1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
76 <term><option>-fglasgow-exts</option>:</term>
77 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
79 <para>This simultaneously enables all of the extensions to
80 Haskell 98 described in <xref
81 linkend="ghc-language-features"/>, except where otherwise
84 <para>New reserved words: <literal>forall</literal> (only in
85 types), <literal>mdo</literal>.</para>
87 <para>Other syntax stolen:
88 <replaceable>varid</replaceable>{<literal>#</literal>},
89 <replaceable>char</replaceable><literal>#</literal>,
90 <replaceable>string</replaceable><literal>#</literal>,
91 <replaceable>integer</replaceable><literal>#</literal>,
92 <replaceable>float</replaceable><literal>#</literal>,
93 <replaceable>float</replaceable><literal>##</literal>,
94 <literal>(#</literal>, <literal>#)</literal>,
95 <literal>|)</literal>, <literal>{|</literal>.</para>
100 <term><option>-ffi</option> and <option>-fffi</option>:</term>
101 <indexterm><primary><option>-ffi</option></primary></indexterm>
102 <indexterm><primary><option>-fffi</option></primary></indexterm>
104 <para>This option enables the language extension defined in the
105 Haskell 98 Foreign Function Interface Addendum plus deprecated
106 syntax of previous versions of the FFI for backwards
107 compatibility.</para>
109 <para>New reserved words: <literal>foreign</literal>.</para>
114 <term><option>-fno-monomorphism-restriction</option>:</term>
115 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
117 <para> Switch off the Haskell 98 monomorphism restriction.
118 Independent of the <option>-fglasgow-exts</option>
124 <term><option>-fallow-overlapping-instances</option></term>
125 <term><option>-fallow-undecidable-instances</option></term>
126 <term><option>-fallow-incoherent-instances</option></term>
127 <term><option>-fcontext-stack</option></term>
128 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
129 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
130 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
132 <para> See <xref linkend="instance-decls"/>. Only relevant
133 if you also use <option>-fglasgow-exts</option>.</para>
138 <term><option>-finline-phase</option></term>
139 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
141 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
142 you also use <option>-fglasgow-exts</option>.</para>
147 <term><option>-farrows</option></term>
148 <indexterm><primary><option>-farrows</option></primary></indexterm>
150 <para>See <xref linkend="arrow-notation"/>. Independent of
151 <option>-fglasgow-exts</option>.</para>
153 <para>New reserved words/symbols: <literal>rec</literal>,
154 <literal>proc</literal>, <literal>-<</literal>,
155 <literal>>-</literal>, <literal>-<<</literal>,
156 <literal>>>-</literal>.</para>
158 <para>Other syntax stolen: <literal>(|</literal>,
159 <literal>|)</literal>.</para>
164 <term><option>-fgenerics</option></term>
165 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
167 <para>See <xref linkend="generic-classes"/>. Independent of
168 <option>-fglasgow-exts</option>.</para>
173 <term><option>-fno-implicit-prelude</option></term>
175 <para><indexterm><primary>-fno-implicit-prelude
176 option</primary></indexterm> GHC normally imports
177 <filename>Prelude.hi</filename> files for you. If you'd
178 rather it didn't, then give it a
179 <option>-fno-implicit-prelude</option> option. The idea is
180 that you can then import a Prelude of your own. (But don't
181 call it <literal>Prelude</literal>; the Haskell module
182 namespace is flat, and you must not conflict with any
183 Prelude module.)</para>
185 <para>Even though you have not imported the Prelude, most of
186 the built-in syntax still refers to the built-in Haskell
187 Prelude types and values, as specified by the Haskell
188 Report. For example, the type <literal>[Int]</literal>
189 still means <literal>Prelude.[] Int</literal>; tuples
190 continue to refer to the standard Prelude tuples; the
191 translation for list comprehensions continues to use
192 <literal>Prelude.map</literal> etc.</para>
194 <para>However, <option>-fno-implicit-prelude</option> does
195 change the handling of certain built-in syntax: see <xref
196 linkend="rebindable-syntax"/>.</para>
201 <term><option>-fth</option></term>
203 <para>Enables Template Haskell (see <xref
204 linkend="template-haskell"/>). Currently also implied by
205 <option>-fglasgow-exts</option>.</para>
207 <para>Syntax stolen: <literal>[|</literal>,
208 <literal>[e|</literal>, <literal>[p|</literal>,
209 <literal>[d|</literal>, <literal>[t|</literal>,
210 <literal>$(</literal>,
211 <literal>$<replaceable>varid</replaceable></literal>.</para>
216 <term><option>-fimplicit-params</option></term>
218 <para>Enables implicit parameters (see <xref
219 linkend="implicit-parameters"/>). Currently also implied by
220 <option>-fglasgow-exts</option>.</para>
223 <literal>?<replaceable>varid</replaceable></literal>,
224 <literal>%<replaceable>varid</replaceable></literal>.</para>
231 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
232 <!-- included from primitives.sgml -->
233 <!-- &primitives; -->
234 <sect1 id="primitives">
235 <title>Unboxed types and primitive operations</title>
237 <para>GHC is built on a raft of primitive data types and operations.
238 While you really can use this stuff to write fast code,
239 we generally find it a lot less painful, and more satisfying in the
240 long run, to use higher-level language features and libraries. With
241 any luck, the code you write will be optimised to the efficient
242 unboxed version in any case. And if it isn't, we'd like to know
245 <para>We do not currently have good, up-to-date documentation about the
246 primitives, perhaps because they are mainly intended for internal use.
247 There used to be a long section about them here in the User Guide, but it
248 became out of date, and wrong information is worse than none.</para>
250 <para>The Real Truth about what primitive types there are, and what operations
251 work over those types, is held in the file
252 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
253 This file is used directly to generate GHC's primitive-operation definitions, so
254 it is always correct! It is also intended for processing into text.</para>
257 the result of such processing is part of the description of the
259 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
260 Core language</ulink>.
261 So that document is a good place to look for a type-set version.
262 We would be very happy if someone wanted to volunteer to produce an SGML
263 back end to the program that processes <filename>primops.txt</filename> so that
264 we could include the results here in the User Guide.</para>
266 <para>What follows here is a brief summary of some main points.</para>
268 <sect2 id="glasgow-unboxed">
273 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
276 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
277 that values of that type are represented by a pointer to a heap
278 object. The representation of a Haskell <literal>Int</literal>, for
279 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
280 type, however, is represented by the value itself, no pointers or heap
281 allocation are involved.
285 Unboxed types correspond to the “raw machine” types you
286 would use in C: <literal>Int#</literal> (long int),
287 <literal>Double#</literal> (double), <literal>Addr#</literal>
288 (void *), etc. The <emphasis>primitive operations</emphasis>
289 (PrimOps) on these types are what you might expect; e.g.,
290 <literal>(+#)</literal> is addition on
291 <literal>Int#</literal>s, and is the machine-addition that we all
292 know and love—usually one instruction.
296 Primitive (unboxed) types cannot be defined in Haskell, and are
297 therefore built into the language and compiler. Primitive types are
298 always unlifted; that is, a value of a primitive type cannot be
299 bottom. We use the convention that primitive types, values, and
300 operations have a <literal>#</literal> suffix.
304 Primitive values are often represented by a simple bit-pattern, such
305 as <literal>Int#</literal>, <literal>Float#</literal>,
306 <literal>Double#</literal>. But this is not necessarily the case:
307 a primitive value might be represented by a pointer to a
308 heap-allocated object. Examples include
309 <literal>Array#</literal>, the type of primitive arrays. A
310 primitive array is heap-allocated because it is too big a value to fit
311 in a register, and would be too expensive to copy around; in a sense,
312 it is accidental that it is represented by a pointer. If a pointer
313 represents a primitive value, then it really does point to that value:
314 no unevaluated thunks, no indirections…nothing can be at the
315 other end of the pointer than the primitive value.
319 There are some restrictions on the use of primitive types, the main
320 one being that you can't pass a primitive value to a polymorphic
321 function or store one in a polymorphic data type. This rules out
322 things like <literal>[Int#]</literal> (i.e. lists of primitive
323 integers). The reason for this restriction is that polymorphic
324 arguments and constructor fields are assumed to be pointers: if an
325 unboxed integer is stored in one of these, the garbage collector would
326 attempt to follow it, leading to unpredictable space leaks. Or a
327 <function>seq</function> operation on the polymorphic component may
328 attempt to dereference the pointer, with disastrous results. Even
329 worse, the unboxed value might be larger than a pointer
330 (<literal>Double#</literal> for instance).
334 Nevertheless, A numerically-intensive program using unboxed types can
335 go a <emphasis>lot</emphasis> faster than its “standard”
336 counterpart—we saw a threefold speedup on one example.
341 <sect2 id="unboxed-tuples">
342 <title>Unboxed Tuples
346 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
347 they're available by default with <option>-fglasgow-exts</option>. An
348 unboxed tuple looks like this:
360 where <literal>e_1..e_n</literal> are expressions of any
361 type (primitive or non-primitive). The type of an unboxed tuple looks
366 Unboxed tuples are used for functions that need to return multiple
367 values, but they avoid the heap allocation normally associated with
368 using fully-fledged tuples. When an unboxed tuple is returned, the
369 components are put directly into registers or on the stack; the
370 unboxed tuple itself does not have a composite representation. Many
371 of the primitive operations listed in this section return unboxed
376 There are some pretty stringent restrictions on the use of unboxed tuples:
385 Unboxed tuple types are subject to the same restrictions as
386 other unboxed types; i.e. they may not be stored in polymorphic data
387 structures or passed to polymorphic functions.
394 Unboxed tuples may only be constructed as the direct result of
395 a function, and may only be deconstructed with a <literal>case</literal> expression.
396 eg. the following are valid:
400 f x y = (# x+1, y-1 #)
401 g x = case f x x of { (# a, b #) -> a + b }
405 but the following are invalid:
419 No variable can have an unboxed tuple type. This is illegal:
423 f :: (# Int, Int #) -> (# Int, Int #)
428 because <literal>x</literal> has an unboxed tuple type.
438 Note: we may relax some of these restrictions in the future.
442 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
443 tuples to avoid unnecessary allocation during sequences of operations.
450 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
452 <sect1 id="syntax-extns">
453 <title>Syntactic extensions</title>
455 <!-- ====================== HIERARCHICAL MODULES ======================= -->
457 <sect2 id="hierarchical-modules">
458 <title>Hierarchical Modules</title>
460 <para>GHC supports a small extension to the syntax of module
461 names: a module name is allowed to contain a dot
462 <literal>‘.’</literal>. This is also known as the
463 “hierarchical module namespace” extension, because
464 it extends the normally flat Haskell module namespace into a
465 more flexible hierarchy of modules.</para>
467 <para>This extension has very little impact on the language
468 itself; modules names are <emphasis>always</emphasis> fully
469 qualified, so you can just think of the fully qualified module
470 name as <quote>the module name</quote>. In particular, this
471 means that the full module name must be given after the
472 <literal>module</literal> keyword at the beginning of the
473 module; for example, the module <literal>A.B.C</literal> must
476 <programlisting>module A.B.C</programlisting>
479 <para>It is a common strategy to use the <literal>as</literal>
480 keyword to save some typing when using qualified names with
481 hierarchical modules. For example:</para>
484 import qualified Control.Monad.ST.Strict as ST
487 <para>For details on how GHC searches for source and interface
488 files in the presence of hierarchical modules, see <xref
489 linkend="search-path"/>.</para>
491 <para>GHC comes with a large collection of libraries arranged
492 hierarchically; see the accompanying library documentation.
493 There is an ongoing project to create and maintain a stable set
494 of <quote>core</quote> libraries used by several Haskell
495 compilers, and the libraries that GHC comes with represent the
496 current status of that project. For more details, see <ulink
497 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
498 Libraries</ulink>.</para>
502 <!-- ====================== PATTERN GUARDS ======================= -->
504 <sect2 id="pattern-guards">
505 <title>Pattern guards</title>
508 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
509 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.)
513 Suppose we have an abstract data type of finite maps, with a
517 lookup :: FiniteMap -> Int -> Maybe Int
520 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
521 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
525 clunky env var1 var2 | ok1 && ok2 = val1 + val2
526 | otherwise = var1 + var2
537 The auxiliary functions are
541 maybeToBool :: Maybe a -> Bool
542 maybeToBool (Just x) = True
543 maybeToBool Nothing = False
545 expectJust :: Maybe a -> a
546 expectJust (Just x) = x
547 expectJust Nothing = error "Unexpected Nothing"
551 What is <function>clunky</function> doing? The guard <literal>ok1 &&
552 ok2</literal> checks that both lookups succeed, using
553 <function>maybeToBool</function> to convert the <function>Maybe</function>
554 types to booleans. The (lazily evaluated) <function>expectJust</function>
555 calls extract the values from the results of the lookups, and binds the
556 returned values to <varname>val1</varname> and <varname>val2</varname>
557 respectively. If either lookup fails, then clunky takes the
558 <literal>otherwise</literal> case and returns the sum of its arguments.
562 This is certainly legal Haskell, but it is a tremendously verbose and
563 un-obvious way to achieve the desired effect. Arguably, a more direct way
564 to write clunky would be to use case expressions:
568 clunky env var1 var1 = case lookup env var1 of
570 Just val1 -> case lookup env var2 of
572 Just val2 -> val1 + val2
578 This is a bit shorter, but hardly better. Of course, we can rewrite any set
579 of pattern-matching, guarded equations as case expressions; that is
580 precisely what the compiler does when compiling equations! The reason that
581 Haskell provides guarded equations is because they allow us to write down
582 the cases we want to consider, one at a time, independently of each other.
583 This structure is hidden in the case version. Two of the right-hand sides
584 are really the same (<function>fail</function>), and the whole expression
585 tends to become more and more indented.
589 Here is how I would write clunky:
594 | Just val1 <- lookup env var1
595 , Just val2 <- lookup env var2
597 ...other equations for clunky...
601 The semantics should be clear enough. The qualifers are matched in order.
602 For a <literal><-</literal> qualifier, which I call a pattern guard, the
603 right hand side is evaluated and matched against the pattern on the left.
604 If the match fails then the whole guard fails and the next equation is
605 tried. If it succeeds, then the appropriate binding takes place, and the
606 next qualifier is matched, in the augmented environment. Unlike list
607 comprehensions, however, the type of the expression to the right of the
608 <literal><-</literal> is the same as the type of the pattern to its
609 left. The bindings introduced by pattern guards scope over all the
610 remaining guard qualifiers, and over the right hand side of the equation.
614 Just as with list comprehensions, boolean expressions can be freely mixed
615 with among the pattern guards. For example:
626 Haskell's current guards therefore emerge as a special case, in which the
627 qualifier list has just one element, a boolean expression.
631 <!-- ===================== Recursive do-notation =================== -->
633 <sect2 id="mdo-notation">
634 <title>The recursive do-notation
637 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
638 "A recursive do for Haskell",
639 Levent Erkok, John Launchbury",
640 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
643 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
644 that is, the variables bound in a do-expression are visible only in the textually following
645 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
646 group. It turns out that several applications can benefit from recursive bindings in
647 the do-notation, and this extension provides the necessary syntactic support.
650 Here is a simple (yet contrived) example:
653 import Control.Monad.Fix
655 justOnes = mdo xs <- Just (1:xs)
659 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
663 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
666 class Monad m => MonadFix m where
667 mfix :: (a -> m a) -> m a
670 The function <literal>mfix</literal>
671 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
672 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
673 For details, see the above mentioned reference.
676 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
677 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
678 for Haskell's internal state monad (strict and lazy, respectively).
681 There are three important points in using the recursive-do notation:
684 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
685 than <literal>do</literal>).
689 You should <literal>import Control.Monad.Fix</literal>.
690 (Note: Strictly speaking, this import is required only when you need to refer to the name
691 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
692 are encouraged to always import this module when using the mdo-notation.)
696 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
702 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
703 contains up to date information on recursive monadic bindings.
707 Historical note: The old implementation of the mdo-notation (and most
708 of the existing documents) used the name
709 <literal>MonadRec</literal> for the class and the corresponding library.
710 This name is not supported by GHC.
716 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
718 <sect2 id="parallel-list-comprehensions">
719 <title>Parallel List Comprehensions</title>
720 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
722 <indexterm><primary>parallel list comprehensions</primary>
725 <para>Parallel list comprehensions are a natural extension to list
726 comprehensions. List comprehensions can be thought of as a nice
727 syntax for writing maps and filters. Parallel comprehensions
728 extend this to include the zipWith family.</para>
730 <para>A parallel list comprehension has multiple independent
731 branches of qualifier lists, each separated by a `|' symbol. For
732 example, the following zips together two lists:</para>
735 [ (x, y) | x <- xs | y <- ys ]
738 <para>The behavior of parallel list comprehensions follows that of
739 zip, in that the resulting list will have the same length as the
740 shortest branch.</para>
742 <para>We can define parallel list comprehensions by translation to
743 regular comprehensions. Here's the basic idea:</para>
745 <para>Given a parallel comprehension of the form: </para>
748 [ e | p1 <- e11, p2 <- e12, ...
749 | q1 <- e21, q2 <- e22, ...
754 <para>This will be translated to: </para>
757 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
758 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
763 <para>where `zipN' is the appropriate zip for the given number of
768 <sect2 id="rebindable-syntax">
769 <title>Rebindable syntax</title>
772 <para>GHC allows most kinds of built-in syntax to be rebound by
773 the user, to facilitate replacing the <literal>Prelude</literal>
774 with a home-grown version, for example.</para>
776 <para>You may want to define your own numeric class
777 hierarchy. It completely defeats that purpose if the
778 literal "1" means "<literal>Prelude.fromInteger
779 1</literal>", which is what the Haskell Report specifies.
780 So the <option>-fno-implicit-prelude</option> flag causes
781 the following pieces of built-in syntax to refer to
782 <emphasis>whatever is in scope</emphasis>, not the Prelude
787 <para>Integer and fractional literals mean
788 "<literal>fromInteger 1</literal>" and
789 "<literal>fromRational 3.2</literal>", not the
790 Prelude-qualified versions; both in expressions and in
792 <para>However, the standard Prelude <literal>Eq</literal> class
793 is still used for the equality test necessary for literal patterns.</para>
797 <para>Negation (e.g. "<literal>- (f x)</literal>")
798 means "<literal>negate (f x)</literal>" (not
799 <literal>Prelude.negate</literal>).</para>
803 <para>In an n+k pattern, the standard Prelude
804 <literal>Ord</literal> class is still used for comparison,
805 but the necessary subtraction uses whatever
806 "<literal>(-)</literal>" is in scope (not
807 "<literal>Prelude.(-)</literal>").</para>
811 <para>"Do" notation is translated using whatever
812 functions <literal>(>>=)</literal>,
813 <literal>(>>)</literal>, <literal>fail</literal>, and
814 <literal>return</literal>, are in scope (not the Prelude
815 versions). List comprehensions, and parallel array
816 comprehensions, are unaffected. </para></listitem>
819 <para>Be warned: this is an experimental facility, with fewer checks than
820 usual. In particular, it is essential that the functions GHC finds in scope
821 must have the appropriate types, namely:
823 fromInteger :: forall a. (...) => Integer -> a
824 fromRational :: forall a. (...) => Rational -> a
825 negate :: forall a. (...) => a -> a
826 (-) :: forall a. (...) => a -> a -> a
827 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
828 (>>) :: forall m a. (...) => m a -> m b -> m b
829 return :: forall m a. (...) => a -> m a
830 fail :: forall m a. (...) => String -> m a
832 (The (...) part can be any context including the empty context; that part
834 If the functions don't have the right type, very peculiar things may
835 happen. Use <literal>-dcore-lint</literal> to
836 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
842 <!-- TYPE SYSTEM EXTENSIONS -->
843 <sect1 id="type-extensions">
844 <title>Type system extensions</title>
848 <title>Data types and type synonyms</title>
850 <sect3 id="nullary-types">
851 <title>Data types with no constructors</title>
853 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
854 a data type with no constructors. For example:</para>
858 data T a -- T :: * -> *
861 <para>Syntactically, the declaration lacks the "= constrs" part. The
862 type can be parameterised over types of any kind, but if the kind is
863 not <literal>*</literal> then an explicit kind annotation must be used
864 (see <xref linkend="sec-kinding"/>).</para>
866 <para>Such data types have only one value, namely bottom.
867 Nevertheless, they can be useful when defining "phantom types".</para>
870 <sect3 id="infix-tycons">
871 <title>Infix type constructors</title>
874 GHC allows type constructors to be operators, and to be written infix, very much
875 like expressions. More specifically:
878 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
879 The lexical syntax is the same as that for data constructors.
882 Types can be written infix. For example <literal>Int :*: Bool</literal>.
886 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
887 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
890 Fixities may be declared for type constructors just as for data constructors. However,
891 one cannot distinguish between the two in a fixity declaration; a fixity declaration
892 sets the fixity for a data constructor and the corresponding type constructor. For example:
896 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
897 and similarly for <literal>:*:</literal>.
898 <literal>Int `a` Bool</literal>.
901 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
904 Data type and type-synonym declarations can be written infix. E.g.
906 data a :*: b = Foo a b
907 type a :+: b = Either a b
911 The only thing that differs between operators in types and operators in expressions is that
912 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
913 are not allowed in types. Reason: the uniform thing to do would be to make them type
914 variables, but that's not very useful. A less uniform but more useful thing would be to
915 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
916 lists. So for now we just exclude them.
923 <sect3 id="type-synonyms">
924 <title>Liberalised type synonyms</title>
927 Type synonmys are like macros at the type level, and
928 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
929 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
931 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
932 in a type synonym, thus:
934 type Discard a = forall b. Show b => a -> b -> (a, String)
939 g :: Discard Int -> (Int,Bool) -- A rank-2 type
946 You can write an unboxed tuple in a type synonym:
948 type Pr = (# Int, Int #)
956 You can apply a type synonym to a forall type:
958 type Foo a = a -> a -> Bool
960 f :: Foo (forall b. b->b)
962 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
964 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
969 You can apply a type synonym to a partially applied type synonym:
971 type Generic i o = forall x. i x -> o x
976 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
978 foo :: forall x. x -> [x]
986 GHC currently does kind checking before expanding synonyms (though even that
990 After expanding type synonyms, GHC does validity checking on types, looking for
991 the following mal-formedness which isn't detected simply by kind checking:
994 Type constructor applied to a type involving for-alls.
997 Unboxed tuple on left of an arrow.
1000 Partially-applied type synonym.
1004 this will be rejected:
1006 type Pr = (# Int, Int #)
1011 because GHC does not allow unboxed tuples on the left of a function arrow.
1016 <sect3 id="existential-quantification">
1017 <title>Existentially quantified data constructors
1021 The idea of using existential quantification in data type declarations
1022 was suggested by Laufer (I believe, thought doubtless someone will
1023 correct me), and implemented in Hope+. It's been in Lennart
1024 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1025 proved very useful. Here's the idea. Consider the declaration:
1031 data Foo = forall a. MkFoo a (a -> Bool)
1038 The data type <literal>Foo</literal> has two constructors with types:
1044 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1051 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1052 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1053 For example, the following expression is fine:
1059 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1065 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1066 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1067 isUpper</function> packages a character with a compatible function. These
1068 two things are each of type <literal>Foo</literal> and can be put in a list.
1072 What can we do with a value of type <literal>Foo</literal>?. In particular,
1073 what happens when we pattern-match on <function>MkFoo</function>?
1079 f (MkFoo val fn) = ???
1085 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1086 are compatible, the only (useful) thing we can do with them is to
1087 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1094 f (MkFoo val fn) = fn val
1100 What this allows us to do is to package heterogenous values
1101 together with a bunch of functions that manipulate them, and then treat
1102 that collection of packages in a uniform manner. You can express
1103 quite a bit of object-oriented-like programming this way.
1106 <sect4 id="existential">
1107 <title>Why existential?
1111 What has this to do with <emphasis>existential</emphasis> quantification?
1112 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1118 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1124 But Haskell programmers can safely think of the ordinary
1125 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1126 adding a new existential quantification construct.
1132 <title>Type classes</title>
1135 An easy extension (implemented in <command>hbc</command>) is to allow
1136 arbitrary contexts before the constructor. For example:
1142 data Baz = forall a. Eq a => Baz1 a a
1143 | forall b. Show b => Baz2 b (b -> b)
1149 The two constructors have the types you'd expect:
1155 Baz1 :: forall a. Eq a => a -> a -> Baz
1156 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1162 But when pattern matching on <function>Baz1</function> the matched values can be compared
1163 for equality, and when pattern matching on <function>Baz2</function> the first matched
1164 value can be converted to a string (as well as applying the function to it).
1165 So this program is legal:
1172 f (Baz1 p q) | p == q = "Yes"
1174 f (Baz2 v fn) = show (fn v)
1180 Operationally, in a dictionary-passing implementation, the
1181 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1182 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1183 extract it on pattern matching.
1187 Notice the way that the syntax fits smoothly with that used for
1188 universal quantification earlier.
1194 <title>Restrictions</title>
1197 There are several restrictions on the ways in which existentially-quantified
1198 constructors can be use.
1207 When pattern matching, each pattern match introduces a new,
1208 distinct, type for each existential type variable. These types cannot
1209 be unified with any other type, nor can they escape from the scope of
1210 the pattern match. For example, these fragments are incorrect:
1218 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1219 is the result of <function>f1</function>. One way to see why this is wrong is to
1220 ask what type <function>f1</function> has:
1224 f1 :: Foo -> a -- Weird!
1228 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1233 f1 :: forall a. Foo -> a -- Wrong!
1237 The original program is just plain wrong. Here's another sort of error
1241 f2 (Baz1 a b) (Baz1 p q) = a==q
1245 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1246 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1247 from the two <function>Baz1</function> constructors.
1255 You can't pattern-match on an existentially quantified
1256 constructor in a <literal>let</literal> or <literal>where</literal> group of
1257 bindings. So this is illegal:
1261 f3 x = a==b where { Baz1 a b = x }
1264 Instead, use a <literal>case</literal> expression:
1267 f3 x = case x of Baz1 a b -> a==b
1270 In general, you can only pattern-match
1271 on an existentially-quantified constructor in a <literal>case</literal> expression or
1272 in the patterns of a function definition.
1274 The reason for this restriction is really an implementation one.
1275 Type-checking binding groups is already a nightmare without
1276 existentials complicating the picture. Also an existential pattern
1277 binding at the top level of a module doesn't make sense, because it's
1278 not clear how to prevent the existentially-quantified type "escaping".
1279 So for now, there's a simple-to-state restriction. We'll see how
1287 You can't use existential quantification for <literal>newtype</literal>
1288 declarations. So this is illegal:
1292 newtype T = forall a. Ord a => MkT a
1296 Reason: a value of type <literal>T</literal> must be represented as a
1297 pair of a dictionary for <literal>Ord t</literal> and a value of type
1298 <literal>t</literal>. That contradicts the idea that
1299 <literal>newtype</literal> should have no concrete representation.
1300 You can get just the same efficiency and effect by using
1301 <literal>data</literal> instead of <literal>newtype</literal>. If
1302 there is no overloading involved, then there is more of a case for
1303 allowing an existentially-quantified <literal>newtype</literal>,
1304 because the <literal>data</literal> version does carry an
1305 implementation cost, but single-field existentially quantified
1306 constructors aren't much use. So the simple restriction (no
1307 existential stuff on <literal>newtype</literal>) stands, unless there
1308 are convincing reasons to change it.
1316 You can't use <literal>deriving</literal> to define instances of a
1317 data type with existentially quantified data constructors.
1319 Reason: in most cases it would not make sense. For example:#
1322 data T = forall a. MkT [a] deriving( Eq )
1325 To derive <literal>Eq</literal> in the standard way we would need to have equality
1326 between the single component of two <function>MkT</function> constructors:
1330 (MkT a) == (MkT b) = ???
1333 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1334 It's just about possible to imagine examples in which the derived instance
1335 would make sense, but it seems altogether simpler simply to prohibit such
1336 declarations. Define your own instances!
1351 <sect2 id="multi-param-type-classes">
1352 <title>Class declarations</title>
1355 This section documents GHC's implementation of multi-parameter type
1356 classes. There's lots of background in the paper <ulink
1357 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1358 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1359 Jones, Erik Meijer).
1362 There are the following constraints on class declarations:
1367 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1371 class Collection c a where
1372 union :: c a -> c a -> c a
1383 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1384 of "acyclic" involves only the superclass relationships. For example,
1390 op :: D b => a -> b -> b
1393 class C a => D a where { ... }
1397 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1398 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1399 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1406 <emphasis>There are no restrictions on the context in a class declaration
1407 (which introduces superclasses), except that the class hierarchy must
1408 be acyclic</emphasis>. So these class declarations are OK:
1412 class Functor (m k) => FiniteMap m k where
1415 class (Monad m, Monad (t m)) => Transform t m where
1416 lift :: m a -> (t m) a
1426 <emphasis>All of the class type variables must be reachable (in the sense
1427 mentioned in <xref linkend="type-restrictions"/>)
1428 from the free varibles of each method type
1429 </emphasis>. For example:
1433 class Coll s a where
1435 insert :: s -> a -> s
1439 is not OK, because the type of <literal>empty</literal> doesn't mention
1440 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1441 types, and has the same motivation.
1443 Sometimes, offending class declarations exhibit misunderstandings. For
1444 example, <literal>Coll</literal> might be rewritten
1448 class Coll s a where
1450 insert :: s a -> a -> s a
1454 which makes the connection between the type of a collection of
1455 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1456 Occasionally this really doesn't work, in which case you can split the
1464 class CollE s => Coll s a where
1465 insert :: s -> a -> s
1475 <sect3 id="class-method-types">
1476 <title>Class method types</title>
1478 Haskell 98 prohibits class method types to mention constraints on the
1479 class type variable, thus:
1482 fromList :: [a] -> s a
1483 elem :: Eq a => a -> s a -> Bool
1485 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1486 contains the constraint <literal>Eq a</literal>, constrains only the
1487 class type variable (in this case <literal>a</literal>).
1490 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1497 <sect2 id="type-restrictions">
1498 <title>Type signatures</title>
1500 <sect3><title>The context of a type signature</title>
1502 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1503 the form <emphasis>(class type-variable)</emphasis> or
1504 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1505 these type signatures are perfectly OK
1508 g :: Ord (T a ()) => ...
1512 GHC imposes the following restrictions on the constraints in a type signature.
1516 forall tv1..tvn (c1, ...,cn) => type
1519 (Here, we write the "foralls" explicitly, although the Haskell source
1520 language omits them; in Haskell 98, all the free type variables of an
1521 explicit source-language type signature are universally quantified,
1522 except for the class type variables in a class declaration. However,
1523 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1532 <emphasis>Each universally quantified type variable
1533 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1535 A type variable <literal>a</literal> is "reachable" if it it appears
1536 in the same constraint as either a type variable free in in
1537 <literal>type</literal>, or another reachable type variable.
1538 A value with a type that does not obey
1539 this reachability restriction cannot be used without introducing
1540 ambiguity; that is why the type is rejected.
1541 Here, for example, is an illegal type:
1545 forall a. Eq a => Int
1549 When a value with this type was used, the constraint <literal>Eq tv</literal>
1550 would be introduced where <literal>tv</literal> is a fresh type variable, and
1551 (in the dictionary-translation implementation) the value would be
1552 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1553 can never know which instance of <literal>Eq</literal> to use because we never
1554 get any more information about <literal>tv</literal>.
1558 that the reachability condition is weaker than saying that <literal>a</literal> is
1559 functionally dependendent on a type variable free in
1560 <literal>type</literal> (see <xref
1561 linkend="functional-dependencies"/>). The reason for this is there
1562 might be a "hidden" dependency, in a superclass perhaps. So
1563 "reachable" is a conservative approximation to "functionally dependent".
1564 For example, consider:
1566 class C a b | a -> b where ...
1567 class C a b => D a b where ...
1568 f :: forall a b. D a b => a -> a
1570 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1571 but that is not immediately apparent from <literal>f</literal>'s type.
1577 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1578 universally quantified type variables <literal>tvi</literal></emphasis>.
1580 For example, this type is OK because <literal>C a b</literal> mentions the
1581 universally quantified type variable <literal>b</literal>:
1585 forall a. C a b => burble
1589 The next type is illegal because the constraint <literal>Eq b</literal> does not
1590 mention <literal>a</literal>:
1594 forall a. Eq b => burble
1598 The reason for this restriction is milder than the other one. The
1599 excluded types are never useful or necessary (because the offending
1600 context doesn't need to be witnessed at this point; it can be floated
1601 out). Furthermore, floating them out increases sharing. Lastly,
1602 excluding them is a conservative choice; it leaves a patch of
1603 territory free in case we need it later.
1614 <title>For-all hoisting</title>
1616 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1617 end of an arrow, thus:
1619 type Discard a = forall b. a -> b -> a
1621 g :: Int -> Discard Int
1624 Simply expanding the type synonym would give
1626 g :: Int -> (forall b. Int -> b -> Int)
1628 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1630 g :: forall b. Int -> Int -> b -> Int
1632 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1633 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1634 performs the transformation:</emphasis>
1636 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1638 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1640 (In fact, GHC tries to retain as much synonym information as possible for use in
1641 error messages, but that is a usability issue.) This rule applies, of course, whether
1642 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1643 valid way to write <literal>g</literal>'s type signature:
1645 g :: Int -> Int -> forall b. b -> Int
1649 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1652 type Foo a = (?x::Int) => Bool -> a
1657 g :: (?x::Int) => Bool -> Bool -> Int
1665 <sect2 id="instance-decls">
1666 <title>Instance declarations</title>
1669 <title>Overlapping instances</title>
1671 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1676 instance context1 => C type1 where ...
1677 instance context2 => C type2 where ...
1680 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
1683 However, if you give the command line option
1684 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1685 option</primary></indexterm> then overlapping instance declarations are permitted.
1686 However, GHC arranges never to commit to using an instance declaration
1687 if another instance declaration also applies, either now or later.
1693 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1699 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1700 (but not identical to <literal>type1</literal>), or vice versa.
1704 Notice that these rules
1709 make it clear which instance decl to use
1710 (pick the most specific one that matches)
1717 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1718 Reason: you can pick which instance decl
1719 "matches" based on the type.
1724 However the rules are over-conservative. Two instance declarations can overlap,
1725 but it can still be clear in particular situations which to use. For example:
1727 instance C (Int,a) where ...
1728 instance C (a,Bool) where ...
1730 These are rejected by GHC's rules, but it is clear what to do when trying
1731 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1732 cannot apply. Yell if this restriction bites you.
1735 GHC is also conservative about committing to an overlapping instance. For example:
1737 class C a where { op :: a -> a }
1738 instance C [Int] where ...
1739 instance C a => C [a] where ...
1741 f :: C b => [b] -> [b]
1744 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1745 GHC does not commit to the second instance declaration, because in a paricular
1746 call of f, b might be instantiate to Int, so the first instance declaration
1747 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1748 GHC will instead silently pick the second instance, without complaining about
1749 the problem of subsequent instantiations.
1752 Regrettably, GHC doesn't guarantee to detect overlapping instance
1753 declarations if they appear in different modules. GHC can "see" the
1754 instance declarations in the transitive closure of all the modules
1755 imported by the one being compiled, so it can "see" all instance decls
1756 when it is compiling <literal>Main</literal>. However, it currently chooses not
1757 to look at ones that can't possibly be of use in the module currently
1758 being compiled, in the interests of efficiency. (Perhaps we should
1759 change that decision, at least for <literal>Main</literal>.)
1764 <title>Type synonyms in the instance head</title>
1767 <emphasis>Unlike Haskell 98, instance heads may use type
1768 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1769 As always, using a type synonym is just shorthand for
1770 writing the RHS of the type synonym definition. For example:
1774 type Point = (Int,Int)
1775 instance C Point where ...
1776 instance C [Point] where ...
1780 is legal. However, if you added
1784 instance C (Int,Int) where ...
1788 as well, then the compiler will complain about the overlapping
1789 (actually, identical) instance declarations. As always, type synonyms
1790 must be fully applied. You cannot, for example, write:
1795 instance Monad P where ...
1799 This design decision is independent of all the others, and easily
1800 reversed, but it makes sense to me.
1805 <sect3 id="undecidable-instances">
1806 <title>Undecidable instances</title>
1808 <para>An instance declaration must normally obey the following rules:
1810 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1811 an instance declaration <emphasis>must not</emphasis> be a type variable.
1812 For example, these are OK:
1815 instance C Int a where ...
1817 instance D (Int, Int) where ...
1819 instance E [[a]] where ...
1823 instance F a where ...
1825 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1826 For example, this is OK:
1828 instance Stateful (ST s) (MutVar s) where ...
1835 <para>All of the types in the <emphasis>context</emphasis> of
1836 an instance declaration <emphasis>must</emphasis> be type variables.
1839 instance C a b => Eq (a,b) where ...
1843 instance C Int b => Foo b where ...
1849 These restrictions ensure that
1850 context reduction terminates: each reduction step removes one type
1851 constructor. For example, the following would make the type checker
1852 loop if it wasn't excluded:
1854 instance C a => C a where ...
1856 There are two situations in which the rule is a bit of a pain. First,
1857 if one allows overlapping instance declarations then it's quite
1858 convenient to have a "default instance" declaration that applies if
1859 something more specific does not:
1868 Second, sometimes you might want to use the following to get the
1869 effect of a "class synonym":
1873 class (C1 a, C2 a, C3 a) => C a where { }
1875 instance (C1 a, C2 a, C3 a) => C a where { }
1879 This allows you to write shorter signatures:
1891 f :: (C1 a, C2 a, C3 a) => ...
1895 Voluminous correspondence on the Haskell mailing list has convinced me
1896 that it's worth experimenting with more liberal rules. If you use
1897 the experimental flag <option>-fallow-undecidable-instances</option>
1898 <indexterm><primary>-fallow-undecidable-instances
1899 option</primary></indexterm>, you can use arbitrary
1900 types in both an instance context and instance head. Termination is ensured by having a
1901 fixed-depth recursion stack. If you exceed the stack depth you get a
1902 sort of backtrace, and the opportunity to increase the stack depth
1903 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1906 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1907 allowing these idioms interesting idioms.
1914 <sect2 id="implicit-parameters">
1915 <title>Implicit parameters</title>
1917 <para> Implicit paramters are implemented as described in
1918 "Implicit parameters: dynamic scoping with static types",
1919 J Lewis, MB Shields, E Meijer, J Launchbury,
1920 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1924 <para>(Most of the following, stil rather incomplete, documentation is
1925 due to Jeff Lewis.)</para>
1927 <para>Implicit parameter support is enabled with the option
1928 <option>-fimplicit-params</option>.</para>
1931 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1932 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1933 context. In Haskell, all variables are statically bound. Dynamic
1934 binding of variables is a notion that goes back to Lisp, but was later
1935 discarded in more modern incarnations, such as Scheme. Dynamic binding
1936 can be very confusing in an untyped language, and unfortunately, typed
1937 languages, in particular Hindley-Milner typed languages like Haskell,
1938 only support static scoping of variables.
1941 However, by a simple extension to the type class system of Haskell, we
1942 can support dynamic binding. Basically, we express the use of a
1943 dynamically bound variable as a constraint on the type. These
1944 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1945 function uses a dynamically-bound variable <literal>?x</literal>
1946 of type <literal>t'</literal>". For
1947 example, the following expresses the type of a sort function,
1948 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1950 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1952 The dynamic binding constraints are just a new form of predicate in the type class system.
1955 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1956 where <literal>x</literal> is
1957 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1958 Use of this construct also introduces a new
1959 dynamic-binding constraint in the type of the expression.
1960 For example, the following definition
1961 shows how we can define an implicitly parameterized sort function in
1962 terms of an explicitly parameterized <literal>sortBy</literal> function:
1964 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1966 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1972 <title>Implicit-parameter type constraints</title>
1974 Dynamic binding constraints behave just like other type class
1975 constraints in that they are automatically propagated. Thus, when a
1976 function is used, its implicit parameters are inherited by the
1977 function that called it. For example, our <literal>sort</literal> function might be used
1978 to pick out the least value in a list:
1980 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1981 least xs = fst (sort xs)
1983 Without lifting a finger, the <literal>?cmp</literal> parameter is
1984 propagated to become a parameter of <literal>least</literal> as well. With explicit
1985 parameters, the default is that parameters must always be explicit
1986 propagated. With implicit parameters, the default is to always
1990 An implicit-parameter type constraint differs from other type class constraints in the
1991 following way: All uses of a particular implicit parameter must have
1992 the same type. This means that the type of <literal>(?x, ?x)</literal>
1993 is <literal>(?x::a) => (a,a)</literal>, and not
1994 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1998 <para> You can't have an implicit parameter in the context of a class or instance
1999 declaration. For example, both these declarations are illegal:
2001 class (?x::Int) => C a where ...
2002 instance (?x::a) => Foo [a] where ...
2004 Reason: exactly which implicit parameter you pick up depends on exactly where
2005 you invoke a function. But the ``invocation'' of instance declarations is done
2006 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2007 Easiest thing is to outlaw the offending types.</para>
2009 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2011 f :: (?x :: [a]) => Int -> Int
2014 g :: (Read a, Show a) => String -> String
2017 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2018 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2019 quite unambiguous, and fixes the type <literal>a</literal>.
2024 <title>Implicit-parameter bindings</title>
2027 An implicit parameter is <emphasis>bound</emphasis> using the standard
2028 <literal>let</literal> or <literal>where</literal> binding forms.
2029 For example, we define the <literal>min</literal> function by binding
2030 <literal>cmp</literal>.
2033 min = let ?cmp = (<=) in least
2037 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2038 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2039 (including in a list comprehension, or do-notation, or pattern guards),
2040 or a <literal>where</literal> clause.
2041 Note the following points:
2044 An implicit-parameter binding group must be a
2045 collection of simple bindings to implicit-style variables (no
2046 function-style bindings, and no type signatures); these bindings are
2047 neither polymorphic or recursive.
2050 You may not mix implicit-parameter bindings with ordinary bindings in a
2051 single <literal>let</literal>
2052 expression; use two nested <literal>let</literal>s instead.
2053 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2057 You may put multiple implicit-parameter bindings in a
2058 single binding group; but they are <emphasis>not</emphasis> treated
2059 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2060 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2061 parameter. The bindings are not nested, and may be re-ordered without changing
2062 the meaning of the program.
2063 For example, consider:
2065 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2067 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2068 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2070 f :: (?x::Int) => Int -> Int
2079 <sect2 id="linear-implicit-parameters">
2080 <title>Linear implicit parameters</title>
2082 Linear implicit parameters are an idea developed by Koen Claessen,
2083 Mark Shields, and Simon PJ. They address the long-standing
2084 problem that monads seem over-kill for certain sorts of problem, notably:
2087 <listitem> <para> distributing a supply of unique names </para> </listitem>
2088 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2089 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2093 Linear implicit parameters are just like ordinary implicit parameters,
2094 except that they are "linear" -- that is, they cannot be copied, and
2095 must be explicitly "split" instead. Linear implicit parameters are
2096 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2097 (The '/' in the '%' suggests the split!)
2102 import GHC.Exts( Splittable )
2104 data NameSupply = ...
2106 splitNS :: NameSupply -> (NameSupply, NameSupply)
2107 newName :: NameSupply -> Name
2109 instance Splittable NameSupply where
2113 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2114 f env (Lam x e) = Lam x' (f env e)
2117 env' = extend env x x'
2118 ...more equations for f...
2120 Notice that the implicit parameter %ns is consumed
2122 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2123 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2127 So the translation done by the type checker makes
2128 the parameter explicit:
2130 f :: NameSupply -> Env -> Expr -> Expr
2131 f ns env (Lam x e) = Lam x' (f ns1 env e)
2133 (ns1,ns2) = splitNS ns
2135 env = extend env x x'
2137 Notice the call to 'split' introduced by the type checker.
2138 How did it know to use 'splitNS'? Because what it really did
2139 was to introduce a call to the overloaded function 'split',
2140 defined by the class <literal>Splittable</literal>:
2142 class Splittable a where
2145 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2146 split for name supplies. But we can simply write
2152 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2154 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2155 <literal>GHC.Exts</literal>.
2160 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2161 are entirely distinct implicit parameters: you
2162 can use them together and they won't intefere with each other. </para>
2165 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2167 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2168 in the context of a class or instance declaration. </para></listitem>
2172 <sect3><title>Warnings</title>
2175 The monomorphism restriction is even more important than usual.
2176 Consider the example above:
2178 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2179 f env (Lam x e) = Lam x' (f env e)
2182 env' = extend env x x'
2184 If we replaced the two occurrences of x' by (newName %ns), which is
2185 usually a harmless thing to do, we get:
2187 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2188 f env (Lam x e) = Lam (newName %ns) (f env e)
2190 env' = extend env x (newName %ns)
2192 But now the name supply is consumed in <emphasis>three</emphasis> places
2193 (the two calls to newName,and the recursive call to f), so
2194 the result is utterly different. Urk! We don't even have
2198 Well, this is an experimental change. With implicit
2199 parameters we have already lost beta reduction anyway, and
2200 (as John Launchbury puts it) we can't sensibly reason about
2201 Haskell programs without knowing their typing.
2206 <sect3><title>Recursive functions</title>
2207 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2210 foo :: %x::T => Int -> [Int]
2212 foo n = %x : foo (n-1)
2214 where T is some type in class Splittable.</para>
2216 Do you get a list of all the same T's or all different T's
2217 (assuming that split gives two distinct T's back)?
2219 If you supply the type signature, taking advantage of polymorphic
2220 recursion, you get what you'd probably expect. Here's the
2221 translated term, where the implicit param is made explicit:
2224 foo x n = let (x1,x2) = split x
2225 in x1 : foo x2 (n-1)
2227 But if you don't supply a type signature, GHC uses the Hindley
2228 Milner trick of using a single monomorphic instance of the function
2229 for the recursive calls. That is what makes Hindley Milner type inference
2230 work. So the translation becomes
2234 foom n = x : foom (n-1)
2238 Result: 'x' is not split, and you get a list of identical T's. So the
2239 semantics of the program depends on whether or not foo has a type signature.
2242 You may say that this is a good reason to dislike linear implicit parameters
2243 and you'd be right. That is why they are an experimental feature.
2249 <sect2 id="functional-dependencies">
2250 <title>Functional dependencies
2253 <para> Functional dependencies are implemented as described by Mark Jones
2254 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2255 In Proceedings of the 9th European Symposium on Programming,
2256 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2260 Functional dependencies are introduced by a vertical bar in the syntax of a
2261 class declaration; e.g.
2263 class (Monad m) => MonadState s m | m -> s where ...
2265 class Foo a b c | a b -> c where ...
2267 There should be more documentation, but there isn't (yet). Yell if you need it.
2273 <sect2 id="sec-kinding">
2274 <title>Explicitly-kinded quantification</title>
2277 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2278 to give the kind explicitly as (machine-checked) documentation,
2279 just as it is nice to give a type signature for a function. On some occasions,
2280 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2281 John Hughes had to define the data type:
2283 data Set cxt a = Set [a]
2284 | Unused (cxt a -> ())
2286 The only use for the <literal>Unused</literal> constructor was to force the correct
2287 kind for the type variable <literal>cxt</literal>.
2290 GHC now instead allows you to specify the kind of a type variable directly, wherever
2291 a type variable is explicitly bound. Namely:
2293 <listitem><para><literal>data</literal> declarations:
2295 data Set (cxt :: * -> *) a = Set [a]
2296 </screen></para></listitem>
2297 <listitem><para><literal>type</literal> declarations:
2299 type T (f :: * -> *) = f Int
2300 </screen></para></listitem>
2301 <listitem><para><literal>class</literal> declarations:
2303 class (Eq a) => C (f :: * -> *) a where ...
2304 </screen></para></listitem>
2305 <listitem><para><literal>forall</literal>'s in type signatures:
2307 f :: forall (cxt :: * -> *). Set cxt Int
2308 </screen></para></listitem>
2313 The parentheses are required. Some of the spaces are required too, to
2314 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2315 will get a parse error, because "<literal>::*->*</literal>" is a
2316 single lexeme in Haskell.
2320 As part of the same extension, you can put kind annotations in types
2323 f :: (Int :: *) -> Int
2324 g :: forall a. a -> (a :: *)
2328 atype ::= '(' ctype '::' kind ')
2330 The parentheses are required.
2335 <sect2 id="universal-quantification">
2336 <title>Arbitrary-rank polymorphism
2340 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2341 allows us to say exactly what this means. For example:
2349 g :: forall b. (b -> b)
2351 The two are treated identically.
2355 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2356 explicit universal quantification in
2358 For example, all the following types are legal:
2360 f1 :: forall a b. a -> b -> a
2361 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2363 f2 :: (forall a. a->a) -> Int -> Int
2364 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2366 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2368 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2369 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2370 The <literal>forall</literal> makes explicit the universal quantification that
2371 is implicitly added by Haskell.
2374 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2375 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2376 shows, the polymorphic type on the left of the function arrow can be overloaded.
2379 The function <literal>f3</literal> has a rank-3 type;
2380 it has rank-2 types on the left of a function arrow.
2383 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2384 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2385 that restriction has now been lifted.)
2386 In particular, a forall-type (also called a "type scheme"),
2387 including an operational type class context, is legal:
2389 <listitem> <para> On the left of a function arrow </para> </listitem>
2390 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2391 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2392 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2393 field type signatures.</para> </listitem>
2394 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2395 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2397 There is one place you cannot put a <literal>forall</literal>:
2398 you cannot instantiate a type variable with a forall-type. So you cannot
2399 make a forall-type the argument of a type constructor. So these types are illegal:
2401 x1 :: [forall a. a->a]
2402 x2 :: (forall a. a->a, Int)
2403 x3 :: Maybe (forall a. a->a)
2405 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2406 a type variable any more!
2415 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2416 the types of the constructor arguments. Here are several examples:
2422 data T a = T1 (forall b. b -> b -> b) a
2424 data MonadT m = MkMonad { return :: forall a. a -> m a,
2425 bind :: forall a b. m a -> (a -> m b) -> m b
2428 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2434 The constructors have rank-2 types:
2440 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2441 MkMonad :: forall m. (forall a. a -> m a)
2442 -> (forall a b. m a -> (a -> m b) -> m b)
2444 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2450 Notice that you don't need to use a <literal>forall</literal> if there's an
2451 explicit context. For example in the first argument of the
2452 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2453 prefixed to the argument type. The implicit <literal>forall</literal>
2454 quantifies all type variables that are not already in scope, and are
2455 mentioned in the type quantified over.
2459 As for type signatures, implicit quantification happens for non-overloaded
2460 types too. So if you write this:
2463 data T a = MkT (Either a b) (b -> b)
2466 it's just as if you had written this:
2469 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2472 That is, since the type variable <literal>b</literal> isn't in scope, it's
2473 implicitly universally quantified. (Arguably, it would be better
2474 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2475 where that is what is wanted. Feedback welcomed.)
2479 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2480 the constructor to suitable values, just as usual. For example,
2491 a3 = MkSwizzle reverse
2494 a4 = let r x = Just x
2501 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2502 mkTs f x y = [T1 f x, T1 f y]
2508 The type of the argument can, as usual, be more general than the type
2509 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2510 does not need the <literal>Ord</literal> constraint.)
2514 When you use pattern matching, the bound variables may now have
2515 polymorphic types. For example:
2521 f :: T a -> a -> (a, Char)
2522 f (T1 w k) x = (w k x, w 'c' 'd')
2524 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2525 g (MkSwizzle s) xs f = s (map f (s xs))
2527 h :: MonadT m -> [m a] -> m [a]
2528 h m [] = return m []
2529 h m (x:xs) = bind m x $ \y ->
2530 bind m (h m xs) $ \ys ->
2537 In the function <function>h</function> we use the record selectors <literal>return</literal>
2538 and <literal>bind</literal> to extract the polymorphic bind and return functions
2539 from the <literal>MonadT</literal> data structure, rather than using pattern
2545 <title>Type inference</title>
2548 In general, type inference for arbitrary-rank types is undecideable.
2549 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2550 to get a decidable algorithm by requiring some help from the programmer.
2551 We do not yet have a formal specification of "some help" but the rule is this:
2554 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2555 provides an explicit polymorphic type for x, or GHC's type inference will assume
2556 that x's type has no foralls in it</emphasis>.
2559 What does it mean to "provide" an explicit type for x? You can do that by
2560 giving a type signature for x directly, using a pattern type signature
2561 (<xref linkend="scoped-type-variables"/>), thus:
2563 \ f :: (forall a. a->a) -> (f True, f 'c')
2565 Alternatively, you can give a type signature to the enclosing
2566 context, which GHC can "push down" to find the type for the variable:
2568 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2570 Here the type signature on the expression can be pushed inwards
2571 to give a type signature for f. Similarly, and more commonly,
2572 one can give a type signature for the function itself:
2574 h :: (forall a. a->a) -> (Bool,Char)
2575 h f = (f True, f 'c')
2577 You don't need to give a type signature if the lambda bound variable
2578 is a constructor argument. Here is an example we saw earlier:
2580 f :: T a -> a -> (a, Char)
2581 f (T1 w k) x = (w k x, w 'c' 'd')
2583 Here we do not need to give a type signature to <literal>w</literal>, because
2584 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2591 <sect3 id="implicit-quant">
2592 <title>Implicit quantification</title>
2595 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2596 user-written types, if and only if there is no explicit <literal>forall</literal>,
2597 GHC finds all the type variables mentioned in the type that are not already
2598 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2602 f :: forall a. a -> a
2609 h :: forall b. a -> b -> b
2615 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2618 f :: (a -> a) -> Int
2620 f :: forall a. (a -> a) -> Int
2622 f :: (forall a. a -> a) -> Int
2625 g :: (Ord a => a -> a) -> Int
2626 -- MEANS the illegal type
2627 g :: forall a. (Ord a => a -> a) -> Int
2629 g :: (forall a. Ord a => a -> a) -> Int
2631 The latter produces an illegal type, which you might think is silly,
2632 but at least the rule is simple. If you want the latter type, you
2633 can write your for-alls explicitly. Indeed, doing so is strongly advised
2642 <sect2 id="scoped-type-variables">
2643 <title>Scoped type variables
2647 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2648 variable</emphasis>. For example
2654 f (xs::[a]) = ys ++ ys
2663 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2664 This brings the type variable <literal>a</literal> into scope; it scopes over
2665 all the patterns and right hand sides for this equation for <function>f</function>.
2666 In particular, it is in scope at the type signature for <varname>y</varname>.
2670 Pattern type signatures are completely orthogonal to ordinary, separate
2671 type signatures. The two can be used independently or together.
2672 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2673 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2674 implicitly universally quantified. (If there are no type variables in
2675 scope, all type variables mentioned in the signature are universally
2676 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2677 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2678 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2679 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2680 it becomes possible to do so.
2684 Scoped type variables are implemented in both GHC and Hugs. Where the
2685 implementations differ from the specification below, those differences
2690 So much for the basic idea. Here are the details.
2694 <title>What a pattern type signature means</title>
2696 A type variable brought into scope by a pattern type signature is simply
2697 the name for a type. The restriction they express is that all occurrences
2698 of the same name mean the same type. For example:
2700 f :: [Int] -> Int -> Int
2701 f (xs::[a]) (y::a) = (head xs + y) :: a
2703 The pattern type signatures on the left hand side of
2704 <literal>f</literal> express the fact that <literal>xs</literal>
2705 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2706 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2707 specifies that this expression must have the same type <literal>a</literal>.
2708 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2709 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2710 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2711 rules, which specified that a pattern-bound type variable should be universally quantified.)
2712 For example, all of these are legal:</para>
2715 t (x::a) (y::a) = x+y*2
2717 f (x::a) (y::b) = [x,y] -- a unifies with b
2719 g (x::a) = x + 1::Int -- a unifies with Int
2721 h x = let k (y::a) = [x,y] -- a is free in the
2722 in k x -- environment
2724 k (x::a) True = ... -- a unifies with Int
2725 k (x::Int) False = ...
2728 w (x::a) = x -- a unifies with [b]
2734 <title>Scope and implicit quantification</title>
2742 All the type variables mentioned in a pattern,
2743 that are not already in scope,
2744 are brought into scope by the pattern. We describe this set as
2745 the <emphasis>type variables bound by the pattern</emphasis>.
2748 f (x::a) = let g (y::(a,b)) = fst y
2752 The pattern <literal>(x::a)</literal> brings the type variable
2753 <literal>a</literal> into scope, as well as the term
2754 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2755 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2756 and brings into scope the type variable <literal>b</literal>.
2762 The type variable(s) bound by the pattern have the same scope
2763 as the term variable(s) bound by the pattern. For example:
2766 f (x::a) = <...rhs of f...>
2767 (p::b, q::b) = (1,2)
2768 in <...body of let...>
2770 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2771 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2772 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2773 just like <literal>p</literal> and <literal>q</literal> do.
2774 Indeed, the newly bound type variables also scope over any ordinary, separate
2775 type signatures in the <literal>let</literal> group.
2782 The type variables bound by the pattern may be
2783 mentioned in ordinary type signatures or pattern
2784 type signatures anywhere within their scope.
2791 In ordinary type signatures, any type variable mentioned in the
2792 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2800 Ordinary type signatures do not bring any new type variables
2801 into scope (except in the type signature itself!). So this is illegal:
2808 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2809 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2810 and that is an incorrect typing.
2817 The pattern type signature is a monotype:
2822 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2826 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2827 not to type schemes.
2831 There is no implicit universal quantification on pattern type signatures (in contrast to
2832 ordinary type signatures).
2842 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2843 scope over the methods defined in the <literal>where</literal> part. For example:
2857 (Not implemented in Hugs yet, Dec 98).
2868 <title>Where a pattern type signature can occur</title>
2871 A pattern type signature can occur in any pattern. For example:
2876 A pattern type signature can be on an arbitrary sub-pattern, not
2881 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2890 Pattern type signatures, including the result part, can be used
2891 in lambda abstractions:
2894 (\ (x::a, y) :: a -> x)
2901 Pattern type signatures, including the result part, can be used
2902 in <literal>case</literal> expressions:
2905 case e of { ((x::a, y) :: (a,b)) -> x }
2908 Note that the <literal>-></literal> symbol in a case alternative
2909 leads to difficulties when parsing a type signature in the pattern: in
2910 the absence of the extra parentheses in the example above, the parser
2911 would try to interpret the <literal>-></literal> as a function
2912 arrow and give a parse error later.
2920 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2921 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2922 token or a parenthesised type of some sort). To see why,
2923 consider how one would parse this:
2937 Pattern type signatures can bind existential type variables.
2942 data T = forall a. MkT [a]
2945 f (MkT [t::a]) = MkT t3
2958 Pattern type signatures
2959 can be used in pattern bindings:
2962 f x = let (y, z::a) = x in ...
2963 f1 x = let (y, z::Int) = x in ...
2964 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2965 f3 :: (b->b) = \x -> x
2968 In all such cases, the binding is not generalised over the pattern-bound
2969 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2970 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2971 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2972 In contrast, the binding
2977 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2978 in <literal>f4</literal>'s scope.
2988 <title>Result type signatures</title>
2991 The result type of a function can be given a signature, thus:
2995 f (x::a) :: [a] = [x,x,x]
2999 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3000 result type. Sometimes this is the only way of naming the type variable
3005 f :: Int -> [a] -> [a]
3006 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3007 in \xs -> map g (reverse xs `zip` xs)
3012 The type variables bound in a result type signature scope over the right hand side
3013 of the definition. However, consider this corner-case:
3015 rev1 :: [a] -> [a] = \xs -> reverse xs
3017 foo ys = rev (ys::[a])
3019 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3020 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3021 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3022 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3023 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3026 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3027 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3031 rev1 :: [a] -> [a] = \xs -> reverse xs
3036 Result type signatures are not yet implemented in Hugs.
3043 <sect2 id="deriving-typeable">
3044 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3047 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3048 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3049 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3050 classes <literal>Eq</literal>, <literal>Ord</literal>,
3051 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3054 GHC extends this list with two more classes that may be automatically derived
3055 (provided the <option>-fglasgow-exts</option> flag is specified):
3056 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3057 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3058 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3062 <sect2 id="newtype-deriving">
3063 <title>Generalised derived instances for newtypes</title>
3066 When you define an abstract type using <literal>newtype</literal>, you may want
3067 the new type to inherit some instances from its representation. In
3068 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3069 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3070 other classes you have to write an explicit instance declaration. For
3071 example, if you define
3074 newtype Dollars = Dollars Int
3077 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3078 explicitly define an instance of <literal>Num</literal>:
3081 instance Num Dollars where
3082 Dollars a + Dollars b = Dollars (a+b)
3085 All the instance does is apply and remove the <literal>newtype</literal>
3086 constructor. It is particularly galling that, since the constructor
3087 doesn't appear at run-time, this instance declaration defines a
3088 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3089 dictionary, only slower!
3093 <sect3> <title> Generalising the deriving clause </title>
3095 GHC now permits such instances to be derived instead, so one can write
3097 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3100 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3101 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3102 derives an instance declaration of the form
3105 instance Num Int => Num Dollars
3108 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3112 We can also derive instances of constructor classes in a similar
3113 way. For example, suppose we have implemented state and failure monad
3114 transformers, such that
3117 instance Monad m => Monad (State s m)
3118 instance Monad m => Monad (Failure m)
3120 In Haskell 98, we can define a parsing monad by
3122 type Parser tok m a = State [tok] (Failure m) a
3125 which is automatically a monad thanks to the instance declarations
3126 above. With the extension, we can make the parser type abstract,
3127 without needing to write an instance of class <literal>Monad</literal>, via
3130 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3133 In this case the derived instance declaration is of the form
3135 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3138 Notice that, since <literal>Monad</literal> is a constructor class, the
3139 instance is a <emphasis>partial application</emphasis> of the new type, not the
3140 entire left hand side. We can imagine that the type declaration is
3141 ``eta-converted'' to generate the context of the instance
3146 We can even derive instances of multi-parameter classes, provided the
3147 newtype is the last class parameter. In this case, a ``partial
3148 application'' of the class appears in the <literal>deriving</literal>
3149 clause. For example, given the class
3152 class StateMonad s m | m -> s where ...
3153 instance Monad m => StateMonad s (State s m) where ...
3155 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3157 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3158 deriving (Monad, StateMonad [tok])
3161 The derived instance is obtained by completing the application of the
3162 class to the new type:
3165 instance StateMonad [tok] (State [tok] (Failure m)) =>
3166 StateMonad [tok] (Parser tok m)
3171 As a result of this extension, all derived instances in newtype
3172 declarations are treated uniformly (and implemented just by reusing
3173 the dictionary for the representation type), <emphasis>except</emphasis>
3174 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3175 the newtype and its representation.
3179 <sect3> <title> A more precise specification </title>
3181 Derived instance declarations are constructed as follows. Consider the
3182 declaration (after expansion of any type synonyms)
3185 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3191 <literal>S</literal> is a type constructor,
3194 The <literal>t1...tk</literal> are types,
3197 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3198 the <literal>ti</literal>, and
3201 The <literal>ci</literal> are partial applications of
3202 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3203 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3206 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3207 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3208 should not "look through" the type or its constructor. You can still
3209 derive these classes for a newtype, but it happens in the usual way, not
3210 via this new mechanism.
3213 Then, for each <literal>ci</literal>, the derived instance
3216 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3218 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3219 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3223 As an example which does <emphasis>not</emphasis> work, consider
3225 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3227 Here we cannot derive the instance
3229 instance Monad (State s m) => Monad (NonMonad m)
3232 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3233 and so cannot be "eta-converted" away. It is a good thing that this
3234 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3235 not, in fact, a monad --- for the same reason. Try defining
3236 <literal>>>=</literal> with the correct type: you won't be able to.
3240 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3241 important, since we can only derive instances for the last one. If the
3242 <literal>StateMonad</literal> class above were instead defined as
3245 class StateMonad m s | m -> s where ...
3248 then we would not have been able to derive an instance for the
3249 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3250 classes usually have one "main" parameter for which deriving new
3251 instances is most interesting.
3259 <!-- ==================== End of type system extensions ================= -->
3261 <!-- ====================== TEMPLATE HASKELL ======================= -->
3263 <sect1 id="template-haskell">
3264 <title>Template Haskell</title>
3266 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3267 Template Haskell at <ulink url="http://www.haskell.org/th/">
3268 http://www.haskell.org/th/</ulink>, while
3270 the main technical innovations is discussed in "<ulink
3271 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3272 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3273 The details of the Template Haskell design are still in flux. Make sure you
3274 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3275 (search for the type ExpQ).
3276 [Temporary: many changes to the original design are described in
3277 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3278 Not all of these changes are in GHC 6.2.]
3281 <para> The first example from that paper is set out below as a worked example to help get you started.
3285 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3286 Tim Sheard is going to expand it.)
3290 <title>Syntax</title>
3292 <para> Template Haskell has the following new syntactic
3293 constructions. You need to use the flag
3294 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3295 </indexterm>to switch these syntactic extensions on
3296 (<option>-fth</option> is currently implied by
3297 <option>-fglasgow-exts</option>, but you are encouraged to
3298 specify it explicitly).</para>
3302 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3303 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3304 There must be no space between the "$" and the identifier or parenthesis. This use
3305 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3306 of "." as an infix operator. If you want the infix operator, put spaces around it.
3308 <para> A splice can occur in place of
3310 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3311 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3312 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3314 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3315 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3321 A expression quotation is written in Oxford brackets, thus:
3323 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3324 the quotation has type <literal>Expr</literal>.</para></listitem>
3325 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3326 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3327 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3328 the quotation has type <literal>Type</literal>.</para></listitem>
3329 </itemizedlist></para></listitem>
3332 Reification is written thus:
3334 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3335 has type <literal>Dec</literal>. </para></listitem>
3336 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3337 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3338 <listitem><para> Still to come: fixities </para></listitem>
3340 </itemizedlist></para>
3347 <sect2> <title> Using Template Haskell </title>
3351 The data types and monadic constructor functions for Template Haskell are in the library
3352 <literal>Language.Haskell.THSyntax</literal>.
3356 You can only run a function at compile time if it is imported from another module. That is,
3357 you can't define a function in a module, and call it from within a splice in the same module.
3358 (It would make sense to do so, but it's hard to implement.)
3362 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3365 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3366 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3367 compiles and runs a program, and then looks at the result. So it's important that
3368 the program it compiles produces results whose representations are identical to
3369 those of the compiler itself.
3373 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3374 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3379 <sect2> <title> A Template Haskell Worked Example </title>
3380 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3381 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3388 -- Import our template "pr"
3389 import Printf ( pr )
3391 -- The splice operator $ takes the Haskell source code
3392 -- generated at compile time by "pr" and splices it into
3393 -- the argument of "putStrLn".
3394 main = putStrLn ( $(pr "Hello") )
3400 -- Skeletal printf from the paper.
3401 -- It needs to be in a separate module to the one where
3402 -- you intend to use it.
3404 -- Import some Template Haskell syntax
3405 import Language.Haskell.TH.Syntax
3407 -- Describe a format string
3408 data Format = D | S | L String
3410 -- Parse a format string. This is left largely to you
3411 -- as we are here interested in building our first ever
3412 -- Template Haskell program and not in building printf.
3413 parse :: String -> [Format]
3416 -- Generate Haskell source code from a parsed representation
3417 -- of the format string. This code will be spliced into
3418 -- the module which calls "pr", at compile time.
3419 gen :: [Format] -> ExpQ
3420 gen [D] = [| \n -> show n |]
3421 gen [S] = [| \s -> s |]
3422 gen [L s] = stringE s
3424 -- Here we generate the Haskell code for the splice
3425 -- from an input format string.
3426 pr :: String -> ExpQ
3427 pr s = gen (parse s)
3430 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3433 $ ghc --make -fth main.hs -o main.exe
3436 <para>Run "main.exe" and here is your output:</para>
3447 <!-- ===================== Arrow notation =================== -->
3449 <sect1 id="arrow-notation">
3450 <title>Arrow notation
3453 <para>Arrows are a generalization of monads introduced by John Hughes.
3454 For more details, see
3459 “Generalising Monads to Arrows”,
3460 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3461 pp67–111, May 2000.
3467 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3468 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3474 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3475 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3481 and the arrows web page at
3482 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3483 With the <option>-farrows</option> flag, GHC supports the arrow
3484 notation described in the second of these papers.
3485 What follows is a brief introduction to the notation;
3486 it won't make much sense unless you've read Hughes's paper.
3487 This notation is translated to ordinary Haskell,
3488 using combinators from the
3489 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3493 <para>The extension adds a new kind of expression for defining arrows:
3495 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3496 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3498 where <literal>proc</literal> is a new keyword.
3499 The variables of the pattern are bound in the body of the
3500 <literal>proc</literal>-expression,
3501 which is a new sort of thing called a <firstterm>command</firstterm>.
3502 The syntax of commands is as follows:
3504 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3505 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3506 | <replaceable>cmd</replaceable><superscript>0</superscript>
3508 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3509 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3510 infix operators as for expressions, and
3512 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3513 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3514 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3515 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3516 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3517 | <replaceable>fcmd</replaceable>
3519 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3520 | ( <replaceable>cmd</replaceable> )
3521 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3523 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3524 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3525 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3526 | <replaceable>cmd</replaceable>
3528 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3529 except that the bodies are commands instead of expressions.
3533 Commands produce values, but (like monadic computations)
3534 may yield more than one value,
3535 or none, and may do other things as well.
3536 For the most part, familiarity with monadic notation is a good guide to
3538 However the values of expressions, even monadic ones,
3539 are determined by the values of the variables they contain;
3540 this is not necessarily the case for commands.
3544 A simple example of the new notation is the expression
3546 proc x -> f -< x+1
3548 We call this a <firstterm>procedure</firstterm> or
3549 <firstterm>arrow abstraction</firstterm>.
3550 As with a lambda expression, the variable <literal>x</literal>
3551 is a new variable bound within the <literal>proc</literal>-expression.
3552 It refers to the input to the arrow.
3553 In the above example, <literal>-<</literal> is not an identifier but an
3554 new reserved symbol used for building commands from an expression of arrow
3555 type and an expression to be fed as input to that arrow.
3556 (The weird look will make more sense later.)
3557 It may be read as analogue of application for arrows.
3558 The above example is equivalent to the Haskell expression
3560 arr (\ x -> x+1) >>> f
3562 That would make no sense if the expression to the left of
3563 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3564 More generally, the expression to the left of <literal>-<</literal>
3565 may not involve any <firstterm>local variable</firstterm>,
3566 i.e. a variable bound in the current arrow abstraction.
3567 For such a situation there is a variant <literal>-<<</literal>, as in
3569 proc x -> f x -<< x+1
3571 which is equivalent to
3573 arr (\ x -> (f, x+1)) >>> app
3575 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3577 Such an arrow is equivalent to a monad, so if you're using this form
3578 you may find a monadic formulation more convenient.
3582 <title>do-notation for commands</title>
3585 Another form of command is a form of <literal>do</literal>-notation.
3586 For example, you can write
3595 You can read this much like ordinary <literal>do</literal>-notation,
3596 but with commands in place of monadic expressions.
3597 The first line sends the value of <literal>x+1</literal> as an input to
3598 the arrow <literal>f</literal>, and matches its output against
3599 <literal>y</literal>.
3600 In the next line, the output is discarded.
3601 The arrow <literal>returnA</literal> is defined in the
3602 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3603 module as <literal>arr id</literal>.
3604 The above example is treated as an abbreviation for
3606 arr (\ x -> (x, x)) >>>
3607 first (arr (\ x -> x+1) >>> f) >>>
3608 arr (\ (y, x) -> (y, (x, y))) >>>
3609 first (arr (\ y -> 2*y) >>> g) >>>
3611 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3612 first (arr (\ (x, z) -> x*z) >>> h) >>>
3613 arr (\ (t, z) -> t+z) >>>
3616 Note that variables not used later in the composition are projected out.
3617 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3619 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3620 module, this reduces to
3622 arr (\ x -> (x+1, x)) >>>
3624 arr (\ (y, x) -> (2*y, (x, y))) >>>
3626 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3628 arr (\ (t, z) -> t+z)
3630 which is what you might have written by hand.
3631 With arrow notation, GHC keeps track of all those tuples of variables for you.
3635 Note that although the above translation suggests that
3636 <literal>let</literal>-bound variables like <literal>z</literal> must be
3637 monomorphic, the actual translation produces Core,
3638 so polymorphic variables are allowed.
3642 It's also possible to have mutually recursive bindings,
3643 using the new <literal>rec</literal> keyword, as in the following example:
3645 counter :: ArrowCircuit a => a Bool Int
3646 counter = proc reset -> do
3647 rec output <- returnA -< if reset then 0 else next
3648 next <- delay 0 -< output+1
3649 returnA -< output
3651 The translation of such forms uses the <literal>loop</literal> combinator,
3652 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3658 <title>Conditional commands</title>
3661 In the previous example, we used a conditional expression to construct the
3663 Sometimes we want to conditionally execute different commands, as in
3670 which is translated to
3672 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3673 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3675 Since the translation uses <literal>|||</literal>,
3676 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3680 There are also <literal>case</literal> commands, like
3686 y <- h -< (x1, x2)
3690 The syntax is the same as for <literal>case</literal> expressions,
3691 except that the bodies of the alternatives are commands rather than expressions.
3692 The translation is similar to that of <literal>if</literal> commands.
3698 <title>Defining your own control structures</title>
3701 As we're seen, arrow notation provides constructs,
3702 modelled on those for expressions,
3703 for sequencing, value recursion and conditionals.
3704 But suitable combinators,
3705 which you can define in ordinary Haskell,
3706 may also be used to build new commands out of existing ones.
3707 The basic idea is that a command defines an arrow from environments to values.
3708 These environments assign values to the free local variables of the command.
3709 Thus combinators that produce arrows from arrows
3710 may also be used to build commands from commands.
3711 For example, the <literal>ArrowChoice</literal> class includes a combinator
3713 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3715 so we can use it to build commands:
3717 expr' = proc x -> do
3720 symbol Plus -< ()
3721 y <- term -< ()
3724 symbol Minus -< ()
3725 y <- term -< ()
3728 (The <literal>do</literal> on the first line is needed to prevent the first
3729 <literal><+> ...</literal> from being interpreted as part of the
3730 expression on the previous line.)
3731 This is equivalent to
3733 expr' = (proc x -> returnA -< x)
3734 <+> (proc x -> do
3735 symbol Plus -< ()
3736 y <- term -< ()
3738 <+> (proc x -> do
3739 symbol Minus -< ()
3740 y <- term -< ()
3743 It is essential that this operator be polymorphic in <literal>e</literal>
3744 (representing the environment input to the command
3745 and thence to its subcommands)
3746 and satisfy the corresponding naturality property
3748 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3750 at least for strict <literal>k</literal>.
3751 (This should be automatic if you're not using <literal>seq</literal>.)
3752 This ensures that environments seen by the subcommands are environments
3753 of the whole command,
3754 and also allows the translation to safely trim these environments.
3755 The operator must also not use any variable defined within the current
3760 We could define our own operator
3762 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3763 untilA body cond = proc x ->
3764 if cond x then returnA -< ()
3767 untilA body cond -< x
3769 and use it in the same way.
3770 Of course this infix syntax only makes sense for binary operators;
3771 there is also a more general syntax involving special brackets:
3775 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3782 <title>Primitive constructs</title>
3785 Some operators will need to pass additional inputs to their subcommands.
3786 For example, in an arrow type supporting exceptions,
3787 the operator that attaches an exception handler will wish to pass the
3788 exception that occurred to the handler.
3789 Such an operator might have a type
3791 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3793 where <literal>Ex</literal> is the type of exceptions handled.
3794 You could then use this with arrow notation by writing a command
3796 body `handleA` \ ex -> handler
3798 so that if an exception is raised in the command <literal>body</literal>,
3799 the variable <literal>ex</literal> is bound to the value of the exception
3800 and the command <literal>handler</literal>,
3801 which typically refers to <literal>ex</literal>, is entered.
3802 Though the syntax here looks like a functional lambda,
3803 we are talking about commands, and something different is going on.
3804 The input to the arrow represented by a command consists of values for
3805 the free local variables in the command, plus a stack of anonymous values.
3806 In all the prior examples, this stack was empty.
3807 In the second argument to <literal>handleA</literal>,
3808 this stack consists of one value, the value of the exception.
3809 The command form of lambda merely gives this value a name.
3814 the values on the stack are paired to the right of the environment.
3815 So when designing operators like <literal>handleA</literal> that pass
3816 extra inputs to their subcommands,
3817 More precisely, the type of each argument of the operator (and its result)
3818 should have the form
3820 a (...(e,t1), ... tn) t
3822 where <replaceable>e</replaceable> is a polymorphic variable
3823 (representing the environment)
3824 and <replaceable>ti</replaceable> are the types of the values on the stack,
3825 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3826 The polymorphic variable <replaceable>e</replaceable> must not occur in
3827 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3828 <replaceable>t</replaceable>.
3829 However the arrows involved need not be the same.
3830 Here are some more examples of suitable operators:
3832 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3833 runReader :: ... => a e c -> a' (e,State) c
3834 runState :: ... => a e c -> a' (e,State) (c,State)
3836 We can supply the extra input required by commands built with the last two
3837 by applying them to ordinary expressions, as in
3841 (|runReader (do { ... })|) s
3843 which adds <literal>s</literal> to the stack of inputs to the command
3844 built using <literal>runReader</literal>.
3848 The command versions of lambda abstraction and application are analogous to
3849 the expression versions.
3850 In particular, the beta and eta rules describe equivalences of commands.
3851 These three features (operators, lambda abstraction and application)
3852 are the core of the notation; everything else can be built using them,
3853 though the results would be somewhat clumsy.
3854 For example, we could simulate <literal>do</literal>-notation by defining
3856 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3857 u `bind` f = returnA &&& u >>> f
3859 bind_ :: Arrow a => a e b -> a e c -> a e c
3860 u `bind_` f = u `bind` (arr fst >>> f)
3862 We could simulate <literal>do</literal> by defining
3864 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3865 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3872 <title>Differences with the paper</title>
3877 <para>Instead of a single form of arrow application (arrow tail) with two
3878 translations, the implementation provides two forms
3879 <quote><literal>-<</literal></quote> (first-order)
3880 and <quote><literal>-<<</literal></quote> (higher-order).
3885 <para>User-defined operators are flagged with banana brackets instead of
3886 a new <literal>form</literal> keyword.
3895 <title>Portability</title>
3898 Although only GHC implements arrow notation directly,
3899 there is also a preprocessor
3901 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
3902 that translates arrow notation into Haskell 98
3903 for use with other Haskell systems.
3904 You would still want to check arrow programs with GHC;
3905 tracing type errors in the preprocessor output is not easy.
3906 Modules intended for both GHC and the preprocessor must observe some
3907 additional restrictions:
3912 The module must import
3913 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3919 The preprocessor cannot cope with other Haskell extensions.
3920 These would have to go in separate modules.
3926 Because the preprocessor targets Haskell (rather than Core),
3927 <literal>let</literal>-bound variables are monomorphic.
3938 <!-- ==================== ASSERTIONS ================= -->
3940 <sect1 id="sec-assertions">
3942 <indexterm><primary>Assertions</primary></indexterm>
3946 If you want to make use of assertions in your standard Haskell code, you
3947 could define a function like the following:
3953 assert :: Bool -> a -> a
3954 assert False x = error "assertion failed!"
3961 which works, but gives you back a less than useful error message --
3962 an assertion failed, but which and where?
3966 One way out is to define an extended <function>assert</function> function which also
3967 takes a descriptive string to include in the error message and
3968 perhaps combine this with the use of a pre-processor which inserts
3969 the source location where <function>assert</function> was used.
3973 Ghc offers a helping hand here, doing all of this for you. For every
3974 use of <function>assert</function> in the user's source:
3980 kelvinToC :: Double -> Double
3981 kelvinToC k = assert (k >= 0.0) (k+273.15)
3987 Ghc will rewrite this to also include the source location where the
3994 assert pred val ==> assertError "Main.hs|15" pred val
4000 The rewrite is only performed by the compiler when it spots
4001 applications of <function>Control.Exception.assert</function>, so you
4002 can still define and use your own versions of
4003 <function>assert</function>, should you so wish. If not, import
4004 <literal>Control.Exception</literal> to make use
4005 <function>assert</function> in your code.
4009 To have the compiler ignore uses of assert, use the compiler option
4010 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4011 option</primary></indexterm> That is, expressions of the form
4012 <literal>assert pred e</literal> will be rewritten to
4013 <literal>e</literal>.
4017 Assertion failures can be caught, see the documentation for the
4018 <literal>Control.Exception</literal> library for the details.
4024 <!-- =============================== PRAGMAS =========================== -->
4026 <sect1 id="pragmas">
4027 <title>Pragmas</title>
4029 <indexterm><primary>pragma</primary></indexterm>
4031 <para>GHC supports several pragmas, or instructions to the
4032 compiler placed in the source code. Pragmas don't normally affect
4033 the meaning of the program, but they might affect the efficiency
4034 of the generated code.</para>
4036 <para>Pragmas all take the form
4038 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4040 where <replaceable>word</replaceable> indicates the type of
4041 pragma, and is followed optionally by information specific to that
4042 type of pragma. Case is ignored in
4043 <replaceable>word</replaceable>. The various values for
4044 <replaceable>word</replaceable> that GHC understands are described
4045 in the following sections; any pragma encountered with an
4046 unrecognised <replaceable>word</replaceable> is (silently)
4049 <sect2 id="deprecated-pragma">
4050 <title>DEPRECATED pragma</title>
4051 <indexterm><primary>DEPRECATED</primary>
4054 <para>The DEPRECATED pragma lets you specify that a particular
4055 function, class, or type, is deprecated. There are two
4060 <para>You can deprecate an entire module thus:</para>
4062 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4065 <para>When you compile any module that import
4066 <literal>Wibble</literal>, GHC will print the specified
4071 <para>You can deprecate a function, class, or type, with the
4072 following top-level declaration:</para>
4074 {-# DEPRECATED f, C, T "Don't use these" #-}
4076 <para>When you compile any module that imports and uses any
4077 of the specifed entities, GHC will print the specified
4081 Any use of the deprecated item, or of anything from a deprecated
4082 module, will be flagged with an appropriate message. However,
4083 deprecations are not reported for
4084 (a) uses of a deprecated function within its defining module, and
4085 (b) uses of a deprecated function in an export list.
4086 The latter reduces spurious complaints within a library
4087 in which one module gathers together and re-exports
4088 the exports of several others.
4090 <para>You can suppress the warnings with the flag
4091 <option>-fno-warn-deprecations</option>.</para>
4094 <sect2 id="inline-noinline-pragma">
4095 <title>INLINE and NOINLINE pragmas</title>
4097 <para>These pragmas control the inlining of function
4100 <sect3 id="inline-pragma">
4101 <title>INLINE pragma</title>
4102 <indexterm><primary>INLINE</primary></indexterm>
4104 <para>GHC (with <option>-O</option>, as always) tries to
4105 inline (or “unfold”) functions/values that are
4106 “small enough,” thus avoiding the call overhead
4107 and possibly exposing other more-wonderful optimisations.
4108 Normally, if GHC decides a function is “too
4109 expensive” to inline, it will not do so, nor will it
4110 export that unfolding for other modules to use.</para>
4112 <para>The sledgehammer you can bring to bear is the
4113 <literal>INLINE</literal><indexterm><primary>INLINE
4114 pragma</primary></indexterm> pragma, used thusly:</para>
4117 key_function :: Int -> String -> (Bool, Double)
4119 #ifdef __GLASGOW_HASKELL__
4120 {-# INLINE key_function #-}
4124 <para>(You don't need to do the C pre-processor carry-on
4125 unless you're going to stick the code through HBC—it
4126 doesn't like <literal>INLINE</literal> pragmas.)</para>
4128 <para>The major effect of an <literal>INLINE</literal> pragma
4129 is to declare a function's “cost” to be very low.
4130 The normal unfolding machinery will then be very keen to
4133 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4134 function can be put anywhere its type signature could be
4137 <para><literal>INLINE</literal> pragmas are a particularly
4139 <literal>then</literal>/<literal>return</literal> (or
4140 <literal>bind</literal>/<literal>unit</literal>) functions in
4141 a monad. For example, in GHC's own
4142 <literal>UniqueSupply</literal> monad code, we have:</para>
4145 #ifdef __GLASGOW_HASKELL__
4146 {-# INLINE thenUs #-}
4147 {-# INLINE returnUs #-}
4151 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4152 linkend="noinline-pragma"/>).</para>
4155 <sect3 id="noinline-pragma">
4156 <title>NOINLINE pragma</title>
4158 <indexterm><primary>NOINLINE</primary></indexterm>
4159 <indexterm><primary>NOTINLINE</primary></indexterm>
4161 <para>The <literal>NOINLINE</literal> pragma does exactly what
4162 you'd expect: it stops the named function from being inlined
4163 by the compiler. You shouldn't ever need to do this, unless
4164 you're very cautious about code size.</para>
4166 <para><literal>NOTINLINE</literal> is a synonym for
4167 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4168 specified by Haskell 98 as the standard way to disable
4169 inlining, so it should be used if you want your code to be
4173 <sect3 id="phase-control">
4174 <title>Phase control</title>
4176 <para> Sometimes you want to control exactly when in GHC's
4177 pipeline the INLINE pragma is switched on. Inlining happens
4178 only during runs of the <emphasis>simplifier</emphasis>. Each
4179 run of the simplifier has a different <emphasis>phase
4180 number</emphasis>; the phase number decreases towards zero.
4181 If you use <option>-dverbose-core2core</option> you'll see the
4182 sequence of phase numbers for successive runs of the
4183 simpifier. In an INLINE pragma you can optionally specify a
4184 phase number, thus:</para>
4188 <para>You can say "inline <literal>f</literal> in Phase 2
4189 and all subsequent phases":
4191 {-# INLINE [2] f #-}
4197 <para>You can say "inline <literal>g</literal> in all
4198 phases up to, but not including, Phase 3":
4200 {-# INLINE [~3] g #-}
4206 <para>If you omit the phase indicator, you mean "inline in
4211 <para>You can use a phase number on a NOINLINE pragma too:</para>
4215 <para>You can say "do not inline <literal>f</literal>
4216 until Phase 2; in Phase 2 and subsequently behave as if
4217 there was no pragma at all":
4219 {-# NOINLINE [2] f #-}
4225 <para>You can say "do not inline <literal>g</literal> in
4226 Phase 3 or any subsequent phase; before that, behave as if
4227 there was no pragma":
4229 {-# NOINLINE [~3] g #-}
4235 <para>If you omit the phase indicator, you mean "never
4236 inline this function".</para>
4240 <para>The same phase-numbering control is available for RULES
4241 (<xref linkend="rewrite-rules"/>).</para>
4245 <sect2 id="line-pragma">
4246 <title>LINE pragma</title>
4248 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4249 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4250 <para>This pragma is similar to C's <literal>#line</literal>
4251 pragma, and is mainly for use in automatically generated Haskell
4252 code. It lets you specify the line number and filename of the
4253 original code; for example</para>
4256 {-# LINE 42 "Foo.vhs" #-}
4259 <para>if you'd generated the current file from something called
4260 <filename>Foo.vhs</filename> and this line corresponds to line
4261 42 in the original. GHC will adjust its error messages to refer
4262 to the line/file named in the <literal>LINE</literal>
4266 <sect2 id="options-pragma">
4267 <title>OPTIONS pragma</title>
4268 <indexterm><primary>OPTIONS</primary>
4270 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4273 <para>The <literal>OPTIONS</literal> pragma is used to specify
4274 additional options that are given to the compiler when compiling
4275 this source file. See <xref linkend="source-file-options"/> for
4280 <title>RULES pragma</title>
4282 <para>The RULES pragma lets you specify rewrite rules. It is
4283 described in <xref linkend="rewrite-rules"/>.</para>
4286 <sect2 id="specialize-pragma">
4287 <title>SPECIALIZE pragma</title>
4289 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4290 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4291 <indexterm><primary>overloading, death to</primary></indexterm>
4293 <para>(UK spelling also accepted.) For key overloaded
4294 functions, you can create extra versions (NB: more code space)
4295 specialised to particular types. Thus, if you have an
4296 overloaded function:</para>
4299 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4302 <para>If it is heavily used on lists with
4303 <literal>Widget</literal> keys, you could specialise it as
4307 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4310 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4311 be put anywhere its type signature could be put.</para>
4313 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4314 (a) a specialised version of the function and (b) a rewrite rule
4315 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4316 un-specialised function into a call to the specialised one.</para>
4318 <para>In earlier versions of GHC, it was possible to provide your own
4319 specialised function for a given type:
4322 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4325 This feature has been removed, as it is now subsumed by the
4326 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4330 <sect2 id="specialize-instance-pragma">
4331 <title>SPECIALIZE instance pragma
4335 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4336 <indexterm><primary>overloading, death to</primary></indexterm>
4337 Same idea, except for instance declarations. For example:
4340 instance (Eq a) => Eq (Foo a) where {
4341 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4345 The pragma must occur inside the <literal>where</literal> part
4346 of the instance declaration.
4349 Compatible with HBC, by the way, except perhaps in the placement
4355 <sect2 id="unpack-pragma">
4356 <title>UNPACK pragma</title>
4358 <indexterm><primary>UNPACK</primary></indexterm>
4360 <para>The <literal>UNPACK</literal> indicates to the compiler
4361 that it should unpack the contents of a constructor field into
4362 the constructor itself, removing a level of indirection. For
4366 data T = T {-# UNPACK #-} !Float
4367 {-# UNPACK #-} !Float
4370 <para>will create a constructor <literal>T</literal> containing
4371 two unboxed floats. This may not always be an optimisation: if
4372 the <function>T</function> constructor is scrutinised and the
4373 floats passed to a non-strict function for example, they will
4374 have to be reboxed (this is done automatically by the
4377 <para>Unpacking constructor fields should only be used in
4378 conjunction with <option>-O</option>, in order to expose
4379 unfoldings to the compiler so the reboxing can be removed as
4380 often as possible. For example:</para>
4384 f (T f1 f2) = f1 + f2
4387 <para>The compiler will avoid reboxing <function>f1</function>
4388 and <function>f2</function> by inlining <function>+</function>
4389 on floats, but only when <option>-O</option> is on.</para>
4391 <para>Any single-constructor data is eligible for unpacking; for
4395 data T = T {-# UNPACK #-} !(Int,Int)
4398 <para>will store the two <literal>Int</literal>s directly in the
4399 <function>T</function> constructor, by flattening the pair.
4400 Multi-level unpacking is also supported:</para>
4403 data T = T {-# UNPACK #-} !S
4404 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4407 <para>will store two unboxed <literal>Int#</literal>s
4408 directly in the <function>T</function> constructor. The
4409 unpacker can see through newtypes, too.</para>
4411 <para>If a field cannot be unpacked, you will not get a warning,
4412 so it might be an idea to check the generated code with
4413 <option>-ddump-simpl</option>.</para>
4415 <para>See also the <option>-funbox-strict-fields</option> flag,
4416 which essentially has the effect of adding
4417 <literal>{-# UNPACK #-}</literal> to every strict
4418 constructor field.</para>
4423 <!-- ======================= REWRITE RULES ======================== -->
4425 <sect1 id="rewrite-rules">
4426 <title>Rewrite rules
4428 <indexterm><primary>RULES pagma</primary></indexterm>
4429 <indexterm><primary>pragma, RULES</primary></indexterm>
4430 <indexterm><primary>rewrite rules</primary></indexterm></title>
4433 The programmer can specify rewrite rules as part of the source program
4434 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4435 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4436 and (b) the <option>-frules-off</option> flag
4437 (<xref linkend="options-f"/>) is not specified.
4445 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4452 <title>Syntax</title>
4455 From a syntactic point of view:
4461 There may be zero or more rules in a <literal>RULES</literal> pragma.
4468 Each rule has a name, enclosed in double quotes. The name itself has
4469 no significance at all. It is only used when reporting how many times the rule fired.
4475 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4476 immediately after the name of the rule. Thus:
4479 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4482 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4483 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4492 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4493 is set, so you must lay out your rules starting in the same column as the
4494 enclosing definitions.
4501 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4502 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4503 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4504 by spaces, just like in a type <literal>forall</literal>.
4510 A pattern variable may optionally have a type signature.
4511 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4512 For example, here is the <literal>foldr/build</literal> rule:
4515 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4516 foldr k z (build g) = g k z
4519 Since <function>g</function> has a polymorphic type, it must have a type signature.
4526 The left hand side of a rule must consist of a top-level variable applied
4527 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4530 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4531 "wrong2" forall f. f True = True
4534 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4541 A rule does not need to be in the same module as (any of) the
4542 variables it mentions, though of course they need to be in scope.
4548 Rules are automatically exported from a module, just as instance declarations are.
4559 <title>Semantics</title>
4562 From a semantic point of view:
4568 Rules are only applied if you use the <option>-O</option> flag.
4574 Rules are regarded as left-to-right rewrite rules.
4575 When GHC finds an expression that is a substitution instance of the LHS
4576 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4577 By "a substitution instance" we mean that the LHS can be made equal to the
4578 expression by substituting for the pattern variables.
4585 The LHS and RHS of a rule are typechecked, and must have the
4593 GHC makes absolutely no attempt to verify that the LHS and RHS
4594 of a rule have the same meaning. That is undecideable in general, and
4595 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4602 GHC makes no attempt to make sure that the rules are confluent or
4603 terminating. For example:
4606 "loop" forall x,y. f x y = f y x
4609 This rule will cause the compiler to go into an infinite loop.
4616 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4622 GHC currently uses a very simple, syntactic, matching algorithm
4623 for matching a rule LHS with an expression. It seeks a substitution
4624 which makes the LHS and expression syntactically equal modulo alpha
4625 conversion. The pattern (rule), but not the expression, is eta-expanded if
4626 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4627 But not beta conversion (that's called higher-order matching).
4631 Matching is carried out on GHC's intermediate language, which includes
4632 type abstractions and applications. So a rule only matches if the
4633 types match too. See <xref linkend="rule-spec"/> below.
4639 GHC keeps trying to apply the rules as it optimises the program.
4640 For example, consider:
4649 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4650 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4651 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4652 not be substituted, and the rule would not fire.
4659 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4660 that appears on the LHS of a rule</emphasis>, because once you have substituted
4661 for something you can't match against it (given the simple minded
4662 matching). So if you write the rule
4665 "map/map" forall f,g. map f . map g = map (f.g)
4668 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4669 It will only match something written with explicit use of ".".
4670 Well, not quite. It <emphasis>will</emphasis> match the expression
4676 where <function>wibble</function> is defined:
4679 wibble f g = map f . map g
4682 because <function>wibble</function> will be inlined (it's small).
4684 Later on in compilation, GHC starts inlining even things on the
4685 LHS of rules, but still leaves the rules enabled. This inlining
4686 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4693 All rules are implicitly exported from the module, and are therefore
4694 in force in any module that imports the module that defined the rule, directly
4695 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4696 in force when compiling A.) The situation is very similar to that for instance
4708 <title>List fusion</title>
4711 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4712 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4713 intermediate list should be eliminated entirely.
4717 The following are good producers:
4729 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4735 Explicit lists (e.g. <literal>[True, False]</literal>)
4741 The cons constructor (e.g <literal>3:4:[]</literal>)
4747 <function>++</function>
4753 <function>map</function>
4759 <function>filter</function>
4765 <function>iterate</function>, <function>repeat</function>
4771 <function>zip</function>, <function>zipWith</function>
4780 The following are good consumers:
4792 <function>array</function> (on its second argument)
4798 <function>length</function>
4804 <function>++</function> (on its first argument)
4810 <function>foldr</function>
4816 <function>map</function>
4822 <function>filter</function>
4828 <function>concat</function>
4834 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4840 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4841 will fuse with one but not the other)
4847 <function>partition</function>
4853 <function>head</function>
4859 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4865 <function>sequence_</function>
4871 <function>msum</function>
4877 <function>sortBy</function>
4886 So, for example, the following should generate no intermediate lists:
4889 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4895 This list could readily be extended; if there are Prelude functions that you use
4896 a lot which are not included, please tell us.
4900 If you want to write your own good consumers or producers, look at the
4901 Prelude definitions of the above functions to see how to do so.
4906 <sect2 id="rule-spec">
4907 <title>Specialisation
4911 Rewrite rules can be used to get the same effect as a feature
4912 present in earlier versions of GHC.
4913 For example, suppose that:
4916 genericLookup :: Ord a => Table a b -> a -> b
4917 intLookup :: Table Int b -> Int -> b
4920 where <function>intLookup</function> is an implementation of
4921 <function>genericLookup</function> that works very fast for
4922 keys of type <literal>Int</literal>. You might wish
4923 to tell GHC to use <function>intLookup</function> instead of
4924 <function>genericLookup</function> whenever the latter was called with
4925 type <literal>Table Int b -> Int -> b</literal>.
4926 It used to be possible to write
4929 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
4932 This feature is no longer in GHC, but rewrite rules let you do the same thing:
4935 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
4938 This slightly odd-looking rule instructs GHC to replace
4939 <function>genericLookup</function> by <function>intLookup</function>
4940 <emphasis>whenever the types match</emphasis>.
4941 What is more, this rule does not need to be in the same
4942 file as <function>genericLookup</function>, unlike the
4943 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
4944 have an original definition available to specialise).
4947 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
4948 <function>intLookup</function> really behaves as a specialised version
4949 of <function>genericLookup</function>!!!</para>
4951 <para>An example in which using <literal>RULES</literal> for
4952 specialisation will Win Big:
4955 toDouble :: Real a => a -> Double
4956 toDouble = fromRational . toRational
4958 {-# RULES "toDouble/Int" toDouble = i2d #-}
4959 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4962 The <function>i2d</function> function is virtually one machine
4963 instruction; the default conversion—via an intermediate
4964 <literal>Rational</literal>—is obscenely expensive by
4971 <title>Controlling what's going on</title>
4979 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4985 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4986 If you add <option>-dppr-debug</option> you get a more detailed listing.
4992 The defintion of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
4995 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4996 {-# INLINE build #-}
5000 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5001 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5002 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5003 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5010 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5011 see how to write rules that will do fusion and yet give an efficient
5012 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5022 <sect2 id="core-pragma">
5023 <title>CORE pragma</title>
5025 <indexterm><primary>CORE pragma</primary></indexterm>
5026 <indexterm><primary>pragma, CORE</primary></indexterm>
5027 <indexterm><primary>core, annotation</primary></indexterm>
5030 The external core format supports <quote>Note</quote> annotations;
5031 the <literal>CORE</literal> pragma gives a way to specify what these
5032 should be in your Haskell source code. Syntactically, core
5033 annotations are attached to expressions and take a Haskell string
5034 literal as an argument. The following function definition shows an
5038 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5041 Sematically, this is equivalent to:
5049 However, when external for is generated (via
5050 <option>-fext-core</option>), there will be Notes attached to the
5051 expressions <function>show</function> and <varname>x</varname>.
5052 The core function declaration for <function>f</function> is:
5056 f :: %forall a . GHCziShow.ZCTShow a ->
5057 a -> GHCziBase.ZMZN GHCziBase.Char =
5058 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5060 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5062 (tpl1::GHCziBase.Int ->
5064 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5066 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5067 (tpl3::GHCziBase.ZMZN a ->
5068 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5076 Here, we can see that the function <function>show</function> (which
5077 has been expanded out to a case expression over the Show dictionary)
5078 has a <literal>%note</literal> attached to it, as does the
5079 expression <varname>eta</varname> (which used to be called
5080 <varname>x</varname>).
5087 <sect1 id="generic-classes">
5088 <title>Generic classes</title>
5090 <para>(Note: support for generic classes is currently broken in
5094 The ideas behind this extension are described in detail in "Derivable type classes",
5095 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5096 An example will give the idea:
5104 fromBin :: [Int] -> (a, [Int])
5106 toBin {| Unit |} Unit = []
5107 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5108 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5109 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5111 fromBin {| Unit |} bs = (Unit, bs)
5112 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5113 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5114 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5115 (y,bs'') = fromBin bs'
5118 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5119 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5120 which are defined thus in the library module <literal>Generics</literal>:
5124 data a :+: b = Inl a | Inr b
5125 data a :*: b = a :*: b
5128 Now you can make a data type into an instance of Bin like this:
5130 instance (Bin a, Bin b) => Bin (a,b)
5131 instance Bin a => Bin [a]
5133 That is, just leave off the "where" clause. Of course, you can put in the
5134 where clause and over-ride whichever methods you please.
5138 <title> Using generics </title>
5139 <para>To use generics you need to</para>
5142 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5143 <option>-fgenerics</option> (to generate extra per-data-type code),
5144 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5148 <para>Import the module <literal>Generics</literal> from the
5149 <literal>lang</literal> package. This import brings into
5150 scope the data types <literal>Unit</literal>,
5151 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5152 don't need this import if you don't mention these types
5153 explicitly; for example, if you are simply giving instance
5154 declarations.)</para>
5159 <sect2> <title> Changes wrt the paper </title>
5161 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5162 can be written infix (indeed, you can now use
5163 any operator starting in a colon as an infix type constructor). Also note that
5164 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5165 Finally, note that the syntax of the type patterns in the class declaration
5166 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5167 alone would ambiguous when they appear on right hand sides (an extension we
5168 anticipate wanting).
5172 <sect2> <title>Terminology and restrictions</title>
5174 Terminology. A "generic default method" in a class declaration
5175 is one that is defined using type patterns as above.
5176 A "polymorphic default method" is a default method defined as in Haskell 98.
5177 A "generic class declaration" is a class declaration with at least one
5178 generic default method.
5186 Alas, we do not yet implement the stuff about constructor names and
5193 A generic class can have only one parameter; you can't have a generic
5194 multi-parameter class.
5200 A default method must be defined entirely using type patterns, or entirely
5201 without. So this is illegal:
5204 op :: a -> (a, Bool)
5205 op {| Unit |} Unit = (Unit, True)
5208 However it is perfectly OK for some methods of a generic class to have
5209 generic default methods and others to have polymorphic default methods.
5215 The type variable(s) in the type pattern for a generic method declaration
5216 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:
5220 op {| p :*: q |} (x :*: y) = op (x :: p)
5228 The type patterns in a generic default method must take one of the forms:
5234 where "a" and "b" are type variables. Furthermore, all the type patterns for
5235 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5236 must use the same type variables. So this is illegal:
5240 op {| a :+: b |} (Inl x) = True
5241 op {| p :+: q |} (Inr y) = False
5243 The type patterns must be identical, even in equations for different methods of the class.
5244 So this too is illegal:
5248 op1 {| a :*: b |} (x :*: y) = True
5251 op2 {| p :*: q |} (x :*: y) = False
5253 (The reason for this restriction is that we gather all the equations for a particular type consructor
5254 into a single generic instance declaration.)
5260 A generic method declaration must give a case for each of the three type constructors.
5266 The type for a generic method can be built only from:
5268 <listitem> <para> Function arrows </para> </listitem>
5269 <listitem> <para> Type variables </para> </listitem>
5270 <listitem> <para> Tuples </para> </listitem>
5271 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5273 Here are some example type signatures for generic methods:
5276 op2 :: Bool -> (a,Bool)
5277 op3 :: [Int] -> a -> a
5280 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5284 This restriction is an implementation restriction: we just havn't got around to
5285 implementing the necessary bidirectional maps over arbitrary type constructors.
5286 It would be relatively easy to add specific type constructors, such as Maybe and list,
5287 to the ones that are allowed.</para>
5292 In an instance declaration for a generic class, the idea is that the compiler
5293 will fill in the methods for you, based on the generic templates. However it can only
5298 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5303 No constructor of the instance type has unboxed fields.
5307 (Of course, these things can only arise if you are already using GHC extensions.)
5308 However, you can still give an instance declarations for types which break these rules,
5309 provided you give explicit code to override any generic default methods.
5317 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5318 what the compiler does with generic declarations.
5323 <sect2> <title> Another example </title>
5325 Just to finish with, here's another example I rather like:
5329 nCons {| Unit |} _ = 1
5330 nCons {| a :*: b |} _ = 1
5331 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5334 tag {| Unit |} _ = 1
5335 tag {| a :*: b |} _ = 1
5336 tag {| a :+: b |} (Inl x) = tag x
5337 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5346 ;;; Local Variables: ***
5348 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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