2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. They are all enabled by options; by default GHC
6 understands only plain Haskell 98.
10 Some of the Glasgow extensions serve to give you access to the
11 underlying facilities with which we implement Haskell. Thus, you can
12 get at the Raw Iron, if you are willing to write some non-portable
13 code at a more primitive level. You need not be “stuck”
14 on performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code
16 “under” them. In an extreme case, you can write all your
17 time-critical code in C, and then just glue it together with Haskell!
21 Before you get too carried away working at the lowest level (e.g.,
22 sloshing <literal>MutableByteArray#</literal>s around your
23 program), you may wish to check if there are libraries that provide a
24 “Haskellised veneer” over the features you want. The
25 separate <ulink url="../libraries/index.html">libraries
26 documentation</ulink> describes all the libraries that come with GHC.
29 <!-- LANGUAGE OPTIONS -->
30 <sect1 id="options-language">
31 <title>Language options</title>
33 <indexterm><primary>language</primary><secondary>option</secondary>
35 <indexterm><primary>options</primary><secondary>language</secondary>
37 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
40 <para>These flags control what variation of the language are
41 permitted. Leaving out all of them gives you standard Haskell
44 <para>NB. turning on an option that enables special syntax
45 <emphasis>might</emphasis> cause working Haskell 98 code to fail
46 to compile, perhaps because it uses a variable name which has
47 become a reserved word. So, together with each option below, we
48 list the special syntax which is enabled by this option. We use
49 notation and nonterminal names from the Haskell 98 lexical syntax
50 (see the Haskell 98 Report). There are two classes of special
55 <para>New reserved words and symbols: character sequences
56 which are no longer available for use as identifiers in the
60 <para>Other special syntax: sequences of characters that have
61 a different meaning when this particular option is turned
66 <para>We are only listing syntax changes here that might affect
67 existing working programs (i.e. "stolen" syntax). Many of these
68 extensions will also enable new context-free syntax, but in all
69 cases programs written to use the new syntax would not be
70 compilable without the option enabled.</para>
75 <term><option>-fglasgow-exts</option>:</term>
76 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
78 <para>This simultaneously enables all of the extensions to
79 Haskell 98 described in <xref
80 linkend="ghc-language-features">, except where otherwise
83 <para>New reserved words: <literal>forall</literal> (only in
84 types), <literal>mdo</literal>.</para>
86 <para>Other syntax stolen:
87 <replaceable>varid</replaceable>{<literal>#</literal>},
88 <replaceable>char</replaceable><literal>#</literal>,
89 <replaceable>string</replaceable><literal>#</literal>,
90 <replaceable>integer</replaceable><literal>#</literal>,
91 <replaceable>float</replaceable><literal>#</literal>,
92 <replaceable>float</replaceable><literal>##</literal>,
93 <literal>(#</literal>, <literal>#)</literal>,
94 <literal>|)</literal>, <literal>{|</literal>.</para>
99 <term><option>-ffi</option> and <option>-fffi</option>:</term>
100 <indexterm><primary><option>-ffi</option></primary></indexterm>
101 <indexterm><primary><option>-fffi</option></primary></indexterm>
103 <para>This option enables the language extension defined in the
104 Haskell 98 Foreign Function Interface Addendum plus deprecated
105 syntax of previous versions of the FFI for backwards
106 compatibility.</para>
108 <para>New reserved words: <literal>foreign</literal>.</para>
113 <term><option>-fno-monomorphism-restriction</option>:</term>
114 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
116 <para> Switch off the Haskell 98 monomorphism restriction.
117 Independent of the <option>-fglasgow-exts</option>
123 <term><option>-fallow-overlapping-instances</option></term>
124 <term><option>-fallow-undecidable-instances</option></term>
125 <term><option>-fallow-incoherent-instances</option></term>
126 <term><option>-fcontext-stack</option></term>
127 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
128 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
129 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
131 <para> See <xref LinkEnd="instance-decls">. Only relevant
132 if you also use <option>-fglasgow-exts</option>.</para>
137 <term><option>-finline-phase</option></term>
138 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
140 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
141 you also use <option>-fglasgow-exts</option>.</para>
146 <term><option>-farrows</option></term>
147 <indexterm><primary><option>-farrows</option></primary></indexterm>
149 <para>See <xref LinkEnd="arrow-notation">. Independent of
150 <option>-fglasgow-exts</option>.</para>
152 <para>New reserved words/symbols: <literal>rec</literal>,
153 <literal>proc</literal>, <literal>-<</literal>,
154 <literal>>-</literal>, <literal>-<<</literal>,
155 <literal>>>-</literal>.</para>
157 <para>Other syntax stolen: <literal>(|</literal>,
158 <literal>|)</literal>.</para>
163 <term><option>-fgenerics</option></term>
164 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
166 <para>See <xref LinkEnd="generic-classes">. Independent of
167 <option>-fglasgow-exts</option>.</para>
172 <term><option>-fno-implicit-prelude</option></term>
174 <para><indexterm><primary>-fno-implicit-prelude
175 option</primary></indexterm> GHC normally imports
176 <filename>Prelude.hi</filename> files for you. If you'd
177 rather it didn't, then give it a
178 <option>-fno-implicit-prelude</option> option. The idea is
179 that you can then import a Prelude of your own. (But don't
180 call it <literal>Prelude</literal>; the Haskell module
181 namespace is flat, and you must not conflict with any
182 Prelude module.)</para>
184 <para>Even though you have not imported the Prelude, most of
185 the built-in syntax still refers to the built-in Haskell
186 Prelude types and values, as specified by the Haskell
187 Report. For example, the type <literal>[Int]</literal>
188 still means <literal>Prelude.[] Int</literal>; tuples
189 continue to refer to the standard Prelude tuples; the
190 translation for list comprehensions continues to use
191 <literal>Prelude.map</literal> etc.</para>
193 <para>However, <option>-fno-implicit-prelude</option> does
194 change the handling of certain built-in syntax: see <xref
195 LinkEnd="rebindable-syntax">.</para>
200 <term><option>-fth</option></term>
202 <para>Enables Template Haskell (see <xref
203 linkend="template-haskell">). Currently also implied by
204 <option>-fglasgow-exts</option>.</para>
206 <para>Syntax stolen: <literal>[|</literal>,
207 <literal>[e|</literal>, <literal>[p|</literal>,
208 <literal>[d|</literal>, <literal>[t|</literal>,
209 <literal>$(</literal>,
210 <literal>$<replaceable>varid</replaceable></literal>.</para>
215 <term><option>-fimplicit-params</option></term>
217 <para>Enables implicit parameters (see <xref
218 linkend="implicit-parameters">). Currently also implied by
219 <option>-fglasgow-exts</option>.</para>
222 <literal>?<replaceable>varid</replaceable></literal>,
223 <literal>%<replaceable>varid</replaceable></literal>.</para>
230 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
231 <!-- included from primitives.sgml -->
232 <!-- &primitives; -->
233 <sect1 id="primitives">
234 <title>Unboxed types and primitive operations</title>
236 <para>GHC is built on a raft of primitive data types and operations.
237 While you really can use this stuff to write fast code,
238 we generally find it a lot less painful, and more satisfying in the
239 long run, to use higher-level language features and libraries. With
240 any luck, the code you write will be optimised to the efficient
241 unboxed version in any case. And if it isn't, we'd like to know
244 <para>We do not currently have good, up-to-date documentation about the
245 primitives, perhaps because they are mainly intended for internal use.
246 There used to be a long section about them here in the User Guide, but it
247 became out of date, and wrong information is worse than none.</para>
249 <para>The Real Truth about what primitive types there are, and what operations
250 work over those types, is held in the file
251 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
252 This file is used directly to generate GHC's primitive-operation definitions, so
253 it is always correct! It is also intended for processing into text.</para>
256 the result of such processing is part of the description of the
258 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
259 Core language</ulink>.
260 So that document is a good place to look for a type-set version.
261 We would be very happy if someone wanted to volunteer to produce an SGML
262 back end to the program that processes <filename>primops.txt</filename> so that
263 we could include the results here in the User Guide.</para>
265 <para>What follows here is a brief summary of some main points.</para>
267 <sect2 id="glasgow-unboxed">
272 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
275 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
276 that values of that type are represented by a pointer to a heap
277 object. The representation of a Haskell <literal>Int</literal>, for
278 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
279 type, however, is represented by the value itself, no pointers or heap
280 allocation are involved.
284 Unboxed types correspond to the “raw machine” types you
285 would use in C: <literal>Int#</literal> (long int),
286 <literal>Double#</literal> (double), <literal>Addr#</literal>
287 (void *), etc. The <emphasis>primitive operations</emphasis>
288 (PrimOps) on these types are what you might expect; e.g.,
289 <literal>(+#)</literal> is addition on
290 <literal>Int#</literal>s, and is the machine-addition that we all
291 know and love—usually one instruction.
295 Primitive (unboxed) types cannot be defined in Haskell, and are
296 therefore built into the language and compiler. Primitive types are
297 always unlifted; that is, a value of a primitive type cannot be
298 bottom. We use the convention that primitive types, values, and
299 operations have a <literal>#</literal> suffix.
303 Primitive values are often represented by a simple bit-pattern, such
304 as <literal>Int#</literal>, <literal>Float#</literal>,
305 <literal>Double#</literal>. But this is not necessarily the case:
306 a primitive value might be represented by a pointer to a
307 heap-allocated object. Examples include
308 <literal>Array#</literal>, the type of primitive arrays. A
309 primitive array is heap-allocated because it is too big a value to fit
310 in a register, and would be too expensive to copy around; in a sense,
311 it is accidental that it is represented by a pointer. If a pointer
312 represents a primitive value, then it really does point to that value:
313 no unevaluated thunks, no indirections…nothing can be at the
314 other end of the pointer than the primitive value.
318 There are some restrictions on the use of primitive types, the main
319 one being that you can't pass a primitive value to a polymorphic
320 function or store one in a polymorphic data type. This rules out
321 things like <literal>[Int#]</literal> (i.e. lists of primitive
322 integers). The reason for this restriction is that polymorphic
323 arguments and constructor fields are assumed to be pointers: if an
324 unboxed integer is stored in one of these, the garbage collector would
325 attempt to follow it, leading to unpredictable space leaks. Or a
326 <function>seq</function> operation on the polymorphic component may
327 attempt to dereference the pointer, with disastrous results. Even
328 worse, the unboxed value might be larger than a pointer
329 (<literal>Double#</literal> for instance).
333 Nevertheless, A numerically-intensive program using unboxed types can
334 go a <emphasis>lot</emphasis> faster than its “standard”
335 counterpart—we saw a threefold speedup on one example.
340 <sect2 id="unboxed-tuples">
341 <title>Unboxed Tuples
345 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
346 they're available by default with <option>-fglasgow-exts</option>. An
347 unboxed tuple looks like this:
359 where <literal>e_1..e_n</literal> are expressions of any
360 type (primitive or non-primitive). The type of an unboxed tuple looks
365 Unboxed tuples are used for functions that need to return multiple
366 values, but they avoid the heap allocation normally associated with
367 using fully-fledged tuples. When an unboxed tuple is returned, the
368 components are put directly into registers or on the stack; the
369 unboxed tuple itself does not have a composite representation. Many
370 of the primitive operations listed in this section return unboxed
375 There are some pretty stringent restrictions on the use of unboxed tuples:
384 Unboxed tuple types are subject to the same restrictions as
385 other unboxed types; i.e. they may not be stored in polymorphic data
386 structures or passed to polymorphic functions.
393 Unboxed tuples may only be constructed as the direct result of
394 a function, and may only be deconstructed with a <literal>case</literal> expression.
395 eg. the following are valid:
399 f x y = (# x+1, y-1 #)
400 g x = case f x x of { (# a, b #) -> a + b }
404 but the following are invalid:
418 No variable can have an unboxed tuple type. This is illegal:
422 f :: (# Int, Int #) -> (# Int, Int #)
427 because <literal>x</literal> has an unboxed tuple type.
437 Note: we may relax some of these restrictions in the future.
441 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
442 tuples to avoid unnecessary allocation during sequences of operations.
449 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
451 <sect1 id="syntax-extns">
452 <title>Syntactic extensions</title>
454 <!-- ====================== HIERARCHICAL MODULES ======================= -->
456 <sect2 id="hierarchical-modules">
457 <title>Hierarchical Modules</title>
459 <para>GHC supports a small extension to the syntax of module
460 names: a module name is allowed to contain a dot
461 <literal>‘.’</literal>. This is also known as the
462 “hierarchical module namespace” extension, because
463 it extends the normally flat Haskell module namespace into a
464 more flexible hierarchy of modules.</para>
466 <para>This extension has very little impact on the language
467 itself; modules names are <emphasis>always</emphasis> fully
468 qualified, so you can just think of the fully qualified module
469 name as <quote>the module name</quote>. In particular, this
470 means that the full module name must be given after the
471 <literal>module</literal> keyword at the beginning of the
472 module; for example, the module <literal>A.B.C</literal> must
475 <programlisting>module A.B.C</programlisting>
478 <para>It is a common strategy to use the <literal>as</literal>
479 keyword to save some typing when using qualified names with
480 hierarchical modules. For example:</para>
483 import qualified Control.Monad.ST.Strict as ST
486 <para>For details on how GHC searches for source and interface
487 files in the presence of hierarchical modules, see <xref
488 linkend="search-path">.</para>
490 <para>GHC comes with a large collection of libraries arranged
491 hierarchically; see the accompanying library documentation.
492 There is an ongoing project to create and maintain a stable set
493 of <quote>core</quote> libraries used by several Haskell
494 compilers, and the libraries that GHC comes with represent the
495 current status of that project. For more details, see <ulink
496 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
497 Libraries</ulink>.</para>
501 <!-- ====================== PATTERN GUARDS ======================= -->
503 <sect2 id="pattern-guards">
504 <title>Pattern guards</title>
507 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
508 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.)
512 Suppose we have an abstract data type of finite maps, with a
516 lookup :: FiniteMap -> Int -> Maybe Int
519 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
520 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
524 clunky env var1 var2 | ok1 && ok2 = val1 + val2
525 | otherwise = var1 + var2
536 The auxiliary functions are
540 maybeToBool :: Maybe a -> Bool
541 maybeToBool (Just x) = True
542 maybeToBool Nothing = False
544 expectJust :: Maybe a -> a
545 expectJust (Just x) = x
546 expectJust Nothing = error "Unexpected Nothing"
550 What is <function>clunky</function> doing? The guard <literal>ok1 &&
551 ok2</literal> checks that both lookups succeed, using
552 <function>maybeToBool</function> to convert the <function>Maybe</function>
553 types to booleans. The (lazily evaluated) <function>expectJust</function>
554 calls extract the values from the results of the lookups, and binds the
555 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
556 respectively. If either lookup fails, then clunky takes the
557 <literal>otherwise</literal> case and returns the sum of its arguments.
561 This is certainly legal Haskell, but it is a tremendously verbose and
562 un-obvious way to achieve the desired effect. Arguably, a more direct way
563 to write clunky would be to use case expressions:
567 clunky env var1 var1 = case lookup env var1 of
569 Just val1 -> case lookup env var2 of
571 Just val2 -> val1 + val2
577 This is a bit shorter, but hardly better. Of course, we can rewrite any set
578 of pattern-matching, guarded equations as case expressions; that is
579 precisely what the compiler does when compiling equations! The reason that
580 Haskell provides guarded equations is because they allow us to write down
581 the cases we want to consider, one at a time, independently of each other.
582 This structure is hidden in the case version. Two of the right-hand sides
583 are really the same (<function>fail</function>), and the whole expression
584 tends to become more and more indented.
588 Here is how I would write clunky:
593 | Just val1 <- lookup env var1
594 , Just val2 <- lookup env var2
596 ...other equations for clunky...
600 The semantics should be clear enough. The qualifers are matched in order.
601 For a <literal><-</literal> qualifier, which I call a pattern guard, the
602 right hand side is evaluated and matched against the pattern on the left.
603 If the match fails then the whole guard fails and the next equation is
604 tried. If it succeeds, then the appropriate binding takes place, and the
605 next qualifier is matched, in the augmented environment. Unlike list
606 comprehensions, however, the type of the expression to the right of the
607 <literal><-</literal> is the same as the type of the pattern to its
608 left. The bindings introduced by pattern guards scope over all the
609 remaining guard qualifiers, and over the right hand side of the equation.
613 Just as with list comprehensions, boolean expressions can be freely mixed
614 with among the pattern guards. For example:
625 Haskell's current guards therefore emerge as a special case, in which the
626 qualifier list has just one element, a boolean expression.
630 <!-- ===================== Recursive do-notation =================== -->
632 <sect2 id="mdo-notation">
633 <title>The recursive do-notation
636 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
637 "A recursive do for Haskell",
638 Levent Erkok, John Launchbury",
639 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
642 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
643 that is, the variables bound in a do-expression are visible only in the textually following
644 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
645 group. It turns out that several applications can benefit from recursive bindings in
646 the do-notation, and this extension provides the necessary syntactic support.
649 Here is a simple (yet contrived) example:
652 import Control.Monad.Fix
654 justOnes = mdo xs <- Just (1:xs)
658 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
662 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
665 class Monad m => MonadFix m where
666 mfix :: (a -> m a) -> m a
669 The function <literal>mfix</literal>
670 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
671 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
672 For details, see the above mentioned reference.
675 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
676 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
677 for Haskell's internal state monad (strict and lazy, respectively).
680 There are three important points in using the recursive-do notation:
683 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
684 than <literal>do</literal>).
688 You should <literal>import Control.Monad.Fix</literal>.
689 (Note: Strictly speaking, this import is required only when you need to refer to the name
690 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
691 are encouraged to always import this module when using the mdo-notation.)
695 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
701 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
702 contains up to date information on recursive monadic bindings.
706 Historical note: The old implementation of the mdo-notation (and most
707 of the existing documents) used the name
708 <literal>MonadRec</literal> for the class and the corresponding library.
709 This name is not supported by GHC.
715 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
717 <sect2 id="parallel-list-comprehensions">
718 <title>Parallel List Comprehensions</title>
719 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
721 <indexterm><primary>parallel list comprehensions</primary>
724 <para>Parallel list comprehensions are a natural extension to list
725 comprehensions. List comprehensions can be thought of as a nice
726 syntax for writing maps and filters. Parallel comprehensions
727 extend this to include the zipWith family.</para>
729 <para>A parallel list comprehension has multiple independent
730 branches of qualifier lists, each separated by a `|' symbol. For
731 example, the following zips together two lists:</para>
734 [ (x, y) | x <- xs | y <- ys ]
737 <para>The behavior of parallel list comprehensions follows that of
738 zip, in that the resulting list will have the same length as the
739 shortest branch.</para>
741 <para>We can define parallel list comprehensions by translation to
742 regular comprehensions. Here's the basic idea:</para>
744 <para>Given a parallel comprehension of the form: </para>
747 [ e | p1 <- e11, p2 <- e12, ...
748 | q1 <- e21, q2 <- e22, ...
753 <para>This will be translated to: </para>
756 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
757 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
762 <para>where `zipN' is the appropriate zip for the given number of
767 <sect2 id="rebindable-syntax">
768 <title>Rebindable syntax</title>
771 <para>GHC allows most kinds of built-in syntax to be rebound by
772 the user, to facilitate replacing the <literal>Prelude</literal>
773 with a home-grown version, for example.</para>
775 <para>You may want to define your own numeric class
776 hierarchy. It completely defeats that purpose if the
777 literal "1" means "<literal>Prelude.fromInteger
778 1</literal>", which is what the Haskell Report specifies.
779 So the <option>-fno-implicit-prelude</option> flag causes
780 the following pieces of built-in syntax to refer to
781 <emphasis>whatever is in scope</emphasis>, not the Prelude
786 <para>Integer and fractional literals mean
787 "<literal>fromInteger 1</literal>" and
788 "<literal>fromRational 3.2</literal>", not the
789 Prelude-qualified versions; both in expressions and in
791 <para>However, the standard Prelude <literal>Eq</literal> class
792 is still used for the equality test necessary for literal patterns.</para>
796 <para>Negation (e.g. "<literal>- (f x)</literal>")
797 means "<literal>negate (f x)</literal>" (not
798 <literal>Prelude.negate</literal>).</para>
802 <para>In an n+k pattern, the standard Prelude
803 <literal>Ord</literal> class is still used for comparison,
804 but the necessary subtraction uses whatever
805 "<literal>(-)</literal>" is in scope (not
806 "<literal>Prelude.(-)</literal>").</para>
810 <para>"Do" notation is translated using whatever
811 functions <literal>(>>=)</literal>,
812 <literal>(>>)</literal>, <literal>fail</literal>, and
813 <literal>return</literal>, are in scope (not the Prelude
814 versions). List comprehensions, and parallel array
815 comprehensions, are unaffected. </para></listitem>
818 <para>Be warned: this is an experimental facility, with fewer checks than
819 usual. In particular, it is essential that the functions GHC finds in scope
820 must have the appropriate types, namely:
822 fromInteger :: forall a. (...) => Integer -> a
823 fromRational :: forall a. (...) => Rational -> a
824 negate :: forall a. (...) => a -> a
825 (-) :: forall a. (...) => a -> a -> a
826 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
827 (>>) :: forall m a. (...) => m a -> m b -> m b
828 return :: forall m a. (...) => a -> m a
829 fail :: forall m a. (...) => String -> m a
831 (The (...) part can be any context including the empty context; that part
833 If the functions don't have the right type, very peculiar things may
834 happen. Use <literal>-dcore-lint</literal> to
835 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
841 <!-- TYPE SYSTEM EXTENSIONS -->
842 <sect1 id="type-extensions">
843 <title>Type system extensions</title>
847 <title>Data types and type synonyms</title>
849 <sect3 id="nullary-types">
850 <title>Data types with no constructors</title>
852 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
853 a data type with no constructors. For example:</para>
857 data T a -- T :: * -> *
860 <para>Syntactically, the declaration lacks the "= constrs" part. The
861 type can be parameterised over types of any kind, but if the kind is
862 not <literal>*</literal> then an explicit kind annotation must be used
863 (see <xref linkend="sec-kinding">).</para>
865 <para>Such data types have only one value, namely bottom.
866 Nevertheless, they can be useful when defining "phantom types".</para>
869 <sect3 id="infix-tycons">
870 <title>Infix type constructors</title>
873 GHC allows type constructors to be operators, and to be written infix, very much
874 like expressions. More specifically:
877 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
878 The lexical syntax is the same as that for data constructors.
881 Types can be written infix. For example <literal>Int :*: Bool</literal>.
885 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
886 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
889 Fixities may be declared for type constructors just as for data constructors. However,
890 one cannot distinguish between the two in a fixity declaration; a fixity declaration
891 sets the fixity for a data constructor and the corresponding type constructor. For example:
895 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
896 and similarly for <literal>:*:</literal>.
897 <literal>Int `a` Bool</literal>.
900 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
903 Data type and type-synonym declarations can be written infix. E.g.
905 data a :*: b = Foo a b
906 type a :+: b = Either a b
910 The only thing that differs between operators in types and operators in expressions is that
911 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
912 are not allowed in types. Reason: the uniform thing to do would be to make them type
913 variables, but that's not very useful. A less uniform but more useful thing would be to
914 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
915 lists. So for now we just exclude them.
922 <sect3 id="type-synonyms">
923 <title>Liberalised type synonyms</title>
926 Type synonmys are like macros at the type level, and
927 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
928 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
930 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
931 in a type synonym, thus:
933 type Discard a = forall b. Show b => a -> b -> (a, String)
938 g :: Discard Int -> (Int,Bool) -- A rank-2 type
945 You can write an unboxed tuple in a type synonym:
947 type Pr = (# Int, Int #)
955 You can apply a type synonym to a forall type:
957 type Foo a = a -> a -> Bool
959 f :: Foo (forall b. b->b)
961 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
963 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
968 You can apply a type synonym to a partially applied type synonym:
970 type Generic i o = forall x. i x -> o x
975 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
977 foo :: forall x. x -> [x]
985 GHC currently does kind checking before expanding synonyms (though even that
989 After expanding type synonyms, GHC does validity checking on types, looking for
990 the following mal-formedness which isn't detected simply by kind checking:
993 Type constructor applied to a type involving for-alls.
996 Unboxed tuple on left of an arrow.
999 Partially-applied type synonym.
1003 this will be rejected:
1005 type Pr = (# Int, Int #)
1010 because GHC does not allow unboxed tuples on the left of a function arrow.
1015 <sect3 id="existential-quantification">
1016 <title>Existentially quantified data constructors
1020 The idea of using existential quantification in data type declarations
1021 was suggested by Laufer (I believe, thought doubtless someone will
1022 correct me), and implemented in Hope+. It's been in Lennart
1023 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1024 proved very useful. Here's the idea. Consider the declaration:
1030 data Foo = forall a. MkFoo a (a -> Bool)
1037 The data type <literal>Foo</literal> has two constructors with types:
1043 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1050 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1051 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1052 For example, the following expression is fine:
1058 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1064 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1065 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1066 isUpper</function> packages a character with a compatible function. These
1067 two things are each of type <literal>Foo</literal> and can be put in a list.
1071 What can we do with a value of type <literal>Foo</literal>?. In particular,
1072 what happens when we pattern-match on <function>MkFoo</function>?
1078 f (MkFoo val fn) = ???
1084 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1085 are compatible, the only (useful) thing we can do with them is to
1086 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1093 f (MkFoo val fn) = fn val
1099 What this allows us to do is to package heterogenous values
1100 together with a bunch of functions that manipulate them, and then treat
1101 that collection of packages in a uniform manner. You can express
1102 quite a bit of object-oriented-like programming this way.
1105 <sect4 id="existential">
1106 <title>Why existential?
1110 What has this to do with <emphasis>existential</emphasis> quantification?
1111 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1117 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1123 But Haskell programmers can safely think of the ordinary
1124 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1125 adding a new existential quantification construct.
1131 <title>Type classes</title>
1134 An easy extension (implemented in <Command>hbc</Command>) is to allow
1135 arbitrary contexts before the constructor. For example:
1141 data Baz = forall a. Eq a => Baz1 a a
1142 | forall b. Show b => Baz2 b (b -> b)
1148 The two constructors have the types you'd expect:
1154 Baz1 :: forall a. Eq a => a -> a -> Baz
1155 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1161 But when pattern matching on <function>Baz1</function> the matched values can be compared
1162 for equality, and when pattern matching on <function>Baz2</function> the first matched
1163 value can be converted to a string (as well as applying the function to it).
1164 So this program is legal:
1171 f (Baz1 p q) | p == q = "Yes"
1173 f (Baz2 v fn) = show (fn v)
1179 Operationally, in a dictionary-passing implementation, the
1180 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1181 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1182 extract it on pattern matching.
1186 Notice the way that the syntax fits smoothly with that used for
1187 universal quantification earlier.
1193 <title>Restrictions</title>
1196 There are several restrictions on the ways in which existentially-quantified
1197 constructors can be use.
1206 When pattern matching, each pattern match introduces a new,
1207 distinct, type for each existential type variable. These types cannot
1208 be unified with any other type, nor can they escape from the scope of
1209 the pattern match. For example, these fragments are incorrect:
1217 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1218 is the result of <function>f1</function>. One way to see why this is wrong is to
1219 ask what type <function>f1</function> has:
1223 f1 :: Foo -> a -- Weird!
1227 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1232 f1 :: forall a. Foo -> a -- Wrong!
1236 The original program is just plain wrong. Here's another sort of error
1240 f2 (Baz1 a b) (Baz1 p q) = a==q
1244 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1245 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1246 from the two <function>Baz1</function> constructors.
1254 You can't pattern-match on an existentially quantified
1255 constructor in a <literal>let</literal> or <literal>where</literal> group of
1256 bindings. So this is illegal:
1260 f3 x = a==b where { Baz1 a b = x }
1263 Instead, use a <literal>case</literal> expression:
1266 f3 x = case x of Baz1 a b -> a==b
1269 In general, you can only pattern-match
1270 on an existentially-quantified constructor in a <literal>case</literal> expression or
1271 in the patterns of a function definition.
1273 The reason for this restriction is really an implementation one.
1274 Type-checking binding groups is already a nightmare without
1275 existentials complicating the picture. Also an existential pattern
1276 binding at the top level of a module doesn't make sense, because it's
1277 not clear how to prevent the existentially-quantified type "escaping".
1278 So for now, there's a simple-to-state restriction. We'll see how
1286 You can't use existential quantification for <literal>newtype</literal>
1287 declarations. So this is illegal:
1291 newtype T = forall a. Ord a => MkT a
1295 Reason: a value of type <literal>T</literal> must be represented as a
1296 pair of a dictionary for <literal>Ord t</literal> and a value of type
1297 <literal>t</literal>. That contradicts the idea that
1298 <literal>newtype</literal> should have no concrete representation.
1299 You can get just the same efficiency and effect by using
1300 <literal>data</literal> instead of <literal>newtype</literal>. If
1301 there is no overloading involved, then there is more of a case for
1302 allowing an existentially-quantified <literal>newtype</literal>,
1303 because the <literal>data</literal> version does carry an
1304 implementation cost, but single-field existentially quantified
1305 constructors aren't much use. So the simple restriction (no
1306 existential stuff on <literal>newtype</literal>) stands, unless there
1307 are convincing reasons to change it.
1315 You can't use <literal>deriving</literal> to define instances of a
1316 data type with existentially quantified data constructors.
1318 Reason: in most cases it would not make sense. For example:#
1321 data T = forall a. MkT [a] deriving( Eq )
1324 To derive <literal>Eq</literal> in the standard way we would need to have equality
1325 between the single component of two <function>MkT</function> constructors:
1329 (MkT a) == (MkT b) = ???
1332 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1333 It's just about possible to imagine examples in which the derived instance
1334 would make sense, but it seems altogether simpler simply to prohibit such
1335 declarations. Define your own instances!
1350 <sect2 id="multi-param-type-classes">
1351 <title>Class declarations</title>
1354 This section documents GHC's implementation of multi-parameter type
1355 classes. There's lots of background in the paper <ULink
1356 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1357 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
1358 Jones, Erik Meijer).
1361 There are the following constraints on class declarations:
1366 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1370 class Collection c a where
1371 union :: c a -> c a -> c a
1382 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1383 of "acyclic" involves only the superclass relationships. For example,
1389 op :: D b => a -> b -> b
1392 class C a => D a where { ... }
1396 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1397 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1398 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1405 <emphasis>There are no restrictions on the context in a class declaration
1406 (which introduces superclasses), except that the class hierarchy must
1407 be acyclic</emphasis>. So these class declarations are OK:
1411 class Functor (m k) => FiniteMap m k where
1414 class (Monad m, Monad (t m)) => Transform t m where
1415 lift :: m a -> (t m) a
1425 <emphasis>All of the class type variables must be reachable (in the sense
1426 mentioned in <xref linkend="type-restrictions">)
1427 from the free varibles of each method type
1428 </emphasis>. For example:
1432 class Coll s a where
1434 insert :: s -> a -> s
1438 is not OK, because the type of <literal>empty</literal> doesn't mention
1439 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1440 types, and has the same motivation.
1442 Sometimes, offending class declarations exhibit misunderstandings. For
1443 example, <literal>Coll</literal> might be rewritten
1447 class Coll s a where
1449 insert :: s a -> a -> s a
1453 which makes the connection between the type of a collection of
1454 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1455 Occasionally this really doesn't work, in which case you can split the
1463 class CollE s => Coll s a where
1464 insert :: s -> a -> s
1474 <sect3 id="class-method-types">
1475 <title>Class method types</title>
1477 Haskell 98 prohibits class method types to mention constraints on the
1478 class type variable, thus:
1481 fromList :: [a] -> s a
1482 elem :: Eq a => a -> s a -> Bool
1484 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1485 contains the constraint <literal>Eq a</literal>, constrains only the
1486 class type variable (in this case <literal>a</literal>).
1489 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1496 <sect2 id="type-restrictions">
1497 <title>Type signatures</title>
1499 <sect3><title>The context of a type signature</title>
1501 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1502 the form <emphasis>(class type-variable)</emphasis> or
1503 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1504 these type signatures are perfectly OK
1507 g :: Ord (T a ()) => ...
1511 GHC imposes the following restrictions on the constraints in a type signature.
1515 forall tv1..tvn (c1, ...,cn) => type
1518 (Here, we write the "foralls" explicitly, although the Haskell source
1519 language omits them; in Haskell 98, all the free type variables of an
1520 explicit source-language type signature are universally quantified,
1521 except for the class type variables in a class declaration. However,
1522 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
1531 <emphasis>Each universally quantified type variable
1532 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1534 A type variable is "reachable" if it it is functionally dependent
1535 (see <xref linkend="functional-dependencies">)
1536 on the type variables free in <literal>type</literal>.
1537 The reason for this is that a value with a type that does not obey
1538 this restriction could not be used without introducing
1540 Here, for example, is an illegal type:
1544 forall a. Eq a => Int
1548 When a value with this type was used, the constraint <literal>Eq tv</literal>
1549 would be introduced where <literal>tv</literal> is a fresh type variable, and
1550 (in the dictionary-translation implementation) the value would be
1551 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1552 can never know which instance of <literal>Eq</literal> to use because we never
1553 get any more information about <literal>tv</literal>.
1560 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1561 universally quantified type variables <literal>tvi</literal></emphasis>.
1563 For example, this type is OK because <literal>C a b</literal> mentions the
1564 universally quantified type variable <literal>b</literal>:
1568 forall a. C a b => burble
1572 The next type is illegal because the constraint <literal>Eq b</literal> does not
1573 mention <literal>a</literal>:
1577 forall a. Eq b => burble
1581 The reason for this restriction is milder than the other one. The
1582 excluded types are never useful or necessary (because the offending
1583 context doesn't need to be witnessed at this point; it can be floated
1584 out). Furthermore, floating them out increases sharing. Lastly,
1585 excluding them is a conservative choice; it leaves a patch of
1586 territory free in case we need it later.
1597 <title>For-all hoisting</title>
1599 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms">) at the right hand
1600 end of an arrow, thus:
1602 type Discard a = forall b. a -> b -> a
1604 g :: Int -> Discard Int
1607 Simply expanding the type synonym would give
1609 g :: Int -> (forall b. Int -> b -> Int)
1611 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1613 g :: forall b. Int -> Int -> b -> Int
1615 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1616 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1617 performs the transformation:</emphasis>
1619 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1621 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1623 (In fact, GHC tries to retain as much synonym information as possible for use in
1624 error messages, but that is a usability issue.) This rule applies, of course, whether
1625 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1626 valid way to write <literal>g</literal>'s type signature:
1628 g :: Int -> Int -> forall b. b -> Int
1632 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1635 type Foo a = (?x::Int) => Bool -> a
1640 g :: (?x::Int) => Bool -> Bool -> Int
1648 <sect2 id="instance-decls">
1649 <title>Instance declarations</title>
1652 <title>Overlapping instances</title>
1654 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1659 instance context1 => C type1 where ...
1660 instance context2 => C type2 where ...
1663 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
1666 However, if you give the command line option
1667 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1668 option</primary></indexterm> then overlapping instance declarations are permitted.
1669 However, GHC arranges never to commit to using an instance declaration
1670 if another instance declaration also applies, either now or later.
1676 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1682 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1683 (but not identical to <literal>type1</literal>), or vice versa.
1687 Notice that these rules
1692 make it clear which instance decl to use
1693 (pick the most specific one that matches)
1700 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1701 Reason: you can pick which instance decl
1702 "matches" based on the type.
1707 However the rules are over-conservative. Two instance declarations can overlap,
1708 but it can still be clear in particular situations which to use. For example:
1710 instance C (Int,a) where ...
1711 instance C (a,Bool) where ...
1713 These are rejected by GHC's rules, but it is clear what to do when trying
1714 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1715 cannot apply. Yell if this restriction bites you.
1718 GHC is also conservative about committing to an overlapping instance. For example:
1720 class C a where { op :: a -> a }
1721 instance C [Int] where ...
1722 instance C a => C [a] where ...
1724 f :: C b => [b] -> [b]
1727 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1728 GHC does not commit to the second instance declaration, because in a paricular
1729 call of f, b might be instantiate to Int, so the first instance declaration
1730 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1731 GHC will instead silently pick the second instance, without complaining about
1732 the problem of subsequent instantiations.
1735 Regrettably, GHC doesn't guarantee to detect overlapping instance
1736 declarations if they appear in different modules. GHC can "see" the
1737 instance declarations in the transitive closure of all the modules
1738 imported by the one being compiled, so it can "see" all instance decls
1739 when it is compiling <literal>Main</literal>. However, it currently chooses not
1740 to look at ones that can't possibly be of use in the module currently
1741 being compiled, in the interests of efficiency. (Perhaps we should
1742 change that decision, at least for <literal>Main</literal>.)
1747 <title>Type synonyms in the instance head</title>
1750 <emphasis>Unlike Haskell 98, instance heads may use type
1751 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1752 As always, using a type synonym is just shorthand for
1753 writing the RHS of the type synonym definition. For example:
1757 type Point = (Int,Int)
1758 instance C Point where ...
1759 instance C [Point] where ...
1763 is legal. However, if you added
1767 instance C (Int,Int) where ...
1771 as well, then the compiler will complain about the overlapping
1772 (actually, identical) instance declarations. As always, type synonyms
1773 must be fully applied. You cannot, for example, write:
1778 instance Monad P where ...
1782 This design decision is independent of all the others, and easily
1783 reversed, but it makes sense to me.
1788 <sect3 id="undecidable-instances">
1789 <title>Undecidable instances</title>
1791 <para>An instance declaration must normally obey the following rules:
1793 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1794 an instance declaration <emphasis>must not</emphasis> be a type variable.
1795 For example, these are OK:
1798 instance C Int a where ...
1800 instance D (Int, Int) where ...
1802 instance E [[a]] where ...
1806 instance F a where ...
1808 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1809 For example, this is OK:
1811 instance Stateful (ST s) (MutVar s) where ...
1818 <para>All of the types in the <emphasis>context</emphasis> of
1819 an instance declaration <emphasis>must</emphasis> be type variables.
1822 instance C a b => Eq (a,b) where ...
1826 instance C Int b => Foo b where ...
1832 These restrictions ensure that
1833 context reduction terminates: each reduction step removes one type
1834 constructor. For example, the following would make the type checker
1835 loop if it wasn't excluded:
1837 instance C a => C a where ...
1839 There are two situations in which the rule is a bit of a pain. First,
1840 if one allows overlapping instance declarations then it's quite
1841 convenient to have a "default instance" declaration that applies if
1842 something more specific does not:
1851 Second, sometimes you might want to use the following to get the
1852 effect of a "class synonym":
1856 class (C1 a, C2 a, C3 a) => C a where { }
1858 instance (C1 a, C2 a, C3 a) => C a where { }
1862 This allows you to write shorter signatures:
1874 f :: (C1 a, C2 a, C3 a) => ...
1878 Voluminous correspondence on the Haskell mailing list has convinced me
1879 that it's worth experimenting with more liberal rules. If you use
1880 the experimental flag <option>-fallow-undecidable-instances</option>
1881 <indexterm><primary>-fallow-undecidable-instances
1882 option</primary></indexterm>, you can use arbitrary
1883 types in both an instance context and instance head. Termination is ensured by having a
1884 fixed-depth recursion stack. If you exceed the stack depth you get a
1885 sort of backtrace, and the opportunity to increase the stack depth
1886 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1889 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1890 allowing these idioms interesting idioms.
1897 <sect2 id="implicit-parameters">
1898 <title>Implicit parameters</title>
1900 <para> Implicit paramters are implemented as described in
1901 "Implicit parameters: dynamic scoping with static types",
1902 J Lewis, MB Shields, E Meijer, J Launchbury,
1903 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1907 <para>(Most of the following, stil rather incomplete, documentation is
1908 due to Jeff Lewis.)</para>
1910 <para>Implicit parameter support is enabled with the option
1911 <option>-fimplicit-params</option>.</para>
1914 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1915 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1916 context. In Haskell, all variables are statically bound. Dynamic
1917 binding of variables is a notion that goes back to Lisp, but was later
1918 discarded in more modern incarnations, such as Scheme. Dynamic binding
1919 can be very confusing in an untyped language, and unfortunately, typed
1920 languages, in particular Hindley-Milner typed languages like Haskell,
1921 only support static scoping of variables.
1924 However, by a simple extension to the type class system of Haskell, we
1925 can support dynamic binding. Basically, we express the use of a
1926 dynamically bound variable as a constraint on the type. These
1927 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1928 function uses a dynamically-bound variable <literal>?x</literal>
1929 of type <literal>t'</literal>". For
1930 example, the following expresses the type of a sort function,
1931 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1933 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1935 The dynamic binding constraints are just a new form of predicate in the type class system.
1938 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1939 where <literal>x</literal> is
1940 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1941 Use of this construct also introduces a new
1942 dynamic-binding constraint in the type of the expression.
1943 For example, the following definition
1944 shows how we can define an implicitly parameterized sort function in
1945 terms of an explicitly parameterized <literal>sortBy</literal> function:
1947 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1949 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1955 <title>Implicit-parameter type constraints</title>
1957 Dynamic binding constraints behave just like other type class
1958 constraints in that they are automatically propagated. Thus, when a
1959 function is used, its implicit parameters are inherited by the
1960 function that called it. For example, our <literal>sort</literal> function might be used
1961 to pick out the least value in a list:
1963 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1964 least xs = fst (sort xs)
1966 Without lifting a finger, the <literal>?cmp</literal> parameter is
1967 propagated to become a parameter of <literal>least</literal> as well. With explicit
1968 parameters, the default is that parameters must always be explicit
1969 propagated. With implicit parameters, the default is to always
1973 An implicit-parameter type constraint differs from other type class constraints in the
1974 following way: All uses of a particular implicit parameter must have
1975 the same type. This means that the type of <literal>(?x, ?x)</literal>
1976 is <literal>(?x::a) => (a,a)</literal>, and not
1977 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1981 <para> You can't have an implicit parameter in the context of a class or instance
1982 declaration. For example, both these declarations are illegal:
1984 class (?x::Int) => C a where ...
1985 instance (?x::a) => Foo [a] where ...
1987 Reason: exactly which implicit parameter you pick up depends on exactly where
1988 you invoke a function. But the ``invocation'' of instance declarations is done
1989 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1990 Easiest thing is to outlaw the offending types.</para>
1992 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1994 f :: (?x :: [a]) => Int -> Int
1997 g :: (Read a, Show a) => String -> String
2000 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2001 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2002 quite unambiguous, and fixes the type <literal>a</literal>.
2007 <title>Implicit-parameter bindings</title>
2010 An implicit parameter is <emphasis>bound</emphasis> using the standard
2011 <literal>let</literal> or <literal>where</literal> binding forms.
2012 For example, we define the <literal>min</literal> function by binding
2013 <literal>cmp</literal>.
2016 min = let ?cmp = (<=) in least
2020 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2021 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2022 (including in a list comprehension, or do-notation, or pattern guards),
2023 or a <literal>where</literal> clause.
2024 Note the following points:
2027 An implicit-parameter binding group must be a
2028 collection of simple bindings to implicit-style variables (no
2029 function-style bindings, and no type signatures); these bindings are
2030 neither polymorphic or recursive.
2033 You may not mix implicit-parameter bindings with ordinary bindings in a
2034 single <literal>let</literal>
2035 expression; use two nested <literal>let</literal>s instead.
2036 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2040 You may put multiple implicit-parameter bindings in a
2041 single binding group; but they are <emphasis>not</emphasis> treated
2042 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2043 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2044 parameter. The bindings are not nested, and may be re-ordered without changing
2045 the meaning of the program.
2046 For example, consider:
2048 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2050 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2051 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2053 f :: (?x::Int) => Int -> Int
2062 <sect2 id="linear-implicit-parameters">
2063 <title>Linear implicit parameters</title>
2065 Linear implicit parameters are an idea developed by Koen Claessen,
2066 Mark Shields, and Simon PJ. They address the long-standing
2067 problem that monads seem over-kill for certain sorts of problem, notably:
2070 <listitem> <para> distributing a supply of unique names </para> </listitem>
2071 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2072 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2076 Linear implicit parameters are just like ordinary implicit parameters,
2077 except that they are "linear" -- that is, they cannot be copied, and
2078 must be explicitly "split" instead. Linear implicit parameters are
2079 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2080 (The '/' in the '%' suggests the split!)
2085 import GHC.Exts( Splittable )
2087 data NameSupply = ...
2089 splitNS :: NameSupply -> (NameSupply, NameSupply)
2090 newName :: NameSupply -> Name
2092 instance Splittable NameSupply where
2096 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2097 f env (Lam x e) = Lam x' (f env e)
2100 env' = extend env x x'
2101 ...more equations for f...
2103 Notice that the implicit parameter %ns is consumed
2105 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2106 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2110 So the translation done by the type checker makes
2111 the parameter explicit:
2113 f :: NameSupply -> Env -> Expr -> Expr
2114 f ns env (Lam x e) = Lam x' (f ns1 env e)
2116 (ns1,ns2) = splitNS ns
2118 env = extend env x x'
2120 Notice the call to 'split' introduced by the type checker.
2121 How did it know to use 'splitNS'? Because what it really did
2122 was to introduce a call to the overloaded function 'split',
2123 defined by the class <literal>Splittable</literal>:
2125 class Splittable a where
2128 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2129 split for name supplies. But we can simply write
2135 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2137 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2138 <literal>GHC.Exts</literal>.
2143 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2144 are entirely distinct implicit parameters: you
2145 can use them together and they won't intefere with each other. </para>
2148 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2150 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2151 in the context of a class or instance declaration. </para></listitem>
2155 <sect3><title>Warnings</title>
2158 The monomorphism restriction is even more important than usual.
2159 Consider the example above:
2161 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2162 f env (Lam x e) = Lam x' (f env e)
2165 env' = extend env x x'
2167 If we replaced the two occurrences of x' by (newName %ns), which is
2168 usually a harmless thing to do, we get:
2170 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2171 f env (Lam x e) = Lam (newName %ns) (f env e)
2173 env' = extend env x (newName %ns)
2175 But now the name supply is consumed in <emphasis>three</emphasis> places
2176 (the two calls to newName,and the recursive call to f), so
2177 the result is utterly different. Urk! We don't even have
2181 Well, this is an experimental change. With implicit
2182 parameters we have already lost beta reduction anyway, and
2183 (as John Launchbury puts it) we can't sensibly reason about
2184 Haskell programs without knowing their typing.
2189 <sect3><title>Recursive functions</title>
2190 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2193 foo :: %x::T => Int -> [Int]
2195 foo n = %x : foo (n-1)
2197 where T is some type in class Splittable.</para>
2199 Do you get a list of all the same T's or all different T's
2200 (assuming that split gives two distinct T's back)?
2202 If you supply the type signature, taking advantage of polymorphic
2203 recursion, you get what you'd probably expect. Here's the
2204 translated term, where the implicit param is made explicit:
2207 foo x n = let (x1,x2) = split x
2208 in x1 : foo x2 (n-1)
2210 But if you don't supply a type signature, GHC uses the Hindley
2211 Milner trick of using a single monomorphic instance of the function
2212 for the recursive calls. That is what makes Hindley Milner type inference
2213 work. So the translation becomes
2217 foom n = x : foom (n-1)
2221 Result: 'x' is not split, and you get a list of identical T's. So the
2222 semantics of the program depends on whether or not foo has a type signature.
2225 You may say that this is a good reason to dislike linear implicit parameters
2226 and you'd be right. That is why they are an experimental feature.
2232 <sect2 id="functional-dependencies">
2233 <title>Functional dependencies
2236 <para> Functional dependencies are implemented as described by Mark Jones
2237 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2238 In Proceedings of the 9th European Symposium on Programming,
2239 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2243 Functional dependencies are introduced by a vertical bar in the syntax of a
2244 class declaration; e.g.
2246 class (Monad m) => MonadState s m | m -> s where ...
2248 class Foo a b c | a b -> c where ...
2250 There should be more documentation, but there isn't (yet). Yell if you need it.
2256 <sect2 id="sec-kinding">
2257 <title>Explicitly-kinded quantification</title>
2260 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2261 to give the kind explicitly as (machine-checked) documentation,
2262 just as it is nice to give a type signature for a function. On some occasions,
2263 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2264 John Hughes had to define the data type:
2266 data Set cxt a = Set [a]
2267 | Unused (cxt a -> ())
2269 The only use for the <literal>Unused</literal> constructor was to force the correct
2270 kind for the type variable <literal>cxt</literal>.
2273 GHC now instead allows you to specify the kind of a type variable directly, wherever
2274 a type variable is explicitly bound. Namely:
2276 <listitem><para><literal>data</literal> declarations:
2278 data Set (cxt :: * -> *) a = Set [a]
2279 </Screen></para></listitem>
2280 <listitem><para><literal>type</literal> declarations:
2282 type T (f :: * -> *) = f Int
2283 </Screen></para></listitem>
2284 <listitem><para><literal>class</literal> declarations:
2286 class (Eq a) => C (f :: * -> *) a where ...
2287 </Screen></para></listitem>
2288 <listitem><para><literal>forall</literal>'s in type signatures:
2290 f :: forall (cxt :: * -> *). Set cxt Int
2291 </Screen></para></listitem>
2296 The parentheses are required. Some of the spaces are required too, to
2297 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2298 will get a parse error, because "<literal>::*->*</literal>" is a
2299 single lexeme in Haskell.
2303 As part of the same extension, you can put kind annotations in types
2306 f :: (Int :: *) -> Int
2307 g :: forall a. a -> (a :: *)
2311 atype ::= '(' ctype '::' kind ')
2313 The parentheses are required.
2318 <sect2 id="universal-quantification">
2319 <title>Arbitrary-rank polymorphism
2323 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2324 allows us to say exactly what this means. For example:
2332 g :: forall b. (b -> b)
2334 The two are treated identically.
2338 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2339 explicit universal quantification in
2341 For example, all the following types are legal:
2343 f1 :: forall a b. a -> b -> a
2344 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2346 f2 :: (forall a. a->a) -> Int -> Int
2347 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2349 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2351 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2352 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2353 The <literal>forall</literal> makes explicit the universal quantification that
2354 is implicitly added by Haskell.
2357 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2358 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2359 shows, the polymorphic type on the left of the function arrow can be overloaded.
2362 The function <literal>f3</literal> has a rank-3 type;
2363 it has rank-2 types on the left of a function arrow.
2366 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2367 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2368 that restriction has now been lifted.)
2369 In particular, a forall-type (also called a "type scheme"),
2370 including an operational type class context, is legal:
2372 <listitem> <para> On the left of a function arrow </para> </listitem>
2373 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
2374 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2375 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2376 field type signatures.</para> </listitem>
2377 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2378 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
2380 There is one place you cannot put a <literal>forall</literal>:
2381 you cannot instantiate a type variable with a forall-type. So you cannot
2382 make a forall-type the argument of a type constructor. So these types are illegal:
2384 x1 :: [forall a. a->a]
2385 x2 :: (forall a. a->a, Int)
2386 x3 :: Maybe (forall a. a->a)
2388 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2389 a type variable any more!
2398 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2399 the types of the constructor arguments. Here are several examples:
2405 data T a = T1 (forall b. b -> b -> b) a
2407 data MonadT m = MkMonad { return :: forall a. a -> m a,
2408 bind :: forall a b. m a -> (a -> m b) -> m b
2411 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2417 The constructors have rank-2 types:
2423 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2424 MkMonad :: forall m. (forall a. a -> m a)
2425 -> (forall a b. m a -> (a -> m b) -> m b)
2427 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2433 Notice that you don't need to use a <literal>forall</literal> if there's an
2434 explicit context. For example in the first argument of the
2435 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2436 prefixed to the argument type. The implicit <literal>forall</literal>
2437 quantifies all type variables that are not already in scope, and are
2438 mentioned in the type quantified over.
2442 As for type signatures, implicit quantification happens for non-overloaded
2443 types too. So if you write this:
2446 data T a = MkT (Either a b) (b -> b)
2449 it's just as if you had written this:
2452 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2455 That is, since the type variable <literal>b</literal> isn't in scope, it's
2456 implicitly universally quantified. (Arguably, it would be better
2457 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2458 where that is what is wanted. Feedback welcomed.)
2462 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2463 the constructor to suitable values, just as usual. For example,
2474 a3 = MkSwizzle reverse
2477 a4 = let r x = Just x
2484 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2485 mkTs f x y = [T1 f x, T1 f y]
2491 The type of the argument can, as usual, be more general than the type
2492 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2493 does not need the <literal>Ord</literal> constraint.)
2497 When you use pattern matching, the bound variables may now have
2498 polymorphic types. For example:
2504 f :: T a -> a -> (a, Char)
2505 f (T1 w k) x = (w k x, w 'c' 'd')
2507 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2508 g (MkSwizzle s) xs f = s (map f (s xs))
2510 h :: MonadT m -> [m a] -> m [a]
2511 h m [] = return m []
2512 h m (x:xs) = bind m x $ \y ->
2513 bind m (h m xs) $ \ys ->
2520 In the function <function>h</function> we use the record selectors <literal>return</literal>
2521 and <literal>bind</literal> to extract the polymorphic bind and return functions
2522 from the <literal>MonadT</literal> data structure, rather than using pattern
2528 <title>Type inference</title>
2531 In general, type inference for arbitrary-rank types is undecideable.
2532 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2533 to get a decidable algorithm by requiring some help from the programmer.
2534 We do not yet have a formal specification of "some help" but the rule is this:
2537 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2538 provides an explicit polymorphic type for x, or GHC's type inference will assume
2539 that x's type has no foralls in it</emphasis>.
2542 What does it mean to "provide" an explicit type for x? You can do that by
2543 giving a type signature for x directly, using a pattern type signature
2544 (<xref linkend="scoped-type-variables">), thus:
2546 \ f :: (forall a. a->a) -> (f True, f 'c')
2548 Alternatively, you can give a type signature to the enclosing
2549 context, which GHC can "push down" to find the type for the variable:
2551 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2553 Here the type signature on the expression can be pushed inwards
2554 to give a type signature for f. Similarly, and more commonly,
2555 one can give a type signature for the function itself:
2557 h :: (forall a. a->a) -> (Bool,Char)
2558 h f = (f True, f 'c')
2560 You don't need to give a type signature if the lambda bound variable
2561 is a constructor argument. Here is an example we saw earlier:
2563 f :: T a -> a -> (a, Char)
2564 f (T1 w k) x = (w k x, w 'c' 'd')
2566 Here we do not need to give a type signature to <literal>w</literal>, because
2567 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2574 <sect3 id="implicit-quant">
2575 <title>Implicit quantification</title>
2578 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2579 user-written types, if and only if there is no explicit <literal>forall</literal>,
2580 GHC finds all the type variables mentioned in the type that are not already
2581 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2585 f :: forall a. a -> a
2592 h :: forall b. a -> b -> b
2598 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2601 f :: (a -> a) -> Int
2603 f :: forall a. (a -> a) -> Int
2605 f :: (forall a. a -> a) -> Int
2608 g :: (Ord a => a -> a) -> Int
2609 -- MEANS the illegal type
2610 g :: forall a. (Ord a => a -> a) -> Int
2612 g :: (forall a. Ord a => a -> a) -> Int
2614 The latter produces an illegal type, which you might think is silly,
2615 but at least the rule is simple. If you want the latter type, you
2616 can write your for-alls explicitly. Indeed, doing so is strongly advised
2625 <sect2 id="scoped-type-variables">
2626 <title>Scoped type variables
2630 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2631 variable</emphasis>. For example
2637 f (xs::[a]) = ys ++ ys
2646 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2647 This brings the type variable <literal>a</literal> into scope; it scopes over
2648 all the patterns and right hand sides for this equation for <function>f</function>.
2649 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2653 Pattern type signatures are completely orthogonal to ordinary, separate
2654 type signatures. The two can be used independently or together.
2655 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2656 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2657 implicitly universally quantified. (If there are no type variables in
2658 scope, all type variables mentioned in the signature are universally
2659 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2660 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2661 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2662 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2663 it becomes possible to do so.
2667 Scoped type variables are implemented in both GHC and Hugs. Where the
2668 implementations differ from the specification below, those differences
2673 So much for the basic idea. Here are the details.
2677 <title>What a pattern type signature means</title>
2679 A type variable brought into scope by a pattern type signature is simply
2680 the name for a type. The restriction they express is that all occurrences
2681 of the same name mean the same type. For example:
2683 f :: [Int] -> Int -> Int
2684 f (xs::[a]) (y::a) = (head xs + y) :: a
2686 The pattern type signatures on the left hand side of
2687 <literal>f</literal> express the fact that <literal>xs</literal>
2688 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2689 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2690 specifies that this expression must have the same type <literal>a</literal>.
2691 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2692 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2693 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2694 rules, which specified that a pattern-bound type variable should be universally quantified.)
2695 For example, all of these are legal:</para>
2698 t (x::a) (y::a) = x+y*2
2700 f (x::a) (y::b) = [x,y] -- a unifies with b
2702 g (x::a) = x + 1::Int -- a unifies with Int
2704 h x = let k (y::a) = [x,y] -- a is free in the
2705 in k x -- environment
2707 k (x::a) True = ... -- a unifies with Int
2708 k (x::Int) False = ...
2711 w (x::a) = x -- a unifies with [b]
2717 <title>Scope and implicit quantification</title>
2725 All the type variables mentioned in a pattern,
2726 that are not already in scope,
2727 are brought into scope by the pattern. We describe this set as
2728 the <emphasis>type variables bound by the pattern</emphasis>.
2731 f (x::a) = let g (y::(a,b)) = fst y
2735 The pattern <literal>(x::a)</literal> brings the type variable
2736 <literal>a</literal> into scope, as well as the term
2737 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2738 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2739 and brings into scope the type variable <literal>b</literal>.
2745 The type variable(s) bound by the pattern have the same scope
2746 as the term variable(s) bound by the pattern. For example:
2749 f (x::a) = <...rhs of f...>
2750 (p::b, q::b) = (1,2)
2751 in <...body of let...>
2753 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2754 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2755 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2756 just like <literal>p</literal> and <literal>q</literal> do.
2757 Indeed, the newly bound type variables also scope over any ordinary, separate
2758 type signatures in the <literal>let</literal> group.
2765 The type variables bound by the pattern may be
2766 mentioned in ordinary type signatures or pattern
2767 type signatures anywhere within their scope.
2774 In ordinary type signatures, any type variable mentioned in the
2775 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2783 Ordinary type signatures do not bring any new type variables
2784 into scope (except in the type signature itself!). So this is illegal:
2791 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2792 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2793 and that is an incorrect typing.
2800 The pattern type signature is a monotype:
2805 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2809 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2810 not to type schemes.
2814 There is no implicit universal quantification on pattern type signatures (in contrast to
2815 ordinary type signatures).
2825 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2826 scope over the methods defined in the <literal>where</literal> part. For example:
2840 (Not implemented in Hugs yet, Dec 98).
2851 <title>Where a pattern type signature can occur</title>
2854 A pattern type signature can occur in any pattern. For example:
2859 A pattern type signature can be on an arbitrary sub-pattern, not
2864 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2873 Pattern type signatures, including the result part, can be used
2874 in lambda abstractions:
2877 (\ (x::a, y) :: a -> x)
2884 Pattern type signatures, including the result part, can be used
2885 in <literal>case</literal> expressions:
2889 case e of { (x::a, y) :: a -> x }
2897 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2898 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2899 token or a parenthesised type of some sort). To see why,
2900 consider how one would parse this:
2914 Pattern type signatures can bind existential type variables.
2919 data T = forall a. MkT [a]
2922 f (MkT [t::a]) = MkT t3
2935 Pattern type signatures
2936 can be used in pattern bindings:
2939 f x = let (y, z::a) = x in ...
2940 f1 x = let (y, z::Int) = x in ...
2941 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2942 f3 :: (b->b) = \x -> x
2945 In all such cases, the binding is not generalised over the pattern-bound
2946 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2947 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2948 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2949 In contrast, the binding
2954 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2955 in <literal>f4</literal>'s scope.
2965 <title>Result type signatures</title>
2968 The result type of a function can be given a signature, thus:
2972 f (x::a) :: [a] = [x,x,x]
2976 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2977 result type. Sometimes this is the only way of naming the type variable
2982 f :: Int -> [a] -> [a]
2983 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2984 in \xs -> map g (reverse xs `zip` xs)
2989 The type variables bound in a result type signature scope over the right hand side
2990 of the definition. However, consider this corner-case:
2992 rev1 :: [a] -> [a] = \xs -> reverse xs
2994 foo ys = rev (ys::[a])
2996 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2997 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2998 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2999 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3000 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3003 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3004 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3008 rev1 :: [a] -> [a] = \xs -> reverse xs
3013 Result type signatures are not yet implemented in Hugs.
3020 <sect2 id="deriving-typeable">
3021 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3024 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3025 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3026 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3027 classes <literal>Eq</literal>, <literal>Ord</literal>,
3028 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3031 GHC extends this list with two more classes that may be automatically derived
3032 (provided the <option>-fglasgow-exts</option> flag is specified):
3033 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3034 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3035 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3039 <sect2 id="newtype-deriving">
3040 <title>Generalised derived instances for newtypes</title>
3043 When you define an abstract type using <literal>newtype</literal>, you may want
3044 the new type to inherit some instances from its representation. In
3045 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3046 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3047 other classes you have to write an explicit instance declaration. For
3048 example, if you define
3051 newtype Dollars = Dollars Int
3054 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3055 explicitly define an instance of <literal>Num</literal>:
3058 instance Num Dollars where
3059 Dollars a + Dollars b = Dollars (a+b)
3062 All the instance does is apply and remove the <literal>newtype</literal>
3063 constructor. It is particularly galling that, since the constructor
3064 doesn't appear at run-time, this instance declaration defines a
3065 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3066 dictionary, only slower!
3070 <sect3> <title> Generalising the deriving clause </title>
3072 GHC now permits such instances to be derived instead, so one can write
3074 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3077 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3078 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3079 derives an instance declaration of the form
3082 instance Num Int => Num Dollars
3085 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3089 We can also derive instances of constructor classes in a similar
3090 way. For example, suppose we have implemented state and failure monad
3091 transformers, such that
3094 instance Monad m => Monad (State s m)
3095 instance Monad m => Monad (Failure m)
3097 In Haskell 98, we can define a parsing monad by
3099 type Parser tok m a = State [tok] (Failure m) a
3102 which is automatically a monad thanks to the instance declarations
3103 above. With the extension, we can make the parser type abstract,
3104 without needing to write an instance of class <literal>Monad</literal>, via
3107 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3110 In this case the derived instance declaration is of the form
3112 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3115 Notice that, since <literal>Monad</literal> is a constructor class, the
3116 instance is a <emphasis>partial application</emphasis> of the new type, not the
3117 entire left hand side. We can imagine that the type declaration is
3118 ``eta-converted'' to generate the context of the instance
3123 We can even derive instances of multi-parameter classes, provided the
3124 newtype is the last class parameter. In this case, a ``partial
3125 application'' of the class appears in the <literal>deriving</literal>
3126 clause. For example, given the class
3129 class StateMonad s m | m -> s where ...
3130 instance Monad m => StateMonad s (State s m) where ...
3132 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3134 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3135 deriving (Monad, StateMonad [tok])
3138 The derived instance is obtained by completing the application of the
3139 class to the new type:
3142 instance StateMonad [tok] (State [tok] (Failure m)) =>
3143 StateMonad [tok] (Parser tok m)
3148 As a result of this extension, all derived instances in newtype
3149 declarations are treated uniformly (and implemented just by reusing
3150 the dictionary for the representation type), <emphasis>except</emphasis>
3151 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3152 the newtype and its representation.
3156 <sect3> <title> A more precise specification </title>
3158 Derived instance declarations are constructed as follows. Consider the
3159 declaration (after expansion of any type synonyms)
3162 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3168 <literal>S</literal> is a type constructor,
3171 The <literal>t1...tk</literal> are types,
3174 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3175 the <literal>ti</literal>, and
3178 The <literal>ci</literal> are partial applications of
3179 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3180 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3183 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3184 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3185 should not "look through" the type or its constructor. You can still
3186 derive these classes for a newtype, but it happens in the usual way, not
3187 via this new mechanism.
3190 Then, for each <literal>ci</literal>, the derived instance
3193 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3195 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3196 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3200 As an example which does <emphasis>not</emphasis> work, consider
3202 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3204 Here we cannot derive the instance
3206 instance Monad (State s m) => Monad (NonMonad m)
3209 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3210 and so cannot be "eta-converted" away. It is a good thing that this
3211 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3212 not, in fact, a monad --- for the same reason. Try defining
3213 <literal>>>=</literal> with the correct type: you won't be able to.
3217 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3218 important, since we can only derive instances for the last one. If the
3219 <literal>StateMonad</literal> class above were instead defined as
3222 class StateMonad m s | m -> s where ...
3225 then we would not have been able to derive an instance for the
3226 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3227 classes usually have one "main" parameter for which deriving new
3228 instances is most interesting.
3236 <!-- ==================== End of type system extensions ================= -->
3238 <!-- ====================== TEMPLATE HASKELL ======================= -->
3240 <sect1 id="template-haskell">
3241 <title>Template Haskell</title>
3243 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3244 Template Haskell at <ulink url="http://www.haskell.org/th/">
3245 http://www.haskell.org/th/</ulink>, while
3247 the main technical innovations is discussed in "<ulink
3248 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3249 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3250 The details of the Template Haskell design are still in flux. Make sure you
3251 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3252 (search for the type ExpQ).
3253 [Temporary: many changes to the original design are described in
3254 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3255 Not all of these changes are in GHC 6.2.]
3258 <para> The first example from that paper is set out below as a worked example to help get you started.
3262 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3263 Tim Sheard is going to expand it.)
3267 <title>Syntax</title>
3269 <para> Template Haskell has the following new syntactic
3270 constructions. You need to use the flag
3271 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3272 </indexterm>to switch these syntactic extensions on
3273 (<option>-fth</option> is currently implied by
3274 <option>-fglasgow-exts</option>, but you are encouraged to
3275 specify it explicitly).</para>
3279 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3280 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3281 There must be no space between the "$" and the identifier or parenthesis. This use
3282 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3283 of "." as an infix operator. If you want the infix operator, put spaces around it.
3285 <para> A splice can occur in place of
3287 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3288 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3289 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3291 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3292 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3298 A expression quotation is written in Oxford brackets, thus:
3300 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3301 the quotation has type <literal>Expr</literal>.</para></listitem>
3302 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3303 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3304 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3305 the quotation has type <literal>Type</literal>.</para></listitem>
3306 </itemizedlist></para></listitem>
3309 Reification is written thus:
3311 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3312 has type <literal>Dec</literal>. </para></listitem>
3313 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3314 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3315 <listitem><para> Still to come: fixities </para></listitem>
3317 </itemizedlist></para>
3324 <sect2> <title> Using Template Haskell </title>
3328 The data types and monadic constructor functions for Template Haskell are in the library
3329 <literal>Language.Haskell.THSyntax</literal>.
3333 You can only run a function at compile time if it is imported from another module. That is,
3334 you can't define a function in a module, and call it from within a splice in the same module.
3335 (It would make sense to do so, but it's hard to implement.)
3339 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3342 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3343 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3344 compiles and runs a program, and then looks at the result. So it's important that
3345 the program it compiles produces results whose representations are identical to
3346 those of the compiler itself.
3350 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3351 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3356 <sect2> <title> A Template Haskell Worked Example </title>
3357 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3358 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3365 -- Import our template "pr"
3366 import Printf ( pr )
3368 -- The splice operator $ takes the Haskell source code
3369 -- generated at compile time by "pr" and splices it into
3370 -- the argument of "putStrLn".
3371 main = putStrLn ( $(pr "Hello") )
3377 -- Skeletal printf from the paper.
3378 -- It needs to be in a separate module to the one where
3379 -- you intend to use it.
3381 -- Import some Template Haskell syntax
3382 import Language.Haskell.THSyntax
3384 -- Describe a format string
3385 data Format = D | S | L String
3387 -- Parse a format string. This is left largely to you
3388 -- as we are here interested in building our first ever
3389 -- Template Haskell program and not in building printf.
3390 parse :: String -> [Format]
3393 -- Generate Haskell source code from a parsed representation
3394 -- of the format string. This code will be spliced into
3395 -- the module which calls "pr", at compile time.
3396 gen :: [Format] -> ExpQ
3397 gen [D] = [| \n -> show n |]
3398 gen [S] = [| \s -> s |]
3399 gen [L s] = stringE s
3401 -- Here we generate the Haskell code for the splice
3402 -- from an input format string.
3403 pr :: String -> ExpQ
3404 pr s = gen (parse s)
3407 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3410 $ ghc --make -fth main.hs -o main.exe
3413 <para>Run "main.exe" and here is your output:</para>
3424 <!-- ===================== Arrow notation =================== -->
3426 <sect1 id="arrow-notation">
3427 <title>Arrow notation
3430 <para>Arrows are a generalization of monads introduced by John Hughes.
3431 For more details, see
3436 “Generalising Monads to Arrows”,
3437 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3438 pp67–111, May 2000.
3444 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3445 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3451 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3452 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3458 and the arrows web page at
3459 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3460 With the <option>-farrows</option> flag, GHC supports the arrow
3461 notation described in the second of these papers.
3462 What follows is a brief introduction to the notation;
3463 it won't make much sense unless you've read Hughes's paper.
3464 This notation is translated to ordinary Haskell,
3465 using combinators from the
3466 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3470 <para>The extension adds a new kind of expression for defining arrows,
3471 of the form <literal>proc pat -> cmd</literal>,
3472 where <literal>proc</literal> is a new keyword.
3473 The variables of the pattern are bound in the body of the
3474 <literal>proc</literal>-expression,
3475 which is a new sort of thing called a <firstterm>command</firstterm>.
3476 The syntax of commands is as follows:
3478 cmd ::= exp1 -< exp2
3479 | exp1 -<< exp2
3480 | do { cstmt1 .. cstmtn ; cmd }
3482 | if exp then cmd1 else cmd2
3483 | case exp of { calts }
3485 | (| aexp cmd1 .. cmdn |)
3486 | \ pat1 .. patn -> cmd
3492 | rec { cstmt1 .. cstmtn }
3495 Commands produce values, but (like monadic computations)
3496 may yield more than one value,
3497 or none, and may do other things as well.
3498 For the most part, familiarity with monadic notation is a good guide to
3500 However the values of expressions, even monadic ones,
3501 are determined by the values of the variables they contain;
3502 this is not necessarily the case for commands.
3506 A simple example of the new notation is the expression
3508 proc x -> f -< x+1
3510 We call this a <firstterm>procedure</firstterm> or
3511 <firstterm>arrow abstraction</firstterm>.
3512 As with a lambda expression, the variable <literal>x</literal>
3513 is a new variable bound within the <literal>proc</literal>-expression.
3514 It refers to the input to the arrow.
3515 In the above example, <literal>-<</literal> is not an identifier but an
3516 new reserved symbol used for building commands from an expression of arrow
3517 type and an expression to be fed as input to that arrow.
3518 (The weird look will make more sense later.)
3519 It may be read as analogue of application for arrows.
3520 The above example is equivalent to the Haskell expression
3522 arr (\ x -> x+1) >>> f
3524 That would make no sense if the expression to the left of
3525 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3526 More generally, the expression to the left of <literal>-<</literal>
3527 may not involve any <firstterm>local variable</firstterm>,
3528 i.e. a variable bound in the current arrow abstraction.
3529 For such a situation there is a variant <literal>-<<</literal>, as in
3531 proc x -> f x -<< x+1
3533 which is equivalent to
3535 arr (\ x -> (f, x+1)) >>> app
3537 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3539 Such an arrow is equivalent to a monad, so if you're using this form
3540 you may find a monadic formulation more convenient.
3544 <title>do-notation for commands</title>
3547 Another form of command is a form of <literal>do</literal>-notation.
3548 For example, you can write
3557 You can read this much like ordinary <literal>do</literal>-notation,
3558 but with commands in place of monadic expressions.
3559 The first line sends the value of <literal>x+1</literal> as an input to
3560 the arrow <literal>f</literal>, and matches its output against
3561 <literal>y</literal>.
3562 In the next line, the output is discarded.
3563 The arrow <literal>returnA</literal> is defined in the
3564 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3565 module as <literal>arr id</literal>.
3566 The above example is treated as an abbreviation for
3568 arr (\ x -> (x, x)) >>>
3569 first (arr (\ x -> x+1) >>> f) >>>
3570 arr (\ (y, x) -> (y, (x, y))) >>>
3571 first (arr (\ y -> 2*y) >>> g) >>>
3573 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3574 first (arr (\ (x, z) -> x*z) >>> h) >>>
3575 arr (\ (t, z) -> t+z) >>>
3578 Note that variables not used later in the composition are projected out.
3579 After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
3581 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3582 module, this reduces to
3584 arr (\ x -> (x+1, x)) >>>
3586 arr (\ (y, x) -> (2*y, (x, y))) >>>
3588 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3590 arr (\ (t, z) -> t+z)
3592 which is what you might have written by hand.
3593 With arrow notation, GHC keeps track of all those tuples of variables for you.
3597 Note that although the above translation suggests that
3598 <literal>let</literal>-bound variables like <literal>z</literal> must be
3599 monomorphic, the actual translation produces Core,
3600 so polymorphic variables are allowed.
3604 It's also possible to have mutually recursive bindings,
3605 using the new <literal>rec</literal> keyword, as in the following example:
3607 counter :: ArrowCircuit a => a Bool Int
3608 counter = proc reset -> do
3609 rec output <- returnA -< if reset then 0 else next
3610 next <- delay 0 -< output+1
3611 returnA -< output
3613 The translation of such forms uses the <literal>loop</literal> combinator,
3614 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3620 <title>Conditional commands</title>
3623 In the previous example, we used a conditional expression to construct the
3625 Sometimes we want to conditionally execute different commands, as in
3632 which is translated to
3634 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3635 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3637 Since the translation uses <literal>|||</literal>,
3638 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3642 There are also <literal>case</literal> commands, like
3648 y <- h -< (x1, x2)
3652 The syntax is the same as for <literal>case</literal> expressions,
3653 except that the bodies of the alternatives are commands rather than expressions.
3654 The translation is similar to that of <literal>if</literal> commands.
3660 <title>Defining your own control structures</title>
3663 As we're seen, arrow notation provides constructs,
3664 modelled on those for expressions,
3665 for sequencing, value recursion and conditionals.
3666 But suitable combinators,
3667 which you can define in ordinary Haskell,
3668 may also be used to build new commands out of existing ones.
3669 The basic idea is that a command defines an arrow from environments to values.
3670 These environments assign values to the free local variables of the command.
3671 Thus combinators that produce arrows from arrows
3672 may also be used to build commands from commands.
3673 For example, the <literal>ArrowChoice</literal> class includes a combinator
3675 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3677 so we can use it to build commands:
3682 symbol Plus -< ()
3683 y <- term -< ()
3686 symbol Minus -< ()
3687 y <- term -< ()
3690 This is equivalent to
3692 expr' = (proc x -> returnA -< x)
3693 <+> (proc x -> do
3694 symbol Plus -< ()
3695 y <- term -< ()
3697 <+> (proc x -> do
3698 symbol Minus -< ()
3699 y <- term -< ()
3702 It is essential that this operator be polymorphic in <literal>e</literal>
3703 (representing the environment input to the command
3704 and thence to its subcommands)
3705 and satisfy the corresponding naturality property
3707 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3709 at least for strict <literal>k</literal>.
3710 (This should be automatic if you're not using <literal>seq</literal>.)
3711 This ensures that environments seen by the subcommands are environments
3712 of the whole command,
3713 and also allows the translation to safely trim these environments.
3714 The operator must also not use any variable defined within the current
3719 We could define our own operator
3721 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3722 untilA body cond = proc x ->
3723 if cond x then returnA -< ()
3726 untilA body cond -< x
3728 and use it in the same way.
3729 Of course this infix syntax only makes sense for binary operators;
3730 there is also a more general syntax involving special brackets:
3734 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3741 <title>Primitive constructs</title>
3744 Some operators will need to pass additional inputs to their subcommands.
3745 For example, in an arrow type supporting exceptions,
3746 the operator that attaches an exception handler will wish to pass the
3747 exception that occurred to the handler.
3748 Such an operator might have a type
3750 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3752 where <literal>Ex</literal> is the type of exceptions handled.
3753 You could then use this with arrow notation by writing a command
3755 body `handleA` \ ex -> handler
3757 so that if an exception is raised in the command <literal>body</literal>,
3758 the variable <literal>ex</literal> is bound to the value of the exception
3759 and the command <literal>handler</literal>,
3760 which typically refers to <literal>ex</literal>, is entered.
3761 Though the syntax here looks like a functional lambda,
3762 we are talking about commands, and something different is going on.
3763 The input to the arrow represented by a command consists of values for
3764 the free local variables in the command, plus a stack of anonymous values.
3765 In all the prior examples, this stack was empty.
3766 In the second argument to <literal>handleA</literal>,
3767 this stack consists of one value, the value of the exception.
3768 The command form of lambda merely gives this value a name.
3773 the values on the stack are paired to the right of the environment.
3774 So when designing operators like <literal>handleA</literal> that pass
3775 extra inputs to their subcommands,
3776 More precisely, the type of each argument of the operator (and its result)
3777 should have the form
3779 a (...(e,t1), ... tn) t
3781 where <replaceable>e</replaceable> is a polymorphic variable
3782 (representing the environment)
3783 and <replaceable>ti</replaceable> are the types of the values on the stack,
3784 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3785 The polymorphic variable <replaceable>e</replaceable> must not occur in
3786 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3787 <replaceable>t</replaceable>.
3788 However the arrows involved need not be the same.
3789 Here are some more examples of suitable operators:
3791 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3792 runReader :: ... => a e c -> a' (e,State) c
3793 runState :: ... => a e c -> a' (e,State) (c,State)
3795 We can supply the extra input required by commands built with the last two
3796 by applying them to ordinary expressions, as in
3800 (|runReader (do { ... })|) s
3802 which adds <literal>s</literal> to the stack of inputs to the command
3803 built using <literal>runReader</literal>.
3807 The command versions of lambda abstraction and application are analogous to
3808 the expression versions.
3809 In particular, the beta and eta rules describe equivalences of commands.
3810 These three features (operators, lambda abstraction and application)
3811 are the core of the notation; everything else can be built using them,
3812 though the results would be somewhat clumsy.
3813 For example, we could simulate <literal>do</literal>-notation by defining
3815 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3816 u `bind` f = returnA &&& u >>> f
3818 bind_ :: Arrow a => a e b -> a e c -> a e c
3819 u `bind_` f = u `bind` (arr fst >>> f)
3821 We could simulate <literal>do</literal> by defining
3823 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3824 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3831 <title>Differences with the paper</title>
3836 <para>Instead of a single form of arrow application (arrow tail) with two
3837 translations, the implementation provides two forms
3838 <quote><literal>-<</literal></quote> (first-order)
3839 and <quote><literal>-<<</literal></quote> (higher-order).
3844 <para>User-defined operators are flagged with banana brackets instead of
3845 a new <literal>form</literal> keyword.
3854 <title>Portability</title>
3857 Although only GHC implements arrow notation directly,
3858 there is also a preprocessor
3860 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
3861 that translates arrow notation into Haskell 98
3862 for use with other Haskell systems.
3863 You would still want to check arrow programs with GHC;
3864 tracing type errors in the preprocessor output is not easy.
3865 Modules intended for both GHC and the preprocessor must observe some
3866 additional restrictions:
3871 The module must import
3872 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3878 The preprocessor cannot cope with other Haskell extensions.
3879 These would have to go in separate modules.
3885 Because the preprocessor targets Haskell (rather than Core),
3886 <literal>let</literal>-bound variables are monomorphic.
3897 <!-- ==================== ASSERTIONS ================= -->
3899 <sect1 id="sec-assertions">
3901 <indexterm><primary>Assertions</primary></indexterm>
3905 If you want to make use of assertions in your standard Haskell code, you
3906 could define a function like the following:
3912 assert :: Bool -> a -> a
3913 assert False x = error "assertion failed!"
3920 which works, but gives you back a less than useful error message --
3921 an assertion failed, but which and where?
3925 One way out is to define an extended <function>assert</function> function which also
3926 takes a descriptive string to include in the error message and
3927 perhaps combine this with the use of a pre-processor which inserts
3928 the source location where <function>assert</function> was used.
3932 Ghc offers a helping hand here, doing all of this for you. For every
3933 use of <function>assert</function> in the user's source:
3939 kelvinToC :: Double -> Double
3940 kelvinToC k = assert (k >= 0.0) (k+273.15)
3946 Ghc will rewrite this to also include the source location where the
3953 assert pred val ==> assertError "Main.hs|15" pred val
3959 The rewrite is only performed by the compiler when it spots
3960 applications of <function>Control.Exception.assert</function>, so you
3961 can still define and use your own versions of
3962 <function>assert</function>, should you so wish. If not, import
3963 <literal>Control.Exception</literal> to make use
3964 <function>assert</function> in your code.
3968 To have the compiler ignore uses of assert, use the compiler option
3969 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3970 option</primary></indexterm> That is, expressions of the form
3971 <literal>assert pred e</literal> will be rewritten to
3972 <literal>e</literal>.
3976 Assertion failures can be caught, see the documentation for the
3977 <literal>Control.Exception</literal> library for the details.
3983 <!-- =============================== PRAGMAS =========================== -->
3985 <sect1 id="pragmas">
3986 <title>Pragmas</title>
3988 <indexterm><primary>pragma</primary></indexterm>
3990 <para>GHC supports several pragmas, or instructions to the
3991 compiler placed in the source code. Pragmas don't normally affect
3992 the meaning of the program, but they might affect the efficiency
3993 of the generated code.</para>
3995 <para>Pragmas all take the form
3997 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3999 where <replaceable>word</replaceable> indicates the type of
4000 pragma, and is followed optionally by information specific to that
4001 type of pragma. Case is ignored in
4002 <replaceable>word</replaceable>. The various values for
4003 <replaceable>word</replaceable> that GHC understands are described
4004 in the following sections; any pragma encountered with an
4005 unrecognised <replaceable>word</replaceable> is (silently)
4008 <sect2 id="deprecated-pragma">
4009 <title>DEPRECATED pragma</title>
4010 <indexterm><primary>DEPRECATED</primary>
4013 <para>The DEPRECATED pragma lets you specify that a particular
4014 function, class, or type, is deprecated. There are two
4019 <para>You can deprecate an entire module thus:</para>
4021 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4024 <para>When you compile any module that import
4025 <literal>Wibble</literal>, GHC will print the specified
4030 <para>You can deprecate a function, class, or type, with the
4031 following top-level declaration:</para>
4033 {-# DEPRECATED f, C, T "Don't use these" #-}
4035 <para>When you compile any module that imports and uses any
4036 of the specifed entities, GHC will print the specified
4040 Any use of the deprecated item, or of anything from a deprecated
4041 module, will be flagged with an appropriate message. However,
4042 deprecations are not reported for
4043 (a) uses of a deprecated function within its defining module, and
4044 (b) uses of a deprecated function in an export list.
4045 The latter reduces spurious complaints within a library
4046 in which one module gathers together and re-exports
4047 the exports of several others.
4049 <para>You can suppress the warnings with the flag
4050 <option>-fno-warn-deprecations</option>.</para>
4053 <sect2 id="inline-noinline-pragma">
4054 <title>INLINE and NOINLINE pragmas</title>
4056 <para>These pragmas control the inlining of function
4059 <sect3 id="inline-pragma">
4060 <title>INLINE pragma</title>
4061 <indexterm><primary>INLINE</primary></indexterm>
4063 <para>GHC (with <option>-O</option>, as always) tries to
4064 inline (or “unfold”) functions/values that are
4065 “small enough,” thus avoiding the call overhead
4066 and possibly exposing other more-wonderful optimisations.
4067 Normally, if GHC decides a function is “too
4068 expensive” to inline, it will not do so, nor will it
4069 export that unfolding for other modules to use.</para>
4071 <para>The sledgehammer you can bring to bear is the
4072 <literal>INLINE</literal><indexterm><primary>INLINE
4073 pragma</primary></indexterm> pragma, used thusly:</para>
4076 key_function :: Int -> String -> (Bool, Double)
4078 #ifdef __GLASGOW_HASKELL__
4079 {-# INLINE key_function #-}
4083 <para>(You don't need to do the C pre-processor carry-on
4084 unless you're going to stick the code through HBC—it
4085 doesn't like <literal>INLINE</literal> pragmas.)</para>
4087 <para>The major effect of an <literal>INLINE</literal> pragma
4088 is to declare a function's “cost” to be very low.
4089 The normal unfolding machinery will then be very keen to
4092 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4093 function can be put anywhere its type signature could be
4096 <para><literal>INLINE</literal> pragmas are a particularly
4098 <literal>then</literal>/<literal>return</literal> (or
4099 <literal>bind</literal>/<literal>unit</literal>) functions in
4100 a monad. For example, in GHC's own
4101 <literal>UniqueSupply</literal> monad code, we have:</para>
4104 #ifdef __GLASGOW_HASKELL__
4105 {-# INLINE thenUs #-}
4106 {-# INLINE returnUs #-}
4110 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4111 linkend="noinline-pragma">).</para>
4114 <sect3 id="noinline-pragma">
4115 <title>NOINLINE pragma</title>
4117 <indexterm><primary>NOINLINE</primary></indexterm>
4118 <indexterm><primary>NOTINLINE</primary></indexterm>
4120 <para>The <literal>NOINLINE</literal> pragma does exactly what
4121 you'd expect: it stops the named function from being inlined
4122 by the compiler. You shouldn't ever need to do this, unless
4123 you're very cautious about code size.</para>
4125 <para><literal>NOTINLINE</literal> is a synonym for
4126 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4127 specified by Haskell 98 as the standard way to disable
4128 inlining, so it should be used if you want your code to be
4132 <sect3 id="phase-control">
4133 <title>Phase control</title>
4135 <para> Sometimes you want to control exactly when in GHC's
4136 pipeline the INLINE pragma is switched on. Inlining happens
4137 only during runs of the <emphasis>simplifier</emphasis>. Each
4138 run of the simplifier has a different <emphasis>phase
4139 number</emphasis>; the phase number decreases towards zero.
4140 If you use <option>-dverbose-core2core</option> you'll see the
4141 sequence of phase numbers for successive runs of the
4142 simpifier. In an INLINE pragma you can optionally specify a
4143 phase number, thus:</para>
4147 <para>You can say "inline <literal>f</literal> in Phase 2
4148 and all subsequent phases":
4150 {-# INLINE [2] f #-}
4156 <para>You can say "inline <literal>g</literal> in all
4157 phases up to, but not including, Phase 3":
4159 {-# INLINE [~3] g #-}
4165 <para>If you omit the phase indicator, you mean "inline in
4170 <para>You can use a phase number on a NOINLINE pragma too:</para>
4174 <para>You can say "do not inline <literal>f</literal>
4175 until Phase 2; in Phase 2 and subsequently behave as if
4176 there was no pragma at all":
4178 {-# NOINLINE [2] f #-}
4184 <para>You can say "do not inline <literal>g</literal> in
4185 Phase 3 or any subsequent phase; before that, behave as if
4186 there was no pragma":
4188 {-# NOINLINE [~3] g #-}
4194 <para>If you omit the phase indicator, you mean "never
4195 inline this function".</para>
4199 <para>The same phase-numbering control is available for RULES
4200 (<xref LinkEnd="rewrite-rules">).</para>
4204 <sect2 id="line-pragma">
4205 <title>LINE pragma</title>
4207 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4208 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4209 <para>This pragma is similar to C's <literal>#line</literal>
4210 pragma, and is mainly for use in automatically generated Haskell
4211 code. It lets you specify the line number and filename of the
4212 original code; for example</para>
4215 {-# LINE 42 "Foo.vhs" #-}
4218 <para>if you'd generated the current file from something called
4219 <filename>Foo.vhs</filename> and this line corresponds to line
4220 42 in the original. GHC will adjust its error messages to refer
4221 to the line/file named in the <literal>LINE</literal>
4225 <sect2 id="options-pragma">
4226 <title>OPTIONS pragma</title>
4227 <indexterm><primary>OPTIONS</primary>
4229 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4232 <para>The <literal>OPTIONS</literal> pragma is used to specify
4233 additional options that are given to the compiler when compiling
4234 this source file. See <xref linkend="source-file-options"> for
4239 <title>RULES pragma</title>
4241 <para>The RULES pragma lets you specify rewrite rules. It is
4242 described in <xref LinkEnd="rewrite-rules">.</para>
4245 <sect2 id="specialize-pragma">
4246 <title>SPECIALIZE pragma</title>
4248 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4249 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4250 <indexterm><primary>overloading, death to</primary></indexterm>
4252 <para>(UK spelling also accepted.) For key overloaded
4253 functions, you can create extra versions (NB: more code space)
4254 specialised to particular types. Thus, if you have an
4255 overloaded function:</para>
4258 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4261 <para>If it is heavily used on lists with
4262 <literal>Widget</literal> keys, you could specialise it as
4266 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4269 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4270 be put anywhere its type signature could be put.</para>
4272 <para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
4273 version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
4274 rewrites a call to the un-specialised function into a call to the specialised
4275 one. You can, instead, provide your own specialised function and your own rewrite rule.
4276 For example, suppose that:
4278 genericLookup :: Ord a => Table a b -> a -> b
4279 intLookup :: Table Int b -> Int -> b
4281 where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
4282 that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
4284 {-# RULES "intLookup" genericLookup = intLookup #-}
4286 (see <xref linkend="rule-spec">). It is <emphasis>Your
4287 Responsibility</emphasis> to make sure that
4288 <function>intLookup</function> really behaves as a specialised
4289 version of <function>genericLookup</function>!!!</para>
4291 <para>An example in which using <literal>RULES</literal> for
4292 specialisation will Win Big:
4295 toDouble :: Real a => a -> Double
4296 toDouble = fromRational . toRational
4298 {-# RULES "toDouble/Int" toDouble = i2d #-}
4299 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4302 The <function>i2d</function> function is virtually one machine
4303 instruction; the default conversion—via an intermediate
4304 <literal>Rational</literal>—is obscenely expensive by
4309 <sect2 id="specialize-instance-pragma">
4310 <title>SPECIALIZE instance pragma
4314 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4315 <indexterm><primary>overloading, death to</primary></indexterm>
4316 Same idea, except for instance declarations. For example:
4319 instance (Eq a) => Eq (Foo a) where {
4320 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4324 The pragma must occur inside the <literal>where</literal> part
4325 of the instance declaration.
4328 Compatible with HBC, by the way, except perhaps in the placement
4334 <sect2 id="unpack-pragma">
4335 <title>UNPACK pragma</title>
4337 <indexterm><primary>UNPACK</primary></indexterm>
4339 <para>The <literal>UNPACK</literal> indicates to the compiler
4340 that it should unpack the contents of a constructor field into
4341 the constructor itself, removing a level of indirection. For
4345 data T = T {-# UNPACK #-} !Float
4346 {-# UNPACK #-} !Float
4349 <para>will create a constructor <literal>T</literal> containing
4350 two unboxed floats. This may not always be an optimisation: if
4351 the <Function>T</Function> constructor is scrutinised and the
4352 floats passed to a non-strict function for example, they will
4353 have to be reboxed (this is done automatically by the
4356 <para>Unpacking constructor fields should only be used in
4357 conjunction with <option>-O</option>, in order to expose
4358 unfoldings to the compiler so the reboxing can be removed as
4359 often as possible. For example:</para>
4363 f (T f1 f2) = f1 + f2
4366 <para>The compiler will avoid reboxing <Function>f1</Function>
4367 and <Function>f2</Function> by inlining <Function>+</Function>
4368 on floats, but only when <option>-O</option> is on.</para>
4370 <para>Any single-constructor data is eligible for unpacking; for
4374 data T = T {-# UNPACK #-} !(Int,Int)
4377 <para>will store the two <literal>Int</literal>s directly in the
4378 <Function>T</Function> constructor, by flattening the pair.
4379 Multi-level unpacking is also supported:</para>
4382 data T = T {-# UNPACK #-} !S
4383 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4386 <para>will store two unboxed <literal>Int#</literal>s
4387 directly in the <Function>T</Function> constructor. The
4388 unpacker can see through newtypes, too.</para>
4390 <para>If a field cannot be unpacked, you will not get a warning,
4391 so it might be an idea to check the generated code with
4392 <option>-ddump-simpl</option>.</para>
4394 <para>See also the <option>-funbox-strict-fields</option> flag,
4395 which essentially has the effect of adding
4396 <literal>{-# UNPACK #-}</literal> to every strict
4397 constructor field.</para>
4402 <!-- ======================= REWRITE RULES ======================== -->
4404 <sect1 id="rewrite-rules">
4405 <title>Rewrite rules
4407 <indexterm><primary>RULES pagma</primary></indexterm>
4408 <indexterm><primary>pragma, RULES</primary></indexterm>
4409 <indexterm><primary>rewrite rules</primary></indexterm></title>
4412 The programmer can specify rewrite rules as part of the source program
4413 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4414 the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
4415 and (b) the <option>-frules-off</option> flag
4416 (<xref LinkEnd="options-f">) is not specified.
4424 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4431 <title>Syntax</title>
4434 From a syntactic point of view:
4440 There may be zero or more rules in a <literal>RULES</literal> pragma.
4447 Each rule has a name, enclosed in double quotes. The name itself has
4448 no significance at all. It is only used when reporting how many times the rule fired.
4454 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
4455 immediately after the name of the rule. Thus:
4458 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4461 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4462 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4471 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4472 is set, so you must lay out your rules starting in the same column as the
4473 enclosing definitions.
4480 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4481 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4482 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4483 by spaces, just like in a type <literal>forall</literal>.
4489 A pattern variable may optionally have a type signature.
4490 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4491 For example, here is the <literal>foldr/build</literal> rule:
4494 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4495 foldr k z (build g) = g k z
4498 Since <function>g</function> has a polymorphic type, it must have a type signature.
4505 The left hand side of a rule must consist of a top-level variable applied
4506 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4509 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4510 "wrong2" forall f. f True = True
4513 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4520 A rule does not need to be in the same module as (any of) the
4521 variables it mentions, though of course they need to be in scope.
4527 Rules are automatically exported from a module, just as instance declarations are.
4538 <title>Semantics</title>
4541 From a semantic point of view:
4547 Rules are only applied if you use the <option>-O</option> flag.
4553 Rules are regarded as left-to-right rewrite rules.
4554 When GHC finds an expression that is a substitution instance of the LHS
4555 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4556 By "a substitution instance" we mean that the LHS can be made equal to the
4557 expression by substituting for the pattern variables.
4564 The LHS and RHS of a rule are typechecked, and must have the
4572 GHC makes absolutely no attempt to verify that the LHS and RHS
4573 of a rule have the same meaning. That is undecideable in general, and
4574 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4581 GHC makes no attempt to make sure that the rules are confluent or
4582 terminating. For example:
4585 "loop" forall x,y. f x y = f y x
4588 This rule will cause the compiler to go into an infinite loop.
4595 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4601 GHC currently uses a very simple, syntactic, matching algorithm
4602 for matching a rule LHS with an expression. It seeks a substitution
4603 which makes the LHS and expression syntactically equal modulo alpha
4604 conversion. The pattern (rule), but not the expression, is eta-expanded if
4605 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4606 But not beta conversion (that's called higher-order matching).
4610 Matching is carried out on GHC's intermediate language, which includes
4611 type abstractions and applications. So a rule only matches if the
4612 types match too. See <xref LinkEnd="rule-spec"> below.
4618 GHC keeps trying to apply the rules as it optimises the program.
4619 For example, consider:
4628 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4629 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4630 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4631 not be substituted, and the rule would not fire.
4638 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4639 that appears on the LHS of a rule</emphasis>, because once you have substituted
4640 for something you can't match against it (given the simple minded
4641 matching). So if you write the rule
4644 "map/map" forall f,g. map f . map g = map (f.g)
4647 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4648 It will only match something written with explicit use of ".".
4649 Well, not quite. It <emphasis>will</emphasis> match the expression
4655 where <function>wibble</function> is defined:
4658 wibble f g = map f . map g
4661 because <function>wibble</function> will be inlined (it's small).
4663 Later on in compilation, GHC starts inlining even things on the
4664 LHS of rules, but still leaves the rules enabled. This inlining
4665 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4672 All rules are implicitly exported from the module, and are therefore
4673 in force in any module that imports the module that defined the rule, directly
4674 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4675 in force when compiling A.) The situation is very similar to that for instance
4687 <title>List fusion</title>
4690 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4691 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4692 intermediate list should be eliminated entirely.
4696 The following are good producers:
4708 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4714 Explicit lists (e.g. <literal>[True, False]</literal>)
4720 The cons constructor (e.g <literal>3:4:[]</literal>)
4726 <function>++</function>
4732 <function>map</function>
4738 <function>filter</function>
4744 <function>iterate</function>, <function>repeat</function>
4750 <function>zip</function>, <function>zipWith</function>
4759 The following are good consumers:
4771 <function>array</function> (on its second argument)
4777 <function>length</function>
4783 <function>++</function> (on its first argument)
4789 <function>foldr</function>
4795 <function>map</function>
4801 <function>filter</function>
4807 <function>concat</function>
4813 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4819 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4820 will fuse with one but not the other)
4826 <function>partition</function>
4832 <function>head</function>
4838 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4844 <function>sequence_</function>
4850 <function>msum</function>
4856 <function>sortBy</function>
4865 So, for example, the following should generate no intermediate lists:
4868 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4874 This list could readily be extended; if there are Prelude functions that you use
4875 a lot which are not included, please tell us.
4879 If you want to write your own good consumers or producers, look at the
4880 Prelude definitions of the above functions to see how to do so.
4885 <sect2 id="rule-spec">
4886 <title>Specialisation
4890 Rewrite rules can be used to get the same effect as a feature
4891 present in earlier version of GHC:
4894 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4897 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4898 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4899 specialising the original definition of <function>fromIntegral</function> the programmer is
4900 promising that it is safe to use <function>int8ToInt16</function> instead.
4904 This feature is no longer in GHC. But rewrite rules let you do the
4909 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4913 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4914 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4915 GHC adds the type and dictionary applications to get the typed rule
4918 forall (d1::Integral Int8) (d2::Num Int16) .
4919 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4923 this rule does not need to be in the same file as fromIntegral,
4924 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4925 have an original definition available to specialise).
4931 <title>Controlling what's going on</title>
4939 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4945 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4946 If you add <option>-dppr-debug</option> you get a more detailed listing.
4952 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4955 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4956 {-# INLINE build #-}
4960 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4961 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4962 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4963 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4970 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4971 see how to write rules that will do fusion and yet give an efficient
4972 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4982 <sect2 id="core-pragma">
4983 <title>CORE pragma</title>
4985 <indexterm><primary>CORE pragma</primary></indexterm>
4986 <indexterm><primary>pragma, CORE</primary></indexterm>
4987 <indexterm><primary>core, annotation</primary></indexterm>
4990 The external core format supports <quote>Note</quote> annotations;
4991 the <literal>CORE</literal> pragma gives a way to specify what these
4992 should be in your Haskell source code. Syntactically, core
4993 annotations are attached to expressions and take a Haskell string
4994 literal as an argument. The following function definition shows an
4998 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5001 Sematically, this is equivalent to:
5009 However, when external for is generated (via
5010 <option>-fext-core</option>), there will be Notes attached to the
5011 expressions <function>show</function> and <VarName>x</VarName>.
5012 The core function declaration for <function>f</function> is:
5016 f :: %forall a . GHCziShow.ZCTShow a ->
5017 a -> GHCziBase.ZMZN GHCziBase.Char =
5018 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5020 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5022 (tpl1::GHCziBase.Int ->
5024 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5026 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5027 (tpl3::GHCziBase.ZMZN a ->
5028 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5036 Here, we can see that the function <function>show</function> (which
5037 has been expanded out to a case expression over the Show dictionary)
5038 has a <literal>%note</literal> attached to it, as does the
5039 expression <VarName>eta</VarName> (which used to be called
5040 <VarName>x</VarName>).
5047 <sect1 id="generic-classes">
5048 <title>Generic classes</title>
5050 <para>(Note: support for generic classes is currently broken in
5054 The ideas behind this extension are described in detail in "Derivable type classes",
5055 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5056 An example will give the idea:
5064 fromBin :: [Int] -> (a, [Int])
5066 toBin {| Unit |} Unit = []
5067 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5068 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5069 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5071 fromBin {| Unit |} bs = (Unit, bs)
5072 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5073 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5074 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5075 (y,bs'') = fromBin bs'
5078 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5079 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5080 which are defined thus in the library module <literal>Generics</literal>:
5084 data a :+: b = Inl a | Inr b
5085 data a :*: b = a :*: b
5088 Now you can make a data type into an instance of Bin like this:
5090 instance (Bin a, Bin b) => Bin (a,b)
5091 instance Bin a => Bin [a]
5093 That is, just leave off the "where" clause. Of course, you can put in the
5094 where clause and over-ride whichever methods you please.
5098 <title> Using generics </title>
5099 <para>To use generics you need to</para>
5102 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5103 <option>-fgenerics</option> (to generate extra per-data-type code),
5104 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5108 <para>Import the module <literal>Generics</literal> from the
5109 <literal>lang</literal> package. This import brings into
5110 scope the data types <literal>Unit</literal>,
5111 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5112 don't need this import if you don't mention these types
5113 explicitly; for example, if you are simply giving instance
5114 declarations.)</para>
5119 <sect2> <title> Changes wrt the paper </title>
5121 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5122 can be written infix (indeed, you can now use
5123 any operator starting in a colon as an infix type constructor). Also note that
5124 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5125 Finally, note that the syntax of the type patterns in the class declaration
5126 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5127 alone would ambiguous when they appear on right hand sides (an extension we
5128 anticipate wanting).
5132 <sect2> <title>Terminology and restrictions</title>
5134 Terminology. A "generic default method" in a class declaration
5135 is one that is defined using type patterns as above.
5136 A "polymorphic default method" is a default method defined as in Haskell 98.
5137 A "generic class declaration" is a class declaration with at least one
5138 generic default method.
5146 Alas, we do not yet implement the stuff about constructor names and
5153 A generic class can have only one parameter; you can't have a generic
5154 multi-parameter class.
5160 A default method must be defined entirely using type patterns, or entirely
5161 without. So this is illegal:
5164 op :: a -> (a, Bool)
5165 op {| Unit |} Unit = (Unit, True)
5168 However it is perfectly OK for some methods of a generic class to have
5169 generic default methods and others to have polymorphic default methods.
5175 The type variable(s) in the type pattern for a generic method declaration
5176 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:
5180 op {| p :*: q |} (x :*: y) = op (x :: p)
5188 The type patterns in a generic default method must take one of the forms:
5194 where "a" and "b" are type variables. Furthermore, all the type patterns for
5195 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5196 must use the same type variables. So this is illegal:
5200 op {| a :+: b |} (Inl x) = True
5201 op {| p :+: q |} (Inr y) = False
5203 The type patterns must be identical, even in equations for different methods of the class.
5204 So this too is illegal:
5208 op1 {| a :*: b |} (x :*: y) = True
5211 op2 {| p :*: q |} (x :*: y) = False
5213 (The reason for this restriction is that we gather all the equations for a particular type consructor
5214 into a single generic instance declaration.)
5220 A generic method declaration must give a case for each of the three type constructors.
5226 The type for a generic method can be built only from:
5228 <listitem> <para> Function arrows </para> </listitem>
5229 <listitem> <para> Type variables </para> </listitem>
5230 <listitem> <para> Tuples </para> </listitem>
5231 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5233 Here are some example type signatures for generic methods:
5236 op2 :: Bool -> (a,Bool)
5237 op3 :: [Int] -> a -> a
5240 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5244 This restriction is an implementation restriction: we just havn't got around to
5245 implementing the necessary bidirectional maps over arbitrary type constructors.
5246 It would be relatively easy to add specific type constructors, such as Maybe and list,
5247 to the ones that are allowed.</para>
5252 In an instance declaration for a generic class, the idea is that the compiler
5253 will fill in the methods for you, based on the generic templates. However it can only
5258 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5263 No constructor of the instance type has unboxed fields.
5267 (Of course, these things can only arise if you are already using GHC extensions.)
5268 However, you can still give an instance declarations for types which break these rules,
5269 provided you give explicit code to override any generic default methods.
5277 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5278 what the compiler does with generic declarations.
5283 <sect2> <title> Another example </title>
5285 Just to finish with, here's another example I rather like:
5289 nCons {| Unit |} _ = 1
5290 nCons {| a :*: b |} _ = 1
5291 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5294 tag {| Unit |} _ = 1
5295 tag {| a :*: b |} _ = 1
5296 tag {| a :+: b |} (Inl x) = tag x
5297 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5306 ;;; Local Variables: ***
5308 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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