1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum.</para>
111 <para>New reserved words: <literal>foreign</literal>.</para>
117 <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
120 <para> These two flags control how generalisation is done.
121 See <xref linkend="monomorphism"/>.
128 <option>-fextended-default-rules</option>:
129 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
132 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
133 Independent of the <option>-fglasgow-exts</option>
140 <option>-fallow-overlapping-instances</option>
141 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
144 <option>-fallow-undecidable-instances</option>
145 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
148 <option>-fallow-incoherent-instances</option>
149 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
152 <option>-fcontext-stack=N</option>
153 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
156 <para> See <xref linkend="instance-decls"/>. Only relevant
157 if you also use <option>-fglasgow-exts</option>.</para>
163 <option>-finline-phase</option>
164 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
167 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
168 you also use <option>-fglasgow-exts</option>.</para>
174 <option>-farrows</option>
175 <indexterm><primary><option>-farrows</option></primary></indexterm>
178 <para>See <xref linkend="arrow-notation"/>. Independent of
179 <option>-fglasgow-exts</option>.</para>
181 <para>New reserved words/symbols: <literal>rec</literal>,
182 <literal>proc</literal>, <literal>-<</literal>,
183 <literal>>-</literal>, <literal>-<<</literal>,
184 <literal>>>-</literal>.</para>
186 <para>Other syntax stolen: <literal>(|</literal>,
187 <literal>|)</literal>.</para>
193 <option>-fgenerics</option>
194 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
197 <para>See <xref linkend="generic-classes"/>. Independent of
198 <option>-fglasgow-exts</option>.</para>
203 <term><option>-fno-implicit-prelude</option></term>
205 <para><indexterm><primary>-fno-implicit-prelude
206 option</primary></indexterm> GHC normally imports
207 <filename>Prelude.hi</filename> files for you. If you'd
208 rather it didn't, then give it a
209 <option>-fno-implicit-prelude</option> option. The idea is
210 that you can then import a Prelude of your own. (But don't
211 call it <literal>Prelude</literal>; the Haskell module
212 namespace is flat, and you must not conflict with any
213 Prelude module.)</para>
215 <para>Even though you have not imported the Prelude, most of
216 the built-in syntax still refers to the built-in Haskell
217 Prelude types and values, as specified by the Haskell
218 Report. For example, the type <literal>[Int]</literal>
219 still means <literal>Prelude.[] Int</literal>; tuples
220 continue to refer to the standard Prelude tuples; the
221 translation for list comprehensions continues to use
222 <literal>Prelude.map</literal> etc.</para>
224 <para>However, <option>-fno-implicit-prelude</option> does
225 change the handling of certain built-in syntax: see <xref
226 linkend="rebindable-syntax"/>.</para>
231 <term><option>-fimplicit-params</option></term>
233 <para>Enables implicit parameters (see <xref
234 linkend="implicit-parameters"/>). Currently also implied by
235 <option>-fglasgow-exts</option>.</para>
238 <literal>?<replaceable>varid</replaceable></literal>,
239 <literal>%<replaceable>varid</replaceable></literal>.</para>
244 <term><option>-foverloaded-strings</option></term>
246 <para>Enables overloaded string literals (see <xref
247 linkend="overloaded-strings"/>).</para>
252 <term><option>-fscoped-type-variables</option></term>
254 <para>Enables lexically-scoped type variables (see <xref
255 linkend="scoped-type-variables"/>). Implied by
256 <option>-fglasgow-exts</option>.</para>
261 <term><option>-fth</option></term>
263 <para>Enables Template Haskell (see <xref
264 linkend="template-haskell"/>). This flag must
265 be given explicitly; it is no longer implied by
266 <option>-fglasgow-exts</option>.</para>
268 <para>Syntax stolen: <literal>[|</literal>,
269 <literal>[e|</literal>, <literal>[p|</literal>,
270 <literal>[d|</literal>, <literal>[t|</literal>,
271 <literal>$(</literal>,
272 <literal>$<replaceable>varid</replaceable></literal>.</para>
279 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
280 <sect1 id="primitives">
281 <title>Unboxed types and primitive operations</title>
283 <para>GHC is built on a raft of primitive data types and operations.
284 While you really can use this stuff to write fast code,
285 we generally find it a lot less painful, and more satisfying in the
286 long run, to use higher-level language features and libraries. With
287 any luck, the code you write will be optimised to the efficient
288 unboxed version in any case. And if it isn't, we'd like to know
291 <para>We do not currently have good, up-to-date documentation about the
292 primitives, perhaps because they are mainly intended for internal use.
293 There used to be a long section about them here in the User Guide, but it
294 became out of date, and wrong information is worse than none.</para>
296 <para>The Real Truth about what primitive types there are, and what operations
297 work over those types, is held in the file
298 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
299 This file is used directly to generate GHC's primitive-operation definitions, so
300 it is always correct! It is also intended for processing into text.</para>
303 the result of such processing is part of the description of the
305 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
306 Core language</ulink>.
307 So that document is a good place to look for a type-set version.
308 We would be very happy if someone wanted to volunteer to produce an SGML
309 back end to the program that processes <filename>primops.txt</filename> so that
310 we could include the results here in the User Guide.</para>
312 <para>What follows here is a brief summary of some main points.</para>
314 <sect2 id="glasgow-unboxed">
319 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
322 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
323 that values of that type are represented by a pointer to a heap
324 object. The representation of a Haskell <literal>Int</literal>, for
325 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
326 type, however, is represented by the value itself, no pointers or heap
327 allocation are involved.
331 Unboxed types correspond to the “raw machine” types you
332 would use in C: <literal>Int#</literal> (long int),
333 <literal>Double#</literal> (double), <literal>Addr#</literal>
334 (void *), etc. The <emphasis>primitive operations</emphasis>
335 (PrimOps) on these types are what you might expect; e.g.,
336 <literal>(+#)</literal> is addition on
337 <literal>Int#</literal>s, and is the machine-addition that we all
338 know and love—usually one instruction.
342 Primitive (unboxed) types cannot be defined in Haskell, and are
343 therefore built into the language and compiler. Primitive types are
344 always unlifted; that is, a value of a primitive type cannot be
345 bottom. We use the convention that primitive types, values, and
346 operations have a <literal>#</literal> suffix.
350 Primitive values are often represented by a simple bit-pattern, such
351 as <literal>Int#</literal>, <literal>Float#</literal>,
352 <literal>Double#</literal>. But this is not necessarily the case:
353 a primitive value might be represented by a pointer to a
354 heap-allocated object. Examples include
355 <literal>Array#</literal>, the type of primitive arrays. A
356 primitive array is heap-allocated because it is too big a value to fit
357 in a register, and would be too expensive to copy around; in a sense,
358 it is accidental that it is represented by a pointer. If a pointer
359 represents a primitive value, then it really does point to that value:
360 no unevaluated thunks, no indirections…nothing can be at the
361 other end of the pointer than the primitive value.
362 A numerically-intensive program using unboxed types can
363 go a <emphasis>lot</emphasis> faster than its “standard”
364 counterpart—we saw a threefold speedup on one example.
368 There are some restrictions on the use of primitive types:
370 <listitem><para>The main restriction
371 is that you can't pass a primitive value to a polymorphic
372 function or store one in a polymorphic data type. This rules out
373 things like <literal>[Int#]</literal> (i.e. lists of primitive
374 integers). The reason for this restriction is that polymorphic
375 arguments and constructor fields are assumed to be pointers: if an
376 unboxed integer is stored in one of these, the garbage collector would
377 attempt to follow it, leading to unpredictable space leaks. Or a
378 <function>seq</function> operation on the polymorphic component may
379 attempt to dereference the pointer, with disastrous results. Even
380 worse, the unboxed value might be larger than a pointer
381 (<literal>Double#</literal> for instance).
384 <listitem><para> You cannot define a newtype whose representation type
385 (the argument type of the data constructor) is an unboxed type. Thus,
391 <listitem><para> You cannot bind a variable with an unboxed type
392 in a <emphasis>top-level</emphasis> binding.
394 <listitem><para> You cannot bind a variable with an unboxed type
395 in a <emphasis>recursive</emphasis> binding.
397 <listitem><para> You may bind unboxed variables in a (non-recursive,
398 non-top-level) pattern binding, but any such variable causes the entire
400 to become strict. For example:
402 data Foo = Foo Int Int#
404 f x = let (Foo a b, w) = ..rhs.. in ..body..
406 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
408 is strict, and the program behaves as if you had written
410 data Foo = Foo Int Int#
412 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
421 <sect2 id="unboxed-tuples">
422 <title>Unboxed Tuples
426 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
427 they're available by default with <option>-fglasgow-exts</option>. An
428 unboxed tuple looks like this:
440 where <literal>e_1..e_n</literal> are expressions of any
441 type (primitive or non-primitive). The type of an unboxed tuple looks
446 Unboxed tuples are used for functions that need to return multiple
447 values, but they avoid the heap allocation normally associated with
448 using fully-fledged tuples. When an unboxed tuple is returned, the
449 components are put directly into registers or on the stack; the
450 unboxed tuple itself does not have a composite representation. Many
451 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
453 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
454 tuples to avoid unnecessary allocation during sequences of operations.
458 There are some pretty stringent restrictions on the use of unboxed tuples:
463 Values of unboxed tuple types are subject to the same restrictions as
464 other unboxed types; i.e. they may not be stored in polymorphic data
465 structures or passed to polymorphic functions.
472 No variable can have an unboxed tuple type, nor may a constructor or function
473 argument have an unboxed tuple type. The following are all illegal:
477 data Foo = Foo (# Int, Int #)
479 f :: (# Int, Int #) -> (# Int, Int #)
482 g :: (# Int, Int #) -> Int
485 h x = let y = (# x,x #) in ...
492 The typical use of unboxed tuples is simply to return multiple values,
493 binding those multiple results with a <literal>case</literal> expression, thus:
495 f x y = (# x+1, y-1 #)
496 g x = case f x x of { (# a, b #) -> a + b }
498 You can have an unboxed tuple in a pattern binding, thus
500 f x = let (# p,q #) = h x in ..body..
502 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
503 the resulting binding is lazy like any other Haskell pattern binding. The
504 above example desugars like this:
506 f x = let t = case h x o f{ (# p,q #) -> (p,q)
511 Indeed, the bindings can even be recursive.
518 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
520 <sect1 id="syntax-extns">
521 <title>Syntactic extensions</title>
523 <!-- ====================== HIERARCHICAL MODULES ======================= -->
525 <sect2 id="hierarchical-modules">
526 <title>Hierarchical Modules</title>
528 <para>GHC supports a small extension to the syntax of module
529 names: a module name is allowed to contain a dot
530 <literal>‘.’</literal>. This is also known as the
531 “hierarchical module namespace” extension, because
532 it extends the normally flat Haskell module namespace into a
533 more flexible hierarchy of modules.</para>
535 <para>This extension has very little impact on the language
536 itself; modules names are <emphasis>always</emphasis> fully
537 qualified, so you can just think of the fully qualified module
538 name as <quote>the module name</quote>. In particular, this
539 means that the full module name must be given after the
540 <literal>module</literal> keyword at the beginning of the
541 module; for example, the module <literal>A.B.C</literal> must
544 <programlisting>module A.B.C</programlisting>
547 <para>It is a common strategy to use the <literal>as</literal>
548 keyword to save some typing when using qualified names with
549 hierarchical modules. For example:</para>
552 import qualified Control.Monad.ST.Strict as ST
555 <para>For details on how GHC searches for source and interface
556 files in the presence of hierarchical modules, see <xref
557 linkend="search-path"/>.</para>
559 <para>GHC comes with a large collection of libraries arranged
560 hierarchically; see the accompanying <ulink
561 url="../libraries/index.html">library
562 documentation</ulink>. More libraries to install are available
564 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
567 <!-- ====================== PATTERN GUARDS ======================= -->
569 <sect2 id="pattern-guards">
570 <title>Pattern guards</title>
573 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
574 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
578 Suppose we have an abstract data type of finite maps, with a
582 lookup :: FiniteMap -> Int -> Maybe Int
585 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
586 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
590 clunky env var1 var2 | ok1 && ok2 = val1 + val2
591 | otherwise = var1 + var2
602 The auxiliary functions are
606 maybeToBool :: Maybe a -> Bool
607 maybeToBool (Just x) = True
608 maybeToBool Nothing = False
610 expectJust :: Maybe a -> a
611 expectJust (Just x) = x
612 expectJust Nothing = error "Unexpected Nothing"
616 What is <function>clunky</function> doing? The guard <literal>ok1 &&
617 ok2</literal> checks that both lookups succeed, using
618 <function>maybeToBool</function> to convert the <function>Maybe</function>
619 types to booleans. The (lazily evaluated) <function>expectJust</function>
620 calls extract the values from the results of the lookups, and binds the
621 returned values to <varname>val1</varname> and <varname>val2</varname>
622 respectively. If either lookup fails, then clunky takes the
623 <literal>otherwise</literal> case and returns the sum of its arguments.
627 This is certainly legal Haskell, but it is a tremendously verbose and
628 un-obvious way to achieve the desired effect. Arguably, a more direct way
629 to write clunky would be to use case expressions:
633 clunky env var1 var2 = case lookup env var1 of
635 Just val1 -> case lookup env var2 of
637 Just val2 -> val1 + val2
643 This is a bit shorter, but hardly better. Of course, we can rewrite any set
644 of pattern-matching, guarded equations as case expressions; that is
645 precisely what the compiler does when compiling equations! The reason that
646 Haskell provides guarded equations is because they allow us to write down
647 the cases we want to consider, one at a time, independently of each other.
648 This structure is hidden in the case version. Two of the right-hand sides
649 are really the same (<function>fail</function>), and the whole expression
650 tends to become more and more indented.
654 Here is how I would write clunky:
659 | Just val1 <- lookup env var1
660 , Just val2 <- lookup env var2
662 ...other equations for clunky...
666 The semantics should be clear enough. The qualifiers are matched in order.
667 For a <literal><-</literal> qualifier, which I call a pattern guard, the
668 right hand side is evaluated and matched against the pattern on the left.
669 If the match fails then the whole guard fails and the next equation is
670 tried. If it succeeds, then the appropriate binding takes place, and the
671 next qualifier is matched, in the augmented environment. Unlike list
672 comprehensions, however, the type of the expression to the right of the
673 <literal><-</literal> is the same as the type of the pattern to its
674 left. The bindings introduced by pattern guards scope over all the
675 remaining guard qualifiers, and over the right hand side of the equation.
679 Just as with list comprehensions, boolean expressions can be freely mixed
680 with among the pattern guards. For example:
691 Haskell's current guards therefore emerge as a special case, in which the
692 qualifier list has just one element, a boolean expression.
696 <!-- ===================== Recursive do-notation =================== -->
698 <sect2 id="mdo-notation">
699 <title>The recursive do-notation
702 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
703 "A recursive do for Haskell",
704 Levent Erkok, John Launchbury",
705 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
708 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
709 that is, the variables bound in a do-expression are visible only in the textually following
710 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
711 group. It turns out that several applications can benefit from recursive bindings in
712 the do-notation, and this extension provides the necessary syntactic support.
715 Here is a simple (yet contrived) example:
718 import Control.Monad.Fix
720 justOnes = mdo xs <- Just (1:xs)
724 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
728 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
731 class Monad m => MonadFix m where
732 mfix :: (a -> m a) -> m a
735 The function <literal>mfix</literal>
736 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
737 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
738 For details, see the above mentioned reference.
741 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
742 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
743 for Haskell's internal state monad (strict and lazy, respectively).
746 There are three important points in using the recursive-do notation:
749 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
750 than <literal>do</literal>).
754 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
760 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
761 contains up to date information on recursive monadic bindings.
765 Historical note: The old implementation of the mdo-notation (and most
766 of the existing documents) used the name
767 <literal>MonadRec</literal> for the class and the corresponding library.
768 This name is not supported by GHC.
774 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
776 <sect2 id="parallel-list-comprehensions">
777 <title>Parallel List Comprehensions</title>
778 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
780 <indexterm><primary>parallel list comprehensions</primary>
783 <para>Parallel list comprehensions are a natural extension to list
784 comprehensions. List comprehensions can be thought of as a nice
785 syntax for writing maps and filters. Parallel comprehensions
786 extend this to include the zipWith family.</para>
788 <para>A parallel list comprehension has multiple independent
789 branches of qualifier lists, each separated by a `|' symbol. For
790 example, the following zips together two lists:</para>
793 [ (x, y) | x <- xs | y <- ys ]
796 <para>The behavior of parallel list comprehensions follows that of
797 zip, in that the resulting list will have the same length as the
798 shortest branch.</para>
800 <para>We can define parallel list comprehensions by translation to
801 regular comprehensions. Here's the basic idea:</para>
803 <para>Given a parallel comprehension of the form: </para>
806 [ e | p1 <- e11, p2 <- e12, ...
807 | q1 <- e21, q2 <- e22, ...
812 <para>This will be translated to: </para>
815 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
816 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
821 <para>where `zipN' is the appropriate zip for the given number of
826 <sect2 id="rebindable-syntax">
827 <title>Rebindable syntax</title>
830 <para>GHC allows most kinds of built-in syntax to be rebound by
831 the user, to facilitate replacing the <literal>Prelude</literal>
832 with a home-grown version, for example.</para>
834 <para>You may want to define your own numeric class
835 hierarchy. It completely defeats that purpose if the
836 literal "1" means "<literal>Prelude.fromInteger
837 1</literal>", which is what the Haskell Report specifies.
838 So the <option>-fno-implicit-prelude</option> flag causes
839 the following pieces of built-in syntax to refer to
840 <emphasis>whatever is in scope</emphasis>, not the Prelude
845 <para>An integer literal <literal>368</literal> means
846 "<literal>fromInteger (368::Integer)</literal>", rather than
847 "<literal>Prelude.fromInteger (368::Integer)</literal>".
850 <listitem><para>Fractional literals are handed in just the same way,
851 except that the translation is
852 <literal>fromRational (3.68::Rational)</literal>.
855 <listitem><para>The equality test in an overloaded numeric pattern
856 uses whatever <literal>(==)</literal> is in scope.
859 <listitem><para>The subtraction operation, and the
860 greater-than-or-equal test, in <literal>n+k</literal> patterns
861 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
865 <para>Negation (e.g. "<literal>- (f x)</literal>")
866 means "<literal>negate (f x)</literal>", both in numeric
867 patterns, and expressions.
871 <para>"Do" notation is translated using whatever
872 functions <literal>(>>=)</literal>,
873 <literal>(>>)</literal>, and <literal>fail</literal>,
874 are in scope (not the Prelude
875 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
876 comprehensions, are unaffected. </para></listitem>
880 notation (see <xref linkend="arrow-notation"/>)
881 uses whatever <literal>arr</literal>,
882 <literal>(>>>)</literal>, <literal>first</literal>,
883 <literal>app</literal>, <literal>(|||)</literal> and
884 <literal>loop</literal> functions are in scope. But unlike the
885 other constructs, the types of these functions must match the
886 Prelude types very closely. Details are in flux; if you want
890 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
891 even if that is a little unexpected. For emample, the
892 static semantics of the literal <literal>368</literal>
893 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
894 <literal>fromInteger</literal> to have any of the types:
896 fromInteger :: Integer -> Integer
897 fromInteger :: forall a. Foo a => Integer -> a
898 fromInteger :: Num a => a -> Integer
899 fromInteger :: Integer -> Bool -> Bool
903 <para>Be warned: this is an experimental facility, with
904 fewer checks than usual. Use <literal>-dcore-lint</literal>
905 to typecheck the desugared program. If Core Lint is happy
906 you should be all right.</para>
910 <sect2 id="postfix-operators">
911 <title>Postfix operators</title>
914 GHC allows a small extension to the syntax of left operator sections, which
915 allows you to define postfix operators. The extension is this: the left section
919 is equivalent (from the point of view of both type checking and execution) to the expression
923 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
924 The strict Haskell 98 interpretation is that the section is equivalent to
928 That is, the operator must be a function of two arguments. GHC allows it to
929 take only one argument, and that in turn allows you to write the function
932 <para>Since this extension goes beyond Haskell 98, it should really be enabled
933 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
934 change their behaviour, of course.)
936 <para>The extension does not extend to the left-hand side of function
937 definitions; you must define such a function in prefix form.</para>
944 <!-- TYPE SYSTEM EXTENSIONS -->
945 <sect1 id="data-type-extensions">
946 <title>Extensions to data types and type synonyms</title>
948 <sect2 id="nullary-types">
949 <title>Data types with no constructors</title>
951 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
952 a data type with no constructors. For example:</para>
956 data T a -- T :: * -> *
959 <para>Syntactically, the declaration lacks the "= constrs" part. The
960 type can be parameterised over types of any kind, but if the kind is
961 not <literal>*</literal> then an explicit kind annotation must be used
962 (see <xref linkend="kinding"/>).</para>
964 <para>Such data types have only one value, namely bottom.
965 Nevertheless, they can be useful when defining "phantom types".</para>
968 <sect2 id="infix-tycons">
969 <title>Infix type constructors, classes, and type variables</title>
972 GHC allows type constructors, classes, and type variables to be operators, and
973 to be written infix, very much like expressions. More specifically:
976 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
977 The lexical syntax is the same as that for data constructors.
980 Data type and type-synonym declarations can be written infix, parenthesised
981 if you want further arguments. E.g.
983 data a :*: b = Foo a b
984 type a :+: b = Either a b
985 class a :=: b where ...
987 data (a :**: b) x = Baz a b x
988 type (a :++: b) y = Either (a,b) y
992 Types, and class constraints, can be written infix. For example
995 f :: (a :=: b) => a -> b
999 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1000 The lexical syntax is the same as that for variable operators, excluding "(.)",
1001 "(!)", and "(*)". In a binding position, the operator must be
1002 parenthesised. For example:
1004 type T (+) = Int + Int
1008 liftA2 :: Arrow (~>)
1009 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1015 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1016 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1019 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1020 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1021 sets the fixity for a data constructor and the corresponding type constructor. For example:
1025 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1026 and similarly for <literal>:*:</literal>.
1027 <literal>Int `a` Bool</literal>.
1030 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1037 <sect2 id="type-synonyms">
1038 <title>Liberalised type synonyms</title>
1041 Type synonyms are like macros at the type level, and
1042 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1043 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1045 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1046 in a type synonym, thus:
1048 type Discard a = forall b. Show b => a -> b -> (a, String)
1053 g :: Discard Int -> (Int,String) -- A rank-2 type
1060 You can write an unboxed tuple in a type synonym:
1062 type Pr = (# Int, Int #)
1070 You can apply a type synonym to a forall type:
1072 type Foo a = a -> a -> Bool
1074 f :: Foo (forall b. b->b)
1076 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1078 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1083 You can apply a type synonym to a partially applied type synonym:
1085 type Generic i o = forall x. i x -> o x
1088 foo :: Generic Id []
1090 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1092 foo :: forall x. x -> [x]
1100 GHC currently does kind checking before expanding synonyms (though even that
1104 After expanding type synonyms, GHC does validity checking on types, looking for
1105 the following mal-formedness which isn't detected simply by kind checking:
1108 Type constructor applied to a type involving for-alls.
1111 Unboxed tuple on left of an arrow.
1114 Partially-applied type synonym.
1118 this will be rejected:
1120 type Pr = (# Int, Int #)
1125 because GHC does not allow unboxed tuples on the left of a function arrow.
1130 <sect2 id="existential-quantification">
1131 <title>Existentially quantified data constructors
1135 The idea of using existential quantification in data type declarations
1136 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1137 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1138 London, 1991). It was later formalised by Laufer and Odersky
1139 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1140 TOPLAS, 16(5), pp1411-1430, 1994).
1141 It's been in Lennart
1142 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1143 proved very useful. Here's the idea. Consider the declaration:
1149 data Foo = forall a. MkFoo a (a -> Bool)
1156 The data type <literal>Foo</literal> has two constructors with types:
1162 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1169 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1170 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1171 For example, the following expression is fine:
1177 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1183 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1184 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1185 isUpper</function> packages a character with a compatible function. These
1186 two things are each of type <literal>Foo</literal> and can be put in a list.
1190 What can we do with a value of type <literal>Foo</literal>?. In particular,
1191 what happens when we pattern-match on <function>MkFoo</function>?
1197 f (MkFoo val fn) = ???
1203 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1204 are compatible, the only (useful) thing we can do with them is to
1205 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1212 f (MkFoo val fn) = fn val
1218 What this allows us to do is to package heterogenous values
1219 together with a bunch of functions that manipulate them, and then treat
1220 that collection of packages in a uniform manner. You can express
1221 quite a bit of object-oriented-like programming this way.
1224 <sect3 id="existential">
1225 <title>Why existential?
1229 What has this to do with <emphasis>existential</emphasis> quantification?
1230 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1236 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1242 But Haskell programmers can safely think of the ordinary
1243 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1244 adding a new existential quantification construct.
1250 <title>Type classes</title>
1253 An easy extension is to allow
1254 arbitrary contexts before the constructor. For example:
1260 data Baz = forall a. Eq a => Baz1 a a
1261 | forall b. Show b => Baz2 b (b -> b)
1267 The two constructors have the types you'd expect:
1273 Baz1 :: forall a. Eq a => a -> a -> Baz
1274 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1280 But when pattern matching on <function>Baz1</function> the matched values can be compared
1281 for equality, and when pattern matching on <function>Baz2</function> the first matched
1282 value can be converted to a string (as well as applying the function to it).
1283 So this program is legal:
1290 f (Baz1 p q) | p == q = "Yes"
1292 f (Baz2 v fn) = show (fn v)
1298 Operationally, in a dictionary-passing implementation, the
1299 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1300 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1301 extract it on pattern matching.
1305 Notice the way that the syntax fits smoothly with that used for
1306 universal quantification earlier.
1311 <sect3 id="existential-records">
1312 <title>Record Constructors</title>
1315 GHC allows existentials to be used with records syntax as well. For example:
1318 data Counter a = forall self. NewCounter
1320 , _inc :: self -> self
1321 , _display :: self -> IO ()
1325 Here <literal>tag</literal> is a public field, with a well-typed selector
1326 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1327 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1328 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
1329 compile-time error. In other words, <emphasis>GHC defines a record selector function
1330 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1331 (This example used an underscore in the fields for which record selectors
1332 will not be defined, but that is only programming style; GHC ignores them.)
1336 To make use of these hidden fields, we need to create some helper functions:
1339 inc :: Counter a -> Counter a
1340 inc (NewCounter x i d t) = NewCounter
1341 { _this = i x, _inc = i, _display = d, tag = t }
1343 display :: Counter a -> IO ()
1344 display NewCounter{ _this = x, _display = d } = d x
1347 Now we can define counters with different underlying implementations:
1350 counterA :: Counter String
1351 counterA = NewCounter
1352 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1354 counterB :: Counter String
1355 counterB = NewCounter
1356 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1359 display (inc counterA) -- prints "1"
1360 display (inc (inc counterB)) -- prints "##"
1363 At the moment, record update syntax is only supported for Haskell 98 data types,
1364 so the following function does <emphasis>not</emphasis> work:
1367 -- This is invalid; use explicit NewCounter instead for now
1368 setTag :: Counter a -> a -> Counter a
1369 setTag obj t = obj{ tag = t }
1378 <title>Restrictions</title>
1381 There are several restrictions on the ways in which existentially-quantified
1382 constructors can be use.
1391 When pattern matching, each pattern match introduces a new,
1392 distinct, type for each existential type variable. These types cannot
1393 be unified with any other type, nor can they escape from the scope of
1394 the pattern match. For example, these fragments are incorrect:
1402 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1403 is the result of <function>f1</function>. One way to see why this is wrong is to
1404 ask what type <function>f1</function> has:
1408 f1 :: Foo -> a -- Weird!
1412 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1417 f1 :: forall a. Foo -> a -- Wrong!
1421 The original program is just plain wrong. Here's another sort of error
1425 f2 (Baz1 a b) (Baz1 p q) = a==q
1429 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1430 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1431 from the two <function>Baz1</function> constructors.
1439 You can't pattern-match on an existentially quantified
1440 constructor in a <literal>let</literal> or <literal>where</literal> group of
1441 bindings. So this is illegal:
1445 f3 x = a==b where { Baz1 a b = x }
1448 Instead, use a <literal>case</literal> expression:
1451 f3 x = case x of Baz1 a b -> a==b
1454 In general, you can only pattern-match
1455 on an existentially-quantified constructor in a <literal>case</literal> expression or
1456 in the patterns of a function definition.
1458 The reason for this restriction is really an implementation one.
1459 Type-checking binding groups is already a nightmare without
1460 existentials complicating the picture. Also an existential pattern
1461 binding at the top level of a module doesn't make sense, because it's
1462 not clear how to prevent the existentially-quantified type "escaping".
1463 So for now, there's a simple-to-state restriction. We'll see how
1471 You can't use existential quantification for <literal>newtype</literal>
1472 declarations. So this is illegal:
1476 newtype T = forall a. Ord a => MkT a
1480 Reason: a value of type <literal>T</literal> must be represented as a
1481 pair of a dictionary for <literal>Ord t</literal> and a value of type
1482 <literal>t</literal>. That contradicts the idea that
1483 <literal>newtype</literal> should have no concrete representation.
1484 You can get just the same efficiency and effect by using
1485 <literal>data</literal> instead of <literal>newtype</literal>. If
1486 there is no overloading involved, then there is more of a case for
1487 allowing an existentially-quantified <literal>newtype</literal>,
1488 because the <literal>data</literal> version does carry an
1489 implementation cost, but single-field existentially quantified
1490 constructors aren't much use. So the simple restriction (no
1491 existential stuff on <literal>newtype</literal>) stands, unless there
1492 are convincing reasons to change it.
1500 You can't use <literal>deriving</literal> to define instances of a
1501 data type with existentially quantified data constructors.
1503 Reason: in most cases it would not make sense. For example:;
1506 data T = forall a. MkT [a] deriving( Eq )
1509 To derive <literal>Eq</literal> in the standard way we would need to have equality
1510 between the single component of two <function>MkT</function> constructors:
1514 (MkT a) == (MkT b) = ???
1517 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1518 It's just about possible to imagine examples in which the derived instance
1519 would make sense, but it seems altogether simpler simply to prohibit such
1520 declarations. Define your own instances!
1531 <!-- ====================== Generalised algebraic data types ======================= -->
1533 <sect2 id="gadt-style">
1534 <title>Declaring data types with explicit constructor signatures</title>
1536 <para>GHC allows you to declare an algebraic data type by
1537 giving the type signatures of constructors explicitly. For example:
1541 Just :: a -> Maybe a
1543 The form is called a "GADT-style declaration"
1544 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
1545 can only be declared using this form.</para>
1546 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
1547 For example, these two declarations are equivalent:
1549 data Foo = forall a. MkFoo a (a -> Bool)
1550 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
1553 <para>Any data type that can be declared in standard Haskell-98 syntax
1554 can also be declared using GADT-style syntax.
1555 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
1556 they treat class constraints on the data constructors differently.
1557 Specifically, if the constructor is given a type-class context, that
1558 context is made available by pattern matching. For example:
1561 MkSet :: Eq a => [a] -> Set a
1563 makeSet :: Eq a => [a] -> Set a
1564 makeSet xs = MkSet (nub xs)
1566 insert :: a -> Set a -> Set a
1567 insert a (MkSet as) | a `elem` as = MkSet as
1568 | otherwise = MkSet (a:as)
1570 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
1571 gives rise to a <literal>(Eq a)</literal>
1572 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
1573 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
1574 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
1575 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
1576 when pattern-matching that dictionary becomes available for the right-hand side of the match.
1577 In the example, the equality dictionary is used to satisfy the equality constraint
1578 generated by the call to <literal>elem</literal>, so that the type of
1579 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
1581 <para>This behaviour contrasts with Haskell 98's peculiar treament of
1582 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
1583 In Haskell 98 the defintion
1585 data Eq a => Set' a = MkSet' [a]
1587 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
1588 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
1589 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
1590 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
1591 GHC's behaviour is much more useful, as well as much more intuitive.</para>
1593 For example, a possible application of GHC's behaviour is to reify dictionaries:
1595 data NumInst a where
1596 MkNumInst :: Num a => NumInst a
1598 intInst :: NumInst Int
1601 plus :: NumInst a -> a -> a -> a
1602 plus MkNumInst p q = p + q
1604 Here, a value of type <literal>NumInst a</literal> is equivalent
1605 to an explicit <literal>(Num a)</literal> dictionary.
1609 The rest of this section gives further details about GADT-style data
1614 The result type of each data constructor must begin with the type constructor being defined.
1615 If the result type of all constructors
1616 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
1617 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
1618 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
1622 The type signature of
1623 each constructor is independent, and is implicitly universally quantified as usual.
1624 Different constructors may have different universally-quantified type variables
1625 and different type-class constraints.
1626 For example, this is fine:
1629 T1 :: Eq b => b -> T b
1630 T2 :: (Show c, Ix c) => c -> [c] -> T c
1635 Unlike a Haskell-98-style
1636 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
1637 have no scope. Indeed, one can write a kind signature instead:
1639 data Set :: * -> * where ...
1641 or even a mixture of the two:
1643 data Foo a :: (* -> *) -> * where ...
1645 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
1648 data Foo a (b :: * -> *) where ...
1654 You can use strictness annotations, in the obvious places
1655 in the constructor type:
1658 Lit :: !Int -> Term Int
1659 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
1660 Pair :: Term a -> Term b -> Term (a,b)
1665 You can use a <literal>deriving</literal> clause on a GADT-style data type
1666 declaration. For example, these two declarations are equivalent
1668 data Maybe1 a where {
1669 Nothing1 :: Maybe1 a ;
1670 Just1 :: a -> Maybe1 a
1671 } deriving( Eq, Ord )
1673 data Maybe2 a = Nothing2 | Just2 a
1679 You can use record syntax on a GADT-style data type declaration:
1683 Adult { name :: String, children :: [Person] } :: Person
1684 Child { name :: String } :: Person
1686 As usual, for every constructor that has a field <literal>f</literal>, the type of
1687 field <literal>f</literal> must be the same (modulo alpha conversion).
1690 At the moment, record updates are not yet possible with GADT-style declarations,
1691 so support is limited to record construction, selection and pattern matching.
1694 aPerson = Adult { name = "Fred", children = [] }
1696 shortName :: Person -> Bool
1697 hasChildren (Adult { children = kids }) = not (null kids)
1698 hasChildren (Child {}) = False
1703 As in the case of existentials declared using the Haskell-98-like record syntax
1704 (<xref linkend="existential-records"/>),
1705 record-selector functions are generated only for those fields that have well-typed
1707 Here is the example of that section, in GADT-style syntax:
1709 data Counter a where
1710 NewCounter { _this :: self
1711 , _inc :: self -> self
1712 , _display :: self -> IO ()
1717 As before, only one selector function is generated here, that for <literal>tag</literal>.
1718 Nevertheless, you can still use all the field names in pattern matching and record construction.
1720 </itemizedlist></para>
1724 <title>Generalised Algebraic Data Types (GADTs)</title>
1726 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
1727 by allowing constructors to have richer return types. Here is an example:
1730 Lit :: Int -> Term Int
1731 Succ :: Term Int -> Term Int
1732 IsZero :: Term Int -> Term Bool
1733 If :: Term Bool -> Term a -> Term a -> Term a
1734 Pair :: Term a -> Term b -> Term (a,b)
1736 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
1737 case with ordinary data types. This generality allows us to
1738 write a well-typed <literal>eval</literal> function
1739 for these <literal>Terms</literal>:
1743 eval (Succ t) = 1 + eval t
1744 eval (IsZero t) = eval t == 0
1745 eval (If b e1 e2) = if eval b then eval e1 else eval e2
1746 eval (Pair e1 e2) = (eval e1, eval e2)
1748 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
1749 For example, in the right hand side of the equation
1754 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
1755 A precise specification of the type rules is beyond what this user manual aspires to,
1756 but the design closely follows that described in
1758 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
1759 unification-based type inference for GADTs</ulink>,
1761 The general principle is this: <emphasis>type refinement is only carried out
1762 based on user-supplied type annotations</emphasis>.
1763 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
1764 and lots of obscure error messages will
1765 occur. However, the refinement is quite general. For example, if we had:
1767 eval :: Term a -> a -> a
1768 eval (Lit i) j = i+j
1770 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
1771 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
1772 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
1775 These and many other examples are given in papers by Hongwei Xi, and
1776 Tim Sheard. There is a longer introduction
1777 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
1779 <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
1780 may use different notation to that implemented in GHC.
1783 The rest of this section outlines the extensions to GHC that support GADTs.
1786 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
1787 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
1788 The result type of each constructor must begin with the type constructor being defined,
1789 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
1790 For example, in the <literal>Term</literal> data
1791 type above, the type of each constructor must end with <literal>Term ty</literal>, but
1792 the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
1797 You cannot use a <literal>deriving</literal> clause for a GADT; only for
1798 an ordianary data type.
1802 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
1806 Lit { val :: Int } :: Term Int
1807 Succ { num :: Term Int } :: Term Int
1808 Pred { num :: Term Int } :: Term Int
1809 IsZero { arg :: Term Int } :: Term Bool
1810 Pair { arg1 :: Term a
1813 If { cnd :: Term Bool
1818 However, for GADTs there is the following additional constraint:
1819 every constructor that has a field <literal>f</literal> must have
1820 the same result type (modulo alpha conversion)
1821 Hence, in the above example, we cannot merge the <literal>num</literal>
1822 and <literal>arg</literal> fields above into a
1823 single name. Although their field types are both <literal>Term Int</literal>,
1824 their selector functions actually have different types:
1827 num :: Term Int -> Term Int
1828 arg :: Term Bool -> Term Int
1837 <!-- ====================== End of Generalised algebraic data types ======================= -->
1840 <sect2 id="deriving-typeable">
1841 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
1844 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
1845 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
1846 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
1847 classes <literal>Eq</literal>, <literal>Ord</literal>,
1848 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
1851 GHC extends this list with two more classes that may be automatically derived
1852 (provided the <option>-fglasgow-exts</option> flag is specified):
1853 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
1854 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
1855 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
1857 <para>An instance of <literal>Typeable</literal> can only be derived if the
1858 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
1859 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
1861 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
1862 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
1864 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
1865 are used, and only <literal>Typeable1</literal> up to
1866 <literal>Typeable7</literal> are provided in the library.)
1867 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
1868 class, whose kind suits that of the data type constructor, and
1869 then writing the data type instance by hand.
1873 <sect2 id="newtype-deriving">
1874 <title>Generalised derived instances for newtypes</title>
1877 When you define an abstract type using <literal>newtype</literal>, you may want
1878 the new type to inherit some instances from its representation. In
1879 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
1880 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
1881 other classes you have to write an explicit instance declaration. For
1882 example, if you define
1885 newtype Dollars = Dollars Int
1888 and you want to use arithmetic on <literal>Dollars</literal>, you have to
1889 explicitly define an instance of <literal>Num</literal>:
1892 instance Num Dollars where
1893 Dollars a + Dollars b = Dollars (a+b)
1896 All the instance does is apply and remove the <literal>newtype</literal>
1897 constructor. It is particularly galling that, since the constructor
1898 doesn't appear at run-time, this instance declaration defines a
1899 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
1900 dictionary, only slower!
1904 <sect3> <title> Generalising the deriving clause </title>
1906 GHC now permits such instances to be derived instead, so one can write
1908 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
1911 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
1912 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
1913 derives an instance declaration of the form
1916 instance Num Int => Num Dollars
1919 which just adds or removes the <literal>newtype</literal> constructor according to the type.
1923 We can also derive instances of constructor classes in a similar
1924 way. For example, suppose we have implemented state and failure monad
1925 transformers, such that
1928 instance Monad m => Monad (State s m)
1929 instance Monad m => Monad (Failure m)
1931 In Haskell 98, we can define a parsing monad by
1933 type Parser tok m a = State [tok] (Failure m) a
1936 which is automatically a monad thanks to the instance declarations
1937 above. With the extension, we can make the parser type abstract,
1938 without needing to write an instance of class <literal>Monad</literal>, via
1941 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1944 In this case the derived instance declaration is of the form
1946 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
1949 Notice that, since <literal>Monad</literal> is a constructor class, the
1950 instance is a <emphasis>partial application</emphasis> of the new type, not the
1951 entire left hand side. We can imagine that the type declaration is
1952 ``eta-converted'' to generate the context of the instance
1957 We can even derive instances of multi-parameter classes, provided the
1958 newtype is the last class parameter. In this case, a ``partial
1959 application'' of the class appears in the <literal>deriving</literal>
1960 clause. For example, given the class
1963 class StateMonad s m | m -> s where ...
1964 instance Monad m => StateMonad s (State s m) where ...
1966 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
1968 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
1969 deriving (Monad, StateMonad [tok])
1972 The derived instance is obtained by completing the application of the
1973 class to the new type:
1976 instance StateMonad [tok] (State [tok] (Failure m)) =>
1977 StateMonad [tok] (Parser tok m)
1982 As a result of this extension, all derived instances in newtype
1983 declarations are treated uniformly (and implemented just by reusing
1984 the dictionary for the representation type), <emphasis>except</emphasis>
1985 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
1986 the newtype and its representation.
1990 <sect3> <title> A more precise specification </title>
1992 Derived instance declarations are constructed as follows. Consider the
1993 declaration (after expansion of any type synonyms)
1996 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2002 The <literal>ci</literal> are partial applications of
2003 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2004 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2007 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2010 The type <literal>t</literal> is an arbitrary type.
2013 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2014 nor in the <literal>ci</literal>, and
2017 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2018 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2019 should not "look through" the type or its constructor. You can still
2020 derive these classes for a newtype, but it happens in the usual way, not
2021 via this new mechanism.
2024 Then, for each <literal>ci</literal>, the derived instance
2027 instance ci t => ci (T v1...vk)
2029 As an example which does <emphasis>not</emphasis> work, consider
2031 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2033 Here we cannot derive the instance
2035 instance Monad (State s m) => Monad (NonMonad m)
2038 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2039 and so cannot be "eta-converted" away. It is a good thing that this
2040 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2041 not, in fact, a monad --- for the same reason. Try defining
2042 <literal>>>=</literal> with the correct type: you won't be able to.
2046 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2047 important, since we can only derive instances for the last one. If the
2048 <literal>StateMonad</literal> class above were instead defined as
2051 class StateMonad m s | m -> s where ...
2054 then we would not have been able to derive an instance for the
2055 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2056 classes usually have one "main" parameter for which deriving new
2057 instances is most interesting.
2059 <para>Lastly, all of this applies only for classes other than
2060 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2061 and <literal>Data</literal>, for which the built-in derivation applies (section
2062 4.3.3. of the Haskell Report).
2063 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2064 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2065 the standard method is used or the one described here.)
2071 <sect2 id="stand-alone-deriving">
2072 <title>Stand-alone deriving declarations</title>
2075 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
2077 data Foo a = Bar a | Baz String
2079 derive instance Eq (Foo a)
2081 The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
2082 you can use it as a variable name elsewhere.</para>
2083 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2084 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2087 newtype Foo a = MkFoo (State Int a)
2089 derive instance MonadState Int Foo
2091 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2092 (<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
2100 <!-- TYPE SYSTEM EXTENSIONS -->
2101 <sect1 id="other-type-extensions">
2102 <title>Other type system extensions</title>
2104 <sect2 id="multi-param-type-classes">
2105 <title>Class declarations</title>
2108 This section, and the next one, documents GHC's type-class extensions.
2109 There's lots of background in the paper <ulink
2110 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
2111 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
2112 Jones, Erik Meijer).
2115 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2119 <title>Multi-parameter type classes</title>
2121 Multi-parameter type classes are permitted. For example:
2125 class Collection c a where
2126 union :: c a -> c a -> c a
2134 <title>The superclasses of a class declaration</title>
2137 There are no restrictions on the context in a class declaration
2138 (which introduces superclasses), except that the class hierarchy must
2139 be acyclic. So these class declarations are OK:
2143 class Functor (m k) => FiniteMap m k where
2146 class (Monad m, Monad (t m)) => Transform t m where
2147 lift :: m a -> (t m) a
2153 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
2154 of "acyclic" involves only the superclass relationships. For example,
2160 op :: D b => a -> b -> b
2163 class C a => D a where { ... }
2167 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
2168 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
2169 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
2176 <sect3 id="class-method-types">
2177 <title>Class method types</title>
2180 Haskell 98 prohibits class method types to mention constraints on the
2181 class type variable, thus:
2184 fromList :: [a] -> s a
2185 elem :: Eq a => a -> s a -> Bool
2187 The type of <literal>elem</literal> is illegal in Haskell 98, because it
2188 contains the constraint <literal>Eq a</literal>, constrains only the
2189 class type variable (in this case <literal>a</literal>).
2190 GHC lifts this restriction.
2197 <sect2 id="functional-dependencies">
2198 <title>Functional dependencies
2201 <para> Functional dependencies are implemented as described by Mark Jones
2202 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2203 In Proceedings of the 9th European Symposium on Programming,
2204 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2208 Functional dependencies are introduced by a vertical bar in the syntax of a
2209 class declaration; e.g.
2211 class (Monad m) => MonadState s m | m -> s where ...
2213 class Foo a b c | a b -> c where ...
2215 There should be more documentation, but there isn't (yet). Yell if you need it.
2218 <sect3><title>Rules for functional dependencies </title>
2220 In a class declaration, all of the class type variables must be reachable (in the sense
2221 mentioned in <xref linkend="type-restrictions"/>)
2222 from the free variables of each method type.
2226 class Coll s a where
2228 insert :: s -> a -> s
2231 is not OK, because the type of <literal>empty</literal> doesn't mention
2232 <literal>a</literal>. Functional dependencies can make the type variable
2235 class Coll s a | s -> a where
2237 insert :: s -> a -> s
2240 Alternatively <literal>Coll</literal> might be rewritten
2243 class Coll s a where
2245 insert :: s a -> a -> s a
2249 which makes the connection between the type of a collection of
2250 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
2251 Occasionally this really doesn't work, in which case you can split the
2259 class CollE s => Coll s a where
2260 insert :: s -> a -> s
2267 <title>Background on functional dependencies</title>
2269 <para>The following description of the motivation and use of functional dependencies is taken
2270 from the Hugs user manual, reproduced here (with minor changes) by kind
2271 permission of Mark Jones.
2274 Consider the following class, intended as part of a
2275 library for collection types:
2277 class Collects e ce where
2279 insert :: e -> ce -> ce
2280 member :: e -> ce -> Bool
2282 The type variable e used here represents the element type, while ce is the type
2283 of the container itself. Within this framework, we might want to define
2284 instances of this class for lists or characteristic functions (both of which
2285 can be used to represent collections of any equality type), bit sets (which can
2286 be used to represent collections of characters), or hash tables (which can be
2287 used to represent any collection whose elements have a hash function). Omitting
2288 standard implementation details, this would lead to the following declarations:
2290 instance Eq e => Collects e [e] where ...
2291 instance Eq e => Collects e (e -> Bool) where ...
2292 instance Collects Char BitSet where ...
2293 instance (Hashable e, Collects a ce)
2294 => Collects e (Array Int ce) where ...
2296 All this looks quite promising; we have a class and a range of interesting
2297 implementations. Unfortunately, there are some serious problems with the class
2298 declaration. First, the empty function has an ambiguous type:
2300 empty :: Collects e ce => ce
2302 By "ambiguous" we mean that there is a type variable e that appears on the left
2303 of the <literal>=></literal> symbol, but not on the right. The problem with
2304 this is that, according to the theoretical foundations of Haskell overloading,
2305 we cannot guarantee a well-defined semantics for any term with an ambiguous
2309 We can sidestep this specific problem by removing the empty member from the
2310 class declaration. However, although the remaining members, insert and member,
2311 do not have ambiguous types, we still run into problems when we try to use
2312 them. For example, consider the following two functions:
2314 f x y = insert x . insert y
2317 for which GHC infers the following types:
2319 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2320 g :: (Collects Bool c, Collects Char c) => c -> c
2322 Notice that the type for f allows the two parameters x and y to be assigned
2323 different types, even though it attempts to insert each of the two values, one
2324 after the other, into the same collection. If we're trying to model collections
2325 that contain only one type of value, then this is clearly an inaccurate
2326 type. Worse still, the definition for g is accepted, without causing a type
2327 error. As a result, the error in this code will not be flagged at the point
2328 where it appears. Instead, it will show up only when we try to use g, which
2329 might even be in a different module.
2332 <sect4><title>An attempt to use constructor classes</title>
2335 Faced with the problems described above, some Haskell programmers might be
2336 tempted to use something like the following version of the class declaration:
2338 class Collects e c where
2340 insert :: e -> c e -> c e
2341 member :: e -> c e -> Bool
2343 The key difference here is that we abstract over the type constructor c that is
2344 used to form the collection type c e, and not over that collection type itself,
2345 represented by ce in the original class declaration. This avoids the immediate
2346 problems that we mentioned above: empty has type <literal>Collects e c => c
2347 e</literal>, which is not ambiguous.
2350 The function f from the previous section has a more accurate type:
2352 f :: (Collects e c) => e -> e -> c e -> c e
2354 The function g from the previous section is now rejected with a type error as
2355 we would hope because the type of f does not allow the two arguments to have
2357 This, then, is an example of a multiple parameter class that does actually work
2358 quite well in practice, without ambiguity problems.
2359 There is, however, a catch. This version of the Collects class is nowhere near
2360 as general as the original class seemed to be: only one of the four instances
2361 for <literal>Collects</literal>
2362 given above can be used with this version of Collects because only one of
2363 them---the instance for lists---has a collection type that can be written in
2364 the form c e, for some type constructor c, and element type e.
2368 <sect4><title>Adding functional dependencies</title>
2371 To get a more useful version of the Collects class, Hugs provides a mechanism
2372 that allows programmers to specify dependencies between the parameters of a
2373 multiple parameter class (For readers with an interest in theoretical
2374 foundations and previous work: The use of dependency information can be seen
2375 both as a generalization of the proposal for `parametric type classes' that was
2376 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
2377 later framework for "improvement" of qualified types. The
2378 underlying ideas are also discussed in a more theoretical and abstract setting
2379 in a manuscript [implparam], where they are identified as one point in a
2380 general design space for systems of implicit parameterization.).
2382 To start with an abstract example, consider a declaration such as:
2384 class C a b where ...
2386 which tells us simply that C can be thought of as a binary relation on types
2387 (or type constructors, depending on the kinds of a and b). Extra clauses can be
2388 included in the definition of classes to add information about dependencies
2389 between parameters, as in the following examples:
2391 class D a b | a -> b where ...
2392 class E a b | a -> b, b -> a where ...
2394 The notation <literal>a -> b</literal> used here between the | and where
2395 symbols --- not to be
2396 confused with a function type --- indicates that the a parameter uniquely
2397 determines the b parameter, and might be read as "a determines b." Thus D is
2398 not just a relation, but actually a (partial) function. Similarly, from the two
2399 dependencies that are included in the definition of E, we can see that E
2400 represents a (partial) one-one mapping between types.
2403 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
2404 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
2405 m>=0, meaning that the y parameters are uniquely determined by the x
2406 parameters. Spaces can be used as separators if more than one variable appears
2407 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
2408 annotated with multiple dependencies using commas as separators, as in the
2409 definition of E above. Some dependencies that we can write in this notation are
2410 redundant, and will be rejected because they don't serve any useful
2411 purpose, and may instead indicate an error in the program. Examples of
2412 dependencies like this include <literal>a -> a </literal>,
2413 <literal>a -> a a </literal>,
2414 <literal>a -> </literal>, etc. There can also be
2415 some redundancy if multiple dependencies are given, as in
2416 <literal>a->b</literal>,
2417 <literal>b->c </literal>, <literal>a->c </literal>, and
2418 in which some subset implies the remaining dependencies. Examples like this are
2419 not treated as errors. Note that dependencies appear only in class
2420 declarations, and not in any other part of the language. In particular, the
2421 syntax for instance declarations, class constraints, and types is completely
2425 By including dependencies in a class declaration, we provide a mechanism for
2426 the programmer to specify each multiple parameter class more precisely. The
2427 compiler, on the other hand, is responsible for ensuring that the set of
2428 instances that are in scope at any given point in the program is consistent
2429 with any declared dependencies. For example, the following pair of instance
2430 declarations cannot appear together in the same scope because they violate the
2431 dependency for D, even though either one on its own would be acceptable:
2433 instance D Bool Int where ...
2434 instance D Bool Char where ...
2436 Note also that the following declaration is not allowed, even by itself:
2438 instance D [a] b where ...
2440 The problem here is that this instance would allow one particular choice of [a]
2441 to be associated with more than one choice for b, which contradicts the
2442 dependency specified in the definition of D. More generally, this means that,
2443 in any instance of the form:
2445 instance D t s where ...
2447 for some particular types t and s, the only variables that can appear in s are
2448 the ones that appear in t, and hence, if the type t is known, then s will be
2449 uniquely determined.
2452 The benefit of including dependency information is that it allows us to define
2453 more general multiple parameter classes, without ambiguity problems, and with
2454 the benefit of more accurate types. To illustrate this, we return to the
2455 collection class example, and annotate the original definition of <literal>Collects</literal>
2456 with a simple dependency:
2458 class Collects e ce | ce -> e where
2460 insert :: e -> ce -> ce
2461 member :: e -> ce -> Bool
2463 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
2464 determined by the type of the collection ce. Note that both parameters of
2465 Collects are of kind *; there are no constructor classes here. Note too that
2466 all of the instances of Collects that we gave earlier can be used
2467 together with this new definition.
2470 What about the ambiguity problems that we encountered with the original
2471 definition? The empty function still has type Collects e ce => ce, but it is no
2472 longer necessary to regard that as an ambiguous type: Although the variable e
2473 does not appear on the right of the => symbol, the dependency for class
2474 Collects tells us that it is uniquely determined by ce, which does appear on
2475 the right of the => symbol. Hence the context in which empty is used can still
2476 give enough information to determine types for both ce and e, without
2477 ambiguity. More generally, we need only regard a type as ambiguous if it
2478 contains a variable on the left of the => that is not uniquely determined
2479 (either directly or indirectly) by the variables on the right.
2482 Dependencies also help to produce more accurate types for user defined
2483 functions, and hence to provide earlier detection of errors, and less cluttered
2484 types for programmers to work with. Recall the previous definition for a
2487 f x y = insert x y = insert x . insert y
2489 for which we originally obtained a type:
2491 f :: (Collects a c, Collects b c) => a -> b -> c -> c
2493 Given the dependency information that we have for Collects, however, we can
2494 deduce that a and b must be equal because they both appear as the second
2495 parameter in a Collects constraint with the same first parameter c. Hence we
2496 can infer a shorter and more accurate type for f:
2498 f :: (Collects a c) => a -> a -> c -> c
2500 In a similar way, the earlier definition of g will now be flagged as a type error.
2503 Although we have given only a few examples here, it should be clear that the
2504 addition of dependency information can help to make multiple parameter classes
2505 more useful in practice, avoiding ambiguity problems, and allowing more general
2506 sets of instance declarations.
2512 <sect2 id="instance-decls">
2513 <title>Instance declarations</title>
2515 <sect3 id="instance-rules">
2516 <title>Relaxed rules for instance declarations</title>
2518 <para>An instance declaration has the form
2520 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 ...
2522 The part before the "<literal>=></literal>" is the
2523 <emphasis>context</emphasis>, while the part after the
2524 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
2528 In Haskell 98 the head of an instance declaration
2529 must be of the form <literal>C (T a1 ... an)</literal>, where
2530 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
2531 and the <literal>a1 ... an</literal> are distinct type variables.
2532 Furthermore, the assertions in the context of the instance declaration
2533 must be of the form <literal>C a</literal> where <literal>a</literal>
2534 is a type variable that occurs in the head.
2537 The <option>-fglasgow-exts</option> flag loosens these restrictions
2538 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
2539 the context and head of the instance declaration can each consist of arbitrary
2540 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
2544 The Paterson Conditions: for each assertion in the context
2546 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
2547 <listitem><para>The assertion has fewer constructors and variables (taken together
2548 and counting repetitions) than the head</para></listitem>
2552 <listitem><para>The Coverage Condition. For each functional dependency,
2553 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2554 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2555 every type variable in
2556 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2557 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2558 substitution mapping each type variable in the class declaration to the
2559 corresponding type in the instance declaration.
2562 These restrictions ensure that context reduction terminates: each reduction
2563 step makes the problem smaller by at least one
2564 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
2565 if you give the <option>-fallow-undecidable-instances</option>
2566 flag (<xref linkend="undecidable-instances"/>).
2567 You can find lots of background material about the reason for these
2568 restrictions in the paper <ulink
2569 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2570 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2573 For example, these are OK:
2575 instance C Int [a] -- Multiple parameters
2576 instance Eq (S [a]) -- Structured type in head
2578 -- Repeated type variable in head
2579 instance C4 a a => C4 [a] [a]
2580 instance Stateful (ST s) (MutVar s)
2582 -- Head can consist of type variables only
2584 instance (Eq a, Show b) => C2 a b
2586 -- Non-type variables in context
2587 instance Show (s a) => Show (Sized s a)
2588 instance C2 Int a => C3 Bool [a]
2589 instance C2 Int a => C3 [a] b
2593 -- Context assertion no smaller than head
2594 instance C a => C a where ...
2595 -- (C b b) has more more occurrences of b than the head
2596 instance C b b => Foo [b] where ...
2601 The same restrictions apply to instances generated by
2602 <literal>deriving</literal> clauses. Thus the following is accepted:
2604 data MinHeap h a = H a (h a)
2607 because the derived instance
2609 instance (Show a, Show (h a)) => Show (MinHeap h a)
2611 conforms to the above rules.
2615 A useful idiom permitted by the above rules is as follows.
2616 If one allows overlapping instance declarations then it's quite
2617 convenient to have a "default instance" declaration that applies if
2618 something more specific does not:
2626 <sect3 id="undecidable-instances">
2627 <title>Undecidable instances</title>
2630 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2631 For example, sometimes you might want to use the following to get the
2632 effect of a "class synonym":
2634 class (C1 a, C2 a, C3 a) => C a where { }
2636 instance (C1 a, C2 a, C3 a) => C a where { }
2638 This allows you to write shorter signatures:
2644 f :: (C1 a, C2 a, C3 a) => ...
2646 The restrictions on functional dependencies (<xref
2647 linkend="functional-dependencies"/>) are particularly troublesome.
2648 It is tempting to introduce type variables in the context that do not appear in
2649 the head, something that is excluded by the normal rules. For example:
2651 class HasConverter a b | a -> b where
2654 data Foo a = MkFoo a
2656 instance (HasConverter a b,Show b) => Show (Foo a) where
2657 show (MkFoo value) = show (convert value)
2659 This is dangerous territory, however. Here, for example, is a program that would make the
2664 instance F [a] [[a]]
2665 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2667 Similarly, it can be tempting to lift the coverage condition:
2669 class Mul a b c | a b -> c where
2670 (.*.) :: a -> b -> c
2672 instance Mul Int Int Int where (.*.) = (*)
2673 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2674 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2676 The third instance declaration does not obey the coverage condition;
2677 and indeed the (somewhat strange) definition:
2679 f = \ b x y -> if b then x .*. [y] else y
2681 makes instance inference go into a loop, because it requires the constraint
2682 <literal>(Mul a [b] b)</literal>.
2685 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2686 the experimental flag <option>-fallow-undecidable-instances</option>
2687 <indexterm><primary>-fallow-undecidable-instances
2688 option</primary></indexterm>, both the Paterson Conditions and the Coverage Condition
2689 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
2690 fixed-depth recursion stack. If you exceed the stack depth you get a
2691 sort of backtrace, and the opportunity to increase the stack depth
2692 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2698 <sect3 id="instance-overlap">
2699 <title>Overlapping instances</title>
2701 In general, <emphasis>GHC requires that that it be unambiguous which instance
2703 should be used to resolve a type-class constraint</emphasis>. This behaviour
2704 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2705 <indexterm><primary>-fallow-overlapping-instances
2706 </primary></indexterm>
2707 and <option>-fallow-incoherent-instances</option>
2708 <indexterm><primary>-fallow-incoherent-instances
2709 </primary></indexterm>, as this section discusses. Both these
2710 flags are dynamic flags, and can be set on a per-module basis, using
2711 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2713 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2714 it tries to match every instance declaration against the
2716 by instantiating the head of the instance declaration. For example, consider
2719 instance context1 => C Int a where ... -- (A)
2720 instance context2 => C a Bool where ... -- (B)
2721 instance context3 => C Int [a] where ... -- (C)
2722 instance context4 => C Int [Int] where ... -- (D)
2724 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2725 but (C) and (D) do not. When matching, GHC takes
2726 no account of the context of the instance declaration
2727 (<literal>context1</literal> etc).
2728 GHC's default behaviour is that <emphasis>exactly one instance must match the
2729 constraint it is trying to resolve</emphasis>.
2730 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2731 including both declarations (A) and (B), say); an error is only reported if a
2732 particular constraint matches more than one.
2736 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2737 more than one instance to match, provided there is a most specific one. For
2738 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2739 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2740 most-specific match, the program is rejected.
2743 However, GHC is conservative about committing to an overlapping instance. For example:
2748 Suppose that from the RHS of <literal>f</literal> we get the constraint
2749 <literal>C Int [b]</literal>. But
2750 GHC does not commit to instance (C), because in a particular
2751 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2752 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2753 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2754 GHC will instead pick (C), without complaining about
2755 the problem of subsequent instantiations.
2758 The willingness to be overlapped or incoherent is a property of
2759 the <emphasis>instance declaration</emphasis> itself, controlled by the
2760 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2761 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2762 being defined. Neither flag is required in a module that imports and uses the
2763 instance declaration. Specifically, during the lookup process:
2766 An instance declaration is ignored during the lookup process if (a) a more specific
2767 match is found, and (b) the instance declaration was compiled with
2768 <option>-fallow-overlapping-instances</option>. The flag setting for the
2769 more-specific instance does not matter.
2772 Suppose an instance declaration does not matche the constraint being looked up, but
2773 does unify with it, so that it might match when the constraint is further
2774 instantiated. Usually GHC will regard this as a reason for not committing to
2775 some other constraint. But if the instance declaration was compiled with
2776 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2777 check for that declaration.
2780 These rules make it possible for a library author to design a library that relies on
2781 overlapping instances without the library client having to know.
2784 If an instance declaration is compiled without
2785 <option>-fallow-overlapping-instances</option>,
2786 then that instance can never be overlapped. This could perhaps be
2787 inconvenient. Perhaps the rule should instead say that the
2788 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2789 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2790 at a usage site should be permitted regardless of how the instance declarations
2791 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2792 used at the usage site. (Mind you, the exact usage site can occasionally be
2793 hard to pin down.) We are interested to receive feedback on these points.
2795 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2796 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2801 <title>Type synonyms in the instance head</title>
2804 <emphasis>Unlike Haskell 98, instance heads may use type
2805 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2806 As always, using a type synonym is just shorthand for
2807 writing the RHS of the type synonym definition. For example:
2811 type Point = (Int,Int)
2812 instance C Point where ...
2813 instance C [Point] where ...
2817 is legal. However, if you added
2821 instance C (Int,Int) where ...
2825 as well, then the compiler will complain about the overlapping
2826 (actually, identical) instance declarations. As always, type synonyms
2827 must be fully applied. You cannot, for example, write:
2832 instance Monad P where ...
2836 This design decision is independent of all the others, and easily
2837 reversed, but it makes sense to me.
2845 <sect2 id="type-restrictions">
2846 <title>Type signatures</title>
2848 <sect3><title>The context of a type signature</title>
2850 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2851 the form <emphasis>(class type-variable)</emphasis> or
2852 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2853 these type signatures are perfectly OK
2856 g :: Ord (T a ()) => ...
2860 GHC imposes the following restrictions on the constraints in a type signature.
2864 forall tv1..tvn (c1, ...,cn) => type
2867 (Here, we write the "foralls" explicitly, although the Haskell source
2868 language omits them; in Haskell 98, all the free type variables of an
2869 explicit source-language type signature are universally quantified,
2870 except for the class type variables in a class declaration. However,
2871 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2880 <emphasis>Each universally quantified type variable
2881 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2883 A type variable <literal>a</literal> is "reachable" if it it appears
2884 in the same constraint as either a type variable free in in
2885 <literal>type</literal>, or another reachable type variable.
2886 A value with a type that does not obey
2887 this reachability restriction cannot be used without introducing
2888 ambiguity; that is why the type is rejected.
2889 Here, for example, is an illegal type:
2893 forall a. Eq a => Int
2897 When a value with this type was used, the constraint <literal>Eq tv</literal>
2898 would be introduced where <literal>tv</literal> is a fresh type variable, and
2899 (in the dictionary-translation implementation) the value would be
2900 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2901 can never know which instance of <literal>Eq</literal> to use because we never
2902 get any more information about <literal>tv</literal>.
2906 that the reachability condition is weaker than saying that <literal>a</literal> is
2907 functionally dependent on a type variable free in
2908 <literal>type</literal> (see <xref
2909 linkend="functional-dependencies"/>). The reason for this is there
2910 might be a "hidden" dependency, in a superclass perhaps. So
2911 "reachable" is a conservative approximation to "functionally dependent".
2912 For example, consider:
2914 class C a b | a -> b where ...
2915 class C a b => D a b where ...
2916 f :: forall a b. D a b => a -> a
2918 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2919 but that is not immediately apparent from <literal>f</literal>'s type.
2925 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2926 universally quantified type variables <literal>tvi</literal></emphasis>.
2928 For example, this type is OK because <literal>C a b</literal> mentions the
2929 universally quantified type variable <literal>b</literal>:
2933 forall a. C a b => burble
2937 The next type is illegal because the constraint <literal>Eq b</literal> does not
2938 mention <literal>a</literal>:
2942 forall a. Eq b => burble
2946 The reason for this restriction is milder than the other one. The
2947 excluded types are never useful or necessary (because the offending
2948 context doesn't need to be witnessed at this point; it can be floated
2949 out). Furthermore, floating them out increases sharing. Lastly,
2950 excluding them is a conservative choice; it leaves a patch of
2951 territory free in case we need it later.
2965 <sect2 id="implicit-parameters">
2966 <title>Implicit parameters</title>
2968 <para> Implicit parameters are implemented as described in
2969 "Implicit parameters: dynamic scoping with static types",
2970 J Lewis, MB Shields, E Meijer, J Launchbury,
2971 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2975 <para>(Most of the following, stil rather incomplete, documentation is
2976 due to Jeff Lewis.)</para>
2978 <para>Implicit parameter support is enabled with the option
2979 <option>-fimplicit-params</option>.</para>
2982 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2983 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2984 context. In Haskell, all variables are statically bound. Dynamic
2985 binding of variables is a notion that goes back to Lisp, but was later
2986 discarded in more modern incarnations, such as Scheme. Dynamic binding
2987 can be very confusing in an untyped language, and unfortunately, typed
2988 languages, in particular Hindley-Milner typed languages like Haskell,
2989 only support static scoping of variables.
2992 However, by a simple extension to the type class system of Haskell, we
2993 can support dynamic binding. Basically, we express the use of a
2994 dynamically bound variable as a constraint on the type. These
2995 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2996 function uses a dynamically-bound variable <literal>?x</literal>
2997 of type <literal>t'</literal>". For
2998 example, the following expresses the type of a sort function,
2999 implicitly parameterized by a comparison function named <literal>cmp</literal>.
3001 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3003 The dynamic binding constraints are just a new form of predicate in the type class system.
3006 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
3007 where <literal>x</literal> is
3008 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
3009 Use of this construct also introduces a new
3010 dynamic-binding constraint in the type of the expression.
3011 For example, the following definition
3012 shows how we can define an implicitly parameterized sort function in
3013 terms of an explicitly parameterized <literal>sortBy</literal> function:
3015 sortBy :: (a -> a -> Bool) -> [a] -> [a]
3017 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
3023 <title>Implicit-parameter type constraints</title>
3025 Dynamic binding constraints behave just like other type class
3026 constraints in that they are automatically propagated. Thus, when a
3027 function is used, its implicit parameters are inherited by the
3028 function that called it. For example, our <literal>sort</literal> function might be used
3029 to pick out the least value in a list:
3031 least :: (?cmp :: a -> a -> Bool) => [a] -> a
3032 least xs = head (sort xs)
3034 Without lifting a finger, the <literal>?cmp</literal> parameter is
3035 propagated to become a parameter of <literal>least</literal> as well. With explicit
3036 parameters, the default is that parameters must always be explicit
3037 propagated. With implicit parameters, the default is to always
3041 An implicit-parameter type constraint differs from other type class constraints in the
3042 following way: All uses of a particular implicit parameter must have
3043 the same type. This means that the type of <literal>(?x, ?x)</literal>
3044 is <literal>(?x::a) => (a,a)</literal>, and not
3045 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
3049 <para> You can't have an implicit parameter in the context of a class or instance
3050 declaration. For example, both these declarations are illegal:
3052 class (?x::Int) => C a where ...
3053 instance (?x::a) => Foo [a] where ...
3055 Reason: exactly which implicit parameter you pick up depends on exactly where
3056 you invoke a function. But the ``invocation'' of instance declarations is done
3057 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
3058 Easiest thing is to outlaw the offending types.</para>
3060 Implicit-parameter constraints do not cause ambiguity. For example, consider:
3062 f :: (?x :: [a]) => Int -> Int
3065 g :: (Read a, Show a) => String -> String
3068 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
3069 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
3070 quite unambiguous, and fixes the type <literal>a</literal>.
3075 <title>Implicit-parameter bindings</title>
3078 An implicit parameter is <emphasis>bound</emphasis> using the standard
3079 <literal>let</literal> or <literal>where</literal> binding forms.
3080 For example, we define the <literal>min</literal> function by binding
3081 <literal>cmp</literal>.
3084 min = let ?cmp = (<=) in least
3088 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
3089 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
3090 (including in a list comprehension, or do-notation, or pattern guards),
3091 or a <literal>where</literal> clause.
3092 Note the following points:
3095 An implicit-parameter binding group must be a
3096 collection of simple bindings to implicit-style variables (no
3097 function-style bindings, and no type signatures); these bindings are
3098 neither polymorphic or recursive.
3101 You may not mix implicit-parameter bindings with ordinary bindings in a
3102 single <literal>let</literal>
3103 expression; use two nested <literal>let</literal>s instead.
3104 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
3108 You may put multiple implicit-parameter bindings in a
3109 single binding group; but they are <emphasis>not</emphasis> treated
3110 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
3111 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
3112 parameter. The bindings are not nested, and may be re-ordered without changing
3113 the meaning of the program.
3114 For example, consider:
3116 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
3118 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
3119 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
3121 f :: (?x::Int) => Int -> Int
3129 <sect3><title>Implicit parameters and polymorphic recursion</title>
3132 Consider these two definitions:
3135 len1 xs = let ?acc = 0 in len_acc1 xs
3138 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
3143 len2 xs = let ?acc = 0 in len_acc2 xs
3145 len_acc2 :: (?acc :: Int) => [a] -> Int
3147 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
3149 The only difference between the two groups is that in the second group
3150 <literal>len_acc</literal> is given a type signature.
3151 In the former case, <literal>len_acc1</literal> is monomorphic in its own
3152 right-hand side, so the implicit parameter <literal>?acc</literal> is not
3153 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
3154 has a type signature, the recursive call is made to the
3155 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
3156 as an implicit parameter. So we get the following results in GHCi:
3163 Adding a type signature dramatically changes the result! This is a rather
3164 counter-intuitive phenomenon, worth watching out for.
3168 <sect3><title>Implicit parameters and monomorphism</title>
3170 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
3171 Haskell Report) to implicit parameters. For example, consider:
3179 Since the binding for <literal>y</literal> falls under the Monomorphism
3180 Restriction it is not generalised, so the type of <literal>y</literal> is
3181 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
3182 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
3183 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
3184 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
3185 <literal>y</literal> in the body of the <literal>let</literal> will see the
3186 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
3187 <literal>14</literal>.
3192 <!-- ======================= COMMENTED OUT ========================
3194 We intend to remove linear implicit parameters, so I'm at least removing
3195 them from the 6.6 user manual
3197 <sect2 id="linear-implicit-parameters">
3198 <title>Linear implicit parameters</title>
3200 Linear implicit parameters are an idea developed by Koen Claessen,
3201 Mark Shields, and Simon PJ. They address the long-standing
3202 problem that monads seem over-kill for certain sorts of problem, notably:
3205 <listitem> <para> distributing a supply of unique names </para> </listitem>
3206 <listitem> <para> distributing a supply of random numbers </para> </listitem>
3207 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
3211 Linear implicit parameters are just like ordinary implicit parameters,
3212 except that they are "linear"; that is, they cannot be copied, and
3213 must be explicitly "split" instead. Linear implicit parameters are
3214 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
3215 (The '/' in the '%' suggests the split!)
3220 import GHC.Exts( Splittable )
3222 data NameSupply = ...
3224 splitNS :: NameSupply -> (NameSupply, NameSupply)
3225 newName :: NameSupply -> Name
3227 instance Splittable NameSupply where
3231 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3232 f env (Lam x e) = Lam x' (f env e)
3235 env' = extend env x x'
3236 ...more equations for f...
3238 Notice that the implicit parameter %ns is consumed
3240 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
3241 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
3245 So the translation done by the type checker makes
3246 the parameter explicit:
3248 f :: NameSupply -> Env -> Expr -> Expr
3249 f ns env (Lam x e) = Lam x' (f ns1 env e)
3251 (ns1,ns2) = splitNS ns
3253 env = extend env x x'
3255 Notice the call to 'split' introduced by the type checker.
3256 How did it know to use 'splitNS'? Because what it really did
3257 was to introduce a call to the overloaded function 'split',
3258 defined by the class <literal>Splittable</literal>:
3260 class Splittable a where
3263 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
3264 split for name supplies. But we can simply write
3270 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
3272 The <literal>Splittable</literal> class is built into GHC. It's exported by module
3273 <literal>GHC.Exts</literal>.
3278 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
3279 are entirely distinct implicit parameters: you
3280 can use them together and they won't intefere with each other. </para>
3283 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
3285 <listitem> <para>You cannot have implicit parameters (whether linear or not)
3286 in the context of a class or instance declaration. </para></listitem>
3290 <sect3><title>Warnings</title>
3293 The monomorphism restriction is even more important than usual.
3294 Consider the example above:
3296 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3297 f env (Lam x e) = Lam x' (f env e)
3300 env' = extend env x x'
3302 If we replaced the two occurrences of x' by (newName %ns), which is
3303 usually a harmless thing to do, we get:
3305 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
3306 f env (Lam x e) = Lam (newName %ns) (f env e)
3308 env' = extend env x (newName %ns)
3310 But now the name supply is consumed in <emphasis>three</emphasis> places
3311 (the two calls to newName,and the recursive call to f), so
3312 the result is utterly different. Urk! We don't even have
3316 Well, this is an experimental change. With implicit
3317 parameters we have already lost beta reduction anyway, and
3318 (as John Launchbury puts it) we can't sensibly reason about
3319 Haskell programs without knowing their typing.
3324 <sect3><title>Recursive functions</title>
3325 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
3328 foo :: %x::T => Int -> [Int]
3330 foo n = %x : foo (n-1)
3332 where T is some type in class Splittable.</para>
3334 Do you get a list of all the same T's or all different T's
3335 (assuming that split gives two distinct T's back)?
3337 If you supply the type signature, taking advantage of polymorphic
3338 recursion, you get what you'd probably expect. Here's the
3339 translated term, where the implicit param is made explicit:
3342 foo x n = let (x1,x2) = split x
3343 in x1 : foo x2 (n-1)
3345 But if you don't supply a type signature, GHC uses the Hindley
3346 Milner trick of using a single monomorphic instance of the function
3347 for the recursive calls. That is what makes Hindley Milner type inference
3348 work. So the translation becomes
3352 foom n = x : foom (n-1)
3356 Result: 'x' is not split, and you get a list of identical T's. So the
3357 semantics of the program depends on whether or not foo has a type signature.
3360 You may say that this is a good reason to dislike linear implicit parameters
3361 and you'd be right. That is why they are an experimental feature.
3367 ================ END OF Linear Implicit Parameters commented out -->
3369 <sect2 id="kinding">
3370 <title>Explicitly-kinded quantification</title>
3373 Haskell infers the kind of each type variable. Sometimes it is nice to be able
3374 to give the kind explicitly as (machine-checked) documentation,
3375 just as it is nice to give a type signature for a function. On some occasions,
3376 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
3377 John Hughes had to define the data type:
3379 data Set cxt a = Set [a]
3380 | Unused (cxt a -> ())
3382 The only use for the <literal>Unused</literal> constructor was to force the correct
3383 kind for the type variable <literal>cxt</literal>.
3386 GHC now instead allows you to specify the kind of a type variable directly, wherever
3387 a type variable is explicitly bound. Namely:
3389 <listitem><para><literal>data</literal> declarations:
3391 data Set (cxt :: * -> *) a = Set [a]
3392 </screen></para></listitem>
3393 <listitem><para><literal>type</literal> declarations:
3395 type T (f :: * -> *) = f Int
3396 </screen></para></listitem>
3397 <listitem><para><literal>class</literal> declarations:
3399 class (Eq a) => C (f :: * -> *) a where ...
3400 </screen></para></listitem>
3401 <listitem><para><literal>forall</literal>'s in type signatures:
3403 f :: forall (cxt :: * -> *). Set cxt Int
3404 </screen></para></listitem>
3409 The parentheses are required. Some of the spaces are required too, to
3410 separate the lexemes. If you write <literal>(f::*->*)</literal> you
3411 will get a parse error, because "<literal>::*->*</literal>" is a
3412 single lexeme in Haskell.
3416 As part of the same extension, you can put kind annotations in types
3419 f :: (Int :: *) -> Int
3420 g :: forall a. a -> (a :: *)
3424 atype ::= '(' ctype '::' kind ')
3426 The parentheses are required.
3431 <sect2 id="universal-quantification">
3432 <title>Arbitrary-rank polymorphism
3436 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
3437 allows us to say exactly what this means. For example:
3445 g :: forall b. (b -> b)
3447 The two are treated identically.
3451 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
3452 explicit universal quantification in
3454 For example, all the following types are legal:
3456 f1 :: forall a b. a -> b -> a
3457 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
3459 f2 :: (forall a. a->a) -> Int -> Int
3460 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
3462 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
3464 f4 :: Int -> (forall a. a -> a)
3466 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
3467 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
3468 The <literal>forall</literal> makes explicit the universal quantification that
3469 is implicitly added by Haskell.
3472 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
3473 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
3474 shows, the polymorphic type on the left of the function arrow can be overloaded.
3477 The function <literal>f3</literal> has a rank-3 type;
3478 it has rank-2 types on the left of a function arrow.
3481 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
3482 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
3483 that restriction has now been lifted.)
3484 In particular, a forall-type (also called a "type scheme"),
3485 including an operational type class context, is legal:
3487 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
3488 of a function arrow </para> </listitem>
3489 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
3490 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
3491 field type signatures.</para> </listitem>
3492 <listitem> <para> As the type of an implicit parameter </para> </listitem>
3493 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
3495 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
3496 a type variable any more!
3505 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3506 the types of the constructor arguments. Here are several examples:
3512 data T a = T1 (forall b. b -> b -> b) a
3514 data MonadT m = MkMonad { return :: forall a. a -> m a,
3515 bind :: forall a b. m a -> (a -> m b) -> m b
3518 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3524 The constructors have rank-2 types:
3530 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3531 MkMonad :: forall m. (forall a. a -> m a)
3532 -> (forall a b. m a -> (a -> m b) -> m b)
3534 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3540 Notice that you don't need to use a <literal>forall</literal> if there's an
3541 explicit context. For example in the first argument of the
3542 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3543 prefixed to the argument type. The implicit <literal>forall</literal>
3544 quantifies all type variables that are not already in scope, and are
3545 mentioned in the type quantified over.
3549 As for type signatures, implicit quantification happens for non-overloaded
3550 types too. So if you write this:
3553 data T a = MkT (Either a b) (b -> b)
3556 it's just as if you had written this:
3559 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3562 That is, since the type variable <literal>b</literal> isn't in scope, it's
3563 implicitly universally quantified. (Arguably, it would be better
3564 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3565 where that is what is wanted. Feedback welcomed.)
3569 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3570 the constructor to suitable values, just as usual. For example,
3581 a3 = MkSwizzle reverse
3584 a4 = let r x = Just x
3591 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3592 mkTs f x y = [T1 f x, T1 f y]
3598 The type of the argument can, as usual, be more general than the type
3599 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3600 does not need the <literal>Ord</literal> constraint.)
3604 When you use pattern matching, the bound variables may now have
3605 polymorphic types. For example:
3611 f :: T a -> a -> (a, Char)
3612 f (T1 w k) x = (w k x, w 'c' 'd')
3614 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3615 g (MkSwizzle s) xs f = s (map f (s xs))
3617 h :: MonadT m -> [m a] -> m [a]
3618 h m [] = return m []
3619 h m (x:xs) = bind m x $ \y ->
3620 bind m (h m xs) $ \ys ->
3627 In the function <function>h</function> we use the record selectors <literal>return</literal>
3628 and <literal>bind</literal> to extract the polymorphic bind and return functions
3629 from the <literal>MonadT</literal> data structure, rather than using pattern
3635 <title>Type inference</title>
3638 In general, type inference for arbitrary-rank types is undecidable.
3639 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3640 to get a decidable algorithm by requiring some help from the programmer.
3641 We do not yet have a formal specification of "some help" but the rule is this:
3644 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3645 provides an explicit polymorphic type for x, or GHC's type inference will assume
3646 that x's type has no foralls in it</emphasis>.
3649 What does it mean to "provide" an explicit type for x? You can do that by
3650 giving a type signature for x directly, using a pattern type signature
3651 (<xref linkend="scoped-type-variables"/>), thus:
3653 \ f :: (forall a. a->a) -> (f True, f 'c')
3655 Alternatively, you can give a type signature to the enclosing
3656 context, which GHC can "push down" to find the type for the variable:
3658 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3660 Here the type signature on the expression can be pushed inwards
3661 to give a type signature for f. Similarly, and more commonly,
3662 one can give a type signature for the function itself:
3664 h :: (forall a. a->a) -> (Bool,Char)
3665 h f = (f True, f 'c')
3667 You don't need to give a type signature if the lambda bound variable
3668 is a constructor argument. Here is an example we saw earlier:
3670 f :: T a -> a -> (a, Char)
3671 f (T1 w k) x = (w k x, w 'c' 'd')
3673 Here we do not need to give a type signature to <literal>w</literal>, because
3674 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3681 <sect3 id="implicit-quant">
3682 <title>Implicit quantification</title>
3685 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3686 user-written types, if and only if there is no explicit <literal>forall</literal>,
3687 GHC finds all the type variables mentioned in the type that are not already
3688 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3692 f :: forall a. a -> a
3699 h :: forall b. a -> b -> b
3705 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3708 f :: (a -> a) -> Int
3710 f :: forall a. (a -> a) -> Int
3712 f :: (forall a. a -> a) -> Int
3715 g :: (Ord a => a -> a) -> Int
3716 -- MEANS the illegal type
3717 g :: forall a. (Ord a => a -> a) -> Int
3719 g :: (forall a. Ord a => a -> a) -> Int
3721 The latter produces an illegal type, which you might think is silly,
3722 but at least the rule is simple. If you want the latter type, you
3723 can write your for-alls explicitly. Indeed, doing so is strongly advised
3730 <sect2 id="impredicative-polymorphism">
3731 <title>Impredicative polymorphism
3733 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3734 that you can call a polymorphic function at a polymorphic type, and
3735 parameterise data structures over polymorphic types. For example:
3737 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3738 f (Just g) = Just (g [3], g "hello")
3741 Notice here that the <literal>Maybe</literal> type is parameterised by the
3742 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3745 <para>The technical details of this extension are described in the paper
3746 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3747 type inference for higher-rank types and impredicativity</ulink>,
3748 which appeared at ICFP 2006.
3752 <sect2 id="scoped-type-variables">
3753 <title>Lexically scoped type variables
3757 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3758 which some type signatures are simply impossible to write. For example:
3760 f :: forall a. [a] -> [a]
3766 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3767 the entire definition of <literal>f</literal>.
3768 In particular, it is in scope at the type signature for <varname>ys</varname>.
3769 In Haskell 98 it is not possible to declare
3770 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3771 it becomes possible to do so.
3773 <para>Lexically-scoped type variables are enabled by
3774 <option>-fglasgow-exts</option>.
3776 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3777 variables work, compared to earlier releases. Read this section
3781 <title>Overview</title>
3783 <para>The design follows the following principles
3785 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3786 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3787 design.)</para></listitem>
3788 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3789 type variables. This means that every programmer-written type signature
3790 (includin one that contains free scoped type variables) denotes a
3791 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3792 checker, and no inference is involved.</para></listitem>
3793 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3794 changing the program.</para></listitem>
3798 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3800 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3801 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3802 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3803 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3807 In Haskell, a programmer-written type signature is implicitly quantifed over
3808 its free type variables (<ulink
3809 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3811 of the Haskel Report).
3812 Lexically scoped type variables affect this implicit quantification rules
3813 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3814 quantified. For example, if type variable <literal>a</literal> is in scope,
3817 (e :: a -> a) means (e :: a -> a)
3818 (e :: b -> b) means (e :: forall b. b->b)
3819 (e :: a -> b) means (e :: forall b. a->b)
3827 <sect3 id="decl-type-sigs">
3828 <title>Declaration type signatures</title>
3829 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3830 quantification (using <literal>forall</literal>) brings into scope the
3831 explicitly-quantified
3832 type variables, in the definition of the named function(s). For example:
3834 f :: forall a. [a] -> [a]
3835 f (x:xs) = xs ++ [ x :: a ]
3837 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3838 the definition of "<literal>f</literal>".
3840 <para>This only happens if the quantification in <literal>f</literal>'s type
3841 signature is explicit. For example:
3844 g (x:xs) = xs ++ [ x :: a ]
3846 This program will be rejected, because "<literal>a</literal>" does not scope
3847 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3848 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3849 quantification rules.
3853 <sect3 id="exp-type-sigs">
3854 <title>Expression type signatures</title>
3856 <para>An expression type signature that has <emphasis>explicit</emphasis>
3857 quantification (using <literal>forall</literal>) brings into scope the
3858 explicitly-quantified
3859 type variables, in the annotated expression. For example:
3861 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3863 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3864 type variable <literal>s</literal> into scope, in the annotated expression
3865 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3870 <sect3 id="pattern-type-sigs">
3871 <title>Pattern type signatures</title>
3873 A type signature may occur in any pattern; this is a <emphasis>pattern type
3874 signature</emphasis>.
3877 -- f and g assume that 'a' is already in scope
3878 f = \(x::Int, y::a) -> x
3880 h ((x,y) :: (Int,Bool)) = (y,x)
3882 In the case where all the type variables in the pattern type sigature are
3883 already in scope (i.e. bound by the enclosing context), matters are simple: the
3884 signature simply constrains the type of the pattern in the obvious way.
3887 There is only one situation in which you can write a pattern type signature that
3888 mentions a type variable that is not already in scope, namely in pattern match
3889 of an existential data constructor. For example:
3891 data T = forall a. MkT [a]
3894 k (MkT [t::a]) = MkT t3
3898 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3899 variable that is not already in scope. Indeed, it cannot already be in scope,
3900 because it is bound by the pattern match. GHC's rule is that in this situation
3901 (and only then), a pattern type signature can mention a type variable that is
3902 not already in scope; the effect is to bring it into scope, standing for the
3903 existentially-bound type variable.
3906 If this seems a little odd, we think so too. But we must have
3907 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3908 could not name existentially-bound type variables in subequent type signatures.
3911 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3912 signature is allowed to mention a lexical variable that is not already in
3914 For example, both <literal>f</literal> and <literal>g</literal> would be
3915 illegal if <literal>a</literal> was not already in scope.
3921 <!-- ==================== Commented out part about result type signatures
3923 <sect3 id="result-type-sigs">
3924 <title>Result type signatures</title>
3927 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3930 {- f assumes that 'a' is already in scope -}
3931 f x y :: [a] = [x,y,x]
3933 g = \ x :: [Int] -> [3,4]
3935 h :: forall a. [a] -> a
3939 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3940 the result of the function. Similarly, the body of the lambda in the RHS of
3941 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3942 alternative in <literal>h</literal> is <literal>a</literal>.
3944 <para> A result type signature never brings new type variables into scope.</para>
3946 There are a couple of syntactic wrinkles. First, notice that all three
3947 examples would parse quite differently with parentheses:
3949 {- f assumes that 'a' is already in scope -}
3950 f x (y :: [a]) = [x,y,x]
3952 g = \ (x :: [Int]) -> [3,4]
3954 h :: forall a. [a] -> a
3958 Now the signature is on the <emphasis>pattern</emphasis>; and
3959 <literal>h</literal> would certainly be ill-typed (since the pattern
3960 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3962 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
3963 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3964 token or a parenthesised type of some sort). To see why,
3965 consider how one would parse this:
3974 <sect3 id="cls-inst-scoped-tyvars">
3975 <title>Class and instance declarations</title>
3978 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3979 scope over the methods defined in the <literal>where</literal> part. For example:
3997 <sect2 id="typing-binds">
3998 <title>Generalised typing of mutually recursive bindings</title>
4001 The Haskell Report specifies that a group of bindings (at top level, or in a
4002 <literal>let</literal> or <literal>where</literal>) should be sorted into
4003 strongly-connected components, and then type-checked in dependency order
4004 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
4005 Report, Section 4.5.1</ulink>).
4006 As each group is type-checked, any binders of the group that
4008 an explicit type signature are put in the type environment with the specified
4010 and all others are monomorphic until the group is generalised
4011 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
4014 <para>Following a suggestion of Mark Jones, in his paper
4015 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
4017 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
4019 <emphasis>the dependency analysis ignores references to variables that have an explicit
4020 type signature</emphasis>.
4021 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
4022 typecheck. For example, consider:
4024 f :: Eq a => a -> Bool
4025 f x = (x == x) || g True || g "Yes"
4027 g y = (y <= y) || f True
4029 This is rejected by Haskell 98, but under Jones's scheme the definition for
4030 <literal>g</literal> is typechecked first, separately from that for
4031 <literal>f</literal>,
4032 because the reference to <literal>f</literal> in <literal>g</literal>'s right
4033 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
4034 type is generalised, to get
4036 g :: Ord a => a -> Bool
4038 Now, the defintion for <literal>f</literal> is typechecked, with this type for
4039 <literal>g</literal> in the type environment.
4043 The same refined dependency analysis also allows the type signatures of
4044 mutually-recursive functions to have different contexts, something that is illegal in
4045 Haskell 98 (Section 4.5.2, last sentence). With
4046 <option>-fglasgow-exts</option>
4047 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
4048 type signatures; in practice this means that only variables bound by the same
4049 pattern binding must have the same context. For example, this is fine:
4051 f :: Eq a => a -> Bool
4052 f x = (x == x) || g True
4054 g :: Ord a => a -> Bool
4055 g y = (y <= y) || f True
4060 <sect2 id="overloaded-strings">
4061 <title>Overloaded string literals
4065 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4066 string literal has type <literal>String</literal>, but with overloaded string
4067 literals enabled (with <literal>-foverloaded-strings</literal>)
4068 a string literal has type <literal>(IsString a) => a</literal>.
4071 This means that the usual string syntax can be used, e.g., for packed strings
4072 and other variations of string like types. String literals behave very much
4073 like integer literals, i.e., they can be used in both expressions and patterns.
4074 If used in a pattern the literal with be replaced by an equality test, in the same
4075 way as an integer literal is.
4078 The class <literal>IsString</literal> is defined as:
4080 class IsString a where
4081 fromString :: String -> a
4083 The only predefined instance is the obvious one to make strings work as usual:
4085 instance IsString [Char] where
4088 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4089 it explicitly (for exmaple, to give an instance declaration for it), you can import it
4090 from module <literal>GHC.Exts</literal>.
4093 Haskell's defaulting mechanism is extended to cover string literals, when <option>-foverloaded-strings</option> is specified.
4097 Each type in a default declaration must be an
4098 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4102 The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4103 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4104 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4105 <emphasis>or</emphasis> <literal>IsString</literal>.
4114 import GHC.Exts( IsString(..) )
4116 newtype MyString = MyString String deriving (Eq, Show)
4117 instance IsString MyString where
4118 fromString = MyString
4120 greet :: MyString -> MyString
4121 greet "hello" = "world"
4125 print $ greet "hello"
4126 print $ greet "fool"
4130 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4131 to work since it gets translated into an equality comparison.
4135 <sect2 id="type-families">
4136 <title>Type families
4140 GHC supports the definition of type families indexed by types. They may be
4141 seen as an extension of Haskell 98's class-based overloading of values to
4142 types. When type families are declared in classes, they are also known as
4146 There are two forms of type families: data families and type synonym families.
4147 Currently, only the former are fully implemented, while we are still working
4148 on the latter. As a result, the specification of the language extension is
4149 also still to some degree in flux. Hence, a more detailed description of
4150 the language extension and its use is currently available
4151 from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
4152 wiki page on type families</ulink>. The material will be moved to this user's
4153 guide when it has stabilised.
4156 Type families are enabled by the flag <option>-ftype-families</option>.
4163 <!-- ==================== End of type system extensions ================= -->
4165 <!-- ====================== TEMPLATE HASKELL ======================= -->
4167 <sect1 id="template-haskell">
4168 <title>Template Haskell</title>
4170 <para>Template Haskell allows you to do compile-time meta-programming in
4173 the main technical innovations is discussed in "<ulink
4174 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4175 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4178 There is a Wiki page about
4179 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4180 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4184 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4185 Haskell library reference material</ulink>
4186 (search for the type ExpQ).
4187 [Temporary: many changes to the original design are described in
4188 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4189 Not all of these changes are in GHC 6.6.]
4192 <para> The first example from that paper is set out below as a worked example to help get you started.
4196 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4197 Tim Sheard is going to expand it.)
4201 <title>Syntax</title>
4203 <para> Template Haskell has the following new syntactic
4204 constructions. You need to use the flag
4205 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4206 </indexterm>to switch these syntactic extensions on
4207 (<option>-fth</option> is no longer implied by
4208 <option>-fglasgow-exts</option>).</para>
4212 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4213 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4214 There must be no space between the "$" and the identifier or parenthesis. This use
4215 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4216 of "." as an infix operator. If you want the infix operator, put spaces around it.
4218 <para> A splice can occur in place of
4220 <listitem><para> an expression; the spliced expression must
4221 have type <literal>Q Exp</literal></para></listitem>
4222 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4223 <listitem><para> [Planned, but not implemented yet.] a
4224 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4226 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4227 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4233 A expression quotation is written in Oxford brackets, thus:
4235 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4236 the quotation has type <literal>Expr</literal>.</para></listitem>
4237 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4238 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4239 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4240 the quotation has type <literal>Type</literal>.</para></listitem>
4241 </itemizedlist></para></listitem>
4244 Reification is written thus:
4246 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4247 has type <literal>Dec</literal>. </para></listitem>
4248 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4249 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4250 <listitem><para> Still to come: fixities </para></listitem>
4252 </itemizedlist></para>
4259 <sect2> <title> Using Template Haskell </title>
4263 The data types and monadic constructor functions for Template Haskell are in the library
4264 <literal>Language.Haskell.THSyntax</literal>.
4268 You can only run a function at compile time if it is imported from another module. That is,
4269 you can't define a function in a module, and call it from within a splice in the same module.
4270 (It would make sense to do so, but it's hard to implement.)
4274 Furthermore, you can only run a function at compile time if it is imported
4275 from another module <emphasis>that is not part of a mutually-recursive group of modules
4276 that includes the module currently being compiled</emphasis>. For example, when compiling module A,
4277 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
4278 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
4282 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4285 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4286 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4287 compiles and runs a program, and then looks at the result. So it's important that
4288 the program it compiles produces results whose representations are identical to
4289 those of the compiler itself.
4293 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4294 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4299 <sect2> <title> A Template Haskell Worked Example </title>
4300 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4301 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4308 -- Import our template "pr"
4309 import Printf ( pr )
4311 -- The splice operator $ takes the Haskell source code
4312 -- generated at compile time by "pr" and splices it into
4313 -- the argument of "putStrLn".
4314 main = putStrLn ( $(pr "Hello") )
4320 -- Skeletal printf from the paper.
4321 -- It needs to be in a separate module to the one where
4322 -- you intend to use it.
4324 -- Import some Template Haskell syntax
4325 import Language.Haskell.TH
4327 -- Describe a format string
4328 data Format = D | S | L String
4330 -- Parse a format string. This is left largely to you
4331 -- as we are here interested in building our first ever
4332 -- Template Haskell program and not in building printf.
4333 parse :: String -> [Format]
4336 -- Generate Haskell source code from a parsed representation
4337 -- of the format string. This code will be spliced into
4338 -- the module which calls "pr", at compile time.
4339 gen :: [Format] -> ExpQ
4340 gen [D] = [| \n -> show n |]
4341 gen [S] = [| \s -> s |]
4342 gen [L s] = stringE s
4344 -- Here we generate the Haskell code for the splice
4345 -- from an input format string.
4346 pr :: String -> ExpQ
4347 pr s = gen (parse s)
4350 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4353 $ ghc --make -fth main.hs -o main.exe
4356 <para>Run "main.exe" and here is your output:</para>
4366 <title>Using Template Haskell with Profiling</title>
4367 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4369 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4370 interpreter to run the splice expressions. The bytecode interpreter
4371 runs the compiled expression on top of the same runtime on which GHC
4372 itself is running; this means that the compiled code referred to by
4373 the interpreted expression must be compatible with this runtime, and
4374 in particular this means that object code that is compiled for
4375 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4376 expression, because profiled object code is only compatible with the
4377 profiling version of the runtime.</para>
4379 <para>This causes difficulties if you have a multi-module program
4380 containing Template Haskell code and you need to compile it for
4381 profiling, because GHC cannot load the profiled object code and use it
4382 when executing the splices. Fortunately GHC provides a workaround.
4383 The basic idea is to compile the program twice:</para>
4387 <para>Compile the program or library first the normal way, without
4388 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4391 <para>Then compile it again with <option>-prof</option>, and
4392 additionally use <option>-osuf
4393 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4394 to name the object files differentliy (you can choose any suffix
4395 that isn't the normal object suffix here). GHC will automatically
4396 load the object files built in the first step when executing splice
4397 expressions. If you omit the <option>-osuf</option> flag when
4398 building with <option>-prof</option> and Template Haskell is used,
4399 GHC will emit an error message. </para>
4406 <!-- ===================== Arrow notation =================== -->
4408 <sect1 id="arrow-notation">
4409 <title>Arrow notation
4412 <para>Arrows are a generalization of monads introduced by John Hughes.
4413 For more details, see
4418 “Generalising Monads to Arrows”,
4419 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4420 pp67–111, May 2000.
4426 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4427 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4433 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4434 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4440 and the arrows web page at
4441 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4442 With the <option>-farrows</option> flag, GHC supports the arrow
4443 notation described in the second of these papers.
4444 What follows is a brief introduction to the notation;
4445 it won't make much sense unless you've read Hughes's paper.
4446 This notation is translated to ordinary Haskell,
4447 using combinators from the
4448 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4452 <para>The extension adds a new kind of expression for defining arrows:
4454 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4455 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4457 where <literal>proc</literal> is a new keyword.
4458 The variables of the pattern are bound in the body of the
4459 <literal>proc</literal>-expression,
4460 which is a new sort of thing called a <firstterm>command</firstterm>.
4461 The syntax of commands is as follows:
4463 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4464 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4465 | <replaceable>cmd</replaceable><superscript>0</superscript>
4467 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4468 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4469 infix operators as for expressions, and
4471 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4472 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4473 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4474 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4475 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4476 | <replaceable>fcmd</replaceable>
4478 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4479 | ( <replaceable>cmd</replaceable> )
4480 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4482 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4483 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4484 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4485 | <replaceable>cmd</replaceable>
4487 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4488 except that the bodies are commands instead of expressions.
4492 Commands produce values, but (like monadic computations)
4493 may yield more than one value,
4494 or none, and may do other things as well.
4495 For the most part, familiarity with monadic notation is a good guide to
4497 However the values of expressions, even monadic ones,
4498 are determined by the values of the variables they contain;
4499 this is not necessarily the case for commands.
4503 A simple example of the new notation is the expression
4505 proc x -> f -< x+1
4507 We call this a <firstterm>procedure</firstterm> or
4508 <firstterm>arrow abstraction</firstterm>.
4509 As with a lambda expression, the variable <literal>x</literal>
4510 is a new variable bound within the <literal>proc</literal>-expression.
4511 It refers to the input to the arrow.
4512 In the above example, <literal>-<</literal> is not an identifier but an
4513 new reserved symbol used for building commands from an expression of arrow
4514 type and an expression to be fed as input to that arrow.
4515 (The weird look will make more sense later.)
4516 It may be read as analogue of application for arrows.
4517 The above example is equivalent to the Haskell expression
4519 arr (\ x -> x+1) >>> f
4521 That would make no sense if the expression to the left of
4522 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4523 More generally, the expression to the left of <literal>-<</literal>
4524 may not involve any <firstterm>local variable</firstterm>,
4525 i.e. a variable bound in the current arrow abstraction.
4526 For such a situation there is a variant <literal>-<<</literal>, as in
4528 proc x -> f x -<< x+1
4530 which is equivalent to
4532 arr (\ x -> (f x, x+1)) >>> app
4534 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4536 Such an arrow is equivalent to a monad, so if you're using this form
4537 you may find a monadic formulation more convenient.
4541 <title>do-notation for commands</title>
4544 Another form of command is a form of <literal>do</literal>-notation.
4545 For example, you can write
4554 You can read this much like ordinary <literal>do</literal>-notation,
4555 but with commands in place of monadic expressions.
4556 The first line sends the value of <literal>x+1</literal> as an input to
4557 the arrow <literal>f</literal>, and matches its output against
4558 <literal>y</literal>.
4559 In the next line, the output is discarded.
4560 The arrow <function>returnA</function> is defined in the
4561 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4562 module as <literal>arr id</literal>.
4563 The above example is treated as an abbreviation for
4565 arr (\ x -> (x, x)) >>>
4566 first (arr (\ x -> x+1) >>> f) >>>
4567 arr (\ (y, x) -> (y, (x, y))) >>>
4568 first (arr (\ y -> 2*y) >>> g) >>>
4570 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4571 first (arr (\ (x, z) -> x*z) >>> h) >>>
4572 arr (\ (t, z) -> t+z) >>>
4575 Note that variables not used later in the composition are projected out.
4576 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4578 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4579 module, this reduces to
4581 arr (\ x -> (x+1, x)) >>>
4583 arr (\ (y, x) -> (2*y, (x, y))) >>>
4585 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4587 arr (\ (t, z) -> t+z)
4589 which is what you might have written by hand.
4590 With arrow notation, GHC keeps track of all those tuples of variables for you.
4594 Note that although the above translation suggests that
4595 <literal>let</literal>-bound variables like <literal>z</literal> must be
4596 monomorphic, the actual translation produces Core,
4597 so polymorphic variables are allowed.
4601 It's also possible to have mutually recursive bindings,
4602 using the new <literal>rec</literal> keyword, as in the following example:
4604 counter :: ArrowCircuit a => a Bool Int
4605 counter = proc reset -> do
4606 rec output <- returnA -< if reset then 0 else next
4607 next <- delay 0 -< output+1
4608 returnA -< output
4610 The translation of such forms uses the <function>loop</function> combinator,
4611 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4617 <title>Conditional commands</title>
4620 In the previous example, we used a conditional expression to construct the
4622 Sometimes we want to conditionally execute different commands, as in
4629 which is translated to
4631 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4632 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4634 Since the translation uses <function>|||</function>,
4635 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4639 There are also <literal>case</literal> commands, like
4645 y <- h -< (x1, x2)
4649 The syntax is the same as for <literal>case</literal> expressions,
4650 except that the bodies of the alternatives are commands rather than expressions.
4651 The translation is similar to that of <literal>if</literal> commands.
4657 <title>Defining your own control structures</title>
4660 As we're seen, arrow notation provides constructs,
4661 modelled on those for expressions,
4662 for sequencing, value recursion and conditionals.
4663 But suitable combinators,
4664 which you can define in ordinary Haskell,
4665 may also be used to build new commands out of existing ones.
4666 The basic idea is that a command defines an arrow from environments to values.
4667 These environments assign values to the free local variables of the command.
4668 Thus combinators that produce arrows from arrows
4669 may also be used to build commands from commands.
4670 For example, the <literal>ArrowChoice</literal> class includes a combinator
4672 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4674 so we can use it to build commands:
4676 expr' = proc x -> do
4679 symbol Plus -< ()
4680 y <- term -< ()
4683 symbol Minus -< ()
4684 y <- term -< ()
4687 (The <literal>do</literal> on the first line is needed to prevent the first
4688 <literal><+> ...</literal> from being interpreted as part of the
4689 expression on the previous line.)
4690 This is equivalent to
4692 expr' = (proc x -> returnA -< x)
4693 <+> (proc x -> do
4694 symbol Plus -< ()
4695 y <- term -< ()
4697 <+> (proc x -> do
4698 symbol Minus -< ()
4699 y <- term -< ()
4702 It is essential that this operator be polymorphic in <literal>e</literal>
4703 (representing the environment input to the command
4704 and thence to its subcommands)
4705 and satisfy the corresponding naturality property
4707 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4709 at least for strict <literal>k</literal>.
4710 (This should be automatic if you're not using <function>seq</function>.)
4711 This ensures that environments seen by the subcommands are environments
4712 of the whole command,
4713 and also allows the translation to safely trim these environments.
4714 The operator must also not use any variable defined within the current
4719 We could define our own operator
4721 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4722 untilA body cond = proc x ->
4723 if cond x then returnA -< ()
4726 untilA body cond -< x
4728 and use it in the same way.
4729 Of course this infix syntax only makes sense for binary operators;
4730 there is also a more general syntax involving special brackets:
4734 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4741 <title>Primitive constructs</title>
4744 Some operators will need to pass additional inputs to their subcommands.
4745 For example, in an arrow type supporting exceptions,
4746 the operator that attaches an exception handler will wish to pass the
4747 exception that occurred to the handler.
4748 Such an operator might have a type
4750 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4752 where <literal>Ex</literal> is the type of exceptions handled.
4753 You could then use this with arrow notation by writing a command
4755 body `handleA` \ ex -> handler
4757 so that if an exception is raised in the command <literal>body</literal>,
4758 the variable <literal>ex</literal> is bound to the value of the exception
4759 and the command <literal>handler</literal>,
4760 which typically refers to <literal>ex</literal>, is entered.
4761 Though the syntax here looks like a functional lambda,
4762 we are talking about commands, and something different is going on.
4763 The input to the arrow represented by a command consists of values for
4764 the free local variables in the command, plus a stack of anonymous values.
4765 In all the prior examples, this stack was empty.
4766 In the second argument to <function>handleA</function>,
4767 this stack consists of one value, the value of the exception.
4768 The command form of lambda merely gives this value a name.
4773 the values on the stack are paired to the right of the environment.
4774 So operators like <function>handleA</function> that pass
4775 extra inputs to their subcommands can be designed for use with the notation
4776 by pairing the values with the environment in this way.
4777 More precisely, the type of each argument of the operator (and its result)
4778 should have the form
4780 a (...(e,t1), ... tn) t
4782 where <replaceable>e</replaceable> is a polymorphic variable
4783 (representing the environment)
4784 and <replaceable>ti</replaceable> are the types of the values on the stack,
4785 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4786 The polymorphic variable <replaceable>e</replaceable> must not occur in
4787 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4788 <replaceable>t</replaceable>.
4789 However the arrows involved need not be the same.
4790 Here are some more examples of suitable operators:
4792 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4793 runReader :: ... => a e c -> a' (e,State) c
4794 runState :: ... => a e c -> a' (e,State) (c,State)
4796 We can supply the extra input required by commands built with the last two
4797 by applying them to ordinary expressions, as in
4801 (|runReader (do { ... })|) s
4803 which adds <literal>s</literal> to the stack of inputs to the command
4804 built using <function>runReader</function>.
4808 The command versions of lambda abstraction and application are analogous to
4809 the expression versions.
4810 In particular, the beta and eta rules describe equivalences of commands.
4811 These three features (operators, lambda abstraction and application)
4812 are the core of the notation; everything else can be built using them,
4813 though the results would be somewhat clumsy.
4814 For example, we could simulate <literal>do</literal>-notation by defining
4816 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4817 u `bind` f = returnA &&& u >>> f
4819 bind_ :: Arrow a => a e b -> a e c -> a e c
4820 u `bind_` f = u `bind` (arr fst >>> f)
4822 We could simulate <literal>if</literal> by defining
4824 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4825 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4832 <title>Differences with the paper</title>
4837 <para>Instead of a single form of arrow application (arrow tail) with two
4838 translations, the implementation provides two forms
4839 <quote><literal>-<</literal></quote> (first-order)
4840 and <quote><literal>-<<</literal></quote> (higher-order).
4845 <para>User-defined operators are flagged with banana brackets instead of
4846 a new <literal>form</literal> keyword.
4855 <title>Portability</title>
4858 Although only GHC implements arrow notation directly,
4859 there is also a preprocessor
4861 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4862 that translates arrow notation into Haskell 98
4863 for use with other Haskell systems.
4864 You would still want to check arrow programs with GHC;
4865 tracing type errors in the preprocessor output is not easy.
4866 Modules intended for both GHC and the preprocessor must observe some
4867 additional restrictions:
4872 The module must import
4873 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4879 The preprocessor cannot cope with other Haskell extensions.
4880 These would have to go in separate modules.
4886 Because the preprocessor targets Haskell (rather than Core),
4887 <literal>let</literal>-bound variables are monomorphic.
4898 <!-- ==================== BANG PATTERNS ================= -->
4900 <sect1 id="bang-patterns">
4901 <title>Bang patterns
4902 <indexterm><primary>Bang patterns</primary></indexterm>
4904 <para>GHC supports an extension of pattern matching called <emphasis>bang
4905 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4907 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4908 prime feature description</ulink> contains more discussion and examples
4909 than the material below.
4912 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4915 <sect2 id="bang-patterns-informal">
4916 <title>Informal description of bang patterns
4919 The main idea is to add a single new production to the syntax of patterns:
4923 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4924 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4929 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4930 whereas without the bang it would be lazy.
4931 Bang patterns can be nested of course:
4935 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4936 <literal>y</literal>.
4937 A bang only really has an effect if it precedes a variable or wild-card pattern:
4942 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4943 forces evaluation anyway does nothing.
4945 Bang patterns work in <literal>case</literal> expressions too, of course:
4947 g5 x = let y = f x in body
4948 g6 x = case f x of { y -> body }
4949 g7 x = case f x of { !y -> body }
4951 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4952 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4953 result, and then evaluates <literal>body</literal>.
4955 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4956 definitions too. For example:
4960 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4961 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4962 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4963 in a function argument <literal>![x,y]</literal> means the
4964 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4965 is part of the syntax of <literal>let</literal> bindings.
4970 <sect2 id="bang-patterns-sem">
4971 <title>Syntax and semantics
4975 We add a single new production to the syntax of patterns:
4979 There is one problem with syntactic ambiguity. Consider:
4983 Is this a definition of the infix function "<literal>(!)</literal>",
4984 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4985 ambiguity in favour of the latter. If you want to define
4986 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4991 The semantics of Haskell pattern matching is described in <ulink
4992 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4993 Section 3.17.2</ulink> of the Haskell Report. To this description add
4994 one extra item 10, saying:
4995 <itemizedlist><listitem><para>Matching
4996 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4997 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4998 <listitem><para>otherwise, <literal>pat</literal> is matched against
4999 <literal>v</literal></para></listitem>
5001 </para></listitem></itemizedlist>
5002 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
5003 Section 3.17.3</ulink>, add a new case (t):
5005 case v of { !pat -> e; _ -> e' }
5006 = v `seq` case v of { pat -> e; _ -> e' }
5009 That leaves let expressions, whose translation is given in
5010 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
5012 of the Haskell Report.
5013 In the translation box, first apply
5014 the following transformation: for each pattern <literal>pi</literal> that is of
5015 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
5016 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
5017 have a bang at the top, apply the rules in the existing box.
5019 <para>The effect of the let rule is to force complete matching of the pattern
5020 <literal>qi</literal> before evaluation of the body is begun. The bang is
5021 retained in the translated form in case <literal>qi</literal> is a variable,
5029 The let-binding can be recursive. However, it is much more common for
5030 the let-binding to be non-recursive, in which case the following law holds:
5031 <literal>(let !p = rhs in body)</literal>
5033 <literal>(case rhs of !p -> body)</literal>
5036 A pattern with a bang at the outermost level is not allowed at the top level of
5042 <!-- ==================== ASSERTIONS ================= -->
5044 <sect1 id="assertions">
5046 <indexterm><primary>Assertions</primary></indexterm>
5050 If you want to make use of assertions in your standard Haskell code, you
5051 could define a function like the following:
5057 assert :: Bool -> a -> a
5058 assert False x = error "assertion failed!"
5065 which works, but gives you back a less than useful error message --
5066 an assertion failed, but which and where?
5070 One way out is to define an extended <function>assert</function> function which also
5071 takes a descriptive string to include in the error message and
5072 perhaps combine this with the use of a pre-processor which inserts
5073 the source location where <function>assert</function> was used.
5077 Ghc offers a helping hand here, doing all of this for you. For every
5078 use of <function>assert</function> in the user's source:
5084 kelvinToC :: Double -> Double
5085 kelvinToC k = assert (k >= 0.0) (k+273.15)
5091 Ghc will rewrite this to also include the source location where the
5098 assert pred val ==> assertError "Main.hs|15" pred val
5104 The rewrite is only performed by the compiler when it spots
5105 applications of <function>Control.Exception.assert</function>, so you
5106 can still define and use your own versions of
5107 <function>assert</function>, should you so wish. If not, import
5108 <literal>Control.Exception</literal> to make use
5109 <function>assert</function> in your code.
5113 GHC ignores assertions when optimisation is turned on with the
5114 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5115 <literal>assert pred e</literal> will be rewritten to
5116 <literal>e</literal>. You can also disable assertions using the
5117 <option>-fignore-asserts</option>
5118 option<indexterm><primary><option>-fignore-asserts</option></primary>
5119 </indexterm>.</para>
5122 Assertion failures can be caught, see the documentation for the
5123 <literal>Control.Exception</literal> library for the details.
5129 <!-- =============================== PRAGMAS =========================== -->
5131 <sect1 id="pragmas">
5132 <title>Pragmas</title>
5134 <indexterm><primary>pragma</primary></indexterm>
5136 <para>GHC supports several pragmas, or instructions to the
5137 compiler placed in the source code. Pragmas don't normally affect
5138 the meaning of the program, but they might affect the efficiency
5139 of the generated code.</para>
5141 <para>Pragmas all take the form
5143 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5145 where <replaceable>word</replaceable> indicates the type of
5146 pragma, and is followed optionally by information specific to that
5147 type of pragma. Case is ignored in
5148 <replaceable>word</replaceable>. The various values for
5149 <replaceable>word</replaceable> that GHC understands are described
5150 in the following sections; any pragma encountered with an
5151 unrecognised <replaceable>word</replaceable> is (silently)
5154 <sect2 id="deprecated-pragma">
5155 <title>DEPRECATED pragma</title>
5156 <indexterm><primary>DEPRECATED</primary>
5159 <para>The DEPRECATED pragma lets you specify that a particular
5160 function, class, or type, is deprecated. There are two
5165 <para>You can deprecate an entire module thus:</para>
5167 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5170 <para>When you compile any module that import
5171 <literal>Wibble</literal>, GHC will print the specified
5176 <para>You can deprecate a function, class, type, or data constructor, with the
5177 following top-level declaration:</para>
5179 {-# DEPRECATED f, C, T "Don't use these" #-}
5181 <para>When you compile any module that imports and uses any
5182 of the specified entities, GHC will print the specified
5184 <para> You can only depecate entities declared at top level in the module
5185 being compiled, and you can only use unqualified names in the list of
5186 entities being deprecated. A capitalised name, such as <literal>T</literal>
5187 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5188 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5189 both are in scope. If both are in scope, there is currently no way to deprecate
5190 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5193 Any use of the deprecated item, or of anything from a deprecated
5194 module, will be flagged with an appropriate message. However,
5195 deprecations are not reported for
5196 (a) uses of a deprecated function within its defining module, and
5197 (b) uses of a deprecated function in an export list.
5198 The latter reduces spurious complaints within a library
5199 in which one module gathers together and re-exports
5200 the exports of several others.
5202 <para>You can suppress the warnings with the flag
5203 <option>-fno-warn-deprecations</option>.</para>
5206 <sect2 id="include-pragma">
5207 <title>INCLUDE pragma</title>
5209 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5210 of C header files that should be <literal>#include</literal>'d into
5211 the C source code generated by the compiler for the current module (if
5212 compiling via C). For example:</para>
5215 {-# INCLUDE "foo.h" #-}
5216 {-# INCLUDE <stdio.h> #-}</programlisting>
5218 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5219 your source file with any <literal>OPTIONS_GHC</literal>
5222 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5223 to the <option>-#include</option> option (<xref
5224 linkend="options-C-compiler" />), because the
5225 <literal>INCLUDE</literal> pragma is understood by other
5226 compilers. Yet another alternative is to add the include file to each
5227 <literal>foreign import</literal> declaration in your code, but we
5228 don't recommend using this approach with GHC.</para>
5231 <sect2 id="inline-noinline-pragma">
5232 <title>INLINE and NOINLINE pragmas</title>
5234 <para>These pragmas control the inlining of function
5237 <sect3 id="inline-pragma">
5238 <title>INLINE pragma</title>
5239 <indexterm><primary>INLINE</primary></indexterm>
5241 <para>GHC (with <option>-O</option>, as always) tries to
5242 inline (or “unfold”) functions/values that are
5243 “small enough,” thus avoiding the call overhead
5244 and possibly exposing other more-wonderful optimisations.
5245 Normally, if GHC decides a function is “too
5246 expensive” to inline, it will not do so, nor will it
5247 export that unfolding for other modules to use.</para>
5249 <para>The sledgehammer you can bring to bear is the
5250 <literal>INLINE</literal><indexterm><primary>INLINE
5251 pragma</primary></indexterm> pragma, used thusly:</para>
5254 key_function :: Int -> String -> (Bool, Double)
5256 #ifdef __GLASGOW_HASKELL__
5257 {-# INLINE key_function #-}
5261 <para>(You don't need to do the C pre-processor carry-on
5262 unless you're going to stick the code through HBC—it
5263 doesn't like <literal>INLINE</literal> pragmas.)</para>
5265 <para>The major effect of an <literal>INLINE</literal> pragma
5266 is to declare a function's “cost” to be very low.
5267 The normal unfolding machinery will then be very keen to
5270 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5271 function can be put anywhere its type signature could be
5274 <para><literal>INLINE</literal> pragmas are a particularly
5276 <literal>then</literal>/<literal>return</literal> (or
5277 <literal>bind</literal>/<literal>unit</literal>) functions in
5278 a monad. For example, in GHC's own
5279 <literal>UniqueSupply</literal> monad code, we have:</para>
5282 #ifdef __GLASGOW_HASKELL__
5283 {-# INLINE thenUs #-}
5284 {-# INLINE returnUs #-}
5288 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5289 linkend="noinline-pragma"/>).</para>
5292 <sect3 id="noinline-pragma">
5293 <title>NOINLINE pragma</title>
5295 <indexterm><primary>NOINLINE</primary></indexterm>
5296 <indexterm><primary>NOTINLINE</primary></indexterm>
5298 <para>The <literal>NOINLINE</literal> pragma does exactly what
5299 you'd expect: it stops the named function from being inlined
5300 by the compiler. You shouldn't ever need to do this, unless
5301 you're very cautious about code size.</para>
5303 <para><literal>NOTINLINE</literal> is a synonym for
5304 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5305 specified by Haskell 98 as the standard way to disable
5306 inlining, so it should be used if you want your code to be
5310 <sect3 id="phase-control">
5311 <title>Phase control</title>
5313 <para> Sometimes you want to control exactly when in GHC's
5314 pipeline the INLINE pragma is switched on. Inlining happens
5315 only during runs of the <emphasis>simplifier</emphasis>. Each
5316 run of the simplifier has a different <emphasis>phase
5317 number</emphasis>; the phase number decreases towards zero.
5318 If you use <option>-dverbose-core2core</option> you'll see the
5319 sequence of phase numbers for successive runs of the
5320 simplifier. In an INLINE pragma you can optionally specify a
5324 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5325 <literal>f</literal>
5326 until phase <literal>k</literal>, but from phase
5327 <literal>k</literal> onwards be very keen to inline it.
5330 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5331 <literal>f</literal>
5332 until phase <literal>k</literal>, but from phase
5333 <literal>k</literal> onwards do not inline it.
5336 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5337 <literal>f</literal>
5338 until phase <literal>k</literal>, but from phase
5339 <literal>k</literal> onwards be willing to inline it (as if
5340 there was no pragma).
5343 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5344 <literal>f</literal>
5345 until phase <literal>k</literal>, but from phase
5346 <literal>k</literal> onwards do not inline it.
5349 The same information is summarised here:
5351 -- Before phase 2 Phase 2 and later
5352 {-# INLINE [2] f #-} -- No Yes
5353 {-# INLINE [~2] f #-} -- Yes No
5354 {-# NOINLINE [2] f #-} -- No Maybe
5355 {-# NOINLINE [~2] f #-} -- Maybe No
5357 {-# INLINE f #-} -- Yes Yes
5358 {-# NOINLINE f #-} -- No No
5360 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5361 function body is small, or it is applied to interesting-looking arguments etc).
5362 Another way to understand the semantics is this:
5364 <listitem><para>For both INLINE and NOINLINE, the phase number says
5365 when inlining is allowed at all.</para></listitem>
5366 <listitem><para>The INLINE pragma has the additional effect of making the
5367 function body look small, so that when inlining is allowed it is very likely to
5372 <para>The same phase-numbering control is available for RULES
5373 (<xref linkend="rewrite-rules"/>).</para>
5377 <sect2 id="language-pragma">
5378 <title>LANGUAGE pragma</title>
5380 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5381 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5383 <para>This allows language extensions to be enabled in a portable way.
5384 It is the intention that all Haskell compilers support the
5385 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5386 all extensions are supported by all compilers, of
5387 course. The <literal>LANGUAGE</literal> pragma should be used instead
5388 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5390 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5392 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5394 <para>Any extension from the <literal>Extension</literal> type defined in
5396 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>
5400 <sect2 id="line-pragma">
5401 <title>LINE pragma</title>
5403 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5404 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5405 <para>This pragma is similar to C's <literal>#line</literal>
5406 pragma, and is mainly for use in automatically generated Haskell
5407 code. It lets you specify the line number and filename of the
5408 original code; for example</para>
5410 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5412 <para>if you'd generated the current file from something called
5413 <filename>Foo.vhs</filename> and this line corresponds to line
5414 42 in the original. GHC will adjust its error messages to refer
5415 to the line/file named in the <literal>LINE</literal>
5419 <sect2 id="options-pragma">
5420 <title>OPTIONS_GHC pragma</title>
5421 <indexterm><primary>OPTIONS_GHC</primary>
5423 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5426 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5427 additional options that are given to the compiler when compiling
5428 this source file. See <xref linkend="source-file-options"/> for
5431 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5432 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5436 <title>RULES pragma</title>
5438 <para>The RULES pragma lets you specify rewrite rules. It is
5439 described in <xref linkend="rewrite-rules"/>.</para>
5442 <sect2 id="specialize-pragma">
5443 <title>SPECIALIZE pragma</title>
5445 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5446 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5447 <indexterm><primary>overloading, death to</primary></indexterm>
5449 <para>(UK spelling also accepted.) For key overloaded
5450 functions, you can create extra versions (NB: more code space)
5451 specialised to particular types. Thus, if you have an
5452 overloaded function:</para>
5455 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5458 <para>If it is heavily used on lists with
5459 <literal>Widget</literal> keys, you could specialise it as
5463 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5466 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5467 be put anywhere its type signature could be put.</para>
5469 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5470 (a) a specialised version of the function and (b) a rewrite rule
5471 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5472 un-specialised function into a call to the specialised one.</para>
5474 <para>The type in a SPECIALIZE pragma can be any type that is less
5475 polymorphic than the type of the original function. In concrete terms,
5476 if the original function is <literal>f</literal> then the pragma
5478 {-# SPECIALIZE f :: <type> #-}
5480 is valid if and only if the defintion
5482 f_spec :: <type>
5485 is valid. Here are some examples (where we only give the type signature
5486 for the original function, not its code):
5488 f :: Eq a => a -> b -> b
5489 {-# SPECIALISE f :: Int -> b -> b #-}
5491 g :: (Eq a, Ix b) => a -> b -> b
5492 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5494 h :: Eq a => a -> a -> a
5495 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5497 The last of these examples will generate a
5498 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5499 well. If you use this kind of specialisation, let us know how well it works.
5502 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5503 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5504 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5505 The <literal>INLINE</literal> pragma affects the specialised verison of the
5506 function (only), and applies even if the function is recursive. The motivating
5509 -- A GADT for arrays with type-indexed representation
5511 ArrInt :: !Int -> ByteArray# -> Arr Int
5512 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5514 (!:) :: Arr e -> Int -> e
5515 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5516 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5517 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5518 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5520 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5521 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5522 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5523 the specialised function will be inlined. It has two calls to
5524 <literal>(!:)</literal>,
5525 both at type <literal>Int</literal>. Both these calls fire the first
5526 specialisation, whose body is also inlined. The result is a type-based
5527 unrolling of the indexing function.</para>
5528 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5529 on an ordinarily-recursive function.</para>
5531 <para>Note: In earlier versions of GHC, it was possible to provide your own
5532 specialised function for a given type:
5535 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5538 This feature has been removed, as it is now subsumed by the
5539 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5543 <sect2 id="specialize-instance-pragma">
5544 <title>SPECIALIZE instance pragma
5548 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5549 <indexterm><primary>overloading, death to</primary></indexterm>
5550 Same idea, except for instance declarations. For example:
5553 instance (Eq a) => Eq (Foo a) where {
5554 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5558 The pragma must occur inside the <literal>where</literal> part
5559 of the instance declaration.
5562 Compatible with HBC, by the way, except perhaps in the placement
5568 <sect2 id="unpack-pragma">
5569 <title>UNPACK pragma</title>
5571 <indexterm><primary>UNPACK</primary></indexterm>
5573 <para>The <literal>UNPACK</literal> indicates to the compiler
5574 that it should unpack the contents of a constructor field into
5575 the constructor itself, removing a level of indirection. For
5579 data T = T {-# UNPACK #-} !Float
5580 {-# UNPACK #-} !Float
5583 <para>will create a constructor <literal>T</literal> containing
5584 two unboxed floats. This may not always be an optimisation: if
5585 the <function>T</function> constructor is scrutinised and the
5586 floats passed to a non-strict function for example, they will
5587 have to be reboxed (this is done automatically by the
5590 <para>Unpacking constructor fields should only be used in
5591 conjunction with <option>-O</option>, in order to expose
5592 unfoldings to the compiler so the reboxing can be removed as
5593 often as possible. For example:</para>
5597 f (T f1 f2) = f1 + f2
5600 <para>The compiler will avoid reboxing <function>f1</function>
5601 and <function>f2</function> by inlining <function>+</function>
5602 on floats, but only when <option>-O</option> is on.</para>
5604 <para>Any single-constructor data is eligible for unpacking; for
5608 data T = T {-# UNPACK #-} !(Int,Int)
5611 <para>will store the two <literal>Int</literal>s directly in the
5612 <function>T</function> constructor, by flattening the pair.
5613 Multi-level unpacking is also supported:</para>
5616 data T = T {-# UNPACK #-} !S
5617 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5620 <para>will store two unboxed <literal>Int#</literal>s
5621 directly in the <function>T</function> constructor. The
5622 unpacker can see through newtypes, too.</para>
5624 <para>If a field cannot be unpacked, you will not get a warning,
5625 so it might be an idea to check the generated code with
5626 <option>-ddump-simpl</option>.</para>
5628 <para>See also the <option>-funbox-strict-fields</option> flag,
5629 which essentially has the effect of adding
5630 <literal>{-# UNPACK #-}</literal> to every strict
5631 constructor field.</para>
5636 <!-- ======================= REWRITE RULES ======================== -->
5638 <sect1 id="rewrite-rules">
5639 <title>Rewrite rules
5641 <indexterm><primary>RULES pragma</primary></indexterm>
5642 <indexterm><primary>pragma, RULES</primary></indexterm>
5643 <indexterm><primary>rewrite rules</primary></indexterm></title>
5646 The programmer can specify rewrite rules as part of the source program
5647 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5648 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5649 and (b) the <option>-frules-off</option> flag
5650 (<xref linkend="options-f"/>) is not specified, and (c) the
5651 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5660 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5667 <title>Syntax</title>
5670 From a syntactic point of view:
5676 There may be zero or more rules in a <literal>RULES</literal> pragma.
5683 Each rule has a name, enclosed in double quotes. The name itself has
5684 no significance at all. It is only used when reporting how many times the rule fired.
5690 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5691 immediately after the name of the rule. Thus:
5694 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5697 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5698 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5707 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5708 is set, so you must lay out your rules starting in the same column as the
5709 enclosing definitions.
5716 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5717 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5718 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5719 by spaces, just like in a type <literal>forall</literal>.
5725 A pattern variable may optionally have a type signature.
5726 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5727 For example, here is the <literal>foldr/build</literal> rule:
5730 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5731 foldr k z (build g) = g k z
5734 Since <function>g</function> has a polymorphic type, it must have a type signature.
5741 The left hand side of a rule must consist of a top-level variable applied
5742 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5745 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5746 "wrong2" forall f. f True = True
5749 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5756 A rule does not need to be in the same module as (any of) the
5757 variables it mentions, though of course they need to be in scope.
5763 Rules are automatically exported from a module, just as instance declarations are.
5774 <title>Semantics</title>
5777 From a semantic point of view:
5783 Rules are only applied if you use the <option>-O</option> flag.
5789 Rules are regarded as left-to-right rewrite rules.
5790 When GHC finds an expression that is a substitution instance of the LHS
5791 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5792 By "a substitution instance" we mean that the LHS can be made equal to the
5793 expression by substituting for the pattern variables.
5800 The LHS and RHS of a rule are typechecked, and must have the
5808 GHC makes absolutely no attempt to verify that the LHS and RHS
5809 of a rule have the same meaning. That is undecidable in general, and
5810 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5817 GHC makes no attempt to make sure that the rules are confluent or
5818 terminating. For example:
5821 "loop" forall x,y. f x y = f y x
5824 This rule will cause the compiler to go into an infinite loop.
5831 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5837 GHC currently uses a very simple, syntactic, matching algorithm
5838 for matching a rule LHS with an expression. It seeks a substitution
5839 which makes the LHS and expression syntactically equal modulo alpha
5840 conversion. The pattern (rule), but not the expression, is eta-expanded if
5841 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5842 But not beta conversion (that's called higher-order matching).
5846 Matching is carried out on GHC's intermediate language, which includes
5847 type abstractions and applications. So a rule only matches if the
5848 types match too. See <xref linkend="rule-spec"/> below.
5854 GHC keeps trying to apply the rules as it optimises the program.
5855 For example, consider:
5864 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5865 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5866 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5867 not be substituted, and the rule would not fire.
5874 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5875 that appears on the LHS of a rule</emphasis>, because once you have substituted
5876 for something you can't match against it (given the simple minded
5877 matching). So if you write the rule
5880 "map/map" forall f,g. map f . map g = map (f.g)
5883 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5884 It will only match something written with explicit use of ".".
5885 Well, not quite. It <emphasis>will</emphasis> match the expression
5891 where <function>wibble</function> is defined:
5894 wibble f g = map f . map g
5897 because <function>wibble</function> will be inlined (it's small).
5899 Later on in compilation, GHC starts inlining even things on the
5900 LHS of rules, but still leaves the rules enabled. This inlining
5901 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5908 All rules are implicitly exported from the module, and are therefore
5909 in force in any module that imports the module that defined the rule, directly
5910 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5911 in force when compiling A.) The situation is very similar to that for instance
5923 <title>List fusion</title>
5926 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5927 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5928 intermediate list should be eliminated entirely.
5932 The following are good producers:
5944 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5950 Explicit lists (e.g. <literal>[True, False]</literal>)
5956 The cons constructor (e.g <literal>3:4:[]</literal>)
5962 <function>++</function>
5968 <function>map</function>
5974 <function>take</function>, <function>filter</function>
5980 <function>iterate</function>, <function>repeat</function>
5986 <function>zip</function>, <function>zipWith</function>
5995 The following are good consumers:
6007 <function>array</function> (on its second argument)
6013 <function>++</function> (on its first argument)
6019 <function>foldr</function>
6025 <function>map</function>
6031 <function>take</function>, <function>filter</function>
6037 <function>concat</function>
6043 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
6049 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
6050 will fuse with one but not the other)
6056 <function>partition</function>
6062 <function>head</function>
6068 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
6074 <function>sequence_</function>
6080 <function>msum</function>
6086 <function>sortBy</function>
6095 So, for example, the following should generate no intermediate lists:
6098 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6104 This list could readily be extended; if there are Prelude functions that you use
6105 a lot which are not included, please tell us.
6109 If you want to write your own good consumers or producers, look at the
6110 Prelude definitions of the above functions to see how to do so.
6115 <sect2 id="rule-spec">
6116 <title>Specialisation
6120 Rewrite rules can be used to get the same effect as a feature
6121 present in earlier versions of GHC.
6122 For example, suppose that:
6125 genericLookup :: Ord a => Table a b -> a -> b
6126 intLookup :: Table Int b -> Int -> b
6129 where <function>intLookup</function> is an implementation of
6130 <function>genericLookup</function> that works very fast for
6131 keys of type <literal>Int</literal>. You might wish
6132 to tell GHC to use <function>intLookup</function> instead of
6133 <function>genericLookup</function> whenever the latter was called with
6134 type <literal>Table Int b -> Int -> b</literal>.
6135 It used to be possible to write
6138 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6141 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6144 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6147 This slightly odd-looking rule instructs GHC to replace
6148 <function>genericLookup</function> by <function>intLookup</function>
6149 <emphasis>whenever the types match</emphasis>.
6150 What is more, this rule does not need to be in the same
6151 file as <function>genericLookup</function>, unlike the
6152 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6153 have an original definition available to specialise).
6156 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6157 <function>intLookup</function> really behaves as a specialised version
6158 of <function>genericLookup</function>!!!</para>
6160 <para>An example in which using <literal>RULES</literal> for
6161 specialisation will Win Big:
6164 toDouble :: Real a => a -> Double
6165 toDouble = fromRational . toRational
6167 {-# RULES "toDouble/Int" toDouble = i2d #-}
6168 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6171 The <function>i2d</function> function is virtually one machine
6172 instruction; the default conversion—via an intermediate
6173 <literal>Rational</literal>—is obscenely expensive by
6180 <title>Controlling what's going on</title>
6188 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6194 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6195 If you add <option>-dppr-debug</option> you get a more detailed listing.
6201 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6204 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6205 {-# INLINE build #-}
6209 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6210 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6211 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6212 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6219 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6220 see how to write rules that will do fusion and yet give an efficient
6221 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6231 <sect2 id="core-pragma">
6232 <title>CORE pragma</title>
6234 <indexterm><primary>CORE pragma</primary></indexterm>
6235 <indexterm><primary>pragma, CORE</primary></indexterm>
6236 <indexterm><primary>core, annotation</primary></indexterm>
6239 The external core format supports <quote>Note</quote> annotations;
6240 the <literal>CORE</literal> pragma gives a way to specify what these
6241 should be in your Haskell source code. Syntactically, core
6242 annotations are attached to expressions and take a Haskell string
6243 literal as an argument. The following function definition shows an
6247 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6250 Semantically, this is equivalent to:
6258 However, when external for is generated (via
6259 <option>-fext-core</option>), there will be Notes attached to the
6260 expressions <function>show</function> and <varname>x</varname>.
6261 The core function declaration for <function>f</function> is:
6265 f :: %forall a . GHCziShow.ZCTShow a ->
6266 a -> GHCziBase.ZMZN GHCziBase.Char =
6267 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6269 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6271 (tpl1::GHCziBase.Int ->
6273 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6275 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6276 (tpl3::GHCziBase.ZMZN a ->
6277 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6285 Here, we can see that the function <function>show</function> (which
6286 has been expanded out to a case expression over the Show dictionary)
6287 has a <literal>%note</literal> attached to it, as does the
6288 expression <varname>eta</varname> (which used to be called
6289 <varname>x</varname>).
6296 <sect1 id="special-ids">
6297 <title>Special built-in functions</title>
6298 <para>GHC has a few built-in funcions with special behaviour,
6299 described in this section. All are exported by
6300 <literal>GHC.Exts</literal>.</para>
6302 <sect2> <title>The <literal>seq</literal> function </title>
6304 The function <literal>seq</literal> is as described in the Haskell98 Report.
6308 It evaluates its first argument to head normal form, and then returns its
6309 second argument as the result. The reason that it is documented here is
6310 that, despite <literal>seq</literal>'s polymorphism, its
6311 second argument can have an unboxed type, or
6312 can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
6313 or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
6314 to be instantiated to an unboxed type, which is not usually allowed.
6318 <sect2> <title>The <literal>inline</literal> function </title>
6320 The <literal>inline</literal> function is somewhat experimental.
6324 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6325 is inlined, regardless of its size. More precisely, the call
6326 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6328 This allows the programmer to control inlining from
6329 a particular <emphasis>call site</emphasis>
6330 rather than the <emphasis>definition site</emphasis> of the function
6331 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6334 This inlining occurs regardless of the argument to the call
6335 or the size of <literal>f</literal>'s definition; it is unconditional.
6336 The main caveat is that <literal>f</literal>'s definition must be
6337 visible to the compiler. That is, <literal>f</literal> must be
6338 let-bound in the current scope.
6339 If no inlining takes place, the <literal>inline</literal> function
6340 expands to the identity function in Phase zero; so its use imposes
6343 <para> If the function is defined in another
6344 module, GHC only exposes its inlining in the interface file if the
6345 function is sufficiently small that it <emphasis>might</emphasis> be
6346 inlined by the automatic mechanism. There is currently no way to tell
6347 GHC to expose arbitrarily-large functions in the interface file. (This
6348 shortcoming is something that could be fixed, with some kind of pragma.)
6352 <sect2> <title>The <literal>lazy</literal> function </title>
6354 The <literal>lazy</literal> function restrains strictness analysis a little:
6358 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6359 but <literal>lazy</literal> has a magical property so far as strictness
6360 analysis is concerned: it is lazy in its first argument,
6361 even though its semantics is strict. After strictness analysis has run,
6362 calls to <literal>lazy</literal> are inlined to be the identity function.
6365 This behaviour is occasionally useful when controlling evaluation order.
6366 Notably, <literal>lazy</literal> is used in the library definition of
6367 <literal>Control.Parallel.par</literal>:
6370 par x y = case (par# x) of { _ -> lazy y }
6372 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6373 look strict in <literal>y</literal> which would defeat the whole
6374 purpose of <literal>par</literal>.
6377 Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
6383 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6385 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6386 typechecker entirely. It has type
6388 unsafeCoerce# :: a -> b
6390 That is, it allows you to coerce any type into any other type. If you use this
6391 function, you had better get it right, otherwise segmentation faults await.
6392 It is generally used when you want to write a program that you know is
6393 well-typed, but where Haskell's type system is not expressive enough to prove
6394 that it is well typed.
6397 The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
6398 although extremely bad things will happen if you coerce a boxed type
6407 <sect1 id="generic-classes">
6408 <title>Generic classes</title>
6411 The ideas behind this extension are described in detail in "Derivable type classes",
6412 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6413 An example will give the idea:
6421 fromBin :: [Int] -> (a, [Int])
6423 toBin {| Unit |} Unit = []
6424 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6425 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6426 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6428 fromBin {| Unit |} bs = (Unit, bs)
6429 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6430 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6431 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6432 (y,bs'') = fromBin bs'
6435 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6436 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6437 which are defined thus in the library module <literal>Generics</literal>:
6441 data a :+: b = Inl a | Inr b
6442 data a :*: b = a :*: b
6445 Now you can make a data type into an instance of Bin like this:
6447 instance (Bin a, Bin b) => Bin (a,b)
6448 instance Bin a => Bin [a]
6450 That is, just leave off the "where" clause. Of course, you can put in the
6451 where clause and over-ride whichever methods you please.
6455 <title> Using generics </title>
6456 <para>To use generics you need to</para>
6459 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6460 <option>-fgenerics</option> (to generate extra per-data-type code),
6461 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6465 <para>Import the module <literal>Generics</literal> from the
6466 <literal>lang</literal> package. This import brings into
6467 scope the data types <literal>Unit</literal>,
6468 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6469 don't need this import if you don't mention these types
6470 explicitly; for example, if you are simply giving instance
6471 declarations.)</para>
6476 <sect2> <title> Changes wrt the paper </title>
6478 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6479 can be written infix (indeed, you can now use
6480 any operator starting in a colon as an infix type constructor). Also note that
6481 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6482 Finally, note that the syntax of the type patterns in the class declaration
6483 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6484 alone would ambiguous when they appear on right hand sides (an extension we
6485 anticipate wanting).
6489 <sect2> <title>Terminology and restrictions</title>
6491 Terminology. A "generic default method" in a class declaration
6492 is one that is defined using type patterns as above.
6493 A "polymorphic default method" is a default method defined as in Haskell 98.
6494 A "generic class declaration" is a class declaration with at least one
6495 generic default method.
6503 Alas, we do not yet implement the stuff about constructor names and
6510 A generic class can have only one parameter; you can't have a generic
6511 multi-parameter class.
6517 A default method must be defined entirely using type patterns, or entirely
6518 without. So this is illegal:
6521 op :: a -> (a, Bool)
6522 op {| Unit |} Unit = (Unit, True)
6525 However it is perfectly OK for some methods of a generic class to have
6526 generic default methods and others to have polymorphic default methods.
6532 The type variable(s) in the type pattern for a generic method declaration
6533 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:
6537 op {| p :*: q |} (x :*: y) = op (x :: p)
6545 The type patterns in a generic default method must take one of the forms:
6551 where "a" and "b" are type variables. Furthermore, all the type patterns for
6552 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6553 must use the same type variables. So this is illegal:
6557 op {| a :+: b |} (Inl x) = True
6558 op {| p :+: q |} (Inr y) = False
6560 The type patterns must be identical, even in equations for different methods of the class.
6561 So this too is illegal:
6565 op1 {| a :*: b |} (x :*: y) = True
6568 op2 {| p :*: q |} (x :*: y) = False
6570 (The reason for this restriction is that we gather all the equations for a particular type consructor
6571 into a single generic instance declaration.)
6577 A generic method declaration must give a case for each of the three type constructors.
6583 The type for a generic method can be built only from:
6585 <listitem> <para> Function arrows </para> </listitem>
6586 <listitem> <para> Type variables </para> </listitem>
6587 <listitem> <para> Tuples </para> </listitem>
6588 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6590 Here are some example type signatures for generic methods:
6593 op2 :: Bool -> (a,Bool)
6594 op3 :: [Int] -> a -> a
6597 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6601 This restriction is an implementation restriction: we just havn't got around to
6602 implementing the necessary bidirectional maps over arbitrary type constructors.
6603 It would be relatively easy to add specific type constructors, such as Maybe and list,
6604 to the ones that are allowed.</para>
6609 In an instance declaration for a generic class, the idea is that the compiler
6610 will fill in the methods for you, based on the generic templates. However it can only
6615 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6620 No constructor of the instance type has unboxed fields.
6624 (Of course, these things can only arise if you are already using GHC extensions.)
6625 However, you can still give an instance declarations for types which break these rules,
6626 provided you give explicit code to override any generic default methods.
6634 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6635 what the compiler does with generic declarations.
6640 <sect2> <title> Another example </title>
6642 Just to finish with, here's another example I rather like:
6646 nCons {| Unit |} _ = 1
6647 nCons {| a :*: b |} _ = 1
6648 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6651 tag {| Unit |} _ = 1
6652 tag {| a :*: b |} _ = 1
6653 tag {| a :+: b |} (Inl x) = tag x
6654 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6660 <sect1 id="monomorphism">
6661 <title>Control over monomorphism</title>
6663 <para>GHC supports two flags that control the way in which generalisation is
6664 carried out at let and where bindings.
6668 <title>Switching off the dreaded Monomorphism Restriction</title>
6669 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6671 <para>Haskell's monomorphism restriction (see
6672 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6674 of the Haskell Report)
6675 can be completely switched off by
6676 <option>-fno-monomorphism-restriction</option>.
6681 <title>Monomorphic pattern bindings</title>
6682 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6683 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6685 <para> As an experimental change, we are exploring the possibility of
6686 making pattern bindings monomorphic; that is, not generalised at all.
6687 A pattern binding is a binding whose LHS has no function arguments,
6688 and is not a simple variable. For example:
6690 f x = x -- Not a pattern binding
6691 f = \x -> x -- Not a pattern binding
6692 f :: Int -> Int = \x -> x -- Not a pattern binding
6694 (g,h) = e -- A pattern binding
6695 (f) = e -- A pattern binding
6696 [x] = e -- A pattern binding
6698 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6699 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6708 ;;; Local Variables: ***
6710 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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