1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>#</literal>},
91 <replaceable>char</replaceable><literal>#</literal>,
92 <replaceable>string</replaceable><literal>#</literal>,
93 <replaceable>integer</replaceable><literal>#</literal>,
94 <replaceable>float</replaceable><literal>#</literal>,
95 <replaceable>float</replaceable><literal>##</literal>,
96 <literal>(#</literal>, <literal>#)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum plus deprecated
110 syntax of previous versions of the FFI for backwards
111 compatibility.</para>
113 <para>New reserved words: <literal>foreign</literal>.</para>
119 <option>-fno-monomorphism-restriction</option>:
120 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
123 <para> Switch off the Haskell 98 monomorphism restriction.
124 Independent of the <option>-fglasgow-exts</option>
131 <option>-fallow-overlapping-instances</option>
132 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
135 <option>-fallow-undecidable-instances</option>
136 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
139 <option>-fallow-incoherent-instances</option>
140 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
143 <option>-fcontext-stack</option>
144 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
147 <para> See <xref linkend="instance-decls"/>. Only relevant
148 if you also use <option>-fglasgow-exts</option>.</para>
154 <option>-finline-phase</option>
155 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
158 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
159 you also use <option>-fglasgow-exts</option>.</para>
165 <option>-farrows</option>
166 <indexterm><primary><option>-farrows</option></primary></indexterm>
169 <para>See <xref linkend="arrow-notation"/>. Independent of
170 <option>-fglasgow-exts</option>.</para>
172 <para>New reserved words/symbols: <literal>rec</literal>,
173 <literal>proc</literal>, <literal>-<</literal>,
174 <literal>>-</literal>, <literal>-<<</literal>,
175 <literal>>>-</literal>.</para>
177 <para>Other syntax stolen: <literal>(|</literal>,
178 <literal>|)</literal>.</para>
184 <option>-fgenerics</option>
185 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
188 <para>See <xref linkend="generic-classes"/>. Independent of
189 <option>-fglasgow-exts</option>.</para>
194 <term><option>-fno-implicit-prelude</option></term>
196 <para><indexterm><primary>-fno-implicit-prelude
197 option</primary></indexterm> GHC normally imports
198 <filename>Prelude.hi</filename> files for you. If you'd
199 rather it didn't, then give it a
200 <option>-fno-implicit-prelude</option> option. The idea is
201 that you can then import a Prelude of your own. (But don't
202 call it <literal>Prelude</literal>; the Haskell module
203 namespace is flat, and you must not conflict with any
204 Prelude module.)</para>
206 <para>Even though you have not imported the Prelude, most of
207 the built-in syntax still refers to the built-in Haskell
208 Prelude types and values, as specified by the Haskell
209 Report. For example, the type <literal>[Int]</literal>
210 still means <literal>Prelude.[] Int</literal>; tuples
211 continue to refer to the standard Prelude tuples; the
212 translation for list comprehensions continues to use
213 <literal>Prelude.map</literal> etc.</para>
215 <para>However, <option>-fno-implicit-prelude</option> does
216 change the handling of certain built-in syntax: see <xref
217 linkend="rebindable-syntax"/>.</para>
222 <term><option>-fimplicit-params</option></term>
224 <para>Enables implicit parameters (see <xref
225 linkend="implicit-parameters"/>). Currently also implied by
226 <option>-fglasgow-exts</option>.</para>
229 <literal>?<replaceable>varid</replaceable></literal>,
230 <literal>%<replaceable>varid</replaceable></literal>.</para>
235 <term><option>-fscoped-type-variables</option></term>
237 <para>Enables lexically-scoped type variables (see <xref
238 linkend="scoped-type-variables"/>). Implied by
239 <option>-fglasgow-exts</option>.</para>
244 <term><option>-fth</option></term>
246 <para>Enables Template Haskell (see <xref
247 linkend="template-haskell"/>). Currently also implied by
248 <option>-fglasgow-exts</option>.</para>
250 <para>Syntax stolen: <literal>[|</literal>,
251 <literal>[e|</literal>, <literal>[p|</literal>,
252 <literal>[d|</literal>, <literal>[t|</literal>,
253 <literal>$(</literal>,
254 <literal>$<replaceable>varid</replaceable></literal>.</para>
261 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
262 <!-- included from primitives.sgml -->
263 <!-- &primitives; -->
264 <sect1 id="primitives">
265 <title>Unboxed types and primitive operations</title>
267 <para>GHC is built on a raft of primitive data types and operations.
268 While you really can use this stuff to write fast code,
269 we generally find it a lot less painful, and more satisfying in the
270 long run, to use higher-level language features and libraries. With
271 any luck, the code you write will be optimised to the efficient
272 unboxed version in any case. And if it isn't, we'd like to know
275 <para>We do not currently have good, up-to-date documentation about the
276 primitives, perhaps because they are mainly intended for internal use.
277 There used to be a long section about them here in the User Guide, but it
278 became out of date, and wrong information is worse than none.</para>
280 <para>The Real Truth about what primitive types there are, and what operations
281 work over those types, is held in the file
282 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
283 This file is used directly to generate GHC's primitive-operation definitions, so
284 it is always correct! It is also intended for processing into text.</para>
287 the result of such processing is part of the description of the
289 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
290 Core language</ulink>.
291 So that document is a good place to look for a type-set version.
292 We would be very happy if someone wanted to volunteer to produce an SGML
293 back end to the program that processes <filename>primops.txt</filename> so that
294 we could include the results here in the User Guide.</para>
296 <para>What follows here is a brief summary of some main points.</para>
298 <sect2 id="glasgow-unboxed">
303 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
306 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
307 that values of that type are represented by a pointer to a heap
308 object. The representation of a Haskell <literal>Int</literal>, for
309 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
310 type, however, is represented by the value itself, no pointers or heap
311 allocation are involved.
315 Unboxed types correspond to the “raw machine” types you
316 would use in C: <literal>Int#</literal> (long int),
317 <literal>Double#</literal> (double), <literal>Addr#</literal>
318 (void *), etc. The <emphasis>primitive operations</emphasis>
319 (PrimOps) on these types are what you might expect; e.g.,
320 <literal>(+#)</literal> is addition on
321 <literal>Int#</literal>s, and is the machine-addition that we all
322 know and love—usually one instruction.
326 Primitive (unboxed) types cannot be defined in Haskell, and are
327 therefore built into the language and compiler. Primitive types are
328 always unlifted; that is, a value of a primitive type cannot be
329 bottom. We use the convention that primitive types, values, and
330 operations have a <literal>#</literal> suffix.
334 Primitive values are often represented by a simple bit-pattern, such
335 as <literal>Int#</literal>, <literal>Float#</literal>,
336 <literal>Double#</literal>. But this is not necessarily the case:
337 a primitive value might be represented by a pointer to a
338 heap-allocated object. Examples include
339 <literal>Array#</literal>, the type of primitive arrays. A
340 primitive array is heap-allocated because it is too big a value to fit
341 in a register, and would be too expensive to copy around; in a sense,
342 it is accidental that it is represented by a pointer. If a pointer
343 represents a primitive value, then it really does point to that value:
344 no unevaluated thunks, no indirections…nothing can be at the
345 other end of the pointer than the primitive value.
346 A numerically-intensive program using unboxed types can
347 go a <emphasis>lot</emphasis> faster than its “standard”
348 counterpart—we saw a threefold speedup on one example.
352 There are some restrictions on the use of primitive types:
354 <listitem><para>The main restriction
355 is that you can't pass a primitive value to a polymorphic
356 function or store one in a polymorphic data type. This rules out
357 things like <literal>[Int#]</literal> (i.e. lists of primitive
358 integers). The reason for this restriction is that polymorphic
359 arguments and constructor fields are assumed to be pointers: if an
360 unboxed integer is stored in one of these, the garbage collector would
361 attempt to follow it, leading to unpredictable space leaks. Or a
362 <function>seq</function> operation on the polymorphic component may
363 attempt to dereference the pointer, with disastrous results. Even
364 worse, the unboxed value might be larger than a pointer
365 (<literal>Double#</literal> for instance).
368 <listitem><para> You cannot bind a variable with an unboxed type
369 in a <emphasis>top-level</emphasis> binding.
371 <listitem><para> You cannot bind a variable with an unboxed type
372 in a <emphasis>recursive</emphasis> binding.
374 <listitem><para> You may bind unboxed variables in a (non-recursive,
375 non-top-level) pattern binding, but any such variable causes the entire
377 to become strict. For example:
379 data Foo = Foo Int Int#
381 f x = let (Foo a b, w) = ..rhs.. in ..body..
383 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
385 is strict, and the program behaves as if you had written
387 data Foo = Foo Int Int#
389 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
398 <sect2 id="unboxed-tuples">
399 <title>Unboxed Tuples
403 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
404 they're available by default with <option>-fglasgow-exts</option>. An
405 unboxed tuple looks like this:
417 where <literal>e_1..e_n</literal> are expressions of any
418 type (primitive or non-primitive). The type of an unboxed tuple looks
423 Unboxed tuples are used for functions that need to return multiple
424 values, but they avoid the heap allocation normally associated with
425 using fully-fledged tuples. When an unboxed tuple is returned, the
426 components are put directly into registers or on the stack; the
427 unboxed tuple itself does not have a composite representation. Many
428 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
430 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
431 tuples to avoid unnecessary allocation during sequences of operations.
435 There are some pretty stringent restrictions on the use of unboxed tuples:
440 Values of unboxed tuple types are subject to the same restrictions as
441 other unboxed types; i.e. they may not be stored in polymorphic data
442 structures or passed to polymorphic functions.
449 No variable can have an unboxed tuple type, nor may a constructor or function
450 argument have an unboxed tuple type. The following are all illegal:
454 data Foo = Foo (# Int, Int #)
456 f :: (# Int, Int #) -> (# Int, Int #)
459 g :: (# Int, Int #) -> Int
462 h x = let y = (# x,x #) in ...
469 The typical use of unboxed tuples is simply to return multiple values,
470 binding those multiple results with a <literal>case</literal> expression, thus:
472 f x y = (# x+1, y-1 #)
473 g x = case f x x of { (# a, b #) -> a + b }
475 You can have an unboxed tuple in a pattern binding, thus
477 f x = let (# p,q #) = h x in ..body..
479 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
480 the resulting binding is lazy like any other Haskell pattern binding. The
481 above example desugars like this:
483 f x = let t = case h x o f{ (# p,q #) -> (p,q)
488 Indeed, the bindings can even be recursive.
495 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
497 <sect1 id="syntax-extns">
498 <title>Syntactic extensions</title>
500 <!-- ====================== HIERARCHICAL MODULES ======================= -->
502 <sect2 id="hierarchical-modules">
503 <title>Hierarchical Modules</title>
505 <para>GHC supports a small extension to the syntax of module
506 names: a module name is allowed to contain a dot
507 <literal>‘.’</literal>. This is also known as the
508 “hierarchical module namespace” extension, because
509 it extends the normally flat Haskell module namespace into a
510 more flexible hierarchy of modules.</para>
512 <para>This extension has very little impact on the language
513 itself; modules names are <emphasis>always</emphasis> fully
514 qualified, so you can just think of the fully qualified module
515 name as <quote>the module name</quote>. In particular, this
516 means that the full module name must be given after the
517 <literal>module</literal> keyword at the beginning of the
518 module; for example, the module <literal>A.B.C</literal> must
521 <programlisting>module A.B.C</programlisting>
524 <para>It is a common strategy to use the <literal>as</literal>
525 keyword to save some typing when using qualified names with
526 hierarchical modules. For example:</para>
529 import qualified Control.Monad.ST.Strict as ST
532 <para>For details on how GHC searches for source and interface
533 files in the presence of hierarchical modules, see <xref
534 linkend="search-path"/>.</para>
536 <para>GHC comes with a large collection of libraries arranged
537 hierarchically; see the accompanying library documentation.
538 There is an ongoing project to create and maintain a stable set
539 of <quote>core</quote> libraries used by several Haskell
540 compilers, and the libraries that GHC comes with represent the
541 current status of that project. For more details, see <ulink
542 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
543 Libraries</ulink>.</para>
547 <!-- ====================== PATTERN GUARDS ======================= -->
549 <sect2 id="pattern-guards">
550 <title>Pattern guards</title>
553 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
554 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.)
558 Suppose we have an abstract data type of finite maps, with a
562 lookup :: FiniteMap -> Int -> Maybe Int
565 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
566 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
570 clunky env var1 var2 | ok1 && ok2 = val1 + val2
571 | otherwise = var1 + var2
582 The auxiliary functions are
586 maybeToBool :: Maybe a -> Bool
587 maybeToBool (Just x) = True
588 maybeToBool Nothing = False
590 expectJust :: Maybe a -> a
591 expectJust (Just x) = x
592 expectJust Nothing = error "Unexpected Nothing"
596 What is <function>clunky</function> doing? The guard <literal>ok1 &&
597 ok2</literal> checks that both lookups succeed, using
598 <function>maybeToBool</function> to convert the <function>Maybe</function>
599 types to booleans. The (lazily evaluated) <function>expectJust</function>
600 calls extract the values from the results of the lookups, and binds the
601 returned values to <varname>val1</varname> and <varname>val2</varname>
602 respectively. If either lookup fails, then clunky takes the
603 <literal>otherwise</literal> case and returns the sum of its arguments.
607 This is certainly legal Haskell, but it is a tremendously verbose and
608 un-obvious way to achieve the desired effect. Arguably, a more direct way
609 to write clunky would be to use case expressions:
613 clunky env var1 var1 = case lookup env var1 of
615 Just val1 -> case lookup env var2 of
617 Just val2 -> val1 + val2
623 This is a bit shorter, but hardly better. Of course, we can rewrite any set
624 of pattern-matching, guarded equations as case expressions; that is
625 precisely what the compiler does when compiling equations! The reason that
626 Haskell provides guarded equations is because they allow us to write down
627 the cases we want to consider, one at a time, independently of each other.
628 This structure is hidden in the case version. Two of the right-hand sides
629 are really the same (<function>fail</function>), and the whole expression
630 tends to become more and more indented.
634 Here is how I would write clunky:
639 | Just val1 <- lookup env var1
640 , Just val2 <- lookup env var2
642 ...other equations for clunky...
646 The semantics should be clear enough. The qualifiers are matched in order.
647 For a <literal><-</literal> qualifier, which I call a pattern guard, the
648 right hand side is evaluated and matched against the pattern on the left.
649 If the match fails then the whole guard fails and the next equation is
650 tried. If it succeeds, then the appropriate binding takes place, and the
651 next qualifier is matched, in the augmented environment. Unlike list
652 comprehensions, however, the type of the expression to the right of the
653 <literal><-</literal> is the same as the type of the pattern to its
654 left. The bindings introduced by pattern guards scope over all the
655 remaining guard qualifiers, and over the right hand side of the equation.
659 Just as with list comprehensions, boolean expressions can be freely mixed
660 with among the pattern guards. For example:
671 Haskell's current guards therefore emerge as a special case, in which the
672 qualifier list has just one element, a boolean expression.
676 <!-- ===================== Recursive do-notation =================== -->
678 <sect2 id="mdo-notation">
679 <title>The recursive do-notation
682 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
683 "A recursive do for Haskell",
684 Levent Erkok, John Launchbury",
685 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
688 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
689 that is, the variables bound in a do-expression are visible only in the textually following
690 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
691 group. It turns out that several applications can benefit from recursive bindings in
692 the do-notation, and this extension provides the necessary syntactic support.
695 Here is a simple (yet contrived) example:
698 import Control.Monad.Fix
700 justOnes = mdo xs <- Just (1:xs)
704 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
708 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
711 class Monad m => MonadFix m where
712 mfix :: (a -> m a) -> m a
715 The function <literal>mfix</literal>
716 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
717 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
718 For details, see the above mentioned reference.
721 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
722 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
723 for Haskell's internal state monad (strict and lazy, respectively).
726 There are three important points in using the recursive-do notation:
729 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
730 than <literal>do</literal>).
734 You should <literal>import Control.Monad.Fix</literal>.
735 (Note: Strictly speaking, this import is required only when you need to refer to the name
736 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
737 are encouraged to always import this module when using the mdo-notation.)
741 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
747 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
748 contains up to date information on recursive monadic bindings.
752 Historical note: The old implementation of the mdo-notation (and most
753 of the existing documents) used the name
754 <literal>MonadRec</literal> for the class and the corresponding library.
755 This name is not supported by GHC.
761 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
763 <sect2 id="parallel-list-comprehensions">
764 <title>Parallel List Comprehensions</title>
765 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
767 <indexterm><primary>parallel list comprehensions</primary>
770 <para>Parallel list comprehensions are a natural extension to list
771 comprehensions. List comprehensions can be thought of as a nice
772 syntax for writing maps and filters. Parallel comprehensions
773 extend this to include the zipWith family.</para>
775 <para>A parallel list comprehension has multiple independent
776 branches of qualifier lists, each separated by a `|' symbol. For
777 example, the following zips together two lists:</para>
780 [ (x, y) | x <- xs | y <- ys ]
783 <para>The behavior of parallel list comprehensions follows that of
784 zip, in that the resulting list will have the same length as the
785 shortest branch.</para>
787 <para>We can define parallel list comprehensions by translation to
788 regular comprehensions. Here's the basic idea:</para>
790 <para>Given a parallel comprehension of the form: </para>
793 [ e | p1 <- e11, p2 <- e12, ...
794 | q1 <- e21, q2 <- e22, ...
799 <para>This will be translated to: </para>
802 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
803 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
808 <para>where `zipN' is the appropriate zip for the given number of
813 <sect2 id="rebindable-syntax">
814 <title>Rebindable syntax</title>
817 <para>GHC allows most kinds of built-in syntax to be rebound by
818 the user, to facilitate replacing the <literal>Prelude</literal>
819 with a home-grown version, for example.</para>
821 <para>You may want to define your own numeric class
822 hierarchy. It completely defeats that purpose if the
823 literal "1" means "<literal>Prelude.fromInteger
824 1</literal>", which is what the Haskell Report specifies.
825 So the <option>-fno-implicit-prelude</option> flag causes
826 the following pieces of built-in syntax to refer to
827 <emphasis>whatever is in scope</emphasis>, not the Prelude
832 <para>An integer literal <literal>368</literal> means
833 "<literal>fromInteger (368::Integer)</literal>", rather than
834 "<literal>Prelude.fromInteger (368::Integer)</literal>".
837 <listitem><para>Fractional literals are handed in just the same way,
838 except that the translation is
839 <literal>fromRational (3.68::Rational)</literal>.
842 <listitem><para>The equality test in an overloaded numeric pattern
843 uses whatever <literal>(==)</literal> is in scope.
846 <listitem><para>The subtraction operation, and the
847 greater-than-or-equal test, in <literal>n+k</literal> patterns
848 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
852 <para>Negation (e.g. "<literal>- (f x)</literal>")
853 means "<literal>negate (f x)</literal>", both in numeric
854 patterns, and expressions.
858 <para>"Do" notation is translated using whatever
859 functions <literal>(>>=)</literal>,
860 <literal>(>>)</literal>, and <literal>fail</literal>,
861 are in scope (not the Prelude
862 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
863 comprehensions, are unaffected. </para></listitem>
867 notation (see <xref linkend="arrow-notation"/>)
868 uses whatever <literal>arr</literal>,
869 <literal>(>>>)</literal>, <literal>first</literal>,
870 <literal>app</literal>, <literal>(|||)</literal> and
871 <literal>loop</literal> functions are in scope. But unlike the
872 other constructs, the types of these functions must match the
873 Prelude types very closely. Details are in flux; if you want
877 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
878 even if that is a little unexpected. For emample, the
879 static semantics of the literal <literal>368</literal>
880 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
881 <literal>fromInteger</literal> to have any of the types:
883 fromInteger :: Integer -> Integer
884 fromInteger :: forall a. Foo a => Integer -> a
885 fromInteger :: Num a => a -> Integer
886 fromInteger :: Integer -> Bool -> Bool
890 <para>Be warned: this is an experimental facility, with
891 fewer checks than usual. Use <literal>-dcore-lint</literal>
892 to typecheck the desugared program. If Core Lint is happy
893 you should be all right.</para>
899 <!-- TYPE SYSTEM EXTENSIONS -->
900 <sect1 id="type-extensions">
901 <title>Type system extensions</title>
905 <title>Data types and type synonyms</title>
907 <sect3 id="nullary-types">
908 <title>Data types with no constructors</title>
910 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
911 a data type with no constructors. For example:</para>
915 data T a -- T :: * -> *
918 <para>Syntactically, the declaration lacks the "= constrs" part. The
919 type can be parameterised over types of any kind, but if the kind is
920 not <literal>*</literal> then an explicit kind annotation must be used
921 (see <xref linkend="sec-kinding"/>).</para>
923 <para>Such data types have only one value, namely bottom.
924 Nevertheless, they can be useful when defining "phantom types".</para>
927 <sect3 id="infix-tycons">
928 <title>Infix type constructors, classes, and type variables</title>
931 GHC allows type constructors, classes, and type variables to be operators, and
932 to be written infix, very much like expressions. More specifically:
935 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
936 The lexical syntax is the same as that for data constructors.
939 Data type and type-synonym declarations can be written infix, parenthesised
940 if you want further arguments. E.g.
942 data a :*: b = Foo a b
943 type a :+: b = Either a b
944 class a :=: b where ...
946 data (a :**: b) x = Baz a b x
947 type (a :++: b) y = Either (a,b) y
951 Types, and class constraints, can be written infix. For example
954 f :: (a :=: b) => a -> b
958 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
959 The lexical syntax is the same as that for variable operators, excluding "(.)",
960 "(!)", and "(*)". In a binding position, the operator must be
961 parenthesised. For example:
963 type T (+) = Int + Int
968 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
974 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
975 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
978 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
979 one cannot distinguish between the two in a fixity declaration; a fixity declaration
980 sets the fixity for a data constructor and the corresponding type constructor. For example:
984 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
985 and similarly for <literal>:*:</literal>.
986 <literal>Int `a` Bool</literal>.
989 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
996 <sect3 id="type-synonyms">
997 <title>Liberalised type synonyms</title>
1000 Type synonyms are like macros at the type level, and
1001 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1002 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1004 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1005 in a type synonym, thus:
1007 type Discard a = forall b. Show b => a -> b -> (a, String)
1012 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1019 You can write an unboxed tuple in a type synonym:
1021 type Pr = (# Int, Int #)
1029 You can apply a type synonym to a forall type:
1031 type Foo a = a -> a -> Bool
1033 f :: Foo (forall b. b->b)
1035 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1037 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1042 You can apply a type synonym to a partially applied type synonym:
1044 type Generic i o = forall x. i x -> o x
1047 foo :: Generic Id []
1049 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1051 foo :: forall x. x -> [x]
1059 GHC currently does kind checking before expanding synonyms (though even that
1063 After expanding type synonyms, GHC does validity checking on types, looking for
1064 the following mal-formedness which isn't detected simply by kind checking:
1067 Type constructor applied to a type involving for-alls.
1070 Unboxed tuple on left of an arrow.
1073 Partially-applied type synonym.
1077 this will be rejected:
1079 type Pr = (# Int, Int #)
1084 because GHC does not allow unboxed tuples on the left of a function arrow.
1089 <sect3 id="existential-quantification">
1090 <title>Existentially quantified data constructors
1094 The idea of using existential quantification in data type declarations
1095 was suggested by Laufer (I believe, thought doubtless someone will
1096 correct me), and implemented in Hope+. It's been in Lennart
1097 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1098 proved very useful. Here's the idea. Consider the declaration:
1104 data Foo = forall a. MkFoo a (a -> Bool)
1111 The data type <literal>Foo</literal> has two constructors with types:
1117 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1124 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1125 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1126 For example, the following expression is fine:
1132 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1138 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1139 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1140 isUpper</function> packages a character with a compatible function. These
1141 two things are each of type <literal>Foo</literal> and can be put in a list.
1145 What can we do with a value of type <literal>Foo</literal>?. In particular,
1146 what happens when we pattern-match on <function>MkFoo</function>?
1152 f (MkFoo val fn) = ???
1158 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1159 are compatible, the only (useful) thing we can do with them is to
1160 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1167 f (MkFoo val fn) = fn val
1173 What this allows us to do is to package heterogenous values
1174 together with a bunch of functions that manipulate them, and then treat
1175 that collection of packages in a uniform manner. You can express
1176 quite a bit of object-oriented-like programming this way.
1179 <sect4 id="existential">
1180 <title>Why existential?
1184 What has this to do with <emphasis>existential</emphasis> quantification?
1185 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1191 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1197 But Haskell programmers can safely think of the ordinary
1198 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1199 adding a new existential quantification construct.
1205 <title>Type classes</title>
1208 An easy extension (implemented in <command>hbc</command>) is to allow
1209 arbitrary contexts before the constructor. For example:
1215 data Baz = forall a. Eq a => Baz1 a a
1216 | forall b. Show b => Baz2 b (b -> b)
1222 The two constructors have the types you'd expect:
1228 Baz1 :: forall a. Eq a => a -> a -> Baz
1229 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1235 But when pattern matching on <function>Baz1</function> the matched values can be compared
1236 for equality, and when pattern matching on <function>Baz2</function> the first matched
1237 value can be converted to a string (as well as applying the function to it).
1238 So this program is legal:
1245 f (Baz1 p q) | p == q = "Yes"
1247 f (Baz2 v fn) = show (fn v)
1253 Operationally, in a dictionary-passing implementation, the
1254 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1255 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1256 extract it on pattern matching.
1260 Notice the way that the syntax fits smoothly with that used for
1261 universal quantification earlier.
1267 <title>Restrictions</title>
1270 There are several restrictions on the ways in which existentially-quantified
1271 constructors can be use.
1280 When pattern matching, each pattern match introduces a new,
1281 distinct, type for each existential type variable. These types cannot
1282 be unified with any other type, nor can they escape from the scope of
1283 the pattern match. For example, these fragments are incorrect:
1291 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1292 is the result of <function>f1</function>. One way to see why this is wrong is to
1293 ask what type <function>f1</function> has:
1297 f1 :: Foo -> a -- Weird!
1301 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1306 f1 :: forall a. Foo -> a -- Wrong!
1310 The original program is just plain wrong. Here's another sort of error
1314 f2 (Baz1 a b) (Baz1 p q) = a==q
1318 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1319 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1320 from the two <function>Baz1</function> constructors.
1328 You can't pattern-match on an existentially quantified
1329 constructor in a <literal>let</literal> or <literal>where</literal> group of
1330 bindings. So this is illegal:
1334 f3 x = a==b where { Baz1 a b = x }
1337 Instead, use a <literal>case</literal> expression:
1340 f3 x = case x of Baz1 a b -> a==b
1343 In general, you can only pattern-match
1344 on an existentially-quantified constructor in a <literal>case</literal> expression or
1345 in the patterns of a function definition.
1347 The reason for this restriction is really an implementation one.
1348 Type-checking binding groups is already a nightmare without
1349 existentials complicating the picture. Also an existential pattern
1350 binding at the top level of a module doesn't make sense, because it's
1351 not clear how to prevent the existentially-quantified type "escaping".
1352 So for now, there's a simple-to-state restriction. We'll see how
1360 You can't use existential quantification for <literal>newtype</literal>
1361 declarations. So this is illegal:
1365 newtype T = forall a. Ord a => MkT a
1369 Reason: a value of type <literal>T</literal> must be represented as a
1370 pair of a dictionary for <literal>Ord t</literal> and a value of type
1371 <literal>t</literal>. That contradicts the idea that
1372 <literal>newtype</literal> should have no concrete representation.
1373 You can get just the same efficiency and effect by using
1374 <literal>data</literal> instead of <literal>newtype</literal>. If
1375 there is no overloading involved, then there is more of a case for
1376 allowing an existentially-quantified <literal>newtype</literal>,
1377 because the <literal>data</literal> version does carry an
1378 implementation cost, but single-field existentially quantified
1379 constructors aren't much use. So the simple restriction (no
1380 existential stuff on <literal>newtype</literal>) stands, unless there
1381 are convincing reasons to change it.
1389 You can't use <literal>deriving</literal> to define instances of a
1390 data type with existentially quantified data constructors.
1392 Reason: in most cases it would not make sense. For example:#
1395 data T = forall a. MkT [a] deriving( Eq )
1398 To derive <literal>Eq</literal> in the standard way we would need to have equality
1399 between the single component of two <function>MkT</function> constructors:
1403 (MkT a) == (MkT b) = ???
1406 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1407 It's just about possible to imagine examples in which the derived instance
1408 would make sense, but it seems altogether simpler simply to prohibit such
1409 declarations. Define your own instances!
1424 <sect2 id="multi-param-type-classes">
1425 <title>Class declarations</title>
1428 This section documents GHC's implementation of multi-parameter type
1429 classes. There's lots of background in the paper <ulink
1430 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1431 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1432 Jones, Erik Meijer).
1435 There are the following constraints on class declarations:
1440 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1444 class Collection c a where
1445 union :: c a -> c a -> c a
1456 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1457 of "acyclic" involves only the superclass relationships. For example,
1463 op :: D b => a -> b -> b
1466 class C a => D a where { ... }
1470 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1471 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1472 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1479 <emphasis>There are no restrictions on the context in a class declaration
1480 (which introduces superclasses), except that the class hierarchy must
1481 be acyclic</emphasis>. So these class declarations are OK:
1485 class Functor (m k) => FiniteMap m k where
1488 class (Monad m, Monad (t m)) => Transform t m where
1489 lift :: m a -> (t m) a
1499 <emphasis>All of the class type variables must be reachable (in the sense
1500 mentioned in <xref linkend="type-restrictions"/>)
1501 from the free variables of each method type
1502 </emphasis>. For example:
1506 class Coll s a where
1508 insert :: s -> a -> s
1512 is not OK, because the type of <literal>empty</literal> doesn't mention
1513 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1514 types, and has the same motivation.
1516 Sometimes, offending class declarations exhibit misunderstandings. For
1517 example, <literal>Coll</literal> might be rewritten
1521 class Coll s a where
1523 insert :: s a -> a -> s a
1527 which makes the connection between the type of a collection of
1528 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1529 Occasionally this really doesn't work, in which case you can split the
1537 class CollE s => Coll s a where
1538 insert :: s -> a -> s
1548 <sect3 id="class-method-types">
1549 <title>Class method types</title>
1551 Haskell 98 prohibits class method types to mention constraints on the
1552 class type variable, thus:
1555 fromList :: [a] -> s a
1556 elem :: Eq a => a -> s a -> Bool
1558 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1559 contains the constraint <literal>Eq a</literal>, constrains only the
1560 class type variable (in this case <literal>a</literal>).
1563 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1570 <sect2 id="type-restrictions">
1571 <title>Type signatures</title>
1573 <sect3><title>The context of a type signature</title>
1575 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1576 the form <emphasis>(class type-variable)</emphasis> or
1577 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1578 these type signatures are perfectly OK
1581 g :: Ord (T a ()) => ...
1585 GHC imposes the following restrictions on the constraints in a type signature.
1589 forall tv1..tvn (c1, ...,cn) => type
1592 (Here, we write the "foralls" explicitly, although the Haskell source
1593 language omits them; in Haskell 98, all the free type variables of an
1594 explicit source-language type signature are universally quantified,
1595 except for the class type variables in a class declaration. However,
1596 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1605 <emphasis>Each universally quantified type variable
1606 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1608 A type variable <literal>a</literal> is "reachable" if it it appears
1609 in the same constraint as either a type variable free in in
1610 <literal>type</literal>, or another reachable type variable.
1611 A value with a type that does not obey
1612 this reachability restriction cannot be used without introducing
1613 ambiguity; that is why the type is rejected.
1614 Here, for example, is an illegal type:
1618 forall a. Eq a => Int
1622 When a value with this type was used, the constraint <literal>Eq tv</literal>
1623 would be introduced where <literal>tv</literal> is a fresh type variable, and
1624 (in the dictionary-translation implementation) the value would be
1625 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1626 can never know which instance of <literal>Eq</literal> to use because we never
1627 get any more information about <literal>tv</literal>.
1631 that the reachability condition is weaker than saying that <literal>a</literal> is
1632 functionally dependent on a type variable free in
1633 <literal>type</literal> (see <xref
1634 linkend="functional-dependencies"/>). The reason for this is there
1635 might be a "hidden" dependency, in a superclass perhaps. So
1636 "reachable" is a conservative approximation to "functionally dependent".
1637 For example, consider:
1639 class C a b | a -> b where ...
1640 class C a b => D a b where ...
1641 f :: forall a b. D a b => a -> a
1643 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1644 but that is not immediately apparent from <literal>f</literal>'s type.
1650 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1651 universally quantified type variables <literal>tvi</literal></emphasis>.
1653 For example, this type is OK because <literal>C a b</literal> mentions the
1654 universally quantified type variable <literal>b</literal>:
1658 forall a. C a b => burble
1662 The next type is illegal because the constraint <literal>Eq b</literal> does not
1663 mention <literal>a</literal>:
1667 forall a. Eq b => burble
1671 The reason for this restriction is milder than the other one. The
1672 excluded types are never useful or necessary (because the offending
1673 context doesn't need to be witnessed at this point; it can be floated
1674 out). Furthermore, floating them out increases sharing. Lastly,
1675 excluding them is a conservative choice; it leaves a patch of
1676 territory free in case we need it later.
1687 <title>For-all hoisting</title>
1689 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1690 end of an arrow, thus:
1692 type Discard a = forall b. a -> b -> a
1694 g :: Int -> Discard Int
1697 Simply expanding the type synonym would give
1699 g :: Int -> (forall b. Int -> b -> Int)
1701 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1703 g :: forall b. Int -> Int -> b -> Int
1705 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1706 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1707 performs the transformation:</emphasis>
1709 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1711 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1713 (In fact, GHC tries to retain as much synonym information as possible for use in
1714 error messages, but that is a usability issue.) This rule applies, of course, whether
1715 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1716 valid way to write <literal>g</literal>'s type signature:
1718 g :: Int -> Int -> forall b. b -> Int
1722 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1725 type Foo a = (?x::Int) => Bool -> a
1730 g :: (?x::Int) => Bool -> Bool -> Int
1738 <sect2 id="instance-decls">
1739 <title>Instance declarations</title>
1741 <sect3 id="instance-overlap">
1742 <title>Overlapping instances</title>
1744 In general, <emphasis>GHC requires that that it be unambiguous which instance
1746 should be used to resolve a type-class constraint</emphasis>. This behaviour
1747 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1748 <indexterm><primary>-fallow-overlapping-instances
1749 </primary></indexterm>
1750 and <option>-fallow-incoherent-instances</option>
1751 <indexterm><primary>-fallow-incoherent-instances
1752 </primary></indexterm>, as this section discusses.</para>
1754 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1755 it tries to match every instance declaration against the
1757 by instantiating the head of the instance declaration. For example, consider
1760 instance context1 => C Int a where ... -- (A)
1761 instance context2 => C a Bool where ... -- (B)
1762 instance context3 => C Int [a] where ... -- (C)
1763 instance context4 => C Int [Int] where ... -- (D)
1765 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
1766 but (C) and (D) do not. When matching, GHC takes
1767 no account of the context of the instance declaration
1768 (<literal>context1</literal> etc).
1769 GHC's default behaviour is that <emphasis>exactly one instance must match the
1770 constraint it is trying to resolve</emphasis>.
1771 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1772 including both declarations (A) and (B), say); an error is only reported if a
1773 particular constraint matches more than one.
1777 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1778 more than one instance to match, provided there is a most specific one. For
1779 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1780 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1781 most-specific match, the program is rejected.
1784 However, GHC is conservative about committing to an overlapping instance. For example:
1789 Suppose that from the RHS of <literal>f</literal> we get the constraint
1790 <literal>C Int [b]</literal>. But
1791 GHC does not commit to instance (C), because in a particular
1792 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1793 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1794 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1795 GHC will instead pick (C), without complaining about
1796 the problem of subsequent instantiations.
1799 The willingness to be overlapped or incoherent is a property of
1800 the <emphasis>instance declaration</emphasis> itself, controlled by the
1801 presence or otherwise of the <option>-fallow-overlapping-instances</option>
1802 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
1803 being defined. Neither flag is required in a module that imports and uses the
1804 instance declaration. Specifically, during the lookup process:
1807 An instance declaration is ignored during the lookup process if (a) a more specific
1808 match is found, and (b) the instance declaration was compiled with
1809 <option>-fallow-overlapping-instances</option>. The flag setting for the
1810 more-specific instance does not matter.
1813 Suppose an instance declaration does not matche the constraint being looked up, but
1814 does unify with it, so that it might match when the constraint is further
1815 instantiated. Usually GHC will regard this as a reason for not committing to
1816 some other constraint. But if the instance declaration was compiled with
1817 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
1818 check for that declaration.
1821 All this makes it possible for a library author to design a library that relies on
1822 overlapping instances without the library client having to know.
1824 <para>The <option>-fallow-incoherent-instances</option> flag implies the
1825 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
1830 <title>Type synonyms in the instance head</title>
1833 <emphasis>Unlike Haskell 98, instance heads may use type
1834 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1835 As always, using a type synonym is just shorthand for
1836 writing the RHS of the type synonym definition. For example:
1840 type Point = (Int,Int)
1841 instance C Point where ...
1842 instance C [Point] where ...
1846 is legal. However, if you added
1850 instance C (Int,Int) where ...
1854 as well, then the compiler will complain about the overlapping
1855 (actually, identical) instance declarations. As always, type synonyms
1856 must be fully applied. You cannot, for example, write:
1861 instance Monad P where ...
1865 This design decision is independent of all the others, and easily
1866 reversed, but it makes sense to me.
1871 <sect3 id="undecidable-instances">
1872 <title>Undecidable instances</title>
1874 <para>An instance declaration must normally obey the following rules:
1876 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1877 an instance declaration <emphasis>must not</emphasis> be a type variable.
1878 For example, these are OK:
1881 instance C Int a where ...
1883 instance D (Int, Int) where ...
1885 instance E [[a]] where ...
1889 instance F a where ...
1891 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1892 For example, this is OK:
1894 instance Stateful (ST s) (MutVar s) where ...
1901 <para>All of the types in the <emphasis>context</emphasis> of
1902 an instance declaration <emphasis>must</emphasis> be type variables.
1905 instance C a b => Eq (a,b) where ...
1909 instance C Int b => Foo b where ...
1915 These restrictions ensure that
1916 context reduction terminates: each reduction step removes one type
1917 constructor. For example, the following would make the type checker
1918 loop if it wasn't excluded:
1920 instance C a => C a where ...
1922 There are two situations in which the rule is a bit of a pain. First,
1923 if one allows overlapping instance declarations then it's quite
1924 convenient to have a "default instance" declaration that applies if
1925 something more specific does not:
1934 Second, sometimes you might want to use the following to get the
1935 effect of a "class synonym":
1939 class (C1 a, C2 a, C3 a) => C a where { }
1941 instance (C1 a, C2 a, C3 a) => C a where { }
1945 This allows you to write shorter signatures:
1957 f :: (C1 a, C2 a, C3 a) => ...
1961 Voluminous correspondence on the Haskell mailing list has convinced me
1962 that it's worth experimenting with more liberal rules. If you use
1963 the experimental flag <option>-fallow-undecidable-instances</option>
1964 <indexterm><primary>-fallow-undecidable-instances
1965 option</primary></indexterm>, you can use arbitrary
1966 types in both an instance context and instance head. Termination is ensured by having a
1967 fixed-depth recursion stack. If you exceed the stack depth you get a
1968 sort of backtrace, and the opportunity to increase the stack depth
1969 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1972 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1973 allowing these idioms interesting idioms.
1980 <sect2 id="implicit-parameters">
1981 <title>Implicit parameters</title>
1983 <para> Implicit parameters are implemented as described in
1984 "Implicit parameters: dynamic scoping with static types",
1985 J Lewis, MB Shields, E Meijer, J Launchbury,
1986 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1990 <para>(Most of the following, stil rather incomplete, documentation is
1991 due to Jeff Lewis.)</para>
1993 <para>Implicit parameter support is enabled with the option
1994 <option>-fimplicit-params</option>.</para>
1997 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1998 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1999 context. In Haskell, all variables are statically bound. Dynamic
2000 binding of variables is a notion that goes back to Lisp, but was later
2001 discarded in more modern incarnations, such as Scheme. Dynamic binding
2002 can be very confusing in an untyped language, and unfortunately, typed
2003 languages, in particular Hindley-Milner typed languages like Haskell,
2004 only support static scoping of variables.
2007 However, by a simple extension to the type class system of Haskell, we
2008 can support dynamic binding. Basically, we express the use of a
2009 dynamically bound variable as a constraint on the type. These
2010 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2011 function uses a dynamically-bound variable <literal>?x</literal>
2012 of type <literal>t'</literal>". For
2013 example, the following expresses the type of a sort function,
2014 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2016 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2018 The dynamic binding constraints are just a new form of predicate in the type class system.
2021 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2022 where <literal>x</literal> is
2023 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2024 Use of this construct also introduces a new
2025 dynamic-binding constraint in the type of the expression.
2026 For example, the following definition
2027 shows how we can define an implicitly parameterized sort function in
2028 terms of an explicitly parameterized <literal>sortBy</literal> function:
2030 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2032 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2038 <title>Implicit-parameter type constraints</title>
2040 Dynamic binding constraints behave just like other type class
2041 constraints in that they are automatically propagated. Thus, when a
2042 function is used, its implicit parameters are inherited by the
2043 function that called it. For example, our <literal>sort</literal> function might be used
2044 to pick out the least value in a list:
2046 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2047 least xs = fst (sort xs)
2049 Without lifting a finger, the <literal>?cmp</literal> parameter is
2050 propagated to become a parameter of <literal>least</literal> as well. With explicit
2051 parameters, the default is that parameters must always be explicit
2052 propagated. With implicit parameters, the default is to always
2056 An implicit-parameter type constraint differs from other type class constraints in the
2057 following way: All uses of a particular implicit parameter must have
2058 the same type. This means that the type of <literal>(?x, ?x)</literal>
2059 is <literal>(?x::a) => (a,a)</literal>, and not
2060 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2064 <para> You can't have an implicit parameter in the context of a class or instance
2065 declaration. For example, both these declarations are illegal:
2067 class (?x::Int) => C a where ...
2068 instance (?x::a) => Foo [a] where ...
2070 Reason: exactly which implicit parameter you pick up depends on exactly where
2071 you invoke a function. But the ``invocation'' of instance declarations is done
2072 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2073 Easiest thing is to outlaw the offending types.</para>
2075 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2077 f :: (?x :: [a]) => Int -> Int
2080 g :: (Read a, Show a) => String -> String
2083 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2084 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2085 quite unambiguous, and fixes the type <literal>a</literal>.
2090 <title>Implicit-parameter bindings</title>
2093 An implicit parameter is <emphasis>bound</emphasis> using the standard
2094 <literal>let</literal> or <literal>where</literal> binding forms.
2095 For example, we define the <literal>min</literal> function by binding
2096 <literal>cmp</literal>.
2099 min = let ?cmp = (<=) in least
2103 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2104 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2105 (including in a list comprehension, or do-notation, or pattern guards),
2106 or a <literal>where</literal> clause.
2107 Note the following points:
2110 An implicit-parameter binding group must be a
2111 collection of simple bindings to implicit-style variables (no
2112 function-style bindings, and no type signatures); these bindings are
2113 neither polymorphic or recursive.
2116 You may not mix implicit-parameter bindings with ordinary bindings in a
2117 single <literal>let</literal>
2118 expression; use two nested <literal>let</literal>s instead.
2119 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2123 You may put multiple implicit-parameter bindings in a
2124 single binding group; but they are <emphasis>not</emphasis> treated
2125 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2126 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2127 parameter. The bindings are not nested, and may be re-ordered without changing
2128 the meaning of the program.
2129 For example, consider:
2131 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2133 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2134 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2136 f :: (?x::Int) => Int -> Int
2144 <sect3><title>Implicit parameters and polymorphic recursion</title>
2147 Consider these two definitions:
2150 len1 xs = let ?acc = 0 in len_acc1 xs
2153 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2158 len2 xs = let ?acc = 0 in len_acc2 xs
2160 len_acc2 :: (?acc :: Int) => [a] -> Int
2162 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2164 The only difference between the two groups is that in the second group
2165 <literal>len_acc</literal> is given a type signature.
2166 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2167 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2168 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2169 has a type signature, the recursive call is made to the
2170 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2171 as an implicit parameter. So we get the following results in GHCi:
2178 Adding a type signature dramatically changes the result! This is a rather
2179 counter-intuitive phenomenon, worth watching out for.
2183 <sect3><title>Implicit parameters and monomorphism</title>
2185 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2186 Haskell Report) to implicit parameters. For example, consider:
2194 Since the binding for <literal>y</literal> falls under the Monomorphism
2195 Restriction it is not generalised, so the type of <literal>y</literal> is
2196 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2197 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2198 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2199 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2200 <literal>y</literal> in the body of the <literal>let</literal> will see the
2201 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2202 <literal>14</literal>.
2207 <sect2 id="linear-implicit-parameters">
2208 <title>Linear implicit parameters</title>
2210 Linear implicit parameters are an idea developed by Koen Claessen,
2211 Mark Shields, and Simon PJ. They address the long-standing
2212 problem that monads seem over-kill for certain sorts of problem, notably:
2215 <listitem> <para> distributing a supply of unique names </para> </listitem>
2216 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2217 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2221 Linear implicit parameters are just like ordinary implicit parameters,
2222 except that they are "linear" -- that is, they cannot be copied, and
2223 must be explicitly "split" instead. Linear implicit parameters are
2224 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2225 (The '/' in the '%' suggests the split!)
2230 import GHC.Exts( Splittable )
2232 data NameSupply = ...
2234 splitNS :: NameSupply -> (NameSupply, NameSupply)
2235 newName :: NameSupply -> Name
2237 instance Splittable NameSupply where
2241 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2242 f env (Lam x e) = Lam x' (f env e)
2245 env' = extend env x x'
2246 ...more equations for f...
2248 Notice that the implicit parameter %ns is consumed
2250 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2251 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2255 So the translation done by the type checker makes
2256 the parameter explicit:
2258 f :: NameSupply -> Env -> Expr -> Expr
2259 f ns env (Lam x e) = Lam x' (f ns1 env e)
2261 (ns1,ns2) = splitNS ns
2263 env = extend env x x'
2265 Notice the call to 'split' introduced by the type checker.
2266 How did it know to use 'splitNS'? Because what it really did
2267 was to introduce a call to the overloaded function 'split',
2268 defined by the class <literal>Splittable</literal>:
2270 class Splittable a where
2273 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2274 split for name supplies. But we can simply write
2280 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2282 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2283 <literal>GHC.Exts</literal>.
2288 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2289 are entirely distinct implicit parameters: you
2290 can use them together and they won't intefere with each other. </para>
2293 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2295 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2296 in the context of a class or instance declaration. </para></listitem>
2300 <sect3><title>Warnings</title>
2303 The monomorphism restriction is even more important than usual.
2304 Consider the example above:
2306 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2307 f env (Lam x e) = Lam x' (f env e)
2310 env' = extend env x x'
2312 If we replaced the two occurrences of x' by (newName %ns), which is
2313 usually a harmless thing to do, we get:
2315 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2316 f env (Lam x e) = Lam (newName %ns) (f env e)
2318 env' = extend env x (newName %ns)
2320 But now the name supply is consumed in <emphasis>three</emphasis> places
2321 (the two calls to newName,and the recursive call to f), so
2322 the result is utterly different. Urk! We don't even have
2326 Well, this is an experimental change. With implicit
2327 parameters we have already lost beta reduction anyway, and
2328 (as John Launchbury puts it) we can't sensibly reason about
2329 Haskell programs without knowing their typing.
2334 <sect3><title>Recursive functions</title>
2335 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2338 foo :: %x::T => Int -> [Int]
2340 foo n = %x : foo (n-1)
2342 where T is some type in class Splittable.</para>
2344 Do you get a list of all the same T's or all different T's
2345 (assuming that split gives two distinct T's back)?
2347 If you supply the type signature, taking advantage of polymorphic
2348 recursion, you get what you'd probably expect. Here's the
2349 translated term, where the implicit param is made explicit:
2352 foo x n = let (x1,x2) = split x
2353 in x1 : foo x2 (n-1)
2355 But if you don't supply a type signature, GHC uses the Hindley
2356 Milner trick of using a single monomorphic instance of the function
2357 for the recursive calls. That is what makes Hindley Milner type inference
2358 work. So the translation becomes
2362 foom n = x : foom (n-1)
2366 Result: 'x' is not split, and you get a list of identical T's. So the
2367 semantics of the program depends on whether or not foo has a type signature.
2370 You may say that this is a good reason to dislike linear implicit parameters
2371 and you'd be right. That is why they are an experimental feature.
2377 <sect2 id="functional-dependencies">
2378 <title>Functional dependencies
2381 <para> Functional dependencies are implemented as described by Mark Jones
2382 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2383 In Proceedings of the 9th European Symposium on Programming,
2384 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2388 Functional dependencies are introduced by a vertical bar in the syntax of a
2389 class declaration; e.g.
2391 class (Monad m) => MonadState s m | m -> s where ...
2393 class Foo a b c | a b -> c where ...
2395 There should be more documentation, but there isn't (yet). Yell if you need it.
2401 <sect2 id="sec-kinding">
2402 <title>Explicitly-kinded quantification</title>
2405 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2406 to give the kind explicitly as (machine-checked) documentation,
2407 just as it is nice to give a type signature for a function. On some occasions,
2408 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2409 John Hughes had to define the data type:
2411 data Set cxt a = Set [a]
2412 | Unused (cxt a -> ())
2414 The only use for the <literal>Unused</literal> constructor was to force the correct
2415 kind for the type variable <literal>cxt</literal>.
2418 GHC now instead allows you to specify the kind of a type variable directly, wherever
2419 a type variable is explicitly bound. Namely:
2421 <listitem><para><literal>data</literal> declarations:
2423 data Set (cxt :: * -> *) a = Set [a]
2424 </screen></para></listitem>
2425 <listitem><para><literal>type</literal> declarations:
2427 type T (f :: * -> *) = f Int
2428 </screen></para></listitem>
2429 <listitem><para><literal>class</literal> declarations:
2431 class (Eq a) => C (f :: * -> *) a where ...
2432 </screen></para></listitem>
2433 <listitem><para><literal>forall</literal>'s in type signatures:
2435 f :: forall (cxt :: * -> *). Set cxt Int
2436 </screen></para></listitem>
2441 The parentheses are required. Some of the spaces are required too, to
2442 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2443 will get a parse error, because "<literal>::*->*</literal>" is a
2444 single lexeme in Haskell.
2448 As part of the same extension, you can put kind annotations in types
2451 f :: (Int :: *) -> Int
2452 g :: forall a. a -> (a :: *)
2456 atype ::= '(' ctype '::' kind ')
2458 The parentheses are required.
2463 <sect2 id="universal-quantification">
2464 <title>Arbitrary-rank polymorphism
2468 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2469 allows us to say exactly what this means. For example:
2477 g :: forall b. (b -> b)
2479 The two are treated identically.
2483 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2484 explicit universal quantification in
2486 For example, all the following types are legal:
2488 f1 :: forall a b. a -> b -> a
2489 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2491 f2 :: (forall a. a->a) -> Int -> Int
2492 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2494 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2496 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2497 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2498 The <literal>forall</literal> makes explicit the universal quantification that
2499 is implicitly added by Haskell.
2502 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2503 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2504 shows, the polymorphic type on the left of the function arrow can be overloaded.
2507 The function <literal>f3</literal> has a rank-3 type;
2508 it has rank-2 types on the left of a function arrow.
2511 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2512 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2513 that restriction has now been lifted.)
2514 In particular, a forall-type (also called a "type scheme"),
2515 including an operational type class context, is legal:
2517 <listitem> <para> On the left of a function arrow </para> </listitem>
2518 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2519 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2520 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2521 field type signatures.</para> </listitem>
2522 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2523 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2525 There is one place you cannot put a <literal>forall</literal>:
2526 you cannot instantiate a type variable with a forall-type. So you cannot
2527 make a forall-type the argument of a type constructor. So these types are illegal:
2529 x1 :: [forall a. a->a]
2530 x2 :: (forall a. a->a, Int)
2531 x3 :: Maybe (forall a. a->a)
2533 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2534 a type variable any more!
2543 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2544 the types of the constructor arguments. Here are several examples:
2550 data T a = T1 (forall b. b -> b -> b) a
2552 data MonadT m = MkMonad { return :: forall a. a -> m a,
2553 bind :: forall a b. m a -> (a -> m b) -> m b
2556 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2562 The constructors have rank-2 types:
2568 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2569 MkMonad :: forall m. (forall a. a -> m a)
2570 -> (forall a b. m a -> (a -> m b) -> m b)
2572 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2578 Notice that you don't need to use a <literal>forall</literal> if there's an
2579 explicit context. For example in the first argument of the
2580 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2581 prefixed to the argument type. The implicit <literal>forall</literal>
2582 quantifies all type variables that are not already in scope, and are
2583 mentioned in the type quantified over.
2587 As for type signatures, implicit quantification happens for non-overloaded
2588 types too. So if you write this:
2591 data T a = MkT (Either a b) (b -> b)
2594 it's just as if you had written this:
2597 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2600 That is, since the type variable <literal>b</literal> isn't in scope, it's
2601 implicitly universally quantified. (Arguably, it would be better
2602 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2603 where that is what is wanted. Feedback welcomed.)
2607 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2608 the constructor to suitable values, just as usual. For example,
2619 a3 = MkSwizzle reverse
2622 a4 = let r x = Just x
2629 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2630 mkTs f x y = [T1 f x, T1 f y]
2636 The type of the argument can, as usual, be more general than the type
2637 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2638 does not need the <literal>Ord</literal> constraint.)
2642 When you use pattern matching, the bound variables may now have
2643 polymorphic types. For example:
2649 f :: T a -> a -> (a, Char)
2650 f (T1 w k) x = (w k x, w 'c' 'd')
2652 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2653 g (MkSwizzle s) xs f = s (map f (s xs))
2655 h :: MonadT m -> [m a] -> m [a]
2656 h m [] = return m []
2657 h m (x:xs) = bind m x $ \y ->
2658 bind m (h m xs) $ \ys ->
2665 In the function <function>h</function> we use the record selectors <literal>return</literal>
2666 and <literal>bind</literal> to extract the polymorphic bind and return functions
2667 from the <literal>MonadT</literal> data structure, rather than using pattern
2673 <title>Type inference</title>
2676 In general, type inference for arbitrary-rank types is undecidable.
2677 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2678 to get a decidable algorithm by requiring some help from the programmer.
2679 We do not yet have a formal specification of "some help" but the rule is this:
2682 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2683 provides an explicit polymorphic type for x, or GHC's type inference will assume
2684 that x's type has no foralls in it</emphasis>.
2687 What does it mean to "provide" an explicit type for x? You can do that by
2688 giving a type signature for x directly, using a pattern type signature
2689 (<xref linkend="scoped-type-variables"/>), thus:
2691 \ f :: (forall a. a->a) -> (f True, f 'c')
2693 Alternatively, you can give a type signature to the enclosing
2694 context, which GHC can "push down" to find the type for the variable:
2696 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2698 Here the type signature on the expression can be pushed inwards
2699 to give a type signature for f. Similarly, and more commonly,
2700 one can give a type signature for the function itself:
2702 h :: (forall a. a->a) -> (Bool,Char)
2703 h f = (f True, f 'c')
2705 You don't need to give a type signature if the lambda bound variable
2706 is a constructor argument. Here is an example we saw earlier:
2708 f :: T a -> a -> (a, Char)
2709 f (T1 w k) x = (w k x, w 'c' 'd')
2711 Here we do not need to give a type signature to <literal>w</literal>, because
2712 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2719 <sect3 id="implicit-quant">
2720 <title>Implicit quantification</title>
2723 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2724 user-written types, if and only if there is no explicit <literal>forall</literal>,
2725 GHC finds all the type variables mentioned in the type that are not already
2726 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2730 f :: forall a. a -> a
2737 h :: forall b. a -> b -> b
2743 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2746 f :: (a -> a) -> Int
2748 f :: forall a. (a -> a) -> Int
2750 f :: (forall a. a -> a) -> Int
2753 g :: (Ord a => a -> a) -> Int
2754 -- MEANS the illegal type
2755 g :: forall a. (Ord a => a -> a) -> Int
2757 g :: (forall a. Ord a => a -> a) -> Int
2759 The latter produces an illegal type, which you might think is silly,
2760 but at least the rule is simple. If you want the latter type, you
2761 can write your for-alls explicitly. Indeed, doing so is strongly advised
2770 <sect2 id="scoped-type-variables">
2771 <title>Scoped type variables
2775 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
2777 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
2778 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
2779 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
2783 f (xs::[a]) = ys ++ ys
2788 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2789 This brings the type variable <literal>a</literal> into scope; it scopes over
2790 all the patterns and right hand sides for this equation for <function>f</function>.
2791 In particular, it is in scope at the type signature for <varname>y</varname>.
2795 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2796 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2797 implicitly universally quantified. (If there are no type variables in
2798 scope, all type variables mentioned in the signature are universally
2799 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2800 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2801 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2802 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2803 it becomes possible to do so.
2807 Scoped type variables are implemented in both GHC and Hugs. Where the
2808 implementations differ from the specification below, those differences
2813 So much for the basic idea. Here are the details.
2817 <title>What a scoped type variable means</title>
2819 A lexically-scoped type variable is simply
2820 the name for a type. The restriction it expresses is that all occurrences
2821 of the same name mean the same type. For example:
2823 f :: [Int] -> Int -> Int
2824 f (xs::[a]) (y::a) = (head xs + y) :: a
2826 The pattern type signatures on the left hand side of
2827 <literal>f</literal> express the fact that <literal>xs</literal>
2828 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2829 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2830 specifies that this expression must have the same type <literal>a</literal>.
2831 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2832 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2833 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2834 rules, which specified that a pattern-bound type variable should be universally quantified.)
2835 For example, all of these are legal:</para>
2838 t (x::a) (y::a) = x+y*2
2840 f (x::a) (y::b) = [x,y] -- a unifies with b
2842 g (x::a) = x + 1::Int -- a unifies with Int
2844 h x = let k (y::a) = [x,y] -- a is free in the
2845 in k x -- environment
2847 k (x::a) True = ... -- a unifies with Int
2848 k (x::Int) False = ...
2851 w (x::a) = x -- a unifies with [b]
2857 <title>Scope and implicit quantification</title>
2865 All the type variables mentioned in a pattern,
2866 that are not already in scope,
2867 are brought into scope by the pattern. We describe this set as
2868 the <emphasis>type variables bound by the pattern</emphasis>.
2871 f (x::a) = let g (y::(a,b)) = fst y
2875 The pattern <literal>(x::a)</literal> brings the type variable
2876 <literal>a</literal> into scope, as well as the term
2877 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2878 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2879 and brings into scope the type variable <literal>b</literal>.
2885 The type variable(s) bound by the pattern have the same scope
2886 as the term variable(s) bound by the pattern. For example:
2889 f (x::a) = <...rhs of f...>
2890 (p::b, q::b) = (1,2)
2891 in <...body of let...>
2893 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2894 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2895 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2896 just like <literal>p</literal> and <literal>q</literal> do.
2897 Indeed, the newly bound type variables also scope over any ordinary, separate
2898 type signatures in the <literal>let</literal> group.
2905 The type variables bound by the pattern may be
2906 mentioned in ordinary type signatures or pattern
2907 type signatures anywhere within their scope.
2914 In ordinary type signatures, any type variable mentioned in the
2915 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2923 Ordinary type signatures do not bring any new type variables
2924 into scope (except in the type signature itself!). So this is illegal:
2931 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2932 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2933 and that is an incorrect typing.
2940 The pattern type signature is a monotype:
2945 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2949 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2950 not to type schemes.
2954 There is no implicit universal quantification on pattern type signatures (in contrast to
2955 ordinary type signatures).
2965 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2966 scope over the methods defined in the <literal>where</literal> part. For example:
2980 (Not implemented in Hugs yet, Dec 98).
2990 <sect3 id="decl-type-sigs">
2991 <title>Declaration type signatures</title>
2992 <para>A declaration type signature that has <emphasis>explicit</emphasis>
2993 quantification (using <literal>forall</literal>) brings into scope the
2994 explicitly-quantified
2995 type variables, in the definition of the named function(s). For example:
2997 f :: forall a. [a] -> [a]
2998 f (x:xs) = xs ++ [ x :: a ]
3000 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3001 the definition of "<literal>f</literal>".
3003 <para>This only happens if the quantification in <literal>f</literal>'s type
3004 signature is explicit. For example:
3007 g (x:xs) = xs ++ [ x :: a ]
3009 This program will be rejected, because "<literal>a</literal>" does not scope
3010 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3011 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3012 quantification rules.
3016 <sect3 id="pattern-type-sigs">
3017 <title>Where a pattern type signature can occur</title>
3020 A pattern type signature can occur in any pattern. For example:
3025 A pattern type signature can be on an arbitrary sub-pattern, not
3030 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3039 Pattern type signatures, including the result part, can be used
3040 in lambda abstractions:
3043 (\ (x::a, y) :: a -> x)
3050 Pattern type signatures, including the result part, can be used
3051 in <literal>case</literal> expressions:
3054 case e of { ((x::a, y) :: (a,b)) -> x }
3057 Note that the <literal>-></literal> symbol in a case alternative
3058 leads to difficulties when parsing a type signature in the pattern: in
3059 the absence of the extra parentheses in the example above, the parser
3060 would try to interpret the <literal>-></literal> as a function
3061 arrow and give a parse error later.
3069 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3070 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3071 token or a parenthesised type of some sort). To see why,
3072 consider how one would parse this:
3086 Pattern type signatures can bind existential type variables.
3091 data T = forall a. MkT [a]
3094 f (MkT [t::a]) = MkT t3
3107 Pattern type signatures
3108 can be used in pattern bindings:
3111 f x = let (y, z::a) = x in ...
3112 f1 x = let (y, z::Int) = x in ...
3113 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3114 f3 :: (b->b) = \x -> x
3117 In all such cases, the binding is not generalised over the pattern-bound
3118 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3119 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3120 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3121 In contrast, the binding
3126 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3127 in <literal>f4</literal>'s scope.
3133 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3134 type signatures. The two can be used independently or together.</para>
3138 <sect3 id="result-type-sigs">
3139 <title>Result type signatures</title>
3142 The result type of a function can be given a signature, thus:
3146 f (x::a) :: [a] = [x,x,x]
3150 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3151 result type. Sometimes this is the only way of naming the type variable
3156 f :: Int -> [a] -> [a]
3157 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3158 in \xs -> map g (reverse xs `zip` xs)
3163 The type variables bound in a result type signature scope over the right hand side
3164 of the definition. However, consider this corner-case:
3166 rev1 :: [a] -> [a] = \xs -> reverse xs
3168 foo ys = rev (ys::[a])
3170 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3171 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3172 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3173 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3174 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3177 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3178 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3182 rev1 :: [a] -> [a] = \xs -> reverse xs
3187 Result type signatures are not yet implemented in Hugs.
3194 <sect2 id="deriving-typeable">
3195 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3198 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3199 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3200 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3201 classes <literal>Eq</literal>, <literal>Ord</literal>,
3202 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3205 GHC extends this list with two more classes that may be automatically derived
3206 (provided the <option>-fglasgow-exts</option> flag is specified):
3207 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3208 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3209 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3213 <sect2 id="newtype-deriving">
3214 <title>Generalised derived instances for newtypes</title>
3217 When you define an abstract type using <literal>newtype</literal>, you may want
3218 the new type to inherit some instances from its representation. In
3219 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3220 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3221 other classes you have to write an explicit instance declaration. For
3222 example, if you define
3225 newtype Dollars = Dollars Int
3228 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3229 explicitly define an instance of <literal>Num</literal>:
3232 instance Num Dollars where
3233 Dollars a + Dollars b = Dollars (a+b)
3236 All the instance does is apply and remove the <literal>newtype</literal>
3237 constructor. It is particularly galling that, since the constructor
3238 doesn't appear at run-time, this instance declaration defines a
3239 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3240 dictionary, only slower!
3244 <sect3> <title> Generalising the deriving clause </title>
3246 GHC now permits such instances to be derived instead, so one can write
3248 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3251 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3252 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3253 derives an instance declaration of the form
3256 instance Num Int => Num Dollars
3259 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3263 We can also derive instances of constructor classes in a similar
3264 way. For example, suppose we have implemented state and failure monad
3265 transformers, such that
3268 instance Monad m => Monad (State s m)
3269 instance Monad m => Monad (Failure m)
3271 In Haskell 98, we can define a parsing monad by
3273 type Parser tok m a = State [tok] (Failure m) a
3276 which is automatically a monad thanks to the instance declarations
3277 above. With the extension, we can make the parser type abstract,
3278 without needing to write an instance of class <literal>Monad</literal>, via
3281 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3284 In this case the derived instance declaration is of the form
3286 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3289 Notice that, since <literal>Monad</literal> is a constructor class, the
3290 instance is a <emphasis>partial application</emphasis> of the new type, not the
3291 entire left hand side. We can imagine that the type declaration is
3292 ``eta-converted'' to generate the context of the instance
3297 We can even derive instances of multi-parameter classes, provided the
3298 newtype is the last class parameter. In this case, a ``partial
3299 application'' of the class appears in the <literal>deriving</literal>
3300 clause. For example, given the class
3303 class StateMonad s m | m -> s where ...
3304 instance Monad m => StateMonad s (State s m) where ...
3306 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3308 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3309 deriving (Monad, StateMonad [tok])
3312 The derived instance is obtained by completing the application of the
3313 class to the new type:
3316 instance StateMonad [tok] (State [tok] (Failure m)) =>
3317 StateMonad [tok] (Parser tok m)
3322 As a result of this extension, all derived instances in newtype
3323 declarations are treated uniformly (and implemented just by reusing
3324 the dictionary for the representation type), <emphasis>except</emphasis>
3325 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3326 the newtype and its representation.
3330 <sect3> <title> A more precise specification </title>
3332 Derived instance declarations are constructed as follows. Consider the
3333 declaration (after expansion of any type synonyms)
3336 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3342 <literal>S</literal> is a type constructor,
3345 The <literal>t1...tk</literal> are types,
3348 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3349 the <literal>ti</literal>, and
3352 The <literal>ci</literal> are partial applications of
3353 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3354 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3357 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3358 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3359 should not "look through" the type or its constructor. You can still
3360 derive these classes for a newtype, but it happens in the usual way, not
3361 via this new mechanism.
3364 Then, for each <literal>ci</literal>, the derived instance
3367 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3369 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3370 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3374 As an example which does <emphasis>not</emphasis> work, consider
3376 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3378 Here we cannot derive the instance
3380 instance Monad (State s m) => Monad (NonMonad m)
3383 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3384 and so cannot be "eta-converted" away. It is a good thing that this
3385 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3386 not, in fact, a monad --- for the same reason. Try defining
3387 <literal>>>=</literal> with the correct type: you won't be able to.
3391 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3392 important, since we can only derive instances for the last one. If the
3393 <literal>StateMonad</literal> class above were instead defined as
3396 class StateMonad m s | m -> s where ...
3399 then we would not have been able to derive an instance for the
3400 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3401 classes usually have one "main" parameter for which deriving new
3402 instances is most interesting.
3404 <para>Lastly, all of this applies only for classes other than
3405 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3406 and <literal>Data</literal>, for which the built-in derivation applies (section
3407 4.3.3. of the Haskell Report).
3408 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3409 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3410 the standard method is used or the one described here.)
3416 <sect2 id="typing-binds">
3417 <title>Generalised typing of mutually recursive bindings</title>
3420 The Haskell Report specifies that a group of bindings (at top level, or in a
3421 <literal>let</literal> or <literal>where</literal>) should be sorted into
3422 strongly-connected components, and then type-checked in dependency order
3423 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3424 Report, Section 4.5.1</ulink>).
3425 As each group is type-checked, any binders of the group that
3427 an explicit type signature are put in the type environment with the specified
3429 and all others are monomorphic until the group is generalised
3430 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3433 <para>Following a suggestion of Mark Jones, in his paper
3434 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3436 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3438 <emphasis>the dependency analysis ignores references to variables that have an explicit
3439 type signature</emphasis>.
3440 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3441 typecheck. For example, consider:
3443 f :: Eq a => a -> Bool
3444 f x = (x == x) || g True || g "Yes"
3446 g y = (y <= y) || f True
3448 This is rejected by Haskell 98, but under Jones's scheme the definition for
3449 <literal>g</literal> is typechecked first, separately from that for
3450 <literal>f</literal>,
3451 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3452 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3453 type is generalised, to get
3455 g :: Ord a => a -> Bool
3457 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3458 <literal>g</literal> in the type environment.
3462 The same refined dependency analysis also allows the type signatures of
3463 mutually-recursive functions to have different contexts, something that is illegal in
3464 Haskell 98 (Section 4.5.2, last sentence). With
3465 <option>-fglasgow-exts</option>
3466 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3467 type signatures; in practice this means that only variables bound by the same
3468 pattern binding must have the same context. For example, this is fine:
3470 f :: Eq a => a -> Bool
3471 f x = (x == x) || g True
3473 g :: Ord a => a -> Bool
3474 g y = (y <= y) || f True
3480 <!-- ==================== End of type system extensions ================= -->
3482 <!-- ====================== Generalised algebraic data types ======================= -->
3485 <title>Generalised Algebraic Data Types</title>
3487 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3488 to give the type signatures of constructors explicitly. For example:
3491 Lit :: Int -> Term Int
3492 Succ :: Term Int -> Term Int
3493 IsZero :: Term Int -> Term Bool
3494 If :: Term Bool -> Term a -> Term a -> Term a
3495 Pair :: Term a -> Term b -> Term (a,b)
3497 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3498 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3499 for these <literal>Terms</literal>:
3503 eval (Succ t) = 1 + eval t
3504 eval (IsZero i) = eval i == 0
3505 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3506 eval (Pair e1 e2) = (eval e2, eval e2)
3508 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3510 <para> The extensions to GHC are these:
3513 Data type declarations have a 'where' form, as exemplified above. The type signature of
3514 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3515 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3516 have no scope. Indeed, one can write a kind signature instead:
3518 data Term :: * -> * where ...
3520 or even a mixture of the two:
3522 data Foo a :: (* -> *) -> * where ...
3524 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3527 data Foo a (b :: * -> *) where ...
3532 There are no restrictions on the type of the data constructor, except that the result
3533 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3534 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3538 You cannot use record syntax on a GADT-style data type declaration. (
3539 It's not clear what these it would mean. For example,
3540 the record selectors might ill-typed.)
3541 However, you can use strictness annotations, in the obvious places
3542 in the constructor type:
3545 Lit :: !Int -> Term Int
3546 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3547 Pair :: Term a -> Term b -> Term (a,b)
3552 You can use a <literal>deriving</literal> clause on a GADT-style data type
3553 declaration, but only if the data type could also have been declared in
3554 Haskell-98 syntax. For example, these two declarations are equivalent
3556 data Maybe1 a where {
3557 Nothing1 :: Maybe a ;
3558 Just1 :: a -> Maybe a
3559 } deriving( Eq, Ord )
3561 data Maybe2 a = Nothing2 | Just2 a
3564 This simply allows you to declare a vanilla Haskell-98 data type using the
3565 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3569 Pattern matching causes type refinement. For example, in the right hand side of the equation
3574 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3575 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3576 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3578 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3579 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3580 occur. However, the refinement is quite general. For example, if we had:
3582 eval :: Term a -> a -> a
3583 eval (Lit i) j = i+j
3585 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3586 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3587 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3593 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3595 data T a = forall b. MkT b (b->a)
3596 data T' a where { MKT :: b -> (b->a) -> T' a }
3601 <!-- ====================== End of Generalised algebraic data types ======================= -->
3603 <!-- ====================== TEMPLATE HASKELL ======================= -->
3605 <sect1 id="template-haskell">
3606 <title>Template Haskell</title>
3608 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3609 Template Haskell at <ulink url="http://www.haskell.org/th/">
3610 http://www.haskell.org/th/</ulink>, while
3612 the main technical innovations is discussed in "<ulink
3613 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3614 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3615 The details of the Template Haskell design are still in flux. Make sure you
3616 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3617 (search for the type ExpQ).
3618 [Temporary: many changes to the original design are described in
3619 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3620 Not all of these changes are in GHC 6.2.]
3623 <para> The first example from that paper is set out below as a worked example to help get you started.
3627 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3628 Tim Sheard is going to expand it.)
3632 <title>Syntax</title>
3634 <para> Template Haskell has the following new syntactic
3635 constructions. You need to use the flag
3636 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3637 </indexterm>to switch these syntactic extensions on
3638 (<option>-fth</option> is currently implied by
3639 <option>-fglasgow-exts</option>, but you are encouraged to
3640 specify it explicitly).</para>
3644 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3645 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3646 There must be no space between the "$" and the identifier or parenthesis. This use
3647 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3648 of "." as an infix operator. If you want the infix operator, put spaces around it.
3650 <para> A splice can occur in place of
3652 <listitem><para> an expression; the spliced expression must
3653 have type <literal>Q Exp</literal></para></listitem>
3654 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3655 <listitem><para> [Planned, but not implemented yet.] a
3656 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
3658 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3659 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3665 A expression quotation is written in Oxford brackets, thus:
3667 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3668 the quotation has type <literal>Expr</literal>.</para></listitem>
3669 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3670 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3671 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
3672 the quotation has type <literal>Type</literal>.</para></listitem>
3673 </itemizedlist></para></listitem>
3676 Reification is written thus:
3678 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3679 has type <literal>Dec</literal>. </para></listitem>
3680 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3681 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3682 <listitem><para> Still to come: fixities </para></listitem>
3684 </itemizedlist></para>
3691 <sect2> <title> Using Template Haskell </title>
3695 The data types and monadic constructor functions for Template Haskell are in the library
3696 <literal>Language.Haskell.THSyntax</literal>.
3700 You can only run a function at compile time if it is imported from another module. That is,
3701 you can't define a function in a module, and call it from within a splice in the same module.
3702 (It would make sense to do so, but it's hard to implement.)
3706 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3709 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3710 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3711 compiles and runs a program, and then looks at the result. So it's important that
3712 the program it compiles produces results whose representations are identical to
3713 those of the compiler itself.
3717 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3718 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3723 <sect2> <title> A Template Haskell Worked Example </title>
3724 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3725 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3732 -- Import our template "pr"
3733 import Printf ( pr )
3735 -- The splice operator $ takes the Haskell source code
3736 -- generated at compile time by "pr" and splices it into
3737 -- the argument of "putStrLn".
3738 main = putStrLn ( $(pr "Hello") )
3744 -- Skeletal printf from the paper.
3745 -- It needs to be in a separate module to the one where
3746 -- you intend to use it.
3748 -- Import some Template Haskell syntax
3749 import Language.Haskell.TH
3751 -- Describe a format string
3752 data Format = D | S | L String
3754 -- Parse a format string. This is left largely to you
3755 -- as we are here interested in building our first ever
3756 -- Template Haskell program and not in building printf.
3757 parse :: String -> [Format]
3760 -- Generate Haskell source code from a parsed representation
3761 -- of the format string. This code will be spliced into
3762 -- the module which calls "pr", at compile time.
3763 gen :: [Format] -> ExpQ
3764 gen [D] = [| \n -> show n |]
3765 gen [S] = [| \s -> s |]
3766 gen [L s] = stringE s
3768 -- Here we generate the Haskell code for the splice
3769 -- from an input format string.
3770 pr :: String -> ExpQ
3771 pr s = gen (parse s)
3774 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3777 $ ghc --make -fth main.hs -o main.exe
3780 <para>Run "main.exe" and here is your output:</para>
3791 <!-- ===================== Arrow notation =================== -->
3793 <sect1 id="arrow-notation">
3794 <title>Arrow notation
3797 <para>Arrows are a generalization of monads introduced by John Hughes.
3798 For more details, see
3803 “Generalising Monads to Arrows”,
3804 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3805 pp67–111, May 2000.
3811 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3812 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3818 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3819 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3825 and the arrows web page at
3826 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3827 With the <option>-farrows</option> flag, GHC supports the arrow
3828 notation described in the second of these papers.
3829 What follows is a brief introduction to the notation;
3830 it won't make much sense unless you've read Hughes's paper.
3831 This notation is translated to ordinary Haskell,
3832 using combinators from the
3833 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3837 <para>The extension adds a new kind of expression for defining arrows:
3839 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3840 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3842 where <literal>proc</literal> is a new keyword.
3843 The variables of the pattern are bound in the body of the
3844 <literal>proc</literal>-expression,
3845 which is a new sort of thing called a <firstterm>command</firstterm>.
3846 The syntax of commands is as follows:
3848 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3849 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3850 | <replaceable>cmd</replaceable><superscript>0</superscript>
3852 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3853 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3854 infix operators as for expressions, and
3856 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3857 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3858 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3859 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3860 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3861 | <replaceable>fcmd</replaceable>
3863 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3864 | ( <replaceable>cmd</replaceable> )
3865 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3867 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3868 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3869 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3870 | <replaceable>cmd</replaceable>
3872 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3873 except that the bodies are commands instead of expressions.
3877 Commands produce values, but (like monadic computations)
3878 may yield more than one value,
3879 or none, and may do other things as well.
3880 For the most part, familiarity with monadic notation is a good guide to
3882 However the values of expressions, even monadic ones,
3883 are determined by the values of the variables they contain;
3884 this is not necessarily the case for commands.
3888 A simple example of the new notation is the expression
3890 proc x -> f -< x+1
3892 We call this a <firstterm>procedure</firstterm> or
3893 <firstterm>arrow abstraction</firstterm>.
3894 As with a lambda expression, the variable <literal>x</literal>
3895 is a new variable bound within the <literal>proc</literal>-expression.
3896 It refers to the input to the arrow.
3897 In the above example, <literal>-<</literal> is not an identifier but an
3898 new reserved symbol used for building commands from an expression of arrow
3899 type and an expression to be fed as input to that arrow.
3900 (The weird look will make more sense later.)
3901 It may be read as analogue of application for arrows.
3902 The above example is equivalent to the Haskell expression
3904 arr (\ x -> x+1) >>> f
3906 That would make no sense if the expression to the left of
3907 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3908 More generally, the expression to the left of <literal>-<</literal>
3909 may not involve any <firstterm>local variable</firstterm>,
3910 i.e. a variable bound in the current arrow abstraction.
3911 For such a situation there is a variant <literal>-<<</literal>, as in
3913 proc x -> f x -<< x+1
3915 which is equivalent to
3917 arr (\ x -> (f x, x+1)) >>> app
3919 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3921 Such an arrow is equivalent to a monad, so if you're using this form
3922 you may find a monadic formulation more convenient.
3926 <title>do-notation for commands</title>
3929 Another form of command is a form of <literal>do</literal>-notation.
3930 For example, you can write
3939 You can read this much like ordinary <literal>do</literal>-notation,
3940 but with commands in place of monadic expressions.
3941 The first line sends the value of <literal>x+1</literal> as an input to
3942 the arrow <literal>f</literal>, and matches its output against
3943 <literal>y</literal>.
3944 In the next line, the output is discarded.
3945 The arrow <function>returnA</function> is defined in the
3946 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3947 module as <literal>arr id</literal>.
3948 The above example is treated as an abbreviation for
3950 arr (\ x -> (x, x)) >>>
3951 first (arr (\ x -> x+1) >>> f) >>>
3952 arr (\ (y, x) -> (y, (x, y))) >>>
3953 first (arr (\ y -> 2*y) >>> g) >>>
3955 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3956 first (arr (\ (x, z) -> x*z) >>> h) >>>
3957 arr (\ (t, z) -> t+z) >>>
3960 Note that variables not used later in the composition are projected out.
3961 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3963 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3964 module, this reduces to
3966 arr (\ x -> (x+1, x)) >>>
3968 arr (\ (y, x) -> (2*y, (x, y))) >>>
3970 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3972 arr (\ (t, z) -> t+z)
3974 which is what you might have written by hand.
3975 With arrow notation, GHC keeps track of all those tuples of variables for you.
3979 Note that although the above translation suggests that
3980 <literal>let</literal>-bound variables like <literal>z</literal> must be
3981 monomorphic, the actual translation produces Core,
3982 so polymorphic variables are allowed.
3986 It's also possible to have mutually recursive bindings,
3987 using the new <literal>rec</literal> keyword, as in the following example:
3989 counter :: ArrowCircuit a => a Bool Int
3990 counter = proc reset -> do
3991 rec output <- returnA -< if reset then 0 else next
3992 next <- delay 0 -< output+1
3993 returnA -< output
3995 The translation of such forms uses the <function>loop</function> combinator,
3996 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4002 <title>Conditional commands</title>
4005 In the previous example, we used a conditional expression to construct the
4007 Sometimes we want to conditionally execute different commands, as in
4014 which is translated to
4016 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4017 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4019 Since the translation uses <function>|||</function>,
4020 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4024 There are also <literal>case</literal> commands, like
4030 y <- h -< (x1, x2)
4034 The syntax is the same as for <literal>case</literal> expressions,
4035 except that the bodies of the alternatives are commands rather than expressions.
4036 The translation is similar to that of <literal>if</literal> commands.
4042 <title>Defining your own control structures</title>
4045 As we're seen, arrow notation provides constructs,
4046 modelled on those for expressions,
4047 for sequencing, value recursion and conditionals.
4048 But suitable combinators,
4049 which you can define in ordinary Haskell,
4050 may also be used to build new commands out of existing ones.
4051 The basic idea is that a command defines an arrow from environments to values.
4052 These environments assign values to the free local variables of the command.
4053 Thus combinators that produce arrows from arrows
4054 may also be used to build commands from commands.
4055 For example, the <literal>ArrowChoice</literal> class includes a combinator
4057 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4059 so we can use it to build commands:
4061 expr' = proc x -> do
4064 symbol Plus -< ()
4065 y <- term -< ()
4068 symbol Minus -< ()
4069 y <- term -< ()
4072 (The <literal>do</literal> on the first line is needed to prevent the first
4073 <literal><+> ...</literal> from being interpreted as part of the
4074 expression on the previous line.)
4075 This is equivalent to
4077 expr' = (proc x -> returnA -< x)
4078 <+> (proc x -> do
4079 symbol Plus -< ()
4080 y <- term -< ()
4082 <+> (proc x -> do
4083 symbol Minus -< ()
4084 y <- term -< ()
4087 It is essential that this operator be polymorphic in <literal>e</literal>
4088 (representing the environment input to the command
4089 and thence to its subcommands)
4090 and satisfy the corresponding naturality property
4092 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4094 at least for strict <literal>k</literal>.
4095 (This should be automatic if you're not using <function>seq</function>.)
4096 This ensures that environments seen by the subcommands are environments
4097 of the whole command,
4098 and also allows the translation to safely trim these environments.
4099 The operator must also not use any variable defined within the current
4104 We could define our own operator
4106 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4107 untilA body cond = proc x ->
4108 if cond x then returnA -< ()
4111 untilA body cond -< x
4113 and use it in the same way.
4114 Of course this infix syntax only makes sense for binary operators;
4115 there is also a more general syntax involving special brackets:
4119 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4126 <title>Primitive constructs</title>
4129 Some operators will need to pass additional inputs to their subcommands.
4130 For example, in an arrow type supporting exceptions,
4131 the operator that attaches an exception handler will wish to pass the
4132 exception that occurred to the handler.
4133 Such an operator might have a type
4135 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4137 where <literal>Ex</literal> is the type of exceptions handled.
4138 You could then use this with arrow notation by writing a command
4140 body `handleA` \ ex -> handler
4142 so that if an exception is raised in the command <literal>body</literal>,
4143 the variable <literal>ex</literal> is bound to the value of the exception
4144 and the command <literal>handler</literal>,
4145 which typically refers to <literal>ex</literal>, is entered.
4146 Though the syntax here looks like a functional lambda,
4147 we are talking about commands, and something different is going on.
4148 The input to the arrow represented by a command consists of values for
4149 the free local variables in the command, plus a stack of anonymous values.
4150 In all the prior examples, this stack was empty.
4151 In the second argument to <function>handleA</function>,
4152 this stack consists of one value, the value of the exception.
4153 The command form of lambda merely gives this value a name.
4158 the values on the stack are paired to the right of the environment.
4159 So operators like <function>handleA</function> that pass
4160 extra inputs to their subcommands can be designed for use with the notation
4161 by pairing the values with the environment in this way.
4162 More precisely, the type of each argument of the operator (and its result)
4163 should have the form
4165 a (...(e,t1), ... tn) t
4167 where <replaceable>e</replaceable> is a polymorphic variable
4168 (representing the environment)
4169 and <replaceable>ti</replaceable> are the types of the values on the stack,
4170 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4171 The polymorphic variable <replaceable>e</replaceable> must not occur in
4172 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4173 <replaceable>t</replaceable>.
4174 However the arrows involved need not be the same.
4175 Here are some more examples of suitable operators:
4177 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4178 runReader :: ... => a e c -> a' (e,State) c
4179 runState :: ... => a e c -> a' (e,State) (c,State)
4181 We can supply the extra input required by commands built with the last two
4182 by applying them to ordinary expressions, as in
4186 (|runReader (do { ... })|) s
4188 which adds <literal>s</literal> to the stack of inputs to the command
4189 built using <function>runReader</function>.
4193 The command versions of lambda abstraction and application are analogous to
4194 the expression versions.
4195 In particular, the beta and eta rules describe equivalences of commands.
4196 These three features (operators, lambda abstraction and application)
4197 are the core of the notation; everything else can be built using them,
4198 though the results would be somewhat clumsy.
4199 For example, we could simulate <literal>do</literal>-notation by defining
4201 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4202 u `bind` f = returnA &&& u >>> f
4204 bind_ :: Arrow a => a e b -> a e c -> a e c
4205 u `bind_` f = u `bind` (arr fst >>> f)
4207 We could simulate <literal>if</literal> by defining
4209 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4210 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4217 <title>Differences with the paper</title>
4222 <para>Instead of a single form of arrow application (arrow tail) with two
4223 translations, the implementation provides two forms
4224 <quote><literal>-<</literal></quote> (first-order)
4225 and <quote><literal>-<<</literal></quote> (higher-order).
4230 <para>User-defined operators are flagged with banana brackets instead of
4231 a new <literal>form</literal> keyword.
4240 <title>Portability</title>
4243 Although only GHC implements arrow notation directly,
4244 there is also a preprocessor
4246 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4247 that translates arrow notation into Haskell 98
4248 for use with other Haskell systems.
4249 You would still want to check arrow programs with GHC;
4250 tracing type errors in the preprocessor output is not easy.
4251 Modules intended for both GHC and the preprocessor must observe some
4252 additional restrictions:
4257 The module must import
4258 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4264 The preprocessor cannot cope with other Haskell extensions.
4265 These would have to go in separate modules.
4271 Because the preprocessor targets Haskell (rather than Core),
4272 <literal>let</literal>-bound variables are monomorphic.
4283 <!-- ==================== ASSERTIONS ================= -->
4285 <sect1 id="sec-assertions">
4287 <indexterm><primary>Assertions</primary></indexterm>
4291 If you want to make use of assertions in your standard Haskell code, you
4292 could define a function like the following:
4298 assert :: Bool -> a -> a
4299 assert False x = error "assertion failed!"
4306 which works, but gives you back a less than useful error message --
4307 an assertion failed, but which and where?
4311 One way out is to define an extended <function>assert</function> function which also
4312 takes a descriptive string to include in the error message and
4313 perhaps combine this with the use of a pre-processor which inserts
4314 the source location where <function>assert</function> was used.
4318 Ghc offers a helping hand here, doing all of this for you. For every
4319 use of <function>assert</function> in the user's source:
4325 kelvinToC :: Double -> Double
4326 kelvinToC k = assert (k >= 0.0) (k+273.15)
4332 Ghc will rewrite this to also include the source location where the
4339 assert pred val ==> assertError "Main.hs|15" pred val
4345 The rewrite is only performed by the compiler when it spots
4346 applications of <function>Control.Exception.assert</function>, so you
4347 can still define and use your own versions of
4348 <function>assert</function>, should you so wish. If not, import
4349 <literal>Control.Exception</literal> to make use
4350 <function>assert</function> in your code.
4354 To have the compiler ignore uses of assert, use the compiler option
4355 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4356 option</primary></indexterm> That is, expressions of the form
4357 <literal>assert pred e</literal> will be rewritten to
4358 <literal>e</literal>.
4362 Assertion failures can be caught, see the documentation for the
4363 <literal>Control.Exception</literal> library for the details.
4369 <!-- =============================== PRAGMAS =========================== -->
4371 <sect1 id="pragmas">
4372 <title>Pragmas</title>
4374 <indexterm><primary>pragma</primary></indexterm>
4376 <para>GHC supports several pragmas, or instructions to the
4377 compiler placed in the source code. Pragmas don't normally affect
4378 the meaning of the program, but they might affect the efficiency
4379 of the generated code.</para>
4381 <para>Pragmas all take the form
4383 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4385 where <replaceable>word</replaceable> indicates the type of
4386 pragma, and is followed optionally by information specific to that
4387 type of pragma. Case is ignored in
4388 <replaceable>word</replaceable>. The various values for
4389 <replaceable>word</replaceable> that GHC understands are described
4390 in the following sections; any pragma encountered with an
4391 unrecognised <replaceable>word</replaceable> is (silently)
4394 <sect2 id="deprecated-pragma">
4395 <title>DEPRECATED pragma</title>
4396 <indexterm><primary>DEPRECATED</primary>
4399 <para>The DEPRECATED pragma lets you specify that a particular
4400 function, class, or type, is deprecated. There are two
4405 <para>You can deprecate an entire module thus:</para>
4407 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4410 <para>When you compile any module that import
4411 <literal>Wibble</literal>, GHC will print the specified
4416 <para>You can deprecate a function, class, type, or data constructor, with the
4417 following top-level declaration:</para>
4419 {-# DEPRECATED f, C, T "Don't use these" #-}
4421 <para>When you compile any module that imports and uses any
4422 of the specified entities, GHC will print the specified
4424 <para> You can only depecate entities declared at top level in the module
4425 being compiled, and you can only use unqualified names in the list of
4426 entities being deprecated. A capitalised name, such as <literal>T</literal>
4427 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4428 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4429 both are in scope. If both are in scope, there is currently no way to deprecate
4430 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4433 Any use of the deprecated item, or of anything from a deprecated
4434 module, will be flagged with an appropriate message. However,
4435 deprecations are not reported for
4436 (a) uses of a deprecated function within its defining module, and
4437 (b) uses of a deprecated function in an export list.
4438 The latter reduces spurious complaints within a library
4439 in which one module gathers together and re-exports
4440 the exports of several others.
4442 <para>You can suppress the warnings with the flag
4443 <option>-fno-warn-deprecations</option>.</para>
4446 <sect2 id="include-pragma">
4447 <title>INCLUDE pragma</title>
4449 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4450 of C header files that should be <literal>#include</literal>'d into
4451 the C source code generated by the compiler for the current module (if
4452 compiling via C). For example:</para>
4455 {-# INCLUDE "foo.h" #-}
4456 {-# INCLUDE <stdio.h> #-}</programlisting>
4458 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4459 your source file with any <literal>OPTIONS_GHC</literal>
4462 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4463 to the <option>-#include</option> option (<xref
4464 linkend="options-C-compiler" />), because the
4465 <literal>INCLUDE</literal> pragma is understood by other
4466 compilers. Yet another alternative is to add the include file to each
4467 <literal>foreign import</literal> declaration in your code, but we
4468 don't recommend using this approach with GHC.</para>
4471 <sect2 id="inline-noinline-pragma">
4472 <title>INLINE and NOINLINE pragmas</title>
4474 <para>These pragmas control the inlining of function
4477 <sect3 id="inline-pragma">
4478 <title>INLINE pragma</title>
4479 <indexterm><primary>INLINE</primary></indexterm>
4481 <para>GHC (with <option>-O</option>, as always) tries to
4482 inline (or “unfold”) functions/values that are
4483 “small enough,” thus avoiding the call overhead
4484 and possibly exposing other more-wonderful optimisations.
4485 Normally, if GHC decides a function is “too
4486 expensive” to inline, it will not do so, nor will it
4487 export that unfolding for other modules to use.</para>
4489 <para>The sledgehammer you can bring to bear is the
4490 <literal>INLINE</literal><indexterm><primary>INLINE
4491 pragma</primary></indexterm> pragma, used thusly:</para>
4494 key_function :: Int -> String -> (Bool, Double)
4496 #ifdef __GLASGOW_HASKELL__
4497 {-# INLINE key_function #-}
4501 <para>(You don't need to do the C pre-processor carry-on
4502 unless you're going to stick the code through HBC—it
4503 doesn't like <literal>INLINE</literal> pragmas.)</para>
4505 <para>The major effect of an <literal>INLINE</literal> pragma
4506 is to declare a function's “cost” to be very low.
4507 The normal unfolding machinery will then be very keen to
4510 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4511 function can be put anywhere its type signature could be
4514 <para><literal>INLINE</literal> pragmas are a particularly
4516 <literal>then</literal>/<literal>return</literal> (or
4517 <literal>bind</literal>/<literal>unit</literal>) functions in
4518 a monad. For example, in GHC's own
4519 <literal>UniqueSupply</literal> monad code, we have:</para>
4522 #ifdef __GLASGOW_HASKELL__
4523 {-# INLINE thenUs #-}
4524 {-# INLINE returnUs #-}
4528 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4529 linkend="noinline-pragma"/>).</para>
4532 <sect3 id="noinline-pragma">
4533 <title>NOINLINE pragma</title>
4535 <indexterm><primary>NOINLINE</primary></indexterm>
4536 <indexterm><primary>NOTINLINE</primary></indexterm>
4538 <para>The <literal>NOINLINE</literal> pragma does exactly what
4539 you'd expect: it stops the named function from being inlined
4540 by the compiler. You shouldn't ever need to do this, unless
4541 you're very cautious about code size.</para>
4543 <para><literal>NOTINLINE</literal> is a synonym for
4544 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4545 specified by Haskell 98 as the standard way to disable
4546 inlining, so it should be used if you want your code to be
4550 <sect3 id="phase-control">
4551 <title>Phase control</title>
4553 <para> Sometimes you want to control exactly when in GHC's
4554 pipeline the INLINE pragma is switched on. Inlining happens
4555 only during runs of the <emphasis>simplifier</emphasis>. Each
4556 run of the simplifier has a different <emphasis>phase
4557 number</emphasis>; the phase number decreases towards zero.
4558 If you use <option>-dverbose-core2core</option> you'll see the
4559 sequence of phase numbers for successive runs of the
4560 simplifier. In an INLINE pragma you can optionally specify a
4561 phase number, thus:</para>
4565 <para>You can say "inline <literal>f</literal> in Phase 2
4566 and all subsequent phases":
4568 {-# INLINE [2] f #-}
4574 <para>You can say "inline <literal>g</literal> in all
4575 phases up to, but not including, Phase 3":
4577 {-# INLINE [~3] g #-}
4583 <para>If you omit the phase indicator, you mean "inline in
4588 <para>You can use a phase number on a NOINLINE pragma too:</para>
4592 <para>You can say "do not inline <literal>f</literal>
4593 until Phase 2; in Phase 2 and subsequently behave as if
4594 there was no pragma at all":
4596 {-# NOINLINE [2] f #-}
4602 <para>You can say "do not inline <literal>g</literal> in
4603 Phase 3 or any subsequent phase; before that, behave as if
4604 there was no pragma":
4606 {-# NOINLINE [~3] g #-}
4612 <para>If you omit the phase indicator, you mean "never
4613 inline this function".</para>
4617 <para>The same phase-numbering control is available for RULES
4618 (<xref linkend="rewrite-rules"/>).</para>
4622 <sect2 id="line-pragma">
4623 <title>LINE pragma</title>
4625 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4626 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4627 <para>This pragma is similar to C's <literal>#line</literal>
4628 pragma, and is mainly for use in automatically generated Haskell
4629 code. It lets you specify the line number and filename of the
4630 original code; for example</para>
4633 {-# LINE 42 "Foo.vhs" #-}
4636 <para>if you'd generated the current file from something called
4637 <filename>Foo.vhs</filename> and this line corresponds to line
4638 42 in the original. GHC will adjust its error messages to refer
4639 to the line/file named in the <literal>LINE</literal>
4643 <sect2 id="options-pragma">
4644 <title>OPTIONS_GHC pragma</title>
4645 <indexterm><primary>OPTIONS_GHC</primary>
4647 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4650 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4651 additional options that are given to the compiler when compiling
4652 this source file. See <xref linkend="source-file-options"/> for
4655 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4656 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4660 <title>RULES pragma</title>
4662 <para>The RULES pragma lets you specify rewrite rules. It is
4663 described in <xref linkend="rewrite-rules"/>.</para>
4666 <sect2 id="specialize-pragma">
4667 <title>SPECIALIZE pragma</title>
4669 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4670 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4671 <indexterm><primary>overloading, death to</primary></indexterm>
4673 <para>(UK spelling also accepted.) For key overloaded
4674 functions, you can create extra versions (NB: more code space)
4675 specialised to particular types. Thus, if you have an
4676 overloaded function:</para>
4679 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4682 <para>If it is heavily used on lists with
4683 <literal>Widget</literal> keys, you could specialise it as
4687 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4690 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4691 be put anywhere its type signature could be put.</para>
4693 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4694 (a) a specialised version of the function and (b) a rewrite rule
4695 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4696 un-specialised function into a call to the specialised one.</para>
4698 <para>The type in a SPECIALIZE pragma can be any type that is less
4699 polymorphic than the type of the original function. In concrete terms,
4700 if the original function is <literal>f</literal> then the pragma
4702 {-# SPECIALIZE f :: <type> #-}
4704 is valid if and only if the defintion
4706 f_spec :: <type>
4709 is valid. Here are some examples (where we only give the type signature
4710 for the original function, not its code):
4712 f :: Eq a => a -> b -> b
4713 {-# SPECIALISE g :: Int -> b -> b #-}
4715 g :: (Eq a, Ix b) => a -> b -> b
4716 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
4718 h :: Eq a => a -> a -> a
4719 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
4721 The last of these examples will generate a
4722 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
4723 well. If you use this kind of specialisation, let us know how well it works.
4726 <para>Note: In earlier versions of GHC, it was possible to provide your own
4727 specialised function for a given type:
4730 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4733 This feature has been removed, as it is now subsumed by the
4734 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4738 <sect2 id="specialize-instance-pragma">
4739 <title>SPECIALIZE instance pragma
4743 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4744 <indexterm><primary>overloading, death to</primary></indexterm>
4745 Same idea, except for instance declarations. For example:
4748 instance (Eq a) => Eq (Foo a) where {
4749 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4753 The pragma must occur inside the <literal>where</literal> part
4754 of the instance declaration.
4757 Compatible with HBC, by the way, except perhaps in the placement
4763 <sect2 id="unpack-pragma">
4764 <title>UNPACK pragma</title>
4766 <indexterm><primary>UNPACK</primary></indexterm>
4768 <para>The <literal>UNPACK</literal> indicates to the compiler
4769 that it should unpack the contents of a constructor field into
4770 the constructor itself, removing a level of indirection. For
4774 data T = T {-# UNPACK #-} !Float
4775 {-# UNPACK #-} !Float
4778 <para>will create a constructor <literal>T</literal> containing
4779 two unboxed floats. This may not always be an optimisation: if
4780 the <function>T</function> constructor is scrutinised and the
4781 floats passed to a non-strict function for example, they will
4782 have to be reboxed (this is done automatically by the
4785 <para>Unpacking constructor fields should only be used in
4786 conjunction with <option>-O</option>, in order to expose
4787 unfoldings to the compiler so the reboxing can be removed as
4788 often as possible. For example:</para>
4792 f (T f1 f2) = f1 + f2
4795 <para>The compiler will avoid reboxing <function>f1</function>
4796 and <function>f2</function> by inlining <function>+</function>
4797 on floats, but only when <option>-O</option> is on.</para>
4799 <para>Any single-constructor data is eligible for unpacking; for
4803 data T = T {-# UNPACK #-} !(Int,Int)
4806 <para>will store the two <literal>Int</literal>s directly in the
4807 <function>T</function> constructor, by flattening the pair.
4808 Multi-level unpacking is also supported:</para>
4811 data T = T {-# UNPACK #-} !S
4812 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4815 <para>will store two unboxed <literal>Int#</literal>s
4816 directly in the <function>T</function> constructor. The
4817 unpacker can see through newtypes, too.</para>
4819 <para>If a field cannot be unpacked, you will not get a warning,
4820 so it might be an idea to check the generated code with
4821 <option>-ddump-simpl</option>.</para>
4823 <para>See also the <option>-funbox-strict-fields</option> flag,
4824 which essentially has the effect of adding
4825 <literal>{-# UNPACK #-}</literal> to every strict
4826 constructor field.</para>
4831 <!-- ======================= REWRITE RULES ======================== -->
4833 <sect1 id="rewrite-rules">
4834 <title>Rewrite rules
4836 <indexterm><primary>RULES pragma</primary></indexterm>
4837 <indexterm><primary>pragma, RULES</primary></indexterm>
4838 <indexterm><primary>rewrite rules</primary></indexterm></title>
4841 The programmer can specify rewrite rules as part of the source program
4842 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4843 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4844 and (b) the <option>-frules-off</option> flag
4845 (<xref linkend="options-f"/>) is not specified.
4853 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4860 <title>Syntax</title>
4863 From a syntactic point of view:
4869 There may be zero or more rules in a <literal>RULES</literal> pragma.
4876 Each rule has a name, enclosed in double quotes. The name itself has
4877 no significance at all. It is only used when reporting how many times the rule fired.
4883 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4884 immediately after the name of the rule. Thus:
4887 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4890 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4891 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4900 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4901 is set, so you must lay out your rules starting in the same column as the
4902 enclosing definitions.
4909 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4910 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4911 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4912 by spaces, just like in a type <literal>forall</literal>.
4918 A pattern variable may optionally have a type signature.
4919 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4920 For example, here is the <literal>foldr/build</literal> rule:
4923 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4924 foldr k z (build g) = g k z
4927 Since <function>g</function> has a polymorphic type, it must have a type signature.
4934 The left hand side of a rule must consist of a top-level variable applied
4935 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4938 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4939 "wrong2" forall f. f True = True
4942 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4949 A rule does not need to be in the same module as (any of) the
4950 variables it mentions, though of course they need to be in scope.
4956 Rules are automatically exported from a module, just as instance declarations are.
4967 <title>Semantics</title>
4970 From a semantic point of view:
4976 Rules are only applied if you use the <option>-O</option> flag.
4982 Rules are regarded as left-to-right rewrite rules.
4983 When GHC finds an expression that is a substitution instance of the LHS
4984 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4985 By "a substitution instance" we mean that the LHS can be made equal to the
4986 expression by substituting for the pattern variables.
4993 The LHS and RHS of a rule are typechecked, and must have the
5001 GHC makes absolutely no attempt to verify that the LHS and RHS
5002 of a rule have the same meaning. That is undecidable in general, and
5003 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5010 GHC makes no attempt to make sure that the rules are confluent or
5011 terminating. For example:
5014 "loop" forall x,y. f x y = f y x
5017 This rule will cause the compiler to go into an infinite loop.
5024 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5030 GHC currently uses a very simple, syntactic, matching algorithm
5031 for matching a rule LHS with an expression. It seeks a substitution
5032 which makes the LHS and expression syntactically equal modulo alpha
5033 conversion. The pattern (rule), but not the expression, is eta-expanded if
5034 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5035 But not beta conversion (that's called higher-order matching).
5039 Matching is carried out on GHC's intermediate language, which includes
5040 type abstractions and applications. So a rule only matches if the
5041 types match too. See <xref linkend="rule-spec"/> below.
5047 GHC keeps trying to apply the rules as it optimises the program.
5048 For example, consider:
5057 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5058 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5059 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5060 not be substituted, and the rule would not fire.
5067 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5068 that appears on the LHS of a rule</emphasis>, because once you have substituted
5069 for something you can't match against it (given the simple minded
5070 matching). So if you write the rule
5073 "map/map" forall f,g. map f . map g = map (f.g)
5076 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5077 It will only match something written with explicit use of ".".
5078 Well, not quite. It <emphasis>will</emphasis> match the expression
5084 where <function>wibble</function> is defined:
5087 wibble f g = map f . map g
5090 because <function>wibble</function> will be inlined (it's small).
5092 Later on in compilation, GHC starts inlining even things on the
5093 LHS of rules, but still leaves the rules enabled. This inlining
5094 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5101 All rules are implicitly exported from the module, and are therefore
5102 in force in any module that imports the module that defined the rule, directly
5103 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5104 in force when compiling A.) The situation is very similar to that for instance
5116 <title>List fusion</title>
5119 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5120 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5121 intermediate list should be eliminated entirely.
5125 The following are good producers:
5137 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5143 Explicit lists (e.g. <literal>[True, False]</literal>)
5149 The cons constructor (e.g <literal>3:4:[]</literal>)
5155 <function>++</function>
5161 <function>map</function>
5167 <function>filter</function>
5173 <function>iterate</function>, <function>repeat</function>
5179 <function>zip</function>, <function>zipWith</function>
5188 The following are good consumers:
5200 <function>array</function> (on its second argument)
5206 <function>length</function>
5212 <function>++</function> (on its first argument)
5218 <function>foldr</function>
5224 <function>map</function>
5230 <function>filter</function>
5236 <function>concat</function>
5242 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5248 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5249 will fuse with one but not the other)
5255 <function>partition</function>
5261 <function>head</function>
5267 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5273 <function>sequence_</function>
5279 <function>msum</function>
5285 <function>sortBy</function>
5294 So, for example, the following should generate no intermediate lists:
5297 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5303 This list could readily be extended; if there are Prelude functions that you use
5304 a lot which are not included, please tell us.
5308 If you want to write your own good consumers or producers, look at the
5309 Prelude definitions of the above functions to see how to do so.
5314 <sect2 id="rule-spec">
5315 <title>Specialisation
5319 Rewrite rules can be used to get the same effect as a feature
5320 present in earlier versions of GHC.
5321 For example, suppose that:
5324 genericLookup :: Ord a => Table a b -> a -> b
5325 intLookup :: Table Int b -> Int -> b
5328 where <function>intLookup</function> is an implementation of
5329 <function>genericLookup</function> that works very fast for
5330 keys of type <literal>Int</literal>. You might wish
5331 to tell GHC to use <function>intLookup</function> instead of
5332 <function>genericLookup</function> whenever the latter was called with
5333 type <literal>Table Int b -> Int -> b</literal>.
5334 It used to be possible to write
5337 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5340 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5343 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5346 This slightly odd-looking rule instructs GHC to replace
5347 <function>genericLookup</function> by <function>intLookup</function>
5348 <emphasis>whenever the types match</emphasis>.
5349 What is more, this rule does not need to be in the same
5350 file as <function>genericLookup</function>, unlike the
5351 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5352 have an original definition available to specialise).
5355 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5356 <function>intLookup</function> really behaves as a specialised version
5357 of <function>genericLookup</function>!!!</para>
5359 <para>An example in which using <literal>RULES</literal> for
5360 specialisation will Win Big:
5363 toDouble :: Real a => a -> Double
5364 toDouble = fromRational . toRational
5366 {-# RULES "toDouble/Int" toDouble = i2d #-}
5367 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5370 The <function>i2d</function> function is virtually one machine
5371 instruction; the default conversion—via an intermediate
5372 <literal>Rational</literal>—is obscenely expensive by
5379 <title>Controlling what's going on</title>
5387 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5393 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5394 If you add <option>-dppr-debug</option> you get a more detailed listing.
5400 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5403 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5404 {-# INLINE build #-}
5408 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5409 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5410 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5411 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5418 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5419 see how to write rules that will do fusion and yet give an efficient
5420 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5430 <sect2 id="core-pragma">
5431 <title>CORE pragma</title>
5433 <indexterm><primary>CORE pragma</primary></indexterm>
5434 <indexterm><primary>pragma, CORE</primary></indexterm>
5435 <indexterm><primary>core, annotation</primary></indexterm>
5438 The external core format supports <quote>Note</quote> annotations;
5439 the <literal>CORE</literal> pragma gives a way to specify what these
5440 should be in your Haskell source code. Syntactically, core
5441 annotations are attached to expressions and take a Haskell string
5442 literal as an argument. The following function definition shows an
5446 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5449 Semantically, this is equivalent to:
5457 However, when external for is generated (via
5458 <option>-fext-core</option>), there will be Notes attached to the
5459 expressions <function>show</function> and <varname>x</varname>.
5460 The core function declaration for <function>f</function> is:
5464 f :: %forall a . GHCziShow.ZCTShow a ->
5465 a -> GHCziBase.ZMZN GHCziBase.Char =
5466 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5468 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5470 (tpl1::GHCziBase.Int ->
5472 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5474 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5475 (tpl3::GHCziBase.ZMZN a ->
5476 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5484 Here, we can see that the function <function>show</function> (which
5485 has been expanded out to a case expression over the Show dictionary)
5486 has a <literal>%note</literal> attached to it, as does the
5487 expression <varname>eta</varname> (which used to be called
5488 <varname>x</varname>).
5495 <sect1 id="generic-classes">
5496 <title>Generic classes</title>
5498 <para>(Note: support for generic classes is currently broken in
5502 The ideas behind this extension are described in detail in "Derivable type classes",
5503 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5504 An example will give the idea:
5512 fromBin :: [Int] -> (a, [Int])
5514 toBin {| Unit |} Unit = []
5515 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5516 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5517 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5519 fromBin {| Unit |} bs = (Unit, bs)
5520 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5521 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5522 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5523 (y,bs'') = fromBin bs'
5526 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5527 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5528 which are defined thus in the library module <literal>Generics</literal>:
5532 data a :+: b = Inl a | Inr b
5533 data a :*: b = a :*: b
5536 Now you can make a data type into an instance of Bin like this:
5538 instance (Bin a, Bin b) => Bin (a,b)
5539 instance Bin a => Bin [a]
5541 That is, just leave off the "where" clause. Of course, you can put in the
5542 where clause and over-ride whichever methods you please.
5546 <title> Using generics </title>
5547 <para>To use generics you need to</para>
5550 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5551 <option>-fgenerics</option> (to generate extra per-data-type code),
5552 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5556 <para>Import the module <literal>Generics</literal> from the
5557 <literal>lang</literal> package. This import brings into
5558 scope the data types <literal>Unit</literal>,
5559 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5560 don't need this import if you don't mention these types
5561 explicitly; for example, if you are simply giving instance
5562 declarations.)</para>
5567 <sect2> <title> Changes wrt the paper </title>
5569 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5570 can be written infix (indeed, you can now use
5571 any operator starting in a colon as an infix type constructor). Also note that
5572 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5573 Finally, note that the syntax of the type patterns in the class declaration
5574 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5575 alone would ambiguous when they appear on right hand sides (an extension we
5576 anticipate wanting).
5580 <sect2> <title>Terminology and restrictions</title>
5582 Terminology. A "generic default method" in a class declaration
5583 is one that is defined using type patterns as above.
5584 A "polymorphic default method" is a default method defined as in Haskell 98.
5585 A "generic class declaration" is a class declaration with at least one
5586 generic default method.
5594 Alas, we do not yet implement the stuff about constructor names and
5601 A generic class can have only one parameter; you can't have a generic
5602 multi-parameter class.
5608 A default method must be defined entirely using type patterns, or entirely
5609 without. So this is illegal:
5612 op :: a -> (a, Bool)
5613 op {| Unit |} Unit = (Unit, True)
5616 However it is perfectly OK for some methods of a generic class to have
5617 generic default methods and others to have polymorphic default methods.
5623 The type variable(s) in the type pattern for a generic method declaration
5624 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:
5628 op {| p :*: q |} (x :*: y) = op (x :: p)
5636 The type patterns in a generic default method must take one of the forms:
5642 where "a" and "b" are type variables. Furthermore, all the type patterns for
5643 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5644 must use the same type variables. So this is illegal:
5648 op {| a :+: b |} (Inl x) = True
5649 op {| p :+: q |} (Inr y) = False
5651 The type patterns must be identical, even in equations for different methods of the class.
5652 So this too is illegal:
5656 op1 {| a :*: b |} (x :*: y) = True
5659 op2 {| p :*: q |} (x :*: y) = False
5661 (The reason for this restriction is that we gather all the equations for a particular type consructor
5662 into a single generic instance declaration.)
5668 A generic method declaration must give a case for each of the three type constructors.
5674 The type for a generic method can be built only from:
5676 <listitem> <para> Function arrows </para> </listitem>
5677 <listitem> <para> Type variables </para> </listitem>
5678 <listitem> <para> Tuples </para> </listitem>
5679 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5681 Here are some example type signatures for generic methods:
5684 op2 :: Bool -> (a,Bool)
5685 op3 :: [Int] -> a -> a
5688 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5692 This restriction is an implementation restriction: we just havn't got around to
5693 implementing the necessary bidirectional maps over arbitrary type constructors.
5694 It would be relatively easy to add specific type constructors, such as Maybe and list,
5695 to the ones that are allowed.</para>
5700 In an instance declaration for a generic class, the idea is that the compiler
5701 will fill in the methods for you, based on the generic templates. However it can only
5706 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5711 No constructor of the instance type has unboxed fields.
5715 (Of course, these things can only arise if you are already using GHC extensions.)
5716 However, you can still give an instance declarations for types which break these rules,
5717 provided you give explicit code to override any generic default methods.
5725 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5726 what the compiler does with generic declarations.
5731 <sect2> <title> Another example </title>
5733 Just to finish with, here's another example I rather like:
5737 nCons {| Unit |} _ = 1
5738 nCons {| a :*: b |} _ = 1
5739 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5742 tag {| Unit |} _ = 1
5743 tag {| a :*: b |} _ = 1
5744 tag {| a :+: b |} (Inl x) = tag x
5745 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5754 ;;; Local Variables: ***
5756 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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