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 <literal>a</literal> is "reachable" if it it appears
1535 in the same constraint as either a type variable free in in
1536 <literal>type</literal>, or another reachable type variable.
1537 A value with a type that does not obey
1538 this reachability restriction cannot be used without introducing
1539 ambiguity; that is why the type is rejected.
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>.
1557 that the reachability condition is weaker than saying that <literal>a</literal> is
1558 functionally dependendent on a type variable free in
1559 <literal>type</literal> (see <xref
1560 linkend="functional-dependencies"/>). The reason for this is there
1561 might be a "hidden" dependency, in a superclass perhaps. So
1562 "reachable" is a conservative approximation to "functionally dependent".
1563 For example, consider:
1565 class C a b | a -> b where ...
1566 class C a b => D a b where ...
1567 f :: forall a b. D a b => a -> a
1569 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1570 but that is not immediately apparent from <literal>f</literal>'s type.
1576 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1577 universally quantified type variables <literal>tvi</literal></emphasis>.
1579 For example, this type is OK because <literal>C a b</literal> mentions the
1580 universally quantified type variable <literal>b</literal>:
1584 forall a. C a b => burble
1588 The next type is illegal because the constraint <literal>Eq b</literal> does not
1589 mention <literal>a</literal>:
1593 forall a. Eq b => burble
1597 The reason for this restriction is milder than the other one. The
1598 excluded types are never useful or necessary (because the offending
1599 context doesn't need to be witnessed at this point; it can be floated
1600 out). Furthermore, floating them out increases sharing. Lastly,
1601 excluding them is a conservative choice; it leaves a patch of
1602 territory free in case we need it later.
1613 <title>For-all hoisting</title>
1615 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1616 end of an arrow, thus:
1618 type Discard a = forall b. a -> b -> a
1620 g :: Int -> Discard Int
1623 Simply expanding the type synonym would give
1625 g :: Int -> (forall b. Int -> b -> Int)
1627 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1629 g :: forall b. Int -> Int -> b -> Int
1631 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1632 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1633 performs the transformation:</emphasis>
1635 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1637 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1639 (In fact, GHC tries to retain as much synonym information as possible for use in
1640 error messages, but that is a usability issue.) This rule applies, of course, whether
1641 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1642 valid way to write <literal>g</literal>'s type signature:
1644 g :: Int -> Int -> forall b. b -> Int
1648 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1651 type Foo a = (?x::Int) => Bool -> a
1656 g :: (?x::Int) => Bool -> Bool -> Int
1664 <sect2 id="instance-decls">
1665 <title>Instance declarations</title>
1668 <title>Overlapping instances</title>
1670 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1675 instance context1 => C type1 where ...
1676 instance context2 => C type2 where ...
1679 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
1682 However, if you give the command line option
1683 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1684 option</primary></indexterm> then overlapping instance declarations are permitted.
1685 However, GHC arranges never to commit to using an instance declaration
1686 if another instance declaration also applies, either now or later.
1692 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1698 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1699 (but not identical to <literal>type1</literal>), or vice versa.
1703 Notice that these rules
1708 make it clear which instance decl to use
1709 (pick the most specific one that matches)
1716 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1717 Reason: you can pick which instance decl
1718 "matches" based on the type.
1723 However the rules are over-conservative. Two instance declarations can overlap,
1724 but it can still be clear in particular situations which to use. For example:
1726 instance C (Int,a) where ...
1727 instance C (a,Bool) where ...
1729 These are rejected by GHC's rules, but it is clear what to do when trying
1730 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1731 cannot apply. Yell if this restriction bites you.
1734 GHC is also conservative about committing to an overlapping instance. For example:
1736 class C a where { op :: a -> a }
1737 instance C [Int] where ...
1738 instance C a => C [a] where ...
1740 f :: C b => [b] -> [b]
1743 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1744 GHC does not commit to the second instance declaration, because in a paricular
1745 call of f, b might be instantiate to Int, so the first instance declaration
1746 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1747 GHC will instead silently pick the second instance, without complaining about
1748 the problem of subsequent instantiations.
1751 Regrettably, GHC doesn't guarantee to detect overlapping instance
1752 declarations if they appear in different modules. GHC can "see" the
1753 instance declarations in the transitive closure of all the modules
1754 imported by the one being compiled, so it can "see" all instance decls
1755 when it is compiling <literal>Main</literal>. However, it currently chooses not
1756 to look at ones that can't possibly be of use in the module currently
1757 being compiled, in the interests of efficiency. (Perhaps we should
1758 change that decision, at least for <literal>Main</literal>.)
1763 <title>Type synonyms in the instance head</title>
1766 <emphasis>Unlike Haskell 98, instance heads may use type
1767 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1768 As always, using a type synonym is just shorthand for
1769 writing the RHS of the type synonym definition. For example:
1773 type Point = (Int,Int)
1774 instance C Point where ...
1775 instance C [Point] where ...
1779 is legal. However, if you added
1783 instance C (Int,Int) where ...
1787 as well, then the compiler will complain about the overlapping
1788 (actually, identical) instance declarations. As always, type synonyms
1789 must be fully applied. You cannot, for example, write:
1794 instance Monad P where ...
1798 This design decision is independent of all the others, and easily
1799 reversed, but it makes sense to me.
1804 <sect3 id="undecidable-instances">
1805 <title>Undecidable instances</title>
1807 <para>An instance declaration must normally obey the following rules:
1809 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1810 an instance declaration <emphasis>must not</emphasis> be a type variable.
1811 For example, these are OK:
1814 instance C Int a where ...
1816 instance D (Int, Int) where ...
1818 instance E [[a]] where ...
1822 instance F a where ...
1824 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1825 For example, this is OK:
1827 instance Stateful (ST s) (MutVar s) where ...
1834 <para>All of the types in the <emphasis>context</emphasis> of
1835 an instance declaration <emphasis>must</emphasis> be type variables.
1838 instance C a b => Eq (a,b) where ...
1842 instance C Int b => Foo b where ...
1848 These restrictions ensure that
1849 context reduction terminates: each reduction step removes one type
1850 constructor. For example, the following would make the type checker
1851 loop if it wasn't excluded:
1853 instance C a => C a where ...
1855 There are two situations in which the rule is a bit of a pain. First,
1856 if one allows overlapping instance declarations then it's quite
1857 convenient to have a "default instance" declaration that applies if
1858 something more specific does not:
1867 Second, sometimes you might want to use the following to get the
1868 effect of a "class synonym":
1872 class (C1 a, C2 a, C3 a) => C a where { }
1874 instance (C1 a, C2 a, C3 a) => C a where { }
1878 This allows you to write shorter signatures:
1890 f :: (C1 a, C2 a, C3 a) => ...
1894 Voluminous correspondence on the Haskell mailing list has convinced me
1895 that it's worth experimenting with more liberal rules. If you use
1896 the experimental flag <option>-fallow-undecidable-instances</option>
1897 <indexterm><primary>-fallow-undecidable-instances
1898 option</primary></indexterm>, you can use arbitrary
1899 types in both an instance context and instance head. Termination is ensured by having a
1900 fixed-depth recursion stack. If you exceed the stack depth you get a
1901 sort of backtrace, and the opportunity to increase the stack depth
1902 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1905 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1906 allowing these idioms interesting idioms.
1913 <sect2 id="implicit-parameters">
1914 <title>Implicit parameters</title>
1916 <para> Implicit paramters are implemented as described in
1917 "Implicit parameters: dynamic scoping with static types",
1918 J Lewis, MB Shields, E Meijer, J Launchbury,
1919 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1923 <para>(Most of the following, stil rather incomplete, documentation is
1924 due to Jeff Lewis.)</para>
1926 <para>Implicit parameter support is enabled with the option
1927 <option>-fimplicit-params</option>.</para>
1930 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1931 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1932 context. In Haskell, all variables are statically bound. Dynamic
1933 binding of variables is a notion that goes back to Lisp, but was later
1934 discarded in more modern incarnations, such as Scheme. Dynamic binding
1935 can be very confusing in an untyped language, and unfortunately, typed
1936 languages, in particular Hindley-Milner typed languages like Haskell,
1937 only support static scoping of variables.
1940 However, by a simple extension to the type class system of Haskell, we
1941 can support dynamic binding. Basically, we express the use of a
1942 dynamically bound variable as a constraint on the type. These
1943 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1944 function uses a dynamically-bound variable <literal>?x</literal>
1945 of type <literal>t'</literal>". For
1946 example, the following expresses the type of a sort function,
1947 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1949 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1951 The dynamic binding constraints are just a new form of predicate in the type class system.
1954 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1955 where <literal>x</literal> is
1956 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1957 Use of this construct also introduces a new
1958 dynamic-binding constraint in the type of the expression.
1959 For example, the following definition
1960 shows how we can define an implicitly parameterized sort function in
1961 terms of an explicitly parameterized <literal>sortBy</literal> function:
1963 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1965 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1971 <title>Implicit-parameter type constraints</title>
1973 Dynamic binding constraints behave just like other type class
1974 constraints in that they are automatically propagated. Thus, when a
1975 function is used, its implicit parameters are inherited by the
1976 function that called it. For example, our <literal>sort</literal> function might be used
1977 to pick out the least value in a list:
1979 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1980 least xs = fst (sort xs)
1982 Without lifting a finger, the <literal>?cmp</literal> parameter is
1983 propagated to become a parameter of <literal>least</literal> as well. With explicit
1984 parameters, the default is that parameters must always be explicit
1985 propagated. With implicit parameters, the default is to always
1989 An implicit-parameter type constraint differs from other type class constraints in the
1990 following way: All uses of a particular implicit parameter must have
1991 the same type. This means that the type of <literal>(?x, ?x)</literal>
1992 is <literal>(?x::a) => (a,a)</literal>, and not
1993 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1997 <para> You can't have an implicit parameter in the context of a class or instance
1998 declaration. For example, both these declarations are illegal:
2000 class (?x::Int) => C a where ...
2001 instance (?x::a) => Foo [a] where ...
2003 Reason: exactly which implicit parameter you pick up depends on exactly where
2004 you invoke a function. But the ``invocation'' of instance declarations is done
2005 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2006 Easiest thing is to outlaw the offending types.</para>
2008 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2010 f :: (?x :: [a]) => Int -> Int
2013 g :: (Read a, Show a) => String -> String
2016 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2017 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2018 quite unambiguous, and fixes the type <literal>a</literal>.
2023 <title>Implicit-parameter bindings</title>
2026 An implicit parameter is <emphasis>bound</emphasis> using the standard
2027 <literal>let</literal> or <literal>where</literal> binding forms.
2028 For example, we define the <literal>min</literal> function by binding
2029 <literal>cmp</literal>.
2032 min = let ?cmp = (<=) in least
2036 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2037 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2038 (including in a list comprehension, or do-notation, or pattern guards),
2039 or a <literal>where</literal> clause.
2040 Note the following points:
2043 An implicit-parameter binding group must be a
2044 collection of simple bindings to implicit-style variables (no
2045 function-style bindings, and no type signatures); these bindings are
2046 neither polymorphic or recursive.
2049 You may not mix implicit-parameter bindings with ordinary bindings in a
2050 single <literal>let</literal>
2051 expression; use two nested <literal>let</literal>s instead.
2052 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2056 You may put multiple implicit-parameter bindings in a
2057 single binding group; but they are <emphasis>not</emphasis> treated
2058 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2059 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2060 parameter. The bindings are not nested, and may be re-ordered without changing
2061 the meaning of the program.
2062 For example, consider:
2064 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2066 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2067 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2069 f :: (?x::Int) => Int -> Int
2078 <sect2 id="linear-implicit-parameters">
2079 <title>Linear implicit parameters</title>
2081 Linear implicit parameters are an idea developed by Koen Claessen,
2082 Mark Shields, and Simon PJ. They address the long-standing
2083 problem that monads seem over-kill for certain sorts of problem, notably:
2086 <listitem> <para> distributing a supply of unique names </para> </listitem>
2087 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2088 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2092 Linear implicit parameters are just like ordinary implicit parameters,
2093 except that they are "linear" -- that is, they cannot be copied, and
2094 must be explicitly "split" instead. Linear implicit parameters are
2095 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2096 (The '/' in the '%' suggests the split!)
2101 import GHC.Exts( Splittable )
2103 data NameSupply = ...
2105 splitNS :: NameSupply -> (NameSupply, NameSupply)
2106 newName :: NameSupply -> Name
2108 instance Splittable NameSupply where
2112 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2113 f env (Lam x e) = Lam x' (f env e)
2116 env' = extend env x x'
2117 ...more equations for f...
2119 Notice that the implicit parameter %ns is consumed
2121 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2122 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2126 So the translation done by the type checker makes
2127 the parameter explicit:
2129 f :: NameSupply -> Env -> Expr -> Expr
2130 f ns env (Lam x e) = Lam x' (f ns1 env e)
2132 (ns1,ns2) = splitNS ns
2134 env = extend env x x'
2136 Notice the call to 'split' introduced by the type checker.
2137 How did it know to use 'splitNS'? Because what it really did
2138 was to introduce a call to the overloaded function 'split',
2139 defined by the class <literal>Splittable</literal>:
2141 class Splittable a where
2144 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2145 split for name supplies. But we can simply write
2151 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2153 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2154 <literal>GHC.Exts</literal>.
2159 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2160 are entirely distinct implicit parameters: you
2161 can use them together and they won't intefere with each other. </para>
2164 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2166 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2167 in the context of a class or instance declaration. </para></listitem>
2171 <sect3><title>Warnings</title>
2174 The monomorphism restriction is even more important than usual.
2175 Consider the example above:
2177 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2178 f env (Lam x e) = Lam x' (f env e)
2181 env' = extend env x x'
2183 If we replaced the two occurrences of x' by (newName %ns), which is
2184 usually a harmless thing to do, we get:
2186 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2187 f env (Lam x e) = Lam (newName %ns) (f env e)
2189 env' = extend env x (newName %ns)
2191 But now the name supply is consumed in <emphasis>three</emphasis> places
2192 (the two calls to newName,and the recursive call to f), so
2193 the result is utterly different. Urk! We don't even have
2197 Well, this is an experimental change. With implicit
2198 parameters we have already lost beta reduction anyway, and
2199 (as John Launchbury puts it) we can't sensibly reason about
2200 Haskell programs without knowing their typing.
2205 <sect3><title>Recursive functions</title>
2206 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2209 foo :: %x::T => Int -> [Int]
2211 foo n = %x : foo (n-1)
2213 where T is some type in class Splittable.</para>
2215 Do you get a list of all the same T's or all different T's
2216 (assuming that split gives two distinct T's back)?
2218 If you supply the type signature, taking advantage of polymorphic
2219 recursion, you get what you'd probably expect. Here's the
2220 translated term, where the implicit param is made explicit:
2223 foo x n = let (x1,x2) = split x
2224 in x1 : foo x2 (n-1)
2226 But if you don't supply a type signature, GHC uses the Hindley
2227 Milner trick of using a single monomorphic instance of the function
2228 for the recursive calls. That is what makes Hindley Milner type inference
2229 work. So the translation becomes
2233 foom n = x : foom (n-1)
2237 Result: 'x' is not split, and you get a list of identical T's. So the
2238 semantics of the program depends on whether or not foo has a type signature.
2241 You may say that this is a good reason to dislike linear implicit parameters
2242 and you'd be right. That is why they are an experimental feature.
2248 <sect2 id="functional-dependencies">
2249 <title>Functional dependencies
2252 <para> Functional dependencies are implemented as described by Mark Jones
2253 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2254 In Proceedings of the 9th European Symposium on Programming,
2255 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2259 Functional dependencies are introduced by a vertical bar in the syntax of a
2260 class declaration; e.g.
2262 class (Monad m) => MonadState s m | m -> s where ...
2264 class Foo a b c | a b -> c where ...
2266 There should be more documentation, but there isn't (yet). Yell if you need it.
2272 <sect2 id="sec-kinding">
2273 <title>Explicitly-kinded quantification</title>
2276 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2277 to give the kind explicitly as (machine-checked) documentation,
2278 just as it is nice to give a type signature for a function. On some occasions,
2279 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2280 John Hughes had to define the data type:
2282 data Set cxt a = Set [a]
2283 | Unused (cxt a -> ())
2285 The only use for the <literal>Unused</literal> constructor was to force the correct
2286 kind for the type variable <literal>cxt</literal>.
2289 GHC now instead allows you to specify the kind of a type variable directly, wherever
2290 a type variable is explicitly bound. Namely:
2292 <listitem><para><literal>data</literal> declarations:
2294 data Set (cxt :: * -> *) a = Set [a]
2295 </screen></para></listitem>
2296 <listitem><para><literal>type</literal> declarations:
2298 type T (f :: * -> *) = f Int
2299 </screen></para></listitem>
2300 <listitem><para><literal>class</literal> declarations:
2302 class (Eq a) => C (f :: * -> *) a where ...
2303 </screen></para></listitem>
2304 <listitem><para><literal>forall</literal>'s in type signatures:
2306 f :: forall (cxt :: * -> *). Set cxt Int
2307 </screen></para></listitem>
2312 The parentheses are required. Some of the spaces are required too, to
2313 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2314 will get a parse error, because "<literal>::*->*</literal>" is a
2315 single lexeme in Haskell.
2319 As part of the same extension, you can put kind annotations in types
2322 f :: (Int :: *) -> Int
2323 g :: forall a. a -> (a :: *)
2327 atype ::= '(' ctype '::' kind ')
2329 The parentheses are required.
2334 <sect2 id="universal-quantification">
2335 <title>Arbitrary-rank polymorphism
2339 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2340 allows us to say exactly what this means. For example:
2348 g :: forall b. (b -> b)
2350 The two are treated identically.
2354 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2355 explicit universal quantification in
2357 For example, all the following types are legal:
2359 f1 :: forall a b. a -> b -> a
2360 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2362 f2 :: (forall a. a->a) -> Int -> Int
2363 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2365 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2367 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2368 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2369 The <literal>forall</literal> makes explicit the universal quantification that
2370 is implicitly added by Haskell.
2373 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2374 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2375 shows, the polymorphic type on the left of the function arrow can be overloaded.
2378 The function <literal>f3</literal> has a rank-3 type;
2379 it has rank-2 types on the left of a function arrow.
2382 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2383 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2384 that restriction has now been lifted.)
2385 In particular, a forall-type (also called a "type scheme"),
2386 including an operational type class context, is legal:
2388 <listitem> <para> On the left of a function arrow </para> </listitem>
2389 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2390 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2391 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2392 field type signatures.</para> </listitem>
2393 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2394 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2396 There is one place you cannot put a <literal>forall</literal>:
2397 you cannot instantiate a type variable with a forall-type. So you cannot
2398 make a forall-type the argument of a type constructor. So these types are illegal:
2400 x1 :: [forall a. a->a]
2401 x2 :: (forall a. a->a, Int)
2402 x3 :: Maybe (forall a. a->a)
2404 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2405 a type variable any more!
2414 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2415 the types of the constructor arguments. Here are several examples:
2421 data T a = T1 (forall b. b -> b -> b) a
2423 data MonadT m = MkMonad { return :: forall a. a -> m a,
2424 bind :: forall a b. m a -> (a -> m b) -> m b
2427 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2433 The constructors have rank-2 types:
2439 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2440 MkMonad :: forall m. (forall a. a -> m a)
2441 -> (forall a b. m a -> (a -> m b) -> m b)
2443 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2449 Notice that you don't need to use a <literal>forall</literal> if there's an
2450 explicit context. For example in the first argument of the
2451 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2452 prefixed to the argument type. The implicit <literal>forall</literal>
2453 quantifies all type variables that are not already in scope, and are
2454 mentioned in the type quantified over.
2458 As for type signatures, implicit quantification happens for non-overloaded
2459 types too. So if you write this:
2462 data T a = MkT (Either a b) (b -> b)
2465 it's just as if you had written this:
2468 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2471 That is, since the type variable <literal>b</literal> isn't in scope, it's
2472 implicitly universally quantified. (Arguably, it would be better
2473 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2474 where that is what is wanted. Feedback welcomed.)
2478 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2479 the constructor to suitable values, just as usual. For example,
2490 a3 = MkSwizzle reverse
2493 a4 = let r x = Just x
2500 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2501 mkTs f x y = [T1 f x, T1 f y]
2507 The type of the argument can, as usual, be more general than the type
2508 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2509 does not need the <literal>Ord</literal> constraint.)
2513 When you use pattern matching, the bound variables may now have
2514 polymorphic types. For example:
2520 f :: T a -> a -> (a, Char)
2521 f (T1 w k) x = (w k x, w 'c' 'd')
2523 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2524 g (MkSwizzle s) xs f = s (map f (s xs))
2526 h :: MonadT m -> [m a] -> m [a]
2527 h m [] = return m []
2528 h m (x:xs) = bind m x $ \y ->
2529 bind m (h m xs) $ \ys ->
2536 In the function <function>h</function> we use the record selectors <literal>return</literal>
2537 and <literal>bind</literal> to extract the polymorphic bind and return functions
2538 from the <literal>MonadT</literal> data structure, rather than using pattern
2544 <title>Type inference</title>
2547 In general, type inference for arbitrary-rank types is undecideable.
2548 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2549 to get a decidable algorithm by requiring some help from the programmer.
2550 We do not yet have a formal specification of "some help" but the rule is this:
2553 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2554 provides an explicit polymorphic type for x, or GHC's type inference will assume
2555 that x's type has no foralls in it</emphasis>.
2558 What does it mean to "provide" an explicit type for x? You can do that by
2559 giving a type signature for x directly, using a pattern type signature
2560 (<xref linkend="scoped-type-variables"/>), thus:
2562 \ f :: (forall a. a->a) -> (f True, f 'c')
2564 Alternatively, you can give a type signature to the enclosing
2565 context, which GHC can "push down" to find the type for the variable:
2567 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2569 Here the type signature on the expression can be pushed inwards
2570 to give a type signature for f. Similarly, and more commonly,
2571 one can give a type signature for the function itself:
2573 h :: (forall a. a->a) -> (Bool,Char)
2574 h f = (f True, f 'c')
2576 You don't need to give a type signature if the lambda bound variable
2577 is a constructor argument. Here is an example we saw earlier:
2579 f :: T a -> a -> (a, Char)
2580 f (T1 w k) x = (w k x, w 'c' 'd')
2582 Here we do not need to give a type signature to <literal>w</literal>, because
2583 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2590 <sect3 id="implicit-quant">
2591 <title>Implicit quantification</title>
2594 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2595 user-written types, if and only if there is no explicit <literal>forall</literal>,
2596 GHC finds all the type variables mentioned in the type that are not already
2597 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2601 f :: forall a. a -> a
2608 h :: forall b. a -> b -> b
2614 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2617 f :: (a -> a) -> Int
2619 f :: forall a. (a -> a) -> Int
2621 f :: (forall a. a -> a) -> Int
2624 g :: (Ord a => a -> a) -> Int
2625 -- MEANS the illegal type
2626 g :: forall a. (Ord a => a -> a) -> Int
2628 g :: (forall a. Ord a => a -> a) -> Int
2630 The latter produces an illegal type, which you might think is silly,
2631 but at least the rule is simple. If you want the latter type, you
2632 can write your for-alls explicitly. Indeed, doing so is strongly advised
2641 <sect2 id="scoped-type-variables">
2642 <title>Scoped type variables
2646 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2647 variable</emphasis>. For example
2653 f (xs::[a]) = ys ++ ys
2662 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2663 This brings the type variable <literal>a</literal> into scope; it scopes over
2664 all the patterns and right hand sides for this equation for <function>f</function>.
2665 In particular, it is in scope at the type signature for <varname>y</varname>.
2669 Pattern type signatures are completely orthogonal to ordinary, separate
2670 type signatures. The two can be used independently or together.
2671 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2672 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2673 implicitly universally quantified. (If there are no type variables in
2674 scope, all type variables mentioned in the signature are universally
2675 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2676 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2677 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2678 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2679 it becomes possible to do so.
2683 Scoped type variables are implemented in both GHC and Hugs. Where the
2684 implementations differ from the specification below, those differences
2689 So much for the basic idea. Here are the details.
2693 <title>What a pattern type signature means</title>
2695 A type variable brought into scope by a pattern type signature is simply
2696 the name for a type. The restriction they express is that all occurrences
2697 of the same name mean the same type. For example:
2699 f :: [Int] -> Int -> Int
2700 f (xs::[a]) (y::a) = (head xs + y) :: a
2702 The pattern type signatures on the left hand side of
2703 <literal>f</literal> express the fact that <literal>xs</literal>
2704 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2705 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2706 specifies that this expression must have the same type <literal>a</literal>.
2707 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2708 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2709 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2710 rules, which specified that a pattern-bound type variable should be universally quantified.)
2711 For example, all of these are legal:</para>
2714 t (x::a) (y::a) = x+y*2
2716 f (x::a) (y::b) = [x,y] -- a unifies with b
2718 g (x::a) = x + 1::Int -- a unifies with Int
2720 h x = let k (y::a) = [x,y] -- a is free in the
2721 in k x -- environment
2723 k (x::a) True = ... -- a unifies with Int
2724 k (x::Int) False = ...
2727 w (x::a) = x -- a unifies with [b]
2733 <title>Scope and implicit quantification</title>
2741 All the type variables mentioned in a pattern,
2742 that are not already in scope,
2743 are brought into scope by the pattern. We describe this set as
2744 the <emphasis>type variables bound by the pattern</emphasis>.
2747 f (x::a) = let g (y::(a,b)) = fst y
2751 The pattern <literal>(x::a)</literal> brings the type variable
2752 <literal>a</literal> into scope, as well as the term
2753 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2754 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2755 and brings into scope the type variable <literal>b</literal>.
2761 The type variable(s) bound by the pattern have the same scope
2762 as the term variable(s) bound by the pattern. For example:
2765 f (x::a) = <...rhs of f...>
2766 (p::b, q::b) = (1,2)
2767 in <...body of let...>
2769 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2770 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2771 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2772 just like <literal>p</literal> and <literal>q</literal> do.
2773 Indeed, the newly bound type variables also scope over any ordinary, separate
2774 type signatures in the <literal>let</literal> group.
2781 The type variables bound by the pattern may be
2782 mentioned in ordinary type signatures or pattern
2783 type signatures anywhere within their scope.
2790 In ordinary type signatures, any type variable mentioned in the
2791 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2799 Ordinary type signatures do not bring any new type variables
2800 into scope (except in the type signature itself!). So this is illegal:
2807 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2808 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2809 and that is an incorrect typing.
2816 The pattern type signature is a monotype:
2821 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2825 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2826 not to type schemes.
2830 There is no implicit universal quantification on pattern type signatures (in contrast to
2831 ordinary type signatures).
2841 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2842 scope over the methods defined in the <literal>where</literal> part. For example:
2856 (Not implemented in Hugs yet, Dec 98).
2867 <title>Where a pattern type signature can occur</title>
2870 A pattern type signature can occur in any pattern. For example:
2875 A pattern type signature can be on an arbitrary sub-pattern, not
2880 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2889 Pattern type signatures, including the result part, can be used
2890 in lambda abstractions:
2893 (\ (x::a, y) :: a -> x)
2900 Pattern type signatures, including the result part, can be used
2901 in <literal>case</literal> expressions:
2904 case e of { ((x::a, y) :: (a,b)) -> x }
2907 Note that the <literal>-></literal> symbol in a case alternative
2908 leads to difficulties when parsing a type signature in the pattern: in
2909 the absence of the extra parentheses in the example above, the parser
2910 would try to interpret the <literal>-></literal> as a function
2911 arrow and give a parse error later.
2919 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2920 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2921 token or a parenthesised type of some sort). To see why,
2922 consider how one would parse this:
2936 Pattern type signatures can bind existential type variables.
2941 data T = forall a. MkT [a]
2944 f (MkT [t::a]) = MkT t3
2957 Pattern type signatures
2958 can be used in pattern bindings:
2961 f x = let (y, z::a) = x in ...
2962 f1 x = let (y, z::Int) = x in ...
2963 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2964 f3 :: (b->b) = \x -> x
2967 In all such cases, the binding is not generalised over the pattern-bound
2968 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2969 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2970 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2971 In contrast, the binding
2976 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2977 in <literal>f4</literal>'s scope.
2987 <title>Result type signatures</title>
2990 The result type of a function can be given a signature, thus:
2994 f (x::a) :: [a] = [x,x,x]
2998 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2999 result type. Sometimes this is the only way of naming the type variable
3004 f :: Int -> [a] -> [a]
3005 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3006 in \xs -> map g (reverse xs `zip` xs)
3011 The type variables bound in a result type signature scope over the right hand side
3012 of the definition. However, consider this corner-case:
3014 rev1 :: [a] -> [a] = \xs -> reverse xs
3016 foo ys = rev (ys::[a])
3018 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3019 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3020 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3021 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3022 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3025 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3026 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3030 rev1 :: [a] -> [a] = \xs -> reverse xs
3035 Result type signatures are not yet implemented in Hugs.
3042 <sect2 id="deriving-typeable">
3043 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3046 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3047 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3048 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3049 classes <literal>Eq</literal>, <literal>Ord</literal>,
3050 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3053 GHC extends this list with two more classes that may be automatically derived
3054 (provided the <option>-fglasgow-exts</option> flag is specified):
3055 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3056 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3057 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3061 <sect2 id="newtype-deriving">
3062 <title>Generalised derived instances for newtypes</title>
3065 When you define an abstract type using <literal>newtype</literal>, you may want
3066 the new type to inherit some instances from its representation. In
3067 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3068 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3069 other classes you have to write an explicit instance declaration. For
3070 example, if you define
3073 newtype Dollars = Dollars Int
3076 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3077 explicitly define an instance of <literal>Num</literal>:
3080 instance Num Dollars where
3081 Dollars a + Dollars b = Dollars (a+b)
3084 All the instance does is apply and remove the <literal>newtype</literal>
3085 constructor. It is particularly galling that, since the constructor
3086 doesn't appear at run-time, this instance declaration defines a
3087 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3088 dictionary, only slower!
3092 <sect3> <title> Generalising the deriving clause </title>
3094 GHC now permits such instances to be derived instead, so one can write
3096 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3099 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3100 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3101 derives an instance declaration of the form
3104 instance Num Int => Num Dollars
3107 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3111 We can also derive instances of constructor classes in a similar
3112 way. For example, suppose we have implemented state and failure monad
3113 transformers, such that
3116 instance Monad m => Monad (State s m)
3117 instance Monad m => Monad (Failure m)
3119 In Haskell 98, we can define a parsing monad by
3121 type Parser tok m a = State [tok] (Failure m) a
3124 which is automatically a monad thanks to the instance declarations
3125 above. With the extension, we can make the parser type abstract,
3126 without needing to write an instance of class <literal>Monad</literal>, via
3129 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3132 In this case the derived instance declaration is of the form
3134 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3137 Notice that, since <literal>Monad</literal> is a constructor class, the
3138 instance is a <emphasis>partial application</emphasis> of the new type, not the
3139 entire left hand side. We can imagine that the type declaration is
3140 ``eta-converted'' to generate the context of the instance
3145 We can even derive instances of multi-parameter classes, provided the
3146 newtype is the last class parameter. In this case, a ``partial
3147 application'' of the class appears in the <literal>deriving</literal>
3148 clause. For example, given the class
3151 class StateMonad s m | m -> s where ...
3152 instance Monad m => StateMonad s (State s m) where ...
3154 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3156 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3157 deriving (Monad, StateMonad [tok])
3160 The derived instance is obtained by completing the application of the
3161 class to the new type:
3164 instance StateMonad [tok] (State [tok] (Failure m)) =>
3165 StateMonad [tok] (Parser tok m)
3170 As a result of this extension, all derived instances in newtype
3171 declarations are treated uniformly (and implemented just by reusing
3172 the dictionary for the representation type), <emphasis>except</emphasis>
3173 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3174 the newtype and its representation.
3178 <sect3> <title> A more precise specification </title>
3180 Derived instance declarations are constructed as follows. Consider the
3181 declaration (after expansion of any type synonyms)
3184 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3190 <literal>S</literal> is a type constructor,
3193 The <literal>t1...tk</literal> are types,
3196 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3197 the <literal>ti</literal>, and
3200 The <literal>ci</literal> are partial applications of
3201 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3202 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3205 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3206 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3207 should not "look through" the type or its constructor. You can still
3208 derive these classes for a newtype, but it happens in the usual way, not
3209 via this new mechanism.
3212 Then, for each <literal>ci</literal>, the derived instance
3215 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3217 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3218 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3222 As an example which does <emphasis>not</emphasis> work, consider
3224 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3226 Here we cannot derive the instance
3228 instance Monad (State s m) => Monad (NonMonad m)
3231 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3232 and so cannot be "eta-converted" away. It is a good thing that this
3233 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3234 not, in fact, a monad --- for the same reason. Try defining
3235 <literal>>>=</literal> with the correct type: you won't be able to.
3239 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3240 important, since we can only derive instances for the last one. If the
3241 <literal>StateMonad</literal> class above were instead defined as
3244 class StateMonad m s | m -> s where ...
3247 then we would not have been able to derive an instance for the
3248 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3249 classes usually have one "main" parameter for which deriving new
3250 instances is most interesting.
3258 <!-- ==================== End of type system extensions ================= -->
3260 <!-- ====================== TEMPLATE HASKELL ======================= -->
3262 <sect1 id="template-haskell">
3263 <title>Template Haskell</title>
3265 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3266 Template Haskell at <ulink url="http://www.haskell.org/th/">
3267 http://www.haskell.org/th/</ulink>, while
3269 the main technical innovations is discussed in "<ulink
3270 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3271 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3272 The details of the Template Haskell design are still in flux. Make sure you
3273 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3274 (search for the type ExpQ).
3275 [Temporary: many changes to the original design are described in
3276 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3277 Not all of these changes are in GHC 6.2.]
3280 <para> The first example from that paper is set out below as a worked example to help get you started.
3284 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3285 Tim Sheard is going to expand it.)
3289 <title>Syntax</title>
3291 <para> Template Haskell has the following new syntactic
3292 constructions. You need to use the flag
3293 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3294 </indexterm>to switch these syntactic extensions on
3295 (<option>-fth</option> is currently implied by
3296 <option>-fglasgow-exts</option>, but you are encouraged to
3297 specify it explicitly).</para>
3301 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3302 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3303 There must be no space between the "$" and the identifier or parenthesis. This use
3304 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3305 of "." as an infix operator. If you want the infix operator, put spaces around it.
3307 <para> A splice can occur in place of
3309 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3310 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3311 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3313 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3314 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3320 A expression quotation is written in Oxford brackets, thus:
3322 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3323 the quotation has type <literal>Expr</literal>.</para></listitem>
3324 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3325 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3326 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3327 the quotation has type <literal>Type</literal>.</para></listitem>
3328 </itemizedlist></para></listitem>
3331 Reification is written thus:
3333 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3334 has type <literal>Dec</literal>. </para></listitem>
3335 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3336 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3337 <listitem><para> Still to come: fixities </para></listitem>
3339 </itemizedlist></para>
3346 <sect2> <title> Using Template Haskell </title>
3350 The data types and monadic constructor functions for Template Haskell are in the library
3351 <literal>Language.Haskell.THSyntax</literal>.
3355 You can only run a function at compile time if it is imported from another module. That is,
3356 you can't define a function in a module, and call it from within a splice in the same module.
3357 (It would make sense to do so, but it's hard to implement.)
3361 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3364 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3365 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3366 compiles and runs a program, and then looks at the result. So it's important that
3367 the program it compiles produces results whose representations are identical to
3368 those of the compiler itself.
3372 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3373 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3378 <sect2> <title> A Template Haskell Worked Example </title>
3379 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3380 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3387 -- Import our template "pr"
3388 import Printf ( pr )
3390 -- The splice operator $ takes the Haskell source code
3391 -- generated at compile time by "pr" and splices it into
3392 -- the argument of "putStrLn".
3393 main = putStrLn ( $(pr "Hello") )
3399 -- Skeletal printf from the paper.
3400 -- It needs to be in a separate module to the one where
3401 -- you intend to use it.
3403 -- Import some Template Haskell syntax
3404 import Language.Haskell.TH.Syntax
3406 -- Describe a format string
3407 data Format = D | S | L String
3409 -- Parse a format string. This is left largely to you
3410 -- as we are here interested in building our first ever
3411 -- Template Haskell program and not in building printf.
3412 parse :: String -> [Format]
3415 -- Generate Haskell source code from a parsed representation
3416 -- of the format string. This code will be spliced into
3417 -- the module which calls "pr", at compile time.
3418 gen :: [Format] -> ExpQ
3419 gen [D] = [| \n -> show n |]
3420 gen [S] = [| \s -> s |]
3421 gen [L s] = stringE s
3423 -- Here we generate the Haskell code for the splice
3424 -- from an input format string.
3425 pr :: String -> ExpQ
3426 pr s = gen (parse s)
3429 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3432 $ ghc --make -fth main.hs -o main.exe
3435 <para>Run "main.exe" and here is your output:</para>
3446 <!-- ===================== Arrow notation =================== -->
3448 <sect1 id="arrow-notation">
3449 <title>Arrow notation
3452 <para>Arrows are a generalization of monads introduced by John Hughes.
3453 For more details, see
3458 “Generalising Monads to Arrows”,
3459 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3460 pp67–111, May 2000.
3466 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3467 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3473 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3474 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3480 and the arrows web page at
3481 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3482 With the <option>-farrows</option> flag, GHC supports the arrow
3483 notation described in the second of these papers.
3484 What follows is a brief introduction to the notation;
3485 it won't make much sense unless you've read Hughes's paper.
3486 This notation is translated to ordinary Haskell,
3487 using combinators from the
3488 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3492 <para>The extension adds a new kind of expression for defining arrows:
3494 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3495 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3497 where <literal>proc</literal> is a new keyword.
3498 The variables of the pattern are bound in the body of the
3499 <literal>proc</literal>-expression,
3500 which is a new sort of thing called a <firstterm>command</firstterm>.
3501 The syntax of commands is as follows:
3503 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3504 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3505 | <replaceable>cmd</replaceable><superscript>0</superscript>
3507 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3508 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3509 infix operators as for expressions, and
3511 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3512 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3513 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3514 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3515 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3516 | <replaceable>fcmd</replaceable>
3518 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3519 | ( <replaceable>cmd</replaceable> )
3520 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3522 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3523 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3524 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3525 | <replaceable>cmd</replaceable>
3527 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3528 except that the bodies are commands instead of expressions.
3532 Commands produce values, but (like monadic computations)
3533 may yield more than one value,
3534 or none, and may do other things as well.
3535 For the most part, familiarity with monadic notation is a good guide to
3537 However the values of expressions, even monadic ones,
3538 are determined by the values of the variables they contain;
3539 this is not necessarily the case for commands.
3543 A simple example of the new notation is the expression
3545 proc x -> f -< x+1
3547 We call this a <firstterm>procedure</firstterm> or
3548 <firstterm>arrow abstraction</firstterm>.
3549 As with a lambda expression, the variable <literal>x</literal>
3550 is a new variable bound within the <literal>proc</literal>-expression.
3551 It refers to the input to the arrow.
3552 In the above example, <literal>-<</literal> is not an identifier but an
3553 new reserved symbol used for building commands from an expression of arrow
3554 type and an expression to be fed as input to that arrow.
3555 (The weird look will make more sense later.)
3556 It may be read as analogue of application for arrows.
3557 The above example is equivalent to the Haskell expression
3559 arr (\ x -> x+1) >>> f
3561 That would make no sense if the expression to the left of
3562 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3563 More generally, the expression to the left of <literal>-<</literal>
3564 may not involve any <firstterm>local variable</firstterm>,
3565 i.e. a variable bound in the current arrow abstraction.
3566 For such a situation there is a variant <literal>-<<</literal>, as in
3568 proc x -> f x -<< x+1
3570 which is equivalent to
3572 arr (\ x -> (f, x+1)) >>> app
3574 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3576 Such an arrow is equivalent to a monad, so if you're using this form
3577 you may find a monadic formulation more convenient.
3581 <title>do-notation for commands</title>
3584 Another form of command is a form of <literal>do</literal>-notation.
3585 For example, you can write
3594 You can read this much like ordinary <literal>do</literal>-notation,
3595 but with commands in place of monadic expressions.
3596 The first line sends the value of <literal>x+1</literal> as an input to
3597 the arrow <literal>f</literal>, and matches its output against
3598 <literal>y</literal>.
3599 In the next line, the output is discarded.
3600 The arrow <literal>returnA</literal> is defined in the
3601 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3602 module as <literal>arr id</literal>.
3603 The above example is treated as an abbreviation for
3605 arr (\ x -> (x, x)) >>>
3606 first (arr (\ x -> x+1) >>> f) >>>
3607 arr (\ (y, x) -> (y, (x, y))) >>>
3608 first (arr (\ y -> 2*y) >>> g) >>>
3610 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3611 first (arr (\ (x, z) -> x*z) >>> h) >>>
3612 arr (\ (t, z) -> t+z) >>>
3615 Note that variables not used later in the composition are projected out.
3616 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3618 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3619 module, this reduces to
3621 arr (\ x -> (x+1, x)) >>>
3623 arr (\ (y, x) -> (2*y, (x, y))) >>>
3625 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3627 arr (\ (t, z) -> t+z)
3629 which is what you might have written by hand.
3630 With arrow notation, GHC keeps track of all those tuples of variables for you.
3634 Note that although the above translation suggests that
3635 <literal>let</literal>-bound variables like <literal>z</literal> must be
3636 monomorphic, the actual translation produces Core,
3637 so polymorphic variables are allowed.
3641 It's also possible to have mutually recursive bindings,
3642 using the new <literal>rec</literal> keyword, as in the following example:
3644 counter :: ArrowCircuit a => a Bool Int
3645 counter = proc reset -> do
3646 rec output <- returnA -< if reset then 0 else next
3647 next <- delay 0 -< output+1
3648 returnA -< output
3650 The translation of such forms uses the <literal>loop</literal> combinator,
3651 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3657 <title>Conditional commands</title>
3660 In the previous example, we used a conditional expression to construct the
3662 Sometimes we want to conditionally execute different commands, as in
3669 which is translated to
3671 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3672 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3674 Since the translation uses <literal>|||</literal>,
3675 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3679 There are also <literal>case</literal> commands, like
3685 y <- h -< (x1, x2)
3689 The syntax is the same as for <literal>case</literal> expressions,
3690 except that the bodies of the alternatives are commands rather than expressions.
3691 The translation is similar to that of <literal>if</literal> commands.
3697 <title>Defining your own control structures</title>
3700 As we're seen, arrow notation provides constructs,
3701 modelled on those for expressions,
3702 for sequencing, value recursion and conditionals.
3703 But suitable combinators,
3704 which you can define in ordinary Haskell,
3705 may also be used to build new commands out of existing ones.
3706 The basic idea is that a command defines an arrow from environments to values.
3707 These environments assign values to the free local variables of the command.
3708 Thus combinators that produce arrows from arrows
3709 may also be used to build commands from commands.
3710 For example, the <literal>ArrowChoice</literal> class includes a combinator
3712 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3714 so we can use it to build commands:
3716 expr' = proc x -> do
3719 symbol Plus -< ()
3720 y <- term -< ()
3723 symbol Minus -< ()
3724 y <- term -< ()
3727 (The <literal>do</literal> on the first line is needed to prevent the first
3728 <literal><+> ...</literal> from being interpreted as part of the
3729 expression on the previous line.)
3730 This is equivalent to
3732 expr' = (proc x -> returnA -< x)
3733 <+> (proc x -> do
3734 symbol Plus -< ()
3735 y <- term -< ()
3737 <+> (proc x -> do
3738 symbol Minus -< ()
3739 y <- term -< ()
3742 It is essential that this operator be polymorphic in <literal>e</literal>
3743 (representing the environment input to the command
3744 and thence to its subcommands)
3745 and satisfy the corresponding naturality property
3747 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3749 at least for strict <literal>k</literal>.
3750 (This should be automatic if you're not using <literal>seq</literal>.)
3751 This ensures that environments seen by the subcommands are environments
3752 of the whole command,
3753 and also allows the translation to safely trim these environments.
3754 The operator must also not use any variable defined within the current
3759 We could define our own operator
3761 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3762 untilA body cond = proc x ->
3763 if cond x then returnA -< ()
3766 untilA body cond -< x
3768 and use it in the same way.
3769 Of course this infix syntax only makes sense for binary operators;
3770 there is also a more general syntax involving special brackets:
3774 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3781 <title>Primitive constructs</title>
3784 Some operators will need to pass additional inputs to their subcommands.
3785 For example, in an arrow type supporting exceptions,
3786 the operator that attaches an exception handler will wish to pass the
3787 exception that occurred to the handler.
3788 Such an operator might have a type
3790 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3792 where <literal>Ex</literal> is the type of exceptions handled.
3793 You could then use this with arrow notation by writing a command
3795 body `handleA` \ ex -> handler
3797 so that if an exception is raised in the command <literal>body</literal>,
3798 the variable <literal>ex</literal> is bound to the value of the exception
3799 and the command <literal>handler</literal>,
3800 which typically refers to <literal>ex</literal>, is entered.
3801 Though the syntax here looks like a functional lambda,
3802 we are talking about commands, and something different is going on.
3803 The input to the arrow represented by a command consists of values for
3804 the free local variables in the command, plus a stack of anonymous values.
3805 In all the prior examples, this stack was empty.
3806 In the second argument to <literal>handleA</literal>,
3807 this stack consists of one value, the value of the exception.
3808 The command form of lambda merely gives this value a name.
3813 the values on the stack are paired to the right of the environment.
3814 So when designing operators like <literal>handleA</literal> that pass
3815 extra inputs to their subcommands,
3816 More precisely, the type of each argument of the operator (and its result)
3817 should have the form
3819 a (...(e,t1), ... tn) t
3821 where <replaceable>e</replaceable> is a polymorphic variable
3822 (representing the environment)
3823 and <replaceable>ti</replaceable> are the types of the values on the stack,
3824 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3825 The polymorphic variable <replaceable>e</replaceable> must not occur in
3826 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3827 <replaceable>t</replaceable>.
3828 However the arrows involved need not be the same.
3829 Here are some more examples of suitable operators:
3831 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3832 runReader :: ... => a e c -> a' (e,State) c
3833 runState :: ... => a e c -> a' (e,State) (c,State)
3835 We can supply the extra input required by commands built with the last two
3836 by applying them to ordinary expressions, as in
3840 (|runReader (do { ... })|) s
3842 which adds <literal>s</literal> to the stack of inputs to the command
3843 built using <literal>runReader</literal>.
3847 The command versions of lambda abstraction and application are analogous to
3848 the expression versions.
3849 In particular, the beta and eta rules describe equivalences of commands.
3850 These three features (operators, lambda abstraction and application)
3851 are the core of the notation; everything else can be built using them,
3852 though the results would be somewhat clumsy.
3853 For example, we could simulate <literal>do</literal>-notation by defining
3855 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3856 u `bind` f = returnA &&& u >>> f
3858 bind_ :: Arrow a => a e b -> a e c -> a e c
3859 u `bind_` f = u `bind` (arr fst >>> f)
3861 We could simulate <literal>do</literal> by defining
3863 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3864 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3871 <title>Differences with the paper</title>
3876 <para>Instead of a single form of arrow application (arrow tail) with two
3877 translations, the implementation provides two forms
3878 <quote><literal>-<</literal></quote> (first-order)
3879 and <quote><literal>-<<</literal></quote> (higher-order).
3884 <para>User-defined operators are flagged with banana brackets instead of
3885 a new <literal>form</literal> keyword.
3894 <title>Portability</title>
3897 Although only GHC implements arrow notation directly,
3898 there is also a preprocessor
3900 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
3901 that translates arrow notation into Haskell 98
3902 for use with other Haskell systems.
3903 You would still want to check arrow programs with GHC;
3904 tracing type errors in the preprocessor output is not easy.
3905 Modules intended for both GHC and the preprocessor must observe some
3906 additional restrictions:
3911 The module must import
3912 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3918 The preprocessor cannot cope with other Haskell extensions.
3919 These would have to go in separate modules.
3925 Because the preprocessor targets Haskell (rather than Core),
3926 <literal>let</literal>-bound variables are monomorphic.
3937 <!-- ==================== ASSERTIONS ================= -->
3939 <sect1 id="sec-assertions">
3941 <indexterm><primary>Assertions</primary></indexterm>
3945 If you want to make use of assertions in your standard Haskell code, you
3946 could define a function like the following:
3952 assert :: Bool -> a -> a
3953 assert False x = error "assertion failed!"
3960 which works, but gives you back a less than useful error message --
3961 an assertion failed, but which and where?
3965 One way out is to define an extended <function>assert</function> function which also
3966 takes a descriptive string to include in the error message and
3967 perhaps combine this with the use of a pre-processor which inserts
3968 the source location where <function>assert</function> was used.
3972 Ghc offers a helping hand here, doing all of this for you. For every
3973 use of <function>assert</function> in the user's source:
3979 kelvinToC :: Double -> Double
3980 kelvinToC k = assert (k >= 0.0) (k+273.15)
3986 Ghc will rewrite this to also include the source location where the
3993 assert pred val ==> assertError "Main.hs|15" pred val
3999 The rewrite is only performed by the compiler when it spots
4000 applications of <function>Control.Exception.assert</function>, so you
4001 can still define and use your own versions of
4002 <function>assert</function>, should you so wish. If not, import
4003 <literal>Control.Exception</literal> to make use
4004 <function>assert</function> in your code.
4008 To have the compiler ignore uses of assert, use the compiler option
4009 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4010 option</primary></indexterm> That is, expressions of the form
4011 <literal>assert pred e</literal> will be rewritten to
4012 <literal>e</literal>.
4016 Assertion failures can be caught, see the documentation for the
4017 <literal>Control.Exception</literal> library for the details.
4023 <!-- =============================== PRAGMAS =========================== -->
4025 <sect1 id="pragmas">
4026 <title>Pragmas</title>
4028 <indexterm><primary>pragma</primary></indexterm>
4030 <para>GHC supports several pragmas, or instructions to the
4031 compiler placed in the source code. Pragmas don't normally affect
4032 the meaning of the program, but they might affect the efficiency
4033 of the generated code.</para>
4035 <para>Pragmas all take the form
4037 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4039 where <replaceable>word</replaceable> indicates the type of
4040 pragma, and is followed optionally by information specific to that
4041 type of pragma. Case is ignored in
4042 <replaceable>word</replaceable>. The various values for
4043 <replaceable>word</replaceable> that GHC understands are described
4044 in the following sections; any pragma encountered with an
4045 unrecognised <replaceable>word</replaceable> is (silently)
4048 <sect2 id="deprecated-pragma">
4049 <title>DEPRECATED pragma</title>
4050 <indexterm><primary>DEPRECATED</primary>
4053 <para>The DEPRECATED pragma lets you specify that a particular
4054 function, class, or type, is deprecated. There are two
4059 <para>You can deprecate an entire module thus:</para>
4061 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4064 <para>When you compile any module that import
4065 <literal>Wibble</literal>, GHC will print the specified
4070 <para>You can deprecate a function, class, or type, with the
4071 following top-level declaration:</para>
4073 {-# DEPRECATED f, C, T "Don't use these" #-}
4075 <para>When you compile any module that imports and uses any
4076 of the specifed entities, GHC will print the specified
4080 Any use of the deprecated item, or of anything from a deprecated
4081 module, will be flagged with an appropriate message. However,
4082 deprecations are not reported for
4083 (a) uses of a deprecated function within its defining module, and
4084 (b) uses of a deprecated function in an export list.
4085 The latter reduces spurious complaints within a library
4086 in which one module gathers together and re-exports
4087 the exports of several others.
4089 <para>You can suppress the warnings with the flag
4090 <option>-fno-warn-deprecations</option>.</para>
4093 <sect2 id="inline-noinline-pragma">
4094 <title>INLINE and NOINLINE pragmas</title>
4096 <para>These pragmas control the inlining of function
4099 <sect3 id="inline-pragma">
4100 <title>INLINE pragma</title>
4101 <indexterm><primary>INLINE</primary></indexterm>
4103 <para>GHC (with <option>-O</option>, as always) tries to
4104 inline (or “unfold”) functions/values that are
4105 “small enough,” thus avoiding the call overhead
4106 and possibly exposing other more-wonderful optimisations.
4107 Normally, if GHC decides a function is “too
4108 expensive” to inline, it will not do so, nor will it
4109 export that unfolding for other modules to use.</para>
4111 <para>The sledgehammer you can bring to bear is the
4112 <literal>INLINE</literal><indexterm><primary>INLINE
4113 pragma</primary></indexterm> pragma, used thusly:</para>
4116 key_function :: Int -> String -> (Bool, Double)
4118 #ifdef __GLASGOW_HASKELL__
4119 {-# INLINE key_function #-}
4123 <para>(You don't need to do the C pre-processor carry-on
4124 unless you're going to stick the code through HBC—it
4125 doesn't like <literal>INLINE</literal> pragmas.)</para>
4127 <para>The major effect of an <literal>INLINE</literal> pragma
4128 is to declare a function's “cost” to be very low.
4129 The normal unfolding machinery will then be very keen to
4132 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4133 function can be put anywhere its type signature could be
4136 <para><literal>INLINE</literal> pragmas are a particularly
4138 <literal>then</literal>/<literal>return</literal> (or
4139 <literal>bind</literal>/<literal>unit</literal>) functions in
4140 a monad. For example, in GHC's own
4141 <literal>UniqueSupply</literal> monad code, we have:</para>
4144 #ifdef __GLASGOW_HASKELL__
4145 {-# INLINE thenUs #-}
4146 {-# INLINE returnUs #-}
4150 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4151 linkend="noinline-pragma"/>).</para>
4154 <sect3 id="noinline-pragma">
4155 <title>NOINLINE pragma</title>
4157 <indexterm><primary>NOINLINE</primary></indexterm>
4158 <indexterm><primary>NOTINLINE</primary></indexterm>
4160 <para>The <literal>NOINLINE</literal> pragma does exactly what
4161 you'd expect: it stops the named function from being inlined
4162 by the compiler. You shouldn't ever need to do this, unless
4163 you're very cautious about code size.</para>
4165 <para><literal>NOTINLINE</literal> is a synonym for
4166 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4167 specified by Haskell 98 as the standard way to disable
4168 inlining, so it should be used if you want your code to be
4172 <sect3 id="phase-control">
4173 <title>Phase control</title>
4175 <para> Sometimes you want to control exactly when in GHC's
4176 pipeline the INLINE pragma is switched on. Inlining happens
4177 only during runs of the <emphasis>simplifier</emphasis>. Each
4178 run of the simplifier has a different <emphasis>phase
4179 number</emphasis>; the phase number decreases towards zero.
4180 If you use <option>-dverbose-core2core</option> you'll see the
4181 sequence of phase numbers for successive runs of the
4182 simpifier. In an INLINE pragma you can optionally specify a
4183 phase number, thus:</para>
4187 <para>You can say "inline <literal>f</literal> in Phase 2
4188 and all subsequent phases":
4190 {-# INLINE [2] f #-}
4196 <para>You can say "inline <literal>g</literal> in all
4197 phases up to, but not including, Phase 3":
4199 {-# INLINE [~3] g #-}
4205 <para>If you omit the phase indicator, you mean "inline in
4210 <para>You can use a phase number on a NOINLINE pragma too:</para>
4214 <para>You can say "do not inline <literal>f</literal>
4215 until Phase 2; in Phase 2 and subsequently behave as if
4216 there was no pragma at all":
4218 {-# NOINLINE [2] f #-}
4224 <para>You can say "do not inline <literal>g</literal> in
4225 Phase 3 or any subsequent phase; before that, behave as if
4226 there was no pragma":
4228 {-# NOINLINE [~3] g #-}
4234 <para>If you omit the phase indicator, you mean "never
4235 inline this function".</para>
4239 <para>The same phase-numbering control is available for RULES
4240 (<xref linkend="rewrite-rules"/>).</para>
4244 <sect2 id="line-pragma">
4245 <title>LINE pragma</title>
4247 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4248 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4249 <para>This pragma is similar to C's <literal>#line</literal>
4250 pragma, and is mainly for use in automatically generated Haskell
4251 code. It lets you specify the line number and filename of the
4252 original code; for example</para>
4255 {-# LINE 42 "Foo.vhs" #-}
4258 <para>if you'd generated the current file from something called
4259 <filename>Foo.vhs</filename> and this line corresponds to line
4260 42 in the original. GHC will adjust its error messages to refer
4261 to the line/file named in the <literal>LINE</literal>
4265 <sect2 id="options-pragma">
4266 <title>OPTIONS pragma</title>
4267 <indexterm><primary>OPTIONS</primary>
4269 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4272 <para>The <literal>OPTIONS</literal> pragma is used to specify
4273 additional options that are given to the compiler when compiling
4274 this source file. See <xref linkend="source-file-options"/> for
4279 <title>RULES pragma</title>
4281 <para>The RULES pragma lets you specify rewrite rules. It is
4282 described in <xref linkend="rewrite-rules"/>.</para>
4285 <sect2 id="specialize-pragma">
4286 <title>SPECIALIZE pragma</title>
4288 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4289 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4290 <indexterm><primary>overloading, death to</primary></indexterm>
4292 <para>(UK spelling also accepted.) For key overloaded
4293 functions, you can create extra versions (NB: more code space)
4294 specialised to particular types. Thus, if you have an
4295 overloaded function:</para>
4298 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4301 <para>If it is heavily used on lists with
4302 <literal>Widget</literal> keys, you could specialise it as
4306 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4309 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4310 be put anywhere its type signature could be put.</para>
4312 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4313 (a) a specialised version of the function and (b) a rewrite rule
4314 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4315 un-specialised function into a call to the specialised one.</para>
4317 <para>In earlier versions of GHC, it was possible to provide your own
4318 specialised function for a given type:
4321 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4324 This feature has been removed, as it is now subsumed by the
4325 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4329 <sect2 id="specialize-instance-pragma">
4330 <title>SPECIALIZE instance pragma
4334 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4335 <indexterm><primary>overloading, death to</primary></indexterm>
4336 Same idea, except for instance declarations. For example:
4339 instance (Eq a) => Eq (Foo a) where {
4340 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4344 The pragma must occur inside the <literal>where</literal> part
4345 of the instance declaration.
4348 Compatible with HBC, by the way, except perhaps in the placement
4354 <sect2 id="unpack-pragma">
4355 <title>UNPACK pragma</title>
4357 <indexterm><primary>UNPACK</primary></indexterm>
4359 <para>The <literal>UNPACK</literal> indicates to the compiler
4360 that it should unpack the contents of a constructor field into
4361 the constructor itself, removing a level of indirection. For
4365 data T = T {-# UNPACK #-} !Float
4366 {-# UNPACK #-} !Float
4369 <para>will create a constructor <literal>T</literal> containing
4370 two unboxed floats. This may not always be an optimisation: if
4371 the <function>T</function> constructor is scrutinised and the
4372 floats passed to a non-strict function for example, they will
4373 have to be reboxed (this is done automatically by the
4376 <para>Unpacking constructor fields should only be used in
4377 conjunction with <option>-O</option>, in order to expose
4378 unfoldings to the compiler so the reboxing can be removed as
4379 often as possible. For example:</para>
4383 f (T f1 f2) = f1 + f2
4386 <para>The compiler will avoid reboxing <function>f1</function>
4387 and <function>f2</function> by inlining <function>+</function>
4388 on floats, but only when <option>-O</option> is on.</para>
4390 <para>Any single-constructor data is eligible for unpacking; for
4394 data T = T {-# UNPACK #-} !(Int,Int)
4397 <para>will store the two <literal>Int</literal>s directly in the
4398 <function>T</function> constructor, by flattening the pair.
4399 Multi-level unpacking is also supported:</para>
4402 data T = T {-# UNPACK #-} !S
4403 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4406 <para>will store two unboxed <literal>Int#</literal>s
4407 directly in the <function>T</function> constructor. The
4408 unpacker can see through newtypes, too.</para>
4410 <para>If a field cannot be unpacked, you will not get a warning,
4411 so it might be an idea to check the generated code with
4412 <option>-ddump-simpl</option>.</para>
4414 <para>See also the <option>-funbox-strict-fields</option> flag,
4415 which essentially has the effect of adding
4416 <literal>{-# UNPACK #-}</literal> to every strict
4417 constructor field.</para>
4422 <!-- ======================= REWRITE RULES ======================== -->
4424 <sect1 id="rewrite-rules">
4425 <title>Rewrite rules
4427 <indexterm><primary>RULES pagma</primary></indexterm>
4428 <indexterm><primary>pragma, RULES</primary></indexterm>
4429 <indexterm><primary>rewrite rules</primary></indexterm></title>
4432 The programmer can specify rewrite rules as part of the source program
4433 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4434 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4435 and (b) the <option>-frules-off</option> flag
4436 (<xref linkend="options-f"/>) is not specified.
4444 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4451 <title>Syntax</title>
4454 From a syntactic point of view:
4460 There may be zero or more rules in a <literal>RULES</literal> pragma.
4467 Each rule has a name, enclosed in double quotes. The name itself has
4468 no significance at all. It is only used when reporting how many times the rule fired.
4474 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4475 immediately after the name of the rule. Thus:
4478 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4481 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4482 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4491 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4492 is set, so you must lay out your rules starting in the same column as the
4493 enclosing definitions.
4500 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4501 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4502 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4503 by spaces, just like in a type <literal>forall</literal>.
4509 A pattern variable may optionally have a type signature.
4510 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4511 For example, here is the <literal>foldr/build</literal> rule:
4514 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4515 foldr k z (build g) = g k z
4518 Since <function>g</function> has a polymorphic type, it must have a type signature.
4525 The left hand side of a rule must consist of a top-level variable applied
4526 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4529 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4530 "wrong2" forall f. f True = True
4533 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4540 A rule does not need to be in the same module as (any of) the
4541 variables it mentions, though of course they need to be in scope.
4547 Rules are automatically exported from a module, just as instance declarations are.
4558 <title>Semantics</title>
4561 From a semantic point of view:
4567 Rules are only applied if you use the <option>-O</option> flag.
4573 Rules are regarded as left-to-right rewrite rules.
4574 When GHC finds an expression that is a substitution instance of the LHS
4575 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4576 By "a substitution instance" we mean that the LHS can be made equal to the
4577 expression by substituting for the pattern variables.
4584 The LHS and RHS of a rule are typechecked, and must have the
4592 GHC makes absolutely no attempt to verify that the LHS and RHS
4593 of a rule have the same meaning. That is undecideable in general, and
4594 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4601 GHC makes no attempt to make sure that the rules are confluent or
4602 terminating. For example:
4605 "loop" forall x,y. f x y = f y x
4608 This rule will cause the compiler to go into an infinite loop.
4615 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4621 GHC currently uses a very simple, syntactic, matching algorithm
4622 for matching a rule LHS with an expression. It seeks a substitution
4623 which makes the LHS and expression syntactically equal modulo alpha
4624 conversion. The pattern (rule), but not the expression, is eta-expanded if
4625 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4626 But not beta conversion (that's called higher-order matching).
4630 Matching is carried out on GHC's intermediate language, which includes
4631 type abstractions and applications. So a rule only matches if the
4632 types match too. See <xref linkend="rule-spec"/> below.
4638 GHC keeps trying to apply the rules as it optimises the program.
4639 For example, consider:
4648 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4649 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4650 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4651 not be substituted, and the rule would not fire.
4658 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4659 that appears on the LHS of a rule</emphasis>, because once you have substituted
4660 for something you can't match against it (given the simple minded
4661 matching). So if you write the rule
4664 "map/map" forall f,g. map f . map g = map (f.g)
4667 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4668 It will only match something written with explicit use of ".".
4669 Well, not quite. It <emphasis>will</emphasis> match the expression
4675 where <function>wibble</function> is defined:
4678 wibble f g = map f . map g
4681 because <function>wibble</function> will be inlined (it's small).
4683 Later on in compilation, GHC starts inlining even things on the
4684 LHS of rules, but still leaves the rules enabled. This inlining
4685 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4692 All rules are implicitly exported from the module, and are therefore
4693 in force in any module that imports the module that defined the rule, directly
4694 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4695 in force when compiling A.) The situation is very similar to that for instance
4707 <title>List fusion</title>
4710 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4711 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4712 intermediate list should be eliminated entirely.
4716 The following are good producers:
4728 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4734 Explicit lists (e.g. <literal>[True, False]</literal>)
4740 The cons constructor (e.g <literal>3:4:[]</literal>)
4746 <function>++</function>
4752 <function>map</function>
4758 <function>filter</function>
4764 <function>iterate</function>, <function>repeat</function>
4770 <function>zip</function>, <function>zipWith</function>
4779 The following are good consumers:
4791 <function>array</function> (on its second argument)
4797 <function>length</function>
4803 <function>++</function> (on its first argument)
4809 <function>foldr</function>
4815 <function>map</function>
4821 <function>filter</function>
4827 <function>concat</function>
4833 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4839 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4840 will fuse with one but not the other)
4846 <function>partition</function>
4852 <function>head</function>
4858 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4864 <function>sequence_</function>
4870 <function>msum</function>
4876 <function>sortBy</function>
4885 So, for example, the following should generate no intermediate lists:
4888 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4894 This list could readily be extended; if there are Prelude functions that you use
4895 a lot which are not included, please tell us.
4899 If you want to write your own good consumers or producers, look at the
4900 Prelude definitions of the above functions to see how to do so.
4905 <sect2 id="rule-spec">
4906 <title>Specialisation
4910 Rewrite rules can be used to get the same effect as a feature
4911 present in earlier versions of GHC.
4912 For example, suppose that:
4915 genericLookup :: Ord a => Table a b -> a -> b
4916 intLookup :: Table Int b -> Int -> b
4919 where <function>intLookup</function> is an implementation of
4920 <function>genericLookup</function> that works very fast for
4921 keys of type <literal>Int</literal>. You might wish
4922 to tell GHC to use <function>intLookup</function> instead of
4923 <function>genericLookup</function> whenever the latter was called with
4924 type <literal>Table Int b -> Int -> b</literal>.
4925 It used to be possible to write
4928 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
4931 This feature is no longer in GHC, but rewrite rules let you do the same thing:
4934 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
4937 This slightly odd-looking rule instructs GHC to replace
4938 <function>genericLookup</function> by <function>intLookup</function>
4939 <emphasis>whenever the types match</emphasis>.
4940 What is more, this rule does not need to be in the same
4941 file as <function>genericLookup</function>, unlike the
4942 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
4943 have an original definition available to specialise).
4946 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
4947 <function>intLookup</function> really behaves as a specialised version
4948 of <function>genericLookup</function>!!!</para>
4950 <para>An example in which using <literal>RULES</literal> for
4951 specialisation will Win Big:
4954 toDouble :: Real a => a -> Double
4955 toDouble = fromRational . toRational
4957 {-# RULES "toDouble/Int" toDouble = i2d #-}
4958 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4961 The <function>i2d</function> function is virtually one machine
4962 instruction; the default conversion—via an intermediate
4963 <literal>Rational</literal>—is obscenely expensive by
4970 <title>Controlling what's going on</title>
4978 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4984 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4985 If you add <option>-dppr-debug</option> you get a more detailed listing.
4991 The defintion of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
4994 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4995 {-# INLINE build #-}
4999 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5000 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5001 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5002 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5009 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5010 see how to write rules that will do fusion and yet give an efficient
5011 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5021 <sect2 id="core-pragma">
5022 <title>CORE pragma</title>
5024 <indexterm><primary>CORE pragma</primary></indexterm>
5025 <indexterm><primary>pragma, CORE</primary></indexterm>
5026 <indexterm><primary>core, annotation</primary></indexterm>
5029 The external core format supports <quote>Note</quote> annotations;
5030 the <literal>CORE</literal> pragma gives a way to specify what these
5031 should be in your Haskell source code. Syntactically, core
5032 annotations are attached to expressions and take a Haskell string
5033 literal as an argument. The following function definition shows an
5037 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5040 Sematically, this is equivalent to:
5048 However, when external for is generated (via
5049 <option>-fext-core</option>), there will be Notes attached to the
5050 expressions <function>show</function> and <varname>x</varname>.
5051 The core function declaration for <function>f</function> is:
5055 f :: %forall a . GHCziShow.ZCTShow a ->
5056 a -> GHCziBase.ZMZN GHCziBase.Char =
5057 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5059 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5061 (tpl1::GHCziBase.Int ->
5063 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5065 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5066 (tpl3::GHCziBase.ZMZN a ->
5067 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5075 Here, we can see that the function <function>show</function> (which
5076 has been expanded out to a case expression over the Show dictionary)
5077 has a <literal>%note</literal> attached to it, as does the
5078 expression <varname>eta</varname> (which used to be called
5079 <varname>x</varname>).
5086 <sect1 id="generic-classes">
5087 <title>Generic classes</title>
5089 <para>(Note: support for generic classes is currently broken in
5093 The ideas behind this extension are described in detail in "Derivable type classes",
5094 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5095 An example will give the idea:
5103 fromBin :: [Int] -> (a, [Int])
5105 toBin {| Unit |} Unit = []
5106 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5107 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5108 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5110 fromBin {| Unit |} bs = (Unit, bs)
5111 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5112 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5113 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5114 (y,bs'') = fromBin bs'
5117 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5118 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5119 which are defined thus in the library module <literal>Generics</literal>:
5123 data a :+: b = Inl a | Inr b
5124 data a :*: b = a :*: b
5127 Now you can make a data type into an instance of Bin like this:
5129 instance (Bin a, Bin b) => Bin (a,b)
5130 instance Bin a => Bin [a]
5132 That is, just leave off the "where" clause. Of course, you can put in the
5133 where clause and over-ride whichever methods you please.
5137 <title> Using generics </title>
5138 <para>To use generics you need to</para>
5141 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5142 <option>-fgenerics</option> (to generate extra per-data-type code),
5143 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5147 <para>Import the module <literal>Generics</literal> from the
5148 <literal>lang</literal> package. This import brings into
5149 scope the data types <literal>Unit</literal>,
5150 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5151 don't need this import if you don't mention these types
5152 explicitly; for example, if you are simply giving instance
5153 declarations.)</para>
5158 <sect2> <title> Changes wrt the paper </title>
5160 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5161 can be written infix (indeed, you can now use
5162 any operator starting in a colon as an infix type constructor). Also note that
5163 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5164 Finally, note that the syntax of the type patterns in the class declaration
5165 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5166 alone would ambiguous when they appear on right hand sides (an extension we
5167 anticipate wanting).
5171 <sect2> <title>Terminology and restrictions</title>
5173 Terminology. A "generic default method" in a class declaration
5174 is one that is defined using type patterns as above.
5175 A "polymorphic default method" is a default method defined as in Haskell 98.
5176 A "generic class declaration" is a class declaration with at least one
5177 generic default method.
5185 Alas, we do not yet implement the stuff about constructor names and
5192 A generic class can have only one parameter; you can't have a generic
5193 multi-parameter class.
5199 A default method must be defined entirely using type patterns, or entirely
5200 without. So this is illegal:
5203 op :: a -> (a, Bool)
5204 op {| Unit |} Unit = (Unit, True)
5207 However it is perfectly OK for some methods of a generic class to have
5208 generic default methods and others to have polymorphic default methods.
5214 The type variable(s) in the type pattern for a generic method declaration
5215 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:
5219 op {| p :*: q |} (x :*: y) = op (x :: p)
5227 The type patterns in a generic default method must take one of the forms:
5233 where "a" and "b" are type variables. Furthermore, all the type patterns for
5234 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5235 must use the same type variables. So this is illegal:
5239 op {| a :+: b |} (Inl x) = True
5240 op {| p :+: q |} (Inr y) = False
5242 The type patterns must be identical, even in equations for different methods of the class.
5243 So this too is illegal:
5247 op1 {| a :*: b |} (x :*: y) = True
5250 op2 {| p :*: q |} (x :*: y) = False
5252 (The reason for this restriction is that we gather all the equations for a particular type consructor
5253 into a single generic instance declaration.)
5259 A generic method declaration must give a case for each of the three type constructors.
5265 The type for a generic method can be built only from:
5267 <listitem> <para> Function arrows </para> </listitem>
5268 <listitem> <para> Type variables </para> </listitem>
5269 <listitem> <para> Tuples </para> </listitem>
5270 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5272 Here are some example type signatures for generic methods:
5275 op2 :: Bool -> (a,Bool)
5276 op3 :: [Int] -> a -> a
5279 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5283 This restriction is an implementation restriction: we just havn't got around to
5284 implementing the necessary bidirectional maps over arbitrary type constructors.
5285 It would be relatively easy to add specific type constructors, such as Maybe and list,
5286 to the ones that are allowed.</para>
5291 In an instance declaration for a generic class, the idea is that the compiler
5292 will fill in the methods for you, based on the generic templates. However it can only
5297 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5302 No constructor of the instance type has unboxed fields.
5306 (Of course, these things can only arise if you are already using GHC extensions.)
5307 However, you can still give an instance declarations for types which break these rules,
5308 provided you give explicit code to override any generic default methods.
5316 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5317 what the compiler does with generic declarations.
5322 <sect2> <title> Another example </title>
5324 Just to finish with, here's another example I rather like:
5328 nCons {| Unit |} _ = 1
5329 nCons {| a :*: b |} _ = 1
5330 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5333 tag {| Unit |} _ = 1
5334 tag {| a :*: b |} _ = 1
5335 tag {| a :+: b |} (Inl x) = tag x
5336 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5345 ;;; Local Variables: ***
5347 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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