False]</literal>)
5931 The cons constructor (e.g <literal>3:4:[]</literal>)
5937 <function>++</function>
5943 <function>map</function>
5949 <function>take</function>, <function>filter</function>
5955 <function>iterate</function>, <function>repeat</function>
5961 <function>zip</function>, <function>zipWith</function>
5970 The following are good consumers:
5982 <function>array</function> (on its second argument)
5988 <function>++</function> (on its first argument)
5994 <function>foldr</function>
6000 <function>map</function>
6006 <function>take</function>, <function>filter</function>
6012 <function>concat</function>
6018 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6024 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6025 will fuse with one but not the other)
6031 <function>partition</function>
6037 <function>head</function>
6043 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6049 <function>sequence_</function>
6055 <function>msum</function>
6061 <function>sortBy</function>
6070 So, for example, the following should generate no intermediate lists:
6073 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6079 This list could readily be extended; if there are Prelude functions that you use
6080 a lot which are not included, please tell us.
6084 If you want to write your own good consumers or producers, look at the
6085 Prelude definitions of the above functions to see how to do so.
6090 <sect2 id="rule-spec">
6091 <title>Specialisation
6095 Rewrite rules can be used to get the same effect as a feature
6096 present in earlier versions of GHC.
6097 For example, suppose that:
6100 genericLookup :: Ord a => Table a b -> a -> b
6101 intLookup :: Table Int b -> Int -> b
6104 where <function>intLookup</function> is an implementation of
6105 <function>genericLookup</function> that works very fast for
6106 keys of type <literal>Int</literal>. You might wish
6107 to tell GHC to use <function>intLookup</function> instead of
6108 <function>genericLookup</function> whenever the latter was called with
6109 type <literal>Table Int b -> Int -> b</literal>.
6110 It used to be possible to write
6113 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6116 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6119 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6122 This slightly odd-looking rule instructs GHC to replace
6123 <function>genericLookup</function> by <function>intLookup</function>
6124 <emphasis>whenever the types match</emphasis>.
6125 What is more, this rule does not need to be in the same
6126 file as <function>genericLookup</function>, unlike the
6127 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6128 have an original definition available to specialise).
6131 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6132 <function>intLookup</function> really behaves as a specialised version
6133 of <function>genericLookup</function>!!!</para>
6135 <para>An example in which using <literal>RULES</literal> for
6136 specialisation will Win Big:
6139 toDouble :: Real a => a -> Double
6140 toDouble = fromRational . toRational
6142 {-# RULES "toDouble/Int" toDouble = i2d #-}
6143 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6146 The <function>i2d</function> function is virtually one machine
6147 instruction; the default conversion—via an intermediate
6148 <literal>Rational</literal>—is obscenely expensive by
6155 <title>Controlling what's going on</title>
6163 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6169 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6170 If you add <option>-dppr-debug</option> you get a more detailed listing.
6176 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6179 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6180 {-# INLINE build #-}
6184 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6185 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6186 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6187 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6194 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6195 see how to write rules that will do fusion and yet give an efficient
6196 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6206 <sect2 id="core-pragma">
6207 <title>CORE pragma</title>
6209 <indexterm><primary>CORE pragma</primary></indexterm>
6210 <indexterm><primary>pragma, CORE</primary></indexterm>
6211 <indexterm><primary>core, annotation</primary></indexterm>
6214 The external core format supports <quote>Note</quote> annotations;
6215 the <literal>CORE</literal> pragma gives a way to specify what these
6216 should be in your Haskell source code. Syntactically, core
6217 annotations are attached to expressions and take a Haskell string
6218 literal as an argument. The following function definition shows an
6222 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6225 Semantically, this is equivalent to:
6233 However, when external for is generated (via
6234 <option>-fext-core</option>), there will be Notes attached to the
6235 expressions <function>show</function> and <varname>x</varname>.
6236 The core function declaration for <function>f</function> is:
6240 f :: %forall a . GHCziShow.ZCTShow a ->
6241 a -> GHCziBase.ZMZN GHCziBase.Char =
6242 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6244 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6246 (tpl1::GHCziBase.Int ->
6248 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6250 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6251 (tpl3::GHCziBase.ZMZN a ->
6252 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6260 Here, we can see that the function <function>show</function> (which
6261 has been expanded out to a case expression over the Show dictionary)
6262 has a <literal>%note</literal> attached to it, as does the
6263 expression <varname>eta</varname> (which used to be called
6264 <varname>x</varname>).
6271 <sect1 id="special-ids">
6272 <title>Special built-in functions</title>
6273 <para>GHC has a few built-in funcions with special behaviour,
6274 described in this section. All are exported by
6275 <literal>GHC.Exts</literal>.</para>
6277 <sect2> <title>The <literal>seq</literal> function </title>
6279 The function <literal>seq</literal> is as described in the Haskell98 Report.
6283 It evaluates its first argument to head normal form, and then returns its
6284 second argument as the result. The reason that it is documented here is
6285 that, despite <literal>seq</literal>'s polymorphism, its
6286 second argument can have an unboxed type, or
6287 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6288 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6289 to be instantiated to an unboxed type, which is not usually allowed.
6293 <sect2> <title>The <literal>inline</literal> function </title>
6295 The <literal>inline</literal> function is somewhat experimental.
6299 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6300 is inlined, regardless of its size. More precisely, the call
6301 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6303 This allows the programmer to control inlining from
6304 a particular <emphasis>call site</emphasis>
6305 rather than the <emphasis>definition site</emphasis> of the function
6306 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6309 This inlining occurs regardless of the argument to the call
6310 or the size of <literal>f</literal>'s definition; it is unconditional.
6311 The main caveat is that <literal>f</literal>'s definition must be
6312 visible to the compiler. That is, <literal>f</literal> must be
6313 let-bound in the current scope.
6314 If no inlining takes place, the <literal>inline</literal> function
6315 expands to the identity function in Phase zero; so its use imposes
6318 <para> If the function is defined in another
6319 module, GHC only exposes its inlining in the interface file if the
6320 function is sufficiently small that it <emphasis>might</emphasis> be
6321 inlined by the automatic mechanism. There is currently no way to tell
6322 GHC to expose arbitrarily-large functions in the interface file. (This
6323 shortcoming is something that could be fixed, with some kind of pragma.)
6327 <sect2> <title>The <literal>lazy</literal> function </title>
6329 The <literal>lazy</literal> function restrains strictness analysis a little:
6333 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6334 but <literal>lazy</literal> has a magical property so far as strictness
6335 analysis is concerned: it is lazy in its first argument,
6336 even though its semantics is strict. After strictness analysis has run,
6337 calls to <literal>lazy</literal> are inlined to be the identity function.
6340 This behaviour is occasionally useful when controlling evaluation order.
6341 Notably, <literal>lazy</literal> is used in the library definition of
6342 <literal>Control.Parallel.par</literal>:
6345 par x y = case (par# x) of { _ -> lazy y }
6347 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6348 look strict in <literal>y</literal> which would defeat the whole
6349 purpose of <literal>par</literal>.
6352 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6358 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6360 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6361 typechecker entirely. It has type
6363 unsafeCoerce# :: a -> b
6365 That is, it allows you to coerce any type into any other type. If you use this
6366 function, you had better get it right, otherwise segmentation faults await.
6367 It is generally used when you want to write a program that you know is
6368 well-typed, but where Haskell's type system is not expressive enough to prove
6369 that it is well typed.
6372 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6373 although extremely bad things will happen if you coerce a boxed type
6382 <sect1 id="generic-classes">
6383 <title>Generic classes</title>
6386 The ideas behind this extension are described in detail in "Derivable type classes",
6387 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6388 An example will give the idea:
6396 fromBin :: [Int] -> (a, [Int])
6398 toBin {| Unit |} Unit = []
6399 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6400 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6401 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6403 fromBin {| Unit |} bs = (Unit, bs)
6404 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6405 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6406 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6407 (y,bs'') = fromBin bs'
6410 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6411 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6412 which are defined thus in the library module <literal>Generics</literal>:
6416 data a :+: b = Inl a | Inr b
6417 data a :*: b = a :*: b
6420 Now you can make a data type into an instance of Bin like this:
6422 instance (Bin a, Bin b) => Bin (a,b)
6423 instance Bin a => Bin [a]
6425 That is, just leave off the "where" clause. Of course, you can put in the
6426 where clause and over-ride whichever methods you please.
6430 <title> Using generics </title>
6431 <para>To use generics you need to</para>
6434 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6435 <option>-fgenerics</option> (to generate extra per-data-type code),
6436 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6440 <para>Import the module <literal>Generics</literal> from the
6441 <literal>lang</literal> package. This import brings into
6442 scope the data types <literal>Unit</literal>,
6443 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6444 don't need this import if you don't mention these types
6445 explicitly; for example, if you are simply giving instance
6446 declarations.)</para>
6451 <sect2> <title> Changes wrt the paper </title>
6453 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6454 can be written infix (indeed, you can now use
6455 any operator starting in a colon as an infix type constructor). Also note that
6456 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6457 Finally, note that the syntax of the type patterns in the class declaration
6458 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6459 alone would ambiguous when they appear on right hand sides (an extension we
6460 anticipate wanting).
6464 <sect2> <title>Terminology and restrictions</title>
6466 Terminology. A "generic default method" in a class declaration
6467 is one that is defined using type patterns as above.
6468 A "polymorphic default method" is a default method defined as in Haskell 98.
6469 A "generic class declaration" is a class declaration with at least one
6470 generic default method.
6478 Alas, we do not yet implement the stuff about constructor names and
6485 A generic class can have only one parameter; you can't have a generic
6486 multi-parameter class.
6492 A default method must be defined entirely using type patterns, or entirely
6493 without. So this is illegal:
6496 op :: a -> (a, Bool)
6497 op {| Unit |} Unit = (Unit, True)
6500 However it is perfectly OK for some methods of a generic class to have
6501 generic default methods and others to have polymorphic default methods.
6507 The type variable(s) in the type pattern for a generic method declaration
6508 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:
6512 op {| p :*: q |} (x :*: y) = op (x :: p)
6520 The type patterns in a generic default method must take one of the forms:
6526 where "a" and "b" are type variables. Furthermore, all the type patterns for
6527 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6528 must use the same type variables. So this is illegal:
6532 op {| a :+: b |} (Inl x) = True
6533 op {| p :+: q |} (Inr y) = False
6535 The type patterns must be identical, even in equations for different methods of the class.
6536 So this too is illegal:
6540 op1 {| a :*: b |} (x :*: y) = True
6543 op2 {| p :*: q |} (x :*: y) = False
6545 (The reason for this restriction is that we gather all the equations for a particular type consructor
6546 into a single generic instance declaration.)
6552 A generic method declaration must give a case for each of the three type constructors.
6558 The type for a generic method can be built only from:
6560 <listitem> <para> Function arrows </para> </listitem>
6561 <listitem> <para> Type variables </para> </listitem>
6562 <listitem> <para> Tuples </para> </listitem>
6563 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6565 Here are some example type signatures for generic methods:
6568 op2 :: Bool -> (a,Bool)
6569 op3 :: [Int] -> a -> a
6572 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6576 This restriction is an implementation restriction: we just havn't got around to
6577 implementing the necessary bidirectional maps over arbitrary type constructors.
6578 It would be relatively easy to add specific type constructors, such as Maybe and list,
6579 to the ones that are allowed.</para>
6584 In an instance declaration for a generic class, the idea is that the compiler
6585 will fill in the methods for you, based on the generic templates. However it can only
6590 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6595 No constructor of the instance type has unboxed fields.
6599 (Of course, these things can only arise if you are already using GHC extensions.)
6600 However, you can still give an instance declarations for types which break these rules,
6601 provided you give explicit code to override any generic default methods.
6609 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6610 what the compiler does with generic declarations.
6615 <sect2> <title> Another example </title>
6617 Just to finish with, here's another example I rather like:
6621 nCons {| Unit |} _ = 1
6622 nCons {| a :*: b |} _ = 1
6623 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6626 tag {| Unit |} _ = 1
6627 tag {| a :*: b |} _ = 1
6628 tag {| a :+: b |} (Inl x) = tag x
6629 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6635 <sect1 id="monomorphism">
6636 <title>Control over monomorphism</title>
6638 <para>GHC supports two flags that control the way in which generalisation is
6639 carried out at let and where bindings.
6643 <title>Switching off the dreaded Monomorphism Restriction</title>
6644 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6646 <para>Haskell's monomorphism restriction (see
6647 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6649 of the Haskell Report)
6650 can be completely switched off by
6651 <option>-fno-monomorphism-restriction</option>.
6656 <title>Monomorphic pattern bindings</title>
6657 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6658 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6660 <para> As an experimental change, we are exploring the possibility of
6661 making pattern bindings monomorphic; that is, not generalised at all.
6662 A pattern binding is a binding whose LHS has no function arguments,
6663 and is not a simple variable. For example:
6665 f x = x -- Not a pattern binding
6666 f = \x -> x -- Not a pattern binding
6667 f :: Int -> Int = \x -> x -- Not a pattern binding
6669 (g,h) = e -- A pattern binding
6670 (f) = e -- A pattern binding
6671 [x] = e -- A pattern binding
6673 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6674 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6683 ;;; Local Variables: ***
6685 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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