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>Integer and fractional literals mean
833 "<literal>fromInteger 1</literal>" and
834 "<literal>fromRational 3.2</literal>", not the
835 Prelude-qualified versions; both in expressions and in
837 <para>However, the standard Prelude <literal>Eq</literal> class
838 is still used for the equality test necessary for literal patterns.</para>
842 <para>Negation (e.g. "<literal>- (f x)</literal>")
843 means "<literal>negate (f x)</literal>" (not
844 <literal>Prelude.negate</literal>).</para>
848 <para>In an n+k pattern, the standard Prelude
849 <literal>Ord</literal> class is still used for comparison,
850 but the necessary subtraction uses whatever
851 "<literal>(-)</literal>" is in scope (not
852 "<literal>Prelude.(-)</literal>").</para>
856 <para>"Do" notation is translated using whatever
857 functions <literal>(>>=)</literal>,
858 <literal>(>>)</literal>, <literal>fail</literal>, and
859 <literal>return</literal>, are in scope (not the Prelude
860 versions). List comprehensions, and parallel array
861 comprehensions, are unaffected. </para></listitem>
864 <para>Similarly recursive do notation (see
865 <xref linkend="mdo-notation"/>) uses whatever
866 <literal>mfix</literal> function is in scope, and arrow
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.</para>
875 <para>The functions with these names that GHC finds in scope
876 must have types matching those of the originals, namely:
878 fromInteger :: Integer -> N
879 fromRational :: Rational -> N
882 (>>=) :: forall a b. M a -> (a -> M b) -> M b
883 (>>) :: forall a b. M a -> M b -> M b
884 return :: forall a. a -> M a
885 fail :: forall a. String -> M a
887 (Here <literal>N</literal> may be any type,
888 and <literal>M</literal> any type constructor.)</para>
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</title>
931 GHC allows type constructors to be operators, and to be written infix, very much
932 like expressions. More specifically:
935 A type constructor 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 Types can be written infix. For example <literal>Int :*: Bool</literal>.
943 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
944 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
947 Fixities may be declared for type constructors just as for data constructors. However,
948 one cannot distinguish between the two in a fixity declaration; a fixity declaration
949 sets the fixity for a data constructor and the corresponding type constructor. For example:
953 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
954 and similarly for <literal>:*:</literal>.
955 <literal>Int `a` Bool</literal>.
958 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
961 Data type and type-synonym declarations can be written infix. E.g.
963 data a :*: b = Foo a b
964 type a :+: b = Either a b
968 The only thing that differs between operators in types and operators in expressions is that
969 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
970 are not allowed in types. Reason: the uniform thing to do would be to make them type
971 variables, but that's not very useful. A less uniform but more useful thing would be to
972 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
973 lists. So for now we just exclude them.
980 <sect3 id="type-synonyms">
981 <title>Liberalised type synonyms</title>
984 Type synonyms are like macros at the type level, and
985 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
986 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
988 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
989 in a type synonym, thus:
991 type Discard a = forall b. Show b => a -> b -> (a, String)
996 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1003 You can write an unboxed tuple in a type synonym:
1005 type Pr = (# Int, Int #)
1013 You can apply a type synonym to a forall type:
1015 type Foo a = a -> a -> Bool
1017 f :: Foo (forall b. b->b)
1019 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1021 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1026 You can apply a type synonym to a partially applied type synonym:
1028 type Generic i o = forall x. i x -> o x
1031 foo :: Generic Id []
1033 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1035 foo :: forall x. x -> [x]
1043 GHC currently does kind checking before expanding synonyms (though even that
1047 After expanding type synonyms, GHC does validity checking on types, looking for
1048 the following mal-formedness which isn't detected simply by kind checking:
1051 Type constructor applied to a type involving for-alls.
1054 Unboxed tuple on left of an arrow.
1057 Partially-applied type synonym.
1061 this will be rejected:
1063 type Pr = (# Int, Int #)
1068 because GHC does not allow unboxed tuples on the left of a function arrow.
1073 <sect3 id="existential-quantification">
1074 <title>Existentially quantified data constructors
1078 The idea of using existential quantification in data type declarations
1079 was suggested by Laufer (I believe, thought doubtless someone will
1080 correct me), and implemented in Hope+. It's been in Lennart
1081 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1082 proved very useful. Here's the idea. Consider the declaration:
1088 data Foo = forall a. MkFoo a (a -> Bool)
1095 The data type <literal>Foo</literal> has two constructors with types:
1101 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1108 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1109 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1110 For example, the following expression is fine:
1116 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1122 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1123 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1124 isUpper</function> packages a character with a compatible function. These
1125 two things are each of type <literal>Foo</literal> and can be put in a list.
1129 What can we do with a value of type <literal>Foo</literal>?. In particular,
1130 what happens when we pattern-match on <function>MkFoo</function>?
1136 f (MkFoo val fn) = ???
1142 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1143 are compatible, the only (useful) thing we can do with them is to
1144 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1151 f (MkFoo val fn) = fn val
1157 What this allows us to do is to package heterogenous values
1158 together with a bunch of functions that manipulate them, and then treat
1159 that collection of packages in a uniform manner. You can express
1160 quite a bit of object-oriented-like programming this way.
1163 <sect4 id="existential">
1164 <title>Why existential?
1168 What has this to do with <emphasis>existential</emphasis> quantification?
1169 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1175 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1181 But Haskell programmers can safely think of the ordinary
1182 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1183 adding a new existential quantification construct.
1189 <title>Type classes</title>
1192 An easy extension (implemented in <command>hbc</command>) is to allow
1193 arbitrary contexts before the constructor. For example:
1199 data Baz = forall a. Eq a => Baz1 a a
1200 | forall b. Show b => Baz2 b (b -> b)
1206 The two constructors have the types you'd expect:
1212 Baz1 :: forall a. Eq a => a -> a -> Baz
1213 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1219 But when pattern matching on <function>Baz1</function> the matched values can be compared
1220 for equality, and when pattern matching on <function>Baz2</function> the first matched
1221 value can be converted to a string (as well as applying the function to it).
1222 So this program is legal:
1229 f (Baz1 p q) | p == q = "Yes"
1231 f (Baz2 v fn) = show (fn v)
1237 Operationally, in a dictionary-passing implementation, the
1238 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1239 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1240 extract it on pattern matching.
1244 Notice the way that the syntax fits smoothly with that used for
1245 universal quantification earlier.
1251 <title>Restrictions</title>
1254 There are several restrictions on the ways in which existentially-quantified
1255 constructors can be use.
1264 When pattern matching, each pattern match introduces a new,
1265 distinct, type for each existential type variable. These types cannot
1266 be unified with any other type, nor can they escape from the scope of
1267 the pattern match. For example, these fragments are incorrect:
1275 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1276 is the result of <function>f1</function>. One way to see why this is wrong is to
1277 ask what type <function>f1</function> has:
1281 f1 :: Foo -> a -- Weird!
1285 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1290 f1 :: forall a. Foo -> a -- Wrong!
1294 The original program is just plain wrong. Here's another sort of error
1298 f2 (Baz1 a b) (Baz1 p q) = a==q
1302 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1303 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1304 from the two <function>Baz1</function> constructors.
1312 You can't pattern-match on an existentially quantified
1313 constructor in a <literal>let</literal> or <literal>where</literal> group of
1314 bindings. So this is illegal:
1318 f3 x = a==b where { Baz1 a b = x }
1321 Instead, use a <literal>case</literal> expression:
1324 f3 x = case x of Baz1 a b -> a==b
1327 In general, you can only pattern-match
1328 on an existentially-quantified constructor in a <literal>case</literal> expression or
1329 in the patterns of a function definition.
1331 The reason for this restriction is really an implementation one.
1332 Type-checking binding groups is already a nightmare without
1333 existentials complicating the picture. Also an existential pattern
1334 binding at the top level of a module doesn't make sense, because it's
1335 not clear how to prevent the existentially-quantified type "escaping".
1336 So for now, there's a simple-to-state restriction. We'll see how
1344 You can't use existential quantification for <literal>newtype</literal>
1345 declarations. So this is illegal:
1349 newtype T = forall a. Ord a => MkT a
1353 Reason: a value of type <literal>T</literal> must be represented as a
1354 pair of a dictionary for <literal>Ord t</literal> and a value of type
1355 <literal>t</literal>. That contradicts the idea that
1356 <literal>newtype</literal> should have no concrete representation.
1357 You can get just the same efficiency and effect by using
1358 <literal>data</literal> instead of <literal>newtype</literal>. If
1359 there is no overloading involved, then there is more of a case for
1360 allowing an existentially-quantified <literal>newtype</literal>,
1361 because the <literal>data</literal> version does carry an
1362 implementation cost, but single-field existentially quantified
1363 constructors aren't much use. So the simple restriction (no
1364 existential stuff on <literal>newtype</literal>) stands, unless there
1365 are convincing reasons to change it.
1373 You can't use <literal>deriving</literal> to define instances of a
1374 data type with existentially quantified data constructors.
1376 Reason: in most cases it would not make sense. For example:#
1379 data T = forall a. MkT [a] deriving( Eq )
1382 To derive <literal>Eq</literal> in the standard way we would need to have equality
1383 between the single component of two <function>MkT</function> constructors:
1387 (MkT a) == (MkT b) = ???
1390 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1391 It's just about possible to imagine examples in which the derived instance
1392 would make sense, but it seems altogether simpler simply to prohibit such
1393 declarations. Define your own instances!
1408 <sect2 id="multi-param-type-classes">
1409 <title>Class declarations</title>
1412 This section documents GHC's implementation of multi-parameter type
1413 classes. There's lots of background in the paper <ulink
1414 url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1415 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1416 Jones, Erik Meijer).
1419 There are the following constraints on class declarations:
1424 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1428 class Collection c a where
1429 union :: c a -> c a -> c a
1440 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1441 of "acyclic" involves only the superclass relationships. For example,
1447 op :: D b => a -> b -> b
1450 class C a => D a where { ... }
1454 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1455 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1456 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1463 <emphasis>There are no restrictions on the context in a class declaration
1464 (which introduces superclasses), except that the class hierarchy must
1465 be acyclic</emphasis>. So these class declarations are OK:
1469 class Functor (m k) => FiniteMap m k where
1472 class (Monad m, Monad (t m)) => Transform t m where
1473 lift :: m a -> (t m) a
1483 <emphasis>All of the class type variables must be reachable (in the sense
1484 mentioned in <xref linkend="type-restrictions"/>)
1485 from the free variables of each method type
1486 </emphasis>. For example:
1490 class Coll s a where
1492 insert :: s -> a -> s
1496 is not OK, because the type of <literal>empty</literal> doesn't mention
1497 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1498 types, and has the same motivation.
1500 Sometimes, offending class declarations exhibit misunderstandings. For
1501 example, <literal>Coll</literal> might be rewritten
1505 class Coll s a where
1507 insert :: s a -> a -> s a
1511 which makes the connection between the type of a collection of
1512 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1513 Occasionally this really doesn't work, in which case you can split the
1521 class CollE s => Coll s a where
1522 insert :: s -> a -> s
1532 <sect3 id="class-method-types">
1533 <title>Class method types</title>
1535 Haskell 98 prohibits class method types to mention constraints on the
1536 class type variable, thus:
1539 fromList :: [a] -> s a
1540 elem :: Eq a => a -> s a -> Bool
1542 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1543 contains the constraint <literal>Eq a</literal>, constrains only the
1544 class type variable (in this case <literal>a</literal>).
1547 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1554 <sect2 id="type-restrictions">
1555 <title>Type signatures</title>
1557 <sect3><title>The context of a type signature</title>
1559 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1560 the form <emphasis>(class type-variable)</emphasis> or
1561 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1562 these type signatures are perfectly OK
1565 g :: Ord (T a ()) => ...
1569 GHC imposes the following restrictions on the constraints in a type signature.
1573 forall tv1..tvn (c1, ...,cn) => type
1576 (Here, we write the "foralls" explicitly, although the Haskell source
1577 language omits them; in Haskell 98, all the free type variables of an
1578 explicit source-language type signature are universally quantified,
1579 except for the class type variables in a class declaration. However,
1580 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
1589 <emphasis>Each universally quantified type variable
1590 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1592 A type variable <literal>a</literal> is "reachable" if it it appears
1593 in the same constraint as either a type variable free in in
1594 <literal>type</literal>, or another reachable type variable.
1595 A value with a type that does not obey
1596 this reachability restriction cannot be used without introducing
1597 ambiguity; that is why the type is rejected.
1598 Here, for example, is an illegal type:
1602 forall a. Eq a => Int
1606 When a value with this type was used, the constraint <literal>Eq tv</literal>
1607 would be introduced where <literal>tv</literal> is a fresh type variable, and
1608 (in the dictionary-translation implementation) the value would be
1609 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1610 can never know which instance of <literal>Eq</literal> to use because we never
1611 get any more information about <literal>tv</literal>.
1615 that the reachability condition is weaker than saying that <literal>a</literal> is
1616 functionally dependent on a type variable free in
1617 <literal>type</literal> (see <xref
1618 linkend="functional-dependencies"/>). The reason for this is there
1619 might be a "hidden" dependency, in a superclass perhaps. So
1620 "reachable" is a conservative approximation to "functionally dependent".
1621 For example, consider:
1623 class C a b | a -> b where ...
1624 class C a b => D a b where ...
1625 f :: forall a b. D a b => a -> a
1627 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
1628 but that is not immediately apparent from <literal>f</literal>'s type.
1634 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1635 universally quantified type variables <literal>tvi</literal></emphasis>.
1637 For example, this type is OK because <literal>C a b</literal> mentions the
1638 universally quantified type variable <literal>b</literal>:
1642 forall a. C a b => burble
1646 The next type is illegal because the constraint <literal>Eq b</literal> does not
1647 mention <literal>a</literal>:
1651 forall a. Eq b => burble
1655 The reason for this restriction is milder than the other one. The
1656 excluded types are never useful or necessary (because the offending
1657 context doesn't need to be witnessed at this point; it can be floated
1658 out). Furthermore, floating them out increases sharing. Lastly,
1659 excluding them is a conservative choice; it leaves a patch of
1660 territory free in case we need it later.
1671 <title>For-all hoisting</title>
1673 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
1674 end of an arrow, thus:
1676 type Discard a = forall b. a -> b -> a
1678 g :: Int -> Discard Int
1681 Simply expanding the type synonym would give
1683 g :: Int -> (forall b. Int -> b -> Int)
1685 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1687 g :: forall b. Int -> Int -> b -> Int
1689 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1690 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1691 performs the transformation:</emphasis>
1693 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1695 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1697 (In fact, GHC tries to retain as much synonym information as possible for use in
1698 error messages, but that is a usability issue.) This rule applies, of course, whether
1699 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1700 valid way to write <literal>g</literal>'s type signature:
1702 g :: Int -> Int -> forall b. b -> Int
1706 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1709 type Foo a = (?x::Int) => Bool -> a
1714 g :: (?x::Int) => Bool -> Bool -> Int
1722 <sect2 id="instance-decls">
1723 <title>Instance declarations</title>
1726 <title>Overlapping instances</title>
1728 In general, <emphasis>GHC requires that that it be unambiguous which instance
1730 should be used to resolve a type-class constraint</emphasis>. This behaviour
1731 can be modified by two flags: <option>-fallow-overlapping-instances</option>
1732 <indexterm><primary>-fallow-overlapping-instances
1733 </primary></indexterm>
1734 and <option>-fallow-incoherent-instances</option>
1735 <indexterm><primary>-fallow-incoherent-instances
1736 </primary></indexterm>, as this section discusses.</para>
1738 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
1739 it tries to match every instance declaration against the
1741 by instantiating the head of the instance declaration. For example, consider
1744 instance context1 => C Int a where ... -- (A)
1745 instance context2 => C a Bool where ... -- (B)
1746 instance context3 => C Int [a] where ... -- (C)
1747 instance context4 => C Int [Int] where ... -- (D)
1749 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>, but (C) and (D) do not. When matching, GHC takes
1750 no account of the context of the instance declaration
1751 (<literal>context1</literal> etc).
1752 GHC's default behaviour is that <emphasis>exactly one instance must match the
1753 constraint it is trying to resolve</emphasis>.
1754 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
1755 including both declarations (A) and (B), say); an error is only reported if a
1756 particular constraint matches more than one.
1760 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
1761 more than one instance to match, provided there is a most specific one. For
1762 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
1763 (C) and (D), but the last is more specific, and hence is chosen. If there is no
1764 most-specific match, the program is rejected.
1767 However, GHC is conservative about committing to an overlapping instance. For example:
1772 Suppose that from the RHS of <literal>f</literal> we get the constraint
1773 <literal>C Int [b]</literal>. But
1774 GHC does not commit to instance (C), because in a particular
1775 call of <literal>f</literal>, <literal>b</literal> might be instantiate
1776 to <literal>Int</literal>, in which case instance (D) would be more specific still.
1777 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
1778 GHC will instead pick (C), without complaining about
1779 the problem of subsequent instantiations.
1784 <title>Type synonyms in the instance head</title>
1787 <emphasis>Unlike Haskell 98, instance heads may use type
1788 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1789 As always, using a type synonym is just shorthand for
1790 writing the RHS of the type synonym definition. For example:
1794 type Point = (Int,Int)
1795 instance C Point where ...
1796 instance C [Point] where ...
1800 is legal. However, if you added
1804 instance C (Int,Int) where ...
1808 as well, then the compiler will complain about the overlapping
1809 (actually, identical) instance declarations. As always, type synonyms
1810 must be fully applied. You cannot, for example, write:
1815 instance Monad P where ...
1819 This design decision is independent of all the others, and easily
1820 reversed, but it makes sense to me.
1825 <sect3 id="undecidable-instances">
1826 <title>Undecidable instances</title>
1828 <para>An instance declaration must normally obey the following rules:
1830 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1831 an instance declaration <emphasis>must not</emphasis> be a type variable.
1832 For example, these are OK:
1835 instance C Int a where ...
1837 instance D (Int, Int) where ...
1839 instance E [[a]] where ...
1843 instance F a where ...
1845 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1846 For example, this is OK:
1848 instance Stateful (ST s) (MutVar s) where ...
1855 <para>All of the types in the <emphasis>context</emphasis> of
1856 an instance declaration <emphasis>must</emphasis> be type variables.
1859 instance C a b => Eq (a,b) where ...
1863 instance C Int b => Foo b where ...
1869 These restrictions ensure that
1870 context reduction terminates: each reduction step removes one type
1871 constructor. For example, the following would make the type checker
1872 loop if it wasn't excluded:
1874 instance C a => C a where ...
1876 There are two situations in which the rule is a bit of a pain. First,
1877 if one allows overlapping instance declarations then it's quite
1878 convenient to have a "default instance" declaration that applies if
1879 something more specific does not:
1888 Second, sometimes you might want to use the following to get the
1889 effect of a "class synonym":
1893 class (C1 a, C2 a, C3 a) => C a where { }
1895 instance (C1 a, C2 a, C3 a) => C a where { }
1899 This allows you to write shorter signatures:
1911 f :: (C1 a, C2 a, C3 a) => ...
1915 Voluminous correspondence on the Haskell mailing list has convinced me
1916 that it's worth experimenting with more liberal rules. If you use
1917 the experimental flag <option>-fallow-undecidable-instances</option>
1918 <indexterm><primary>-fallow-undecidable-instances
1919 option</primary></indexterm>, you can use arbitrary
1920 types in both an instance context and instance head. Termination is ensured by having a
1921 fixed-depth recursion stack. If you exceed the stack depth you get a
1922 sort of backtrace, and the opportunity to increase the stack depth
1923 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1926 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1927 allowing these idioms interesting idioms.
1934 <sect2 id="implicit-parameters">
1935 <title>Implicit parameters</title>
1937 <para> Implicit parameters are implemented as described in
1938 "Implicit parameters: dynamic scoping with static types",
1939 J Lewis, MB Shields, E Meijer, J Launchbury,
1940 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1944 <para>(Most of the following, stil rather incomplete, documentation is
1945 due to Jeff Lewis.)</para>
1947 <para>Implicit parameter support is enabled with the option
1948 <option>-fimplicit-params</option>.</para>
1951 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1952 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1953 context. In Haskell, all variables are statically bound. Dynamic
1954 binding of variables is a notion that goes back to Lisp, but was later
1955 discarded in more modern incarnations, such as Scheme. Dynamic binding
1956 can be very confusing in an untyped language, and unfortunately, typed
1957 languages, in particular Hindley-Milner typed languages like Haskell,
1958 only support static scoping of variables.
1961 However, by a simple extension to the type class system of Haskell, we
1962 can support dynamic binding. Basically, we express the use of a
1963 dynamically bound variable as a constraint on the type. These
1964 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1965 function uses a dynamically-bound variable <literal>?x</literal>
1966 of type <literal>t'</literal>". For
1967 example, the following expresses the type of a sort function,
1968 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1970 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1972 The dynamic binding constraints are just a new form of predicate in the type class system.
1975 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1976 where <literal>x</literal> is
1977 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1978 Use of this construct also introduces a new
1979 dynamic-binding constraint in the type of the expression.
1980 For example, the following definition
1981 shows how we can define an implicitly parameterized sort function in
1982 terms of an explicitly parameterized <literal>sortBy</literal> function:
1984 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1986 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1992 <title>Implicit-parameter type constraints</title>
1994 Dynamic binding constraints behave just like other type class
1995 constraints in that they are automatically propagated. Thus, when a
1996 function is used, its implicit parameters are inherited by the
1997 function that called it. For example, our <literal>sort</literal> function might be used
1998 to pick out the least value in a list:
2000 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2001 least xs = fst (sort xs)
2003 Without lifting a finger, the <literal>?cmp</literal> parameter is
2004 propagated to become a parameter of <literal>least</literal> as well. With explicit
2005 parameters, the default is that parameters must always be explicit
2006 propagated. With implicit parameters, the default is to always
2010 An implicit-parameter type constraint differs from other type class constraints in the
2011 following way: All uses of a particular implicit parameter must have
2012 the same type. This means that the type of <literal>(?x, ?x)</literal>
2013 is <literal>(?x::a) => (a,a)</literal>, and not
2014 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2018 <para> You can't have an implicit parameter in the context of a class or instance
2019 declaration. For example, both these declarations are illegal:
2021 class (?x::Int) => C a where ...
2022 instance (?x::a) => Foo [a] where ...
2024 Reason: exactly which implicit parameter you pick up depends on exactly where
2025 you invoke a function. But the ``invocation'' of instance declarations is done
2026 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2027 Easiest thing is to outlaw the offending types.</para>
2029 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2031 f :: (?x :: [a]) => Int -> Int
2034 g :: (Read a, Show a) => String -> String
2037 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2038 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2039 quite unambiguous, and fixes the type <literal>a</literal>.
2044 <title>Implicit-parameter bindings</title>
2047 An implicit parameter is <emphasis>bound</emphasis> using the standard
2048 <literal>let</literal> or <literal>where</literal> binding forms.
2049 For example, we define the <literal>min</literal> function by binding
2050 <literal>cmp</literal>.
2053 min = let ?cmp = (<=) in least
2057 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2058 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2059 (including in a list comprehension, or do-notation, or pattern guards),
2060 or a <literal>where</literal> clause.
2061 Note the following points:
2064 An implicit-parameter binding group must be a
2065 collection of simple bindings to implicit-style variables (no
2066 function-style bindings, and no type signatures); these bindings are
2067 neither polymorphic or recursive.
2070 You may not mix implicit-parameter bindings with ordinary bindings in a
2071 single <literal>let</literal>
2072 expression; use two nested <literal>let</literal>s instead.
2073 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2077 You may put multiple implicit-parameter bindings in a
2078 single binding group; but they are <emphasis>not</emphasis> treated
2079 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2080 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2081 parameter. The bindings are not nested, and may be re-ordered without changing
2082 the meaning of the program.
2083 For example, consider:
2085 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2087 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2088 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2090 f :: (?x::Int) => Int -> Int
2099 <sect2 id="linear-implicit-parameters">
2100 <title>Linear implicit parameters</title>
2102 Linear implicit parameters are an idea developed by Koen Claessen,
2103 Mark Shields, and Simon PJ. They address the long-standing
2104 problem that monads seem over-kill for certain sorts of problem, notably:
2107 <listitem> <para> distributing a supply of unique names </para> </listitem>
2108 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2109 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2113 Linear implicit parameters are just like ordinary implicit parameters,
2114 except that they are "linear" -- that is, they cannot be copied, and
2115 must be explicitly "split" instead. Linear implicit parameters are
2116 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2117 (The '/' in the '%' suggests the split!)
2122 import GHC.Exts( Splittable )
2124 data NameSupply = ...
2126 splitNS :: NameSupply -> (NameSupply, NameSupply)
2127 newName :: NameSupply -> Name
2129 instance Splittable NameSupply where
2133 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2134 f env (Lam x e) = Lam x' (f env e)
2137 env' = extend env x x'
2138 ...more equations for f...
2140 Notice that the implicit parameter %ns is consumed
2142 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2143 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2147 So the translation done by the type checker makes
2148 the parameter explicit:
2150 f :: NameSupply -> Env -> Expr -> Expr
2151 f ns env (Lam x e) = Lam x' (f ns1 env e)
2153 (ns1,ns2) = splitNS ns
2155 env = extend env x x'
2157 Notice the call to 'split' introduced by the type checker.
2158 How did it know to use 'splitNS'? Because what it really did
2159 was to introduce a call to the overloaded function 'split',
2160 defined by the class <literal>Splittable</literal>:
2162 class Splittable a where
2165 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2166 split for name supplies. But we can simply write
2172 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2174 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2175 <literal>GHC.Exts</literal>.
2180 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2181 are entirely distinct implicit parameters: you
2182 can use them together and they won't intefere with each other. </para>
2185 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2187 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2188 in the context of a class or instance declaration. </para></listitem>
2192 <sect3><title>Warnings</title>
2195 The monomorphism restriction is even more important than usual.
2196 Consider the example above:
2198 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2199 f env (Lam x e) = Lam x' (f env e)
2202 env' = extend env x x'
2204 If we replaced the two occurrences of x' by (newName %ns), which is
2205 usually a harmless thing to do, we get:
2207 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2208 f env (Lam x e) = Lam (newName %ns) (f env e)
2210 env' = extend env x (newName %ns)
2212 But now the name supply is consumed in <emphasis>three</emphasis> places
2213 (the two calls to newName,and the recursive call to f), so
2214 the result is utterly different. Urk! We don't even have
2218 Well, this is an experimental change. With implicit
2219 parameters we have already lost beta reduction anyway, and
2220 (as John Launchbury puts it) we can't sensibly reason about
2221 Haskell programs without knowing their typing.
2226 <sect3><title>Recursive functions</title>
2227 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2230 foo :: %x::T => Int -> [Int]
2232 foo n = %x : foo (n-1)
2234 where T is some type in class Splittable.</para>
2236 Do you get a list of all the same T's or all different T's
2237 (assuming that split gives two distinct T's back)?
2239 If you supply the type signature, taking advantage of polymorphic
2240 recursion, you get what you'd probably expect. Here's the
2241 translated term, where the implicit param is made explicit:
2244 foo x n = let (x1,x2) = split x
2245 in x1 : foo x2 (n-1)
2247 But if you don't supply a type signature, GHC uses the Hindley
2248 Milner trick of using a single monomorphic instance of the function
2249 for the recursive calls. That is what makes Hindley Milner type inference
2250 work. So the translation becomes
2254 foom n = x : foom (n-1)
2258 Result: 'x' is not split, and you get a list of identical T's. So the
2259 semantics of the program depends on whether or not foo has a type signature.
2262 You may say that this is a good reason to dislike linear implicit parameters
2263 and you'd be right. That is why they are an experimental feature.
2269 <sect2 id="functional-dependencies">
2270 <title>Functional dependencies
2273 <para> Functional dependencies are implemented as described by Mark Jones
2274 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2275 In Proceedings of the 9th European Symposium on Programming,
2276 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2280 Functional dependencies are introduced by a vertical bar in the syntax of a
2281 class declaration; e.g.
2283 class (Monad m) => MonadState s m | m -> s where ...
2285 class Foo a b c | a b -> c where ...
2287 There should be more documentation, but there isn't (yet). Yell if you need it.
2293 <sect2 id="sec-kinding">
2294 <title>Explicitly-kinded quantification</title>
2297 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2298 to give the kind explicitly as (machine-checked) documentation,
2299 just as it is nice to give a type signature for a function. On some occasions,
2300 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2301 John Hughes had to define the data type:
2303 data Set cxt a = Set [a]
2304 | Unused (cxt a -> ())
2306 The only use for the <literal>Unused</literal> constructor was to force the correct
2307 kind for the type variable <literal>cxt</literal>.
2310 GHC now instead allows you to specify the kind of a type variable directly, wherever
2311 a type variable is explicitly bound. Namely:
2313 <listitem><para><literal>data</literal> declarations:
2315 data Set (cxt :: * -> *) a = Set [a]
2316 </screen></para></listitem>
2317 <listitem><para><literal>type</literal> declarations:
2319 type T (f :: * -> *) = f Int
2320 </screen></para></listitem>
2321 <listitem><para><literal>class</literal> declarations:
2323 class (Eq a) => C (f :: * -> *) a where ...
2324 </screen></para></listitem>
2325 <listitem><para><literal>forall</literal>'s in type signatures:
2327 f :: forall (cxt :: * -> *). Set cxt Int
2328 </screen></para></listitem>
2333 The parentheses are required. Some of the spaces are required too, to
2334 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2335 will get a parse error, because "<literal>::*->*</literal>" is a
2336 single lexeme in Haskell.
2340 As part of the same extension, you can put kind annotations in types
2343 f :: (Int :: *) -> Int
2344 g :: forall a. a -> (a :: *)
2348 atype ::= '(' ctype '::' kind ')
2350 The parentheses are required.
2355 <sect2 id="universal-quantification">
2356 <title>Arbitrary-rank polymorphism
2360 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2361 allows us to say exactly what this means. For example:
2369 g :: forall b. (b -> b)
2371 The two are treated identically.
2375 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2376 explicit universal quantification in
2378 For example, all the following types are legal:
2380 f1 :: forall a b. a -> b -> a
2381 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2383 f2 :: (forall a. a->a) -> Int -> Int
2384 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2386 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2388 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2389 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2390 The <literal>forall</literal> makes explicit the universal quantification that
2391 is implicitly added by Haskell.
2394 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2395 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2396 shows, the polymorphic type on the left of the function arrow can be overloaded.
2399 The function <literal>f3</literal> has a rank-3 type;
2400 it has rank-2 types on the left of a function arrow.
2403 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2404 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2405 that restriction has now been lifted.)
2406 In particular, a forall-type (also called a "type scheme"),
2407 including an operational type class context, is legal:
2409 <listitem> <para> On the left of a function arrow </para> </listitem>
2410 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2411 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2412 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2413 field type signatures.</para> </listitem>
2414 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2415 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2417 There is one place you cannot put a <literal>forall</literal>:
2418 you cannot instantiate a type variable with a forall-type. So you cannot
2419 make a forall-type the argument of a type constructor. So these types are illegal:
2421 x1 :: [forall a. a->a]
2422 x2 :: (forall a. a->a, Int)
2423 x3 :: Maybe (forall a. a->a)
2425 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2426 a type variable any more!
2435 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2436 the types of the constructor arguments. Here are several examples:
2442 data T a = T1 (forall b. b -> b -> b) a
2444 data MonadT m = MkMonad { return :: forall a. a -> m a,
2445 bind :: forall a b. m a -> (a -> m b) -> m b
2448 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2454 The constructors have rank-2 types:
2460 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2461 MkMonad :: forall m. (forall a. a -> m a)
2462 -> (forall a b. m a -> (a -> m b) -> m b)
2464 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2470 Notice that you don't need to use a <literal>forall</literal> if there's an
2471 explicit context. For example in the first argument of the
2472 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2473 prefixed to the argument type. The implicit <literal>forall</literal>
2474 quantifies all type variables that are not already in scope, and are
2475 mentioned in the type quantified over.
2479 As for type signatures, implicit quantification happens for non-overloaded
2480 types too. So if you write this:
2483 data T a = MkT (Either a b) (b -> b)
2486 it's just as if you had written this:
2489 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2492 That is, since the type variable <literal>b</literal> isn't in scope, it's
2493 implicitly universally quantified. (Arguably, it would be better
2494 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2495 where that is what is wanted. Feedback welcomed.)
2499 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2500 the constructor to suitable values, just as usual. For example,
2511 a3 = MkSwizzle reverse
2514 a4 = let r x = Just x
2521 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2522 mkTs f x y = [T1 f x, T1 f y]
2528 The type of the argument can, as usual, be more general than the type
2529 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2530 does not need the <literal>Ord</literal> constraint.)
2534 When you use pattern matching, the bound variables may now have
2535 polymorphic types. For example:
2541 f :: T a -> a -> (a, Char)
2542 f (T1 w k) x = (w k x, w 'c' 'd')
2544 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2545 g (MkSwizzle s) xs f = s (map f (s xs))
2547 h :: MonadT m -> [m a] -> m [a]
2548 h m [] = return m []
2549 h m (x:xs) = bind m x $ \y ->
2550 bind m (h m xs) $ \ys ->
2557 In the function <function>h</function> we use the record selectors <literal>return</literal>
2558 and <literal>bind</literal> to extract the polymorphic bind and return functions
2559 from the <literal>MonadT</literal> data structure, rather than using pattern
2565 <title>Type inference</title>
2568 In general, type inference for arbitrary-rank types is undecidable.
2569 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2570 to get a decidable algorithm by requiring some help from the programmer.
2571 We do not yet have a formal specification of "some help" but the rule is this:
2574 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2575 provides an explicit polymorphic type for x, or GHC's type inference will assume
2576 that x's type has no foralls in it</emphasis>.
2579 What does it mean to "provide" an explicit type for x? You can do that by
2580 giving a type signature for x directly, using a pattern type signature
2581 (<xref linkend="scoped-type-variables"/>), thus:
2583 \ f :: (forall a. a->a) -> (f True, f 'c')
2585 Alternatively, you can give a type signature to the enclosing
2586 context, which GHC can "push down" to find the type for the variable:
2588 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2590 Here the type signature on the expression can be pushed inwards
2591 to give a type signature for f. Similarly, and more commonly,
2592 one can give a type signature for the function itself:
2594 h :: (forall a. a->a) -> (Bool,Char)
2595 h f = (f True, f 'c')
2597 You don't need to give a type signature if the lambda bound variable
2598 is a constructor argument. Here is an example we saw earlier:
2600 f :: T a -> a -> (a, Char)
2601 f (T1 w k) x = (w k x, w 'c' 'd')
2603 Here we do not need to give a type signature to <literal>w</literal>, because
2604 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2611 <sect3 id="implicit-quant">
2612 <title>Implicit quantification</title>
2615 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2616 user-written types, if and only if there is no explicit <literal>forall</literal>,
2617 GHC finds all the type variables mentioned in the type that are not already
2618 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2622 f :: forall a. a -> a
2629 h :: forall b. a -> b -> b
2635 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2638 f :: (a -> a) -> Int
2640 f :: forall a. (a -> a) -> Int
2642 f :: (forall a. a -> a) -> Int
2645 g :: (Ord a => a -> a) -> Int
2646 -- MEANS the illegal type
2647 g :: forall a. (Ord a => a -> a) -> Int
2649 g :: (forall a. Ord a => a -> a) -> Int
2651 The latter produces an illegal type, which you might think is silly,
2652 but at least the rule is simple. If you want the latter type, you
2653 can write your for-alls explicitly. Indeed, doing so is strongly advised
2662 <sect2 id="scoped-type-variables">
2663 <title>Scoped type variables
2667 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2668 variable</emphasis>. For example
2674 f (xs::[a]) = ys ++ ys
2683 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
2684 This brings the type variable <literal>a</literal> into scope; it scopes over
2685 all the patterns and right hand sides for this equation for <function>f</function>.
2686 In particular, it is in scope at the type signature for <varname>y</varname>.
2690 Pattern type signatures are completely orthogonal to ordinary, separate
2691 type signatures. The two can be used independently or together.
2692 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
2693 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2694 implicitly universally quantified. (If there are no type variables in
2695 scope, all type variables mentioned in the signature are universally
2696 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
2697 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
2698 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
2699 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
2700 it becomes possible to do so.
2704 Scoped type variables are implemented in both GHC and Hugs. Where the
2705 implementations differ from the specification below, those differences
2710 So much for the basic idea. Here are the details.
2714 <title>What a pattern type signature means</title>
2716 A type variable brought into scope by a pattern type signature is simply
2717 the name for a type. The restriction they express is that all occurrences
2718 of the same name mean the same type. For example:
2720 f :: [Int] -> Int -> Int
2721 f (xs::[a]) (y::a) = (head xs + y) :: a
2723 The pattern type signatures on the left hand side of
2724 <literal>f</literal> express the fact that <literal>xs</literal>
2725 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2726 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2727 specifies that this expression must have the same type <literal>a</literal>.
2728 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2729 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2730 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2731 rules, which specified that a pattern-bound type variable should be universally quantified.)
2732 For example, all of these are legal:</para>
2735 t (x::a) (y::a) = x+y*2
2737 f (x::a) (y::b) = [x,y] -- a unifies with b
2739 g (x::a) = x + 1::Int -- a unifies with Int
2741 h x = let k (y::a) = [x,y] -- a is free in the
2742 in k x -- environment
2744 k (x::a) True = ... -- a unifies with Int
2745 k (x::Int) False = ...
2748 w (x::a) = x -- a unifies with [b]
2754 <title>Scope and implicit quantification</title>
2762 All the type variables mentioned in a pattern,
2763 that are not already in scope,
2764 are brought into scope by the pattern. We describe this set as
2765 the <emphasis>type variables bound by the pattern</emphasis>.
2768 f (x::a) = let g (y::(a,b)) = fst y
2772 The pattern <literal>(x::a)</literal> brings the type variable
2773 <literal>a</literal> into scope, as well as the term
2774 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2775 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2776 and brings into scope the type variable <literal>b</literal>.
2782 The type variable(s) bound by the pattern have the same scope
2783 as the term variable(s) bound by the pattern. For example:
2786 f (x::a) = <...rhs of f...>
2787 (p::b, q::b) = (1,2)
2788 in <...body of let...>
2790 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2791 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2792 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2793 just like <literal>p</literal> and <literal>q</literal> do.
2794 Indeed, the newly bound type variables also scope over any ordinary, separate
2795 type signatures in the <literal>let</literal> group.
2802 The type variables bound by the pattern may be
2803 mentioned in ordinary type signatures or pattern
2804 type signatures anywhere within their scope.
2811 In ordinary type signatures, any type variable mentioned in the
2812 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2820 Ordinary type signatures do not bring any new type variables
2821 into scope (except in the type signature itself!). So this is illegal:
2828 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
2829 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2830 and that is an incorrect typing.
2837 The pattern type signature is a monotype:
2842 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2846 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2847 not to type schemes.
2851 There is no implicit universal quantification on pattern type signatures (in contrast to
2852 ordinary type signatures).
2862 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2863 scope over the methods defined in the <literal>where</literal> part. For example:
2877 (Not implemented in Hugs yet, Dec 98).
2888 <title>Where a pattern type signature can occur</title>
2891 A pattern type signature can occur in any pattern. For example:
2896 A pattern type signature can be on an arbitrary sub-pattern, not
2901 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2910 Pattern type signatures, including the result part, can be used
2911 in lambda abstractions:
2914 (\ (x::a, y) :: a -> x)
2921 Pattern type signatures, including the result part, can be used
2922 in <literal>case</literal> expressions:
2925 case e of { ((x::a, y) :: (a,b)) -> x }
2928 Note that the <literal>-></literal> symbol in a case alternative
2929 leads to difficulties when parsing a type signature in the pattern: in
2930 the absence of the extra parentheses in the example above, the parser
2931 would try to interpret the <literal>-></literal> as a function
2932 arrow and give a parse error later.
2940 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2941 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2942 token or a parenthesised type of some sort). To see why,
2943 consider how one would parse this:
2957 Pattern type signatures can bind existential type variables.
2962 data T = forall a. MkT [a]
2965 f (MkT [t::a]) = MkT t3
2978 Pattern type signatures
2979 can be used in pattern bindings:
2982 f x = let (y, z::a) = x in ...
2983 f1 x = let (y, z::Int) = x in ...
2984 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2985 f3 :: (b->b) = \x -> x
2988 In all such cases, the binding is not generalised over the pattern-bound
2989 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2990 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2991 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2992 In contrast, the binding
2997 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2998 in <literal>f4</literal>'s scope.
3008 <title>Result type signatures</title>
3011 The result type of a function can be given a signature, thus:
3015 f (x::a) :: [a] = [x,x,x]
3019 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3020 result type. Sometimes this is the only way of naming the type variable
3025 f :: Int -> [a] -> [a]
3026 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3027 in \xs -> map g (reverse xs `zip` xs)
3032 The type variables bound in a result type signature scope over the right hand side
3033 of the definition. However, consider this corner-case:
3035 rev1 :: [a] -> [a] = \xs -> reverse xs
3037 foo ys = rev (ys::[a])
3039 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3040 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3041 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3042 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3043 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3046 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3047 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3051 rev1 :: [a] -> [a] = \xs -> reverse xs
3056 Result type signatures are not yet implemented in Hugs.
3063 <sect2 id="deriving-typeable">
3064 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3067 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3068 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3069 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3070 classes <literal>Eq</literal>, <literal>Ord</literal>,
3071 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3074 GHC extends this list with two more classes that may be automatically derived
3075 (provided the <option>-fglasgow-exts</option> flag is specified):
3076 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3077 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
3078 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3082 <sect2 id="newtype-deriving">
3083 <title>Generalised derived instances for newtypes</title>
3086 When you define an abstract type using <literal>newtype</literal>, you may want
3087 the new type to inherit some instances from its representation. In
3088 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3089 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3090 other classes you have to write an explicit instance declaration. For
3091 example, if you define
3094 newtype Dollars = Dollars Int
3097 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3098 explicitly define an instance of <literal>Num</literal>:
3101 instance Num Dollars where
3102 Dollars a + Dollars b = Dollars (a+b)
3105 All the instance does is apply and remove the <literal>newtype</literal>
3106 constructor. It is particularly galling that, since the constructor
3107 doesn't appear at run-time, this instance declaration defines a
3108 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3109 dictionary, only slower!
3113 <sect3> <title> Generalising the deriving clause </title>
3115 GHC now permits such instances to be derived instead, so one can write
3117 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3120 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3121 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3122 derives an instance declaration of the form
3125 instance Num Int => Num Dollars
3128 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3132 We can also derive instances of constructor classes in a similar
3133 way. For example, suppose we have implemented state and failure monad
3134 transformers, such that
3137 instance Monad m => Monad (State s m)
3138 instance Monad m => Monad (Failure m)
3140 In Haskell 98, we can define a parsing monad by
3142 type Parser tok m a = State [tok] (Failure m) a
3145 which is automatically a monad thanks to the instance declarations
3146 above. With the extension, we can make the parser type abstract,
3147 without needing to write an instance of class <literal>Monad</literal>, via
3150 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3153 In this case the derived instance declaration is of the form
3155 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3158 Notice that, since <literal>Monad</literal> is a constructor class, the
3159 instance is a <emphasis>partial application</emphasis> of the new type, not the
3160 entire left hand side. We can imagine that the type declaration is
3161 ``eta-converted'' to generate the context of the instance
3166 We can even derive instances of multi-parameter classes, provided the
3167 newtype is the last class parameter. In this case, a ``partial
3168 application'' of the class appears in the <literal>deriving</literal>
3169 clause. For example, given the class
3172 class StateMonad s m | m -> s where ...
3173 instance Monad m => StateMonad s (State s m) where ...
3175 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3177 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3178 deriving (Monad, StateMonad [tok])
3181 The derived instance is obtained by completing the application of the
3182 class to the new type:
3185 instance StateMonad [tok] (State [tok] (Failure m)) =>
3186 StateMonad [tok] (Parser tok m)
3191 As a result of this extension, all derived instances in newtype
3192 declarations are treated uniformly (and implemented just by reusing
3193 the dictionary for the representation type), <emphasis>except</emphasis>
3194 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3195 the newtype and its representation.
3199 <sect3> <title> A more precise specification </title>
3201 Derived instance declarations are constructed as follows. Consider the
3202 declaration (after expansion of any type synonyms)
3205 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3211 <literal>S</literal> is a type constructor,
3214 The <literal>t1...tk</literal> are types,
3217 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3218 the <literal>ti</literal>, and
3221 The <literal>ci</literal> are partial applications of
3222 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3223 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3226 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3227 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3228 should not "look through" the type or its constructor. You can still
3229 derive these classes for a newtype, but it happens in the usual way, not
3230 via this new mechanism.
3233 Then, for each <literal>ci</literal>, the derived instance
3236 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3238 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3239 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3243 As an example which does <emphasis>not</emphasis> work, consider
3245 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3247 Here we cannot derive the instance
3249 instance Monad (State s m) => Monad (NonMonad m)
3252 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3253 and so cannot be "eta-converted" away. It is a good thing that this
3254 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3255 not, in fact, a monad --- for the same reason. Try defining
3256 <literal>>>=</literal> with the correct type: you won't be able to.
3260 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3261 important, since we can only derive instances for the last one. If the
3262 <literal>StateMonad</literal> class above were instead defined as
3265 class StateMonad m s | m -> s where ...
3268 then we would not have been able to derive an instance for the
3269 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3270 classes usually have one "main" parameter for which deriving new
3271 instances is most interesting.
3279 <!-- ==================== End of type system extensions ================= -->
3281 <!-- ====================== Generalised algebraic data types ======================= -->
3284 <title>Generalised Algebraic Data Types</title>
3286 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3287 to give the type signatures of constructors explicitly. For example:
3290 Lit :: Int -> Term Int
3291 Succ :: Term Int -> Term Int
3292 IsZero :: Term Int -> Term Bool
3293 If :: Term Bool -> Term a -> Term a -> Term a
3294 Pair :: Term a -> Term b -> Term (a,b)
3296 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3297 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3298 for these <literal>Terms</literal>:
3302 eval (Succ t) = 1 + eval t
3303 eval (IsZero i) = eval i == 0
3304 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3305 eval (Pair e1 e2) = (eval e2, eval e2)
3307 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3309 <para> The extensions to GHC are these:
3312 Data type declarations have a 'where' form, as exemplified above. The type signature of
3313 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3314 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3315 have no scope. Indeed, one can write a kind signature instead:
3317 data Term :: * -> * where ...
3319 or even a mixture of the two:
3321 data Foo a :: (* -> *) -> * where ...
3323 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3326 data Foo a (b :: * -> *) where ...
3331 There are no restrictions on the type of the data constructor, except that the result
3332 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3333 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3337 You cannot use a <literal>deriving</literal> clause on a GADT-style data type declaration,
3338 nor can you use record syntax. (It's not clear what these constructs would mean. For example,
3339 the record selectors might ill-typed.) However, you can use strictness annotations, in the obvious places
3340 in the constructor type:
3343 Lit :: !Int -> Term Int
3344 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3345 Pair :: Term a -> Term b -> Term (a,b)
3350 Pattern matching causes type refinement. For example, in the right hand side of the equation
3355 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3356 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3357 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3359 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3360 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3361 occur. However, the refinement is quite general. For example, if we had:
3363 eval :: Term a -> a -> a
3364 eval (Lit i) j = i+j
3366 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3367 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3368 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3374 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3376 data T a = forall b. MkT b (b->a)
3377 data T' a where { MKT :: b -> (b->a) -> T a }
3382 <!-- ====================== End of Generalised algebraic data types ======================= -->
3384 <!-- ====================== TEMPLATE HASKELL ======================= -->
3386 <sect1 id="template-haskell">
3387 <title>Template Haskell</title>
3389 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3390 Template Haskell at <ulink url="http://www.haskell.org/th/">
3391 http://www.haskell.org/th/</ulink>, while
3393 the main technical innovations is discussed in "<ulink
3394 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3395 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3396 The details of the Template Haskell design are still in flux. Make sure you
3397 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3398 (search for the type ExpQ).
3399 [Temporary: many changes to the original design are described in
3400 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3401 Not all of these changes are in GHC 6.2.]
3404 <para> The first example from that paper is set out below as a worked example to help get you started.
3408 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3409 Tim Sheard is going to expand it.)
3413 <title>Syntax</title>
3415 <para> Template Haskell has the following new syntactic
3416 constructions. You need to use the flag
3417 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3418 </indexterm>to switch these syntactic extensions on
3419 (<option>-fth</option> is currently implied by
3420 <option>-fglasgow-exts</option>, but you are encouraged to
3421 specify it explicitly).</para>
3425 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3426 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3427 There must be no space between the "$" and the identifier or parenthesis. This use
3428 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3429 of "." as an infix operator. If you want the infix operator, put spaces around it.
3431 <para> A splice can occur in place of
3433 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3434 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3435 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3437 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3438 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3444 A expression quotation is written in Oxford brackets, thus:
3446 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3447 the quotation has type <literal>Expr</literal>.</para></listitem>
3448 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3449 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3450 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3451 the quotation has type <literal>Type</literal>.</para></listitem>
3452 </itemizedlist></para></listitem>
3455 Reification is written thus:
3457 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3458 has type <literal>Dec</literal>. </para></listitem>
3459 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3460 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3461 <listitem><para> Still to come: fixities </para></listitem>
3463 </itemizedlist></para>
3470 <sect2> <title> Using Template Haskell </title>
3474 The data types and monadic constructor functions for Template Haskell are in the library
3475 <literal>Language.Haskell.THSyntax</literal>.
3479 You can only run a function at compile time if it is imported from another module. That is,
3480 you can't define a function in a module, and call it from within a splice in the same module.
3481 (It would make sense to do so, but it's hard to implement.)
3485 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3488 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3489 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3490 compiles and runs a program, and then looks at the result. So it's important that
3491 the program it compiles produces results whose representations are identical to
3492 those of the compiler itself.
3496 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3497 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3502 <sect2> <title> A Template Haskell Worked Example </title>
3503 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3504 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3511 -- Import our template "pr"
3512 import Printf ( pr )
3514 -- The splice operator $ takes the Haskell source code
3515 -- generated at compile time by "pr" and splices it into
3516 -- the argument of "putStrLn".
3517 main = putStrLn ( $(pr "Hello") )
3523 -- Skeletal printf from the paper.
3524 -- It needs to be in a separate module to the one where
3525 -- you intend to use it.
3527 -- Import some Template Haskell syntax
3528 import Language.Haskell.TH
3530 -- Describe a format string
3531 data Format = D | S | L String
3533 -- Parse a format string. This is left largely to you
3534 -- as we are here interested in building our first ever
3535 -- Template Haskell program and not in building printf.
3536 parse :: String -> [Format]
3539 -- Generate Haskell source code from a parsed representation
3540 -- of the format string. This code will be spliced into
3541 -- the module which calls "pr", at compile time.
3542 gen :: [Format] -> ExpQ
3543 gen [D] = [| \n -> show n |]
3544 gen [S] = [| \s -> s |]
3545 gen [L s] = stringE s
3547 -- Here we generate the Haskell code for the splice
3548 -- from an input format string.
3549 pr :: String -> ExpQ
3550 pr s = gen (parse s)
3553 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3556 $ ghc --make -fth main.hs -o main.exe
3559 <para>Run "main.exe" and here is your output:</para>
3570 <!-- ===================== Arrow notation =================== -->
3572 <sect1 id="arrow-notation">
3573 <title>Arrow notation
3576 <para>Arrows are a generalization of monads introduced by John Hughes.
3577 For more details, see
3582 “Generalising Monads to Arrows”,
3583 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3584 pp67–111, May 2000.
3590 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3591 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3597 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3598 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3604 and the arrows web page at
3605 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3606 With the <option>-farrows</option> flag, GHC supports the arrow
3607 notation described in the second of these papers.
3608 What follows is a brief introduction to the notation;
3609 it won't make much sense unless you've read Hughes's paper.
3610 This notation is translated to ordinary Haskell,
3611 using combinators from the
3612 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3616 <para>The extension adds a new kind of expression for defining arrows:
3618 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
3619 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3621 where <literal>proc</literal> is a new keyword.
3622 The variables of the pattern are bound in the body of the
3623 <literal>proc</literal>-expression,
3624 which is a new sort of thing called a <firstterm>command</firstterm>.
3625 The syntax of commands is as follows:
3627 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
3628 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
3629 | <replaceable>cmd</replaceable><superscript>0</superscript>
3631 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
3632 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
3633 infix operators as for expressions, and
3635 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
3636 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
3637 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
3638 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
3639 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
3640 | <replaceable>fcmd</replaceable>
3642 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
3643 | ( <replaceable>cmd</replaceable> )
3644 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
3646 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
3647 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
3648 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
3649 | <replaceable>cmd</replaceable>
3651 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
3652 except that the bodies are commands instead of expressions.
3656 Commands produce values, but (like monadic computations)
3657 may yield more than one value,
3658 or none, and may do other things as well.
3659 For the most part, familiarity with monadic notation is a good guide to
3661 However the values of expressions, even monadic ones,
3662 are determined by the values of the variables they contain;
3663 this is not necessarily the case for commands.
3667 A simple example of the new notation is the expression
3669 proc x -> f -< x+1
3671 We call this a <firstterm>procedure</firstterm> or
3672 <firstterm>arrow abstraction</firstterm>.
3673 As with a lambda expression, the variable <literal>x</literal>
3674 is a new variable bound within the <literal>proc</literal>-expression.
3675 It refers to the input to the arrow.
3676 In the above example, <literal>-<</literal> is not an identifier but an
3677 new reserved symbol used for building commands from an expression of arrow
3678 type and an expression to be fed as input to that arrow.
3679 (The weird look will make more sense later.)
3680 It may be read as analogue of application for arrows.
3681 The above example is equivalent to the Haskell expression
3683 arr (\ x -> x+1) >>> f
3685 That would make no sense if the expression to the left of
3686 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3687 More generally, the expression to the left of <literal>-<</literal>
3688 may not involve any <firstterm>local variable</firstterm>,
3689 i.e. a variable bound in the current arrow abstraction.
3690 For such a situation there is a variant <literal>-<<</literal>, as in
3692 proc x -> f x -<< x+1
3694 which is equivalent to
3696 arr (\ x -> (f, x+1)) >>> app
3698 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3700 Such an arrow is equivalent to a monad, so if you're using this form
3701 you may find a monadic formulation more convenient.
3705 <title>do-notation for commands</title>
3708 Another form of command is a form of <literal>do</literal>-notation.
3709 For example, you can write
3718 You can read this much like ordinary <literal>do</literal>-notation,
3719 but with commands in place of monadic expressions.
3720 The first line sends the value of <literal>x+1</literal> as an input to
3721 the arrow <literal>f</literal>, and matches its output against
3722 <literal>y</literal>.
3723 In the next line, the output is discarded.
3724 The arrow <function>returnA</function> is defined in the
3725 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3726 module as <literal>arr id</literal>.
3727 The above example is treated as an abbreviation for
3729 arr (\ x -> (x, x)) >>>
3730 first (arr (\ x -> x+1) >>> f) >>>
3731 arr (\ (y, x) -> (y, (x, y))) >>>
3732 first (arr (\ y -> 2*y) >>> g) >>>
3734 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3735 first (arr (\ (x, z) -> x*z) >>> h) >>>
3736 arr (\ (t, z) -> t+z) >>>
3739 Note that variables not used later in the composition are projected out.
3740 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
3742 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3743 module, this reduces to
3745 arr (\ x -> (x+1, x)) >>>
3747 arr (\ (y, x) -> (2*y, (x, y))) >>>
3749 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3751 arr (\ (t, z) -> t+z)
3753 which is what you might have written by hand.
3754 With arrow notation, GHC keeps track of all those tuples of variables for you.
3758 Note that although the above translation suggests that
3759 <literal>let</literal>-bound variables like <literal>z</literal> must be
3760 monomorphic, the actual translation produces Core,
3761 so polymorphic variables are allowed.
3765 It's also possible to have mutually recursive bindings,
3766 using the new <literal>rec</literal> keyword, as in the following example:
3768 counter :: ArrowCircuit a => a Bool Int
3769 counter = proc reset -> do
3770 rec output <- returnA -< if reset then 0 else next
3771 next <- delay 0 -< output+1
3772 returnA -< output
3774 The translation of such forms uses the <function>loop</function> combinator,
3775 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3781 <title>Conditional commands</title>
3784 In the previous example, we used a conditional expression to construct the
3786 Sometimes we want to conditionally execute different commands, as in
3793 which is translated to
3795 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3796 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3798 Since the translation uses <function>|||</function>,
3799 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3803 There are also <literal>case</literal> commands, like
3809 y <- h -< (x1, x2)
3813 The syntax is the same as for <literal>case</literal> expressions,
3814 except that the bodies of the alternatives are commands rather than expressions.
3815 The translation is similar to that of <literal>if</literal> commands.
3821 <title>Defining your own control structures</title>
3824 As we're seen, arrow notation provides constructs,
3825 modelled on those for expressions,
3826 for sequencing, value recursion and conditionals.
3827 But suitable combinators,
3828 which you can define in ordinary Haskell,
3829 may also be used to build new commands out of existing ones.
3830 The basic idea is that a command defines an arrow from environments to values.
3831 These environments assign values to the free local variables of the command.
3832 Thus combinators that produce arrows from arrows
3833 may also be used to build commands from commands.
3834 For example, the <literal>ArrowChoice</literal> class includes a combinator
3836 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3838 so we can use it to build commands:
3840 expr' = proc x -> do
3843 symbol Plus -< ()
3844 y <- term -< ()
3847 symbol Minus -< ()
3848 y <- term -< ()
3851 (The <literal>do</literal> on the first line is needed to prevent the first
3852 <literal><+> ...</literal> from being interpreted as part of the
3853 expression on the previous line.)
3854 This is equivalent to
3856 expr' = (proc x -> returnA -< x)
3857 <+> (proc x -> do
3858 symbol Plus -< ()
3859 y <- term -< ()
3861 <+> (proc x -> do
3862 symbol Minus -< ()
3863 y <- term -< ()
3866 It is essential that this operator be polymorphic in <literal>e</literal>
3867 (representing the environment input to the command
3868 and thence to its subcommands)
3869 and satisfy the corresponding naturality property
3871 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3873 at least for strict <literal>k</literal>.
3874 (This should be automatic if you're not using <function>seq</function>.)
3875 This ensures that environments seen by the subcommands are environments
3876 of the whole command,
3877 and also allows the translation to safely trim these environments.
3878 The operator must also not use any variable defined within the current
3883 We could define our own operator
3885 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3886 untilA body cond = proc x ->
3887 if cond x then returnA -< ()
3890 untilA body cond -< x
3892 and use it in the same way.
3893 Of course this infix syntax only makes sense for binary operators;
3894 there is also a more general syntax involving special brackets:
3898 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3905 <title>Primitive constructs</title>
3908 Some operators will need to pass additional inputs to their subcommands.
3909 For example, in an arrow type supporting exceptions,
3910 the operator that attaches an exception handler will wish to pass the
3911 exception that occurred to the handler.
3912 Such an operator might have a type
3914 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3916 where <literal>Ex</literal> is the type of exceptions handled.
3917 You could then use this with arrow notation by writing a command
3919 body `handleA` \ ex -> handler
3921 so that if an exception is raised in the command <literal>body</literal>,
3922 the variable <literal>ex</literal> is bound to the value of the exception
3923 and the command <literal>handler</literal>,
3924 which typically refers to <literal>ex</literal>, is entered.
3925 Though the syntax here looks like a functional lambda,
3926 we are talking about commands, and something different is going on.
3927 The input to the arrow represented by a command consists of values for
3928 the free local variables in the command, plus a stack of anonymous values.
3929 In all the prior examples, this stack was empty.
3930 In the second argument to <function>handleA</function>,
3931 this stack consists of one value, the value of the exception.
3932 The command form of lambda merely gives this value a name.
3937 the values on the stack are paired to the right of the environment.
3938 So operators like <function>handleA</function> that pass
3939 extra inputs to their subcommands can be designed for use with the notation
3940 by pairing the values with the environment in this way.
3941 More precisely, the type of each argument of the operator (and its result)
3942 should have the form
3944 a (...(e,t1), ... tn) t
3946 where <replaceable>e</replaceable> is a polymorphic variable
3947 (representing the environment)
3948 and <replaceable>ti</replaceable> are the types of the values on the stack,
3949 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3950 The polymorphic variable <replaceable>e</replaceable> must not occur in
3951 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3952 <replaceable>t</replaceable>.
3953 However the arrows involved need not be the same.
3954 Here are some more examples of suitable operators:
3956 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3957 runReader :: ... => a e c -> a' (e,State) c
3958 runState :: ... => a e c -> a' (e,State) (c,State)
3960 We can supply the extra input required by commands built with the last two
3961 by applying them to ordinary expressions, as in
3965 (|runReader (do { ... })|) s
3967 which adds <literal>s</literal> to the stack of inputs to the command
3968 built using <function>runReader</function>.
3972 The command versions of lambda abstraction and application are analogous to
3973 the expression versions.
3974 In particular, the beta and eta rules describe equivalences of commands.
3975 These three features (operators, lambda abstraction and application)
3976 are the core of the notation; everything else can be built using them,
3977 though the results would be somewhat clumsy.
3978 For example, we could simulate <literal>do</literal>-notation by defining
3980 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3981 u `bind` f = returnA &&& u >>> f
3983 bind_ :: Arrow a => a e b -> a e c -> a e c
3984 u `bind_` f = u `bind` (arr fst >>> f)
3986 We could simulate <literal>if</literal> by defining
3988 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3989 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3996 <title>Differences with the paper</title>
4001 <para>Instead of a single form of arrow application (arrow tail) with two
4002 translations, the implementation provides two forms
4003 <quote><literal>-<</literal></quote> (first-order)
4004 and <quote><literal>-<<</literal></quote> (higher-order).
4009 <para>User-defined operators are flagged with banana brackets instead of
4010 a new <literal>form</literal> keyword.
4019 <title>Portability</title>
4022 Although only GHC implements arrow notation directly,
4023 there is also a preprocessor
4025 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4026 that translates arrow notation into Haskell 98
4027 for use with other Haskell systems.
4028 You would still want to check arrow programs with GHC;
4029 tracing type errors in the preprocessor output is not easy.
4030 Modules intended for both GHC and the preprocessor must observe some
4031 additional restrictions:
4036 The module must import
4037 <ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
4043 The preprocessor cannot cope with other Haskell extensions.
4044 These would have to go in separate modules.
4050 Because the preprocessor targets Haskell (rather than Core),
4051 <literal>let</literal>-bound variables are monomorphic.
4062 <!-- ==================== ASSERTIONS ================= -->
4064 <sect1 id="sec-assertions">
4066 <indexterm><primary>Assertions</primary></indexterm>
4070 If you want to make use of assertions in your standard Haskell code, you
4071 could define a function like the following:
4077 assert :: Bool -> a -> a
4078 assert False x = error "assertion failed!"
4085 which works, but gives you back a less than useful error message --
4086 an assertion failed, but which and where?
4090 One way out is to define an extended <function>assert</function> function which also
4091 takes a descriptive string to include in the error message and
4092 perhaps combine this with the use of a pre-processor which inserts
4093 the source location where <function>assert</function> was used.
4097 Ghc offers a helping hand here, doing all of this for you. For every
4098 use of <function>assert</function> in the user's source:
4104 kelvinToC :: Double -> Double
4105 kelvinToC k = assert (k >= 0.0) (k+273.15)
4111 Ghc will rewrite this to also include the source location where the
4118 assert pred val ==> assertError "Main.hs|15" pred val
4124 The rewrite is only performed by the compiler when it spots
4125 applications of <function>Control.Exception.assert</function>, so you
4126 can still define and use your own versions of
4127 <function>assert</function>, should you so wish. If not, import
4128 <literal>Control.Exception</literal> to make use
4129 <function>assert</function> in your code.
4133 To have the compiler ignore uses of assert, use the compiler option
4134 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
4135 option</primary></indexterm> That is, expressions of the form
4136 <literal>assert pred e</literal> will be rewritten to
4137 <literal>e</literal>.
4141 Assertion failures can be caught, see the documentation for the
4142 <literal>Control.Exception</literal> library for the details.
4148 <!-- =============================== PRAGMAS =========================== -->
4150 <sect1 id="pragmas">
4151 <title>Pragmas</title>
4153 <indexterm><primary>pragma</primary></indexterm>
4155 <para>GHC supports several pragmas, or instructions to the
4156 compiler placed in the source code. Pragmas don't normally affect
4157 the meaning of the program, but they might affect the efficiency
4158 of the generated code.</para>
4160 <para>Pragmas all take the form
4162 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4164 where <replaceable>word</replaceable> indicates the type of
4165 pragma, and is followed optionally by information specific to that
4166 type of pragma. Case is ignored in
4167 <replaceable>word</replaceable>. The various values for
4168 <replaceable>word</replaceable> that GHC understands are described
4169 in the following sections; any pragma encountered with an
4170 unrecognised <replaceable>word</replaceable> is (silently)
4173 <sect2 id="deprecated-pragma">
4174 <title>DEPRECATED pragma</title>
4175 <indexterm><primary>DEPRECATED</primary>
4178 <para>The DEPRECATED pragma lets you specify that a particular
4179 function, class, or type, is deprecated. There are two
4184 <para>You can deprecate an entire module thus:</para>
4186 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4189 <para>When you compile any module that import
4190 <literal>Wibble</literal>, GHC will print the specified
4195 <para>You can deprecate a function, class, or type, with the
4196 following top-level declaration:</para>
4198 {-# DEPRECATED f, C, T "Don't use these" #-}
4200 <para>When you compile any module that imports and uses any
4201 of the specified entities, GHC will print the specified
4205 Any use of the deprecated item, or of anything from a deprecated
4206 module, will be flagged with an appropriate message. However,
4207 deprecations are not reported for
4208 (a) uses of a deprecated function within its defining module, and
4209 (b) uses of a deprecated function in an export list.
4210 The latter reduces spurious complaints within a library
4211 in which one module gathers together and re-exports
4212 the exports of several others.
4214 <para>You can suppress the warnings with the flag
4215 <option>-fno-warn-deprecations</option>.</para>
4218 <sect2 id="include-pragma">
4219 <title>INCLUDE pragma</title>
4221 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4222 of C header files that should be <literal>#include</literal>'d into
4223 the C source code generated by the compiler for the current module (if
4224 compiling via C). For example:</para>
4227 {-# INCLUDE "foo.h" #-}
4228 {-# INCLUDE <stdio.h> #-}</programlisting>
4230 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4231 your source file with any <literal>OPTIONS_GHC</literal>
4234 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4235 to the <option>-#include</option> option (<xref
4236 linkend="options-C-compiler" />), because the
4237 <literal>INCLUDE</literal> pragma is understood by other
4238 compilers. Yet another alternative is to add the include file to each
4239 <literal>foreign import</literal> declaration in your code, but we
4240 don't recommend using this approach with GHC.</para>
4243 <sect2 id="inline-noinline-pragma">
4244 <title>INLINE and NOINLINE pragmas</title>
4246 <para>These pragmas control the inlining of function
4249 <sect3 id="inline-pragma">
4250 <title>INLINE pragma</title>
4251 <indexterm><primary>INLINE</primary></indexterm>
4253 <para>GHC (with <option>-O</option>, as always) tries to
4254 inline (or “unfold”) functions/values that are
4255 “small enough,” thus avoiding the call overhead
4256 and possibly exposing other more-wonderful optimisations.
4257 Normally, if GHC decides a function is “too
4258 expensive” to inline, it will not do so, nor will it
4259 export that unfolding for other modules to use.</para>
4261 <para>The sledgehammer you can bring to bear is the
4262 <literal>INLINE</literal><indexterm><primary>INLINE
4263 pragma</primary></indexterm> pragma, used thusly:</para>
4266 key_function :: Int -> String -> (Bool, Double)
4268 #ifdef __GLASGOW_HASKELL__
4269 {-# INLINE key_function #-}
4273 <para>(You don't need to do the C pre-processor carry-on
4274 unless you're going to stick the code through HBC—it
4275 doesn't like <literal>INLINE</literal> pragmas.)</para>
4277 <para>The major effect of an <literal>INLINE</literal> pragma
4278 is to declare a function's “cost” to be very low.
4279 The normal unfolding machinery will then be very keen to
4282 <para>Syntactically, an <literal>INLINE</literal> pragma for a
4283 function can be put anywhere its type signature could be
4286 <para><literal>INLINE</literal> pragmas are a particularly
4288 <literal>then</literal>/<literal>return</literal> (or
4289 <literal>bind</literal>/<literal>unit</literal>) functions in
4290 a monad. For example, in GHC's own
4291 <literal>UniqueSupply</literal> monad code, we have:</para>
4294 #ifdef __GLASGOW_HASKELL__
4295 {-# INLINE thenUs #-}
4296 {-# INLINE returnUs #-}
4300 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4301 linkend="noinline-pragma"/>).</para>
4304 <sect3 id="noinline-pragma">
4305 <title>NOINLINE pragma</title>
4307 <indexterm><primary>NOINLINE</primary></indexterm>
4308 <indexterm><primary>NOTINLINE</primary></indexterm>
4310 <para>The <literal>NOINLINE</literal> pragma does exactly what
4311 you'd expect: it stops the named function from being inlined
4312 by the compiler. You shouldn't ever need to do this, unless
4313 you're very cautious about code size.</para>
4315 <para><literal>NOTINLINE</literal> is a synonym for
4316 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
4317 specified by Haskell 98 as the standard way to disable
4318 inlining, so it should be used if you want your code to be
4322 <sect3 id="phase-control">
4323 <title>Phase control</title>
4325 <para> Sometimes you want to control exactly when in GHC's
4326 pipeline the INLINE pragma is switched on. Inlining happens
4327 only during runs of the <emphasis>simplifier</emphasis>. Each
4328 run of the simplifier has a different <emphasis>phase
4329 number</emphasis>; the phase number decreases towards zero.
4330 If you use <option>-dverbose-core2core</option> you'll see the
4331 sequence of phase numbers for successive runs of the
4332 simplifier. In an INLINE pragma you can optionally specify a
4333 phase number, thus:</para>
4337 <para>You can say "inline <literal>f</literal> in Phase 2
4338 and all subsequent phases":
4340 {-# INLINE [2] f #-}
4346 <para>You can say "inline <literal>g</literal> in all
4347 phases up to, but not including, Phase 3":
4349 {-# INLINE [~3] g #-}
4355 <para>If you omit the phase indicator, you mean "inline in
4360 <para>You can use a phase number on a NOINLINE pragma too:</para>
4364 <para>You can say "do not inline <literal>f</literal>
4365 until Phase 2; in Phase 2 and subsequently behave as if
4366 there was no pragma at all":
4368 {-# NOINLINE [2] f #-}
4374 <para>You can say "do not inline <literal>g</literal> in
4375 Phase 3 or any subsequent phase; before that, behave as if
4376 there was no pragma":
4378 {-# NOINLINE [~3] g #-}
4384 <para>If you omit the phase indicator, you mean "never
4385 inline this function".</para>
4389 <para>The same phase-numbering control is available for RULES
4390 (<xref linkend="rewrite-rules"/>).</para>
4394 <sect2 id="line-pragma">
4395 <title>LINE pragma</title>
4397 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4398 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4399 <para>This pragma is similar to C's <literal>#line</literal>
4400 pragma, and is mainly for use in automatically generated Haskell
4401 code. It lets you specify the line number and filename of the
4402 original code; for example</para>
4405 {-# LINE 42 "Foo.vhs" #-}
4408 <para>if you'd generated the current file from something called
4409 <filename>Foo.vhs</filename> and this line corresponds to line
4410 42 in the original. GHC will adjust its error messages to refer
4411 to the line/file named in the <literal>LINE</literal>
4415 <sect2 id="options-pragma">
4416 <title>OPTIONS_GHC pragma</title>
4417 <indexterm><primary>OPTIONS_GHC</primary>
4419 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
4422 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
4423 additional options that are given to the compiler when compiling
4424 this source file. See <xref linkend="source-file-options"/> for
4427 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
4428 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
4432 <title>RULES pragma</title>
4434 <para>The RULES pragma lets you specify rewrite rules. It is
4435 described in <xref linkend="rewrite-rules"/>.</para>
4438 <sect2 id="specialize-pragma">
4439 <title>SPECIALIZE pragma</title>
4441 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4442 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4443 <indexterm><primary>overloading, death to</primary></indexterm>
4445 <para>(UK spelling also accepted.) For key overloaded
4446 functions, you can create extra versions (NB: more code space)
4447 specialised to particular types. Thus, if you have an
4448 overloaded function:</para>
4451 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4454 <para>If it is heavily used on lists with
4455 <literal>Widget</literal> keys, you could specialise it as
4459 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4462 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4463 be put anywhere its type signature could be put.</para>
4465 <para>A <literal>SPECIALIZE</literal> has the effect of generating
4466 (a) a specialised version of the function and (b) a rewrite rule
4467 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
4468 un-specialised function into a call to the specialised one.</para>
4470 <para>In earlier versions of GHC, it was possible to provide your own
4471 specialised function for a given type:
4474 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
4477 This feature has been removed, as it is now subsumed by the
4478 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
4482 <sect2 id="specialize-instance-pragma">
4483 <title>SPECIALIZE instance pragma
4487 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4488 <indexterm><primary>overloading, death to</primary></indexterm>
4489 Same idea, except for instance declarations. For example:
4492 instance (Eq a) => Eq (Foo a) where {
4493 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4497 The pragma must occur inside the <literal>where</literal> part
4498 of the instance declaration.
4501 Compatible with HBC, by the way, except perhaps in the placement
4507 <sect2 id="unpack-pragma">
4508 <title>UNPACK pragma</title>
4510 <indexterm><primary>UNPACK</primary></indexterm>
4512 <para>The <literal>UNPACK</literal> indicates to the compiler
4513 that it should unpack the contents of a constructor field into
4514 the constructor itself, removing a level of indirection. For
4518 data T = T {-# UNPACK #-} !Float
4519 {-# UNPACK #-} !Float
4522 <para>will create a constructor <literal>T</literal> containing
4523 two unboxed floats. This may not always be an optimisation: if
4524 the <function>T</function> constructor is scrutinised and the
4525 floats passed to a non-strict function for example, they will
4526 have to be reboxed (this is done automatically by the
4529 <para>Unpacking constructor fields should only be used in
4530 conjunction with <option>-O</option>, in order to expose
4531 unfoldings to the compiler so the reboxing can be removed as
4532 often as possible. For example:</para>
4536 f (T f1 f2) = f1 + f2
4539 <para>The compiler will avoid reboxing <function>f1</function>
4540 and <function>f2</function> by inlining <function>+</function>
4541 on floats, but only when <option>-O</option> is on.</para>
4543 <para>Any single-constructor data is eligible for unpacking; for
4547 data T = T {-# UNPACK #-} !(Int,Int)
4550 <para>will store the two <literal>Int</literal>s directly in the
4551 <function>T</function> constructor, by flattening the pair.
4552 Multi-level unpacking is also supported:</para>
4555 data T = T {-# UNPACK #-} !S
4556 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4559 <para>will store two unboxed <literal>Int#</literal>s
4560 directly in the <function>T</function> constructor. The
4561 unpacker can see through newtypes, too.</para>
4563 <para>If a field cannot be unpacked, you will not get a warning,
4564 so it might be an idea to check the generated code with
4565 <option>-ddump-simpl</option>.</para>
4567 <para>See also the <option>-funbox-strict-fields</option> flag,
4568 which essentially has the effect of adding
4569 <literal>{-# UNPACK #-}</literal> to every strict
4570 constructor field.</para>
4575 <!-- ======================= REWRITE RULES ======================== -->
4577 <sect1 id="rewrite-rules">
4578 <title>Rewrite rules
4580 <indexterm><primary>RULES pragma</primary></indexterm>
4581 <indexterm><primary>pragma, RULES</primary></indexterm>
4582 <indexterm><primary>rewrite rules</primary></indexterm></title>
4585 The programmer can specify rewrite rules as part of the source program
4586 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4587 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
4588 and (b) the <option>-frules-off</option> flag
4589 (<xref linkend="options-f"/>) is not specified.
4597 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4604 <title>Syntax</title>
4607 From a syntactic point of view:
4613 There may be zero or more rules in a <literal>RULES</literal> pragma.
4620 Each rule has a name, enclosed in double quotes. The name itself has
4621 no significance at all. It is only used when reporting how many times the rule fired.
4627 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
4628 immediately after the name of the rule. Thus:
4631 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4634 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4635 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4644 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4645 is set, so you must lay out your rules starting in the same column as the
4646 enclosing definitions.
4653 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4654 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4655 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4656 by spaces, just like in a type <literal>forall</literal>.
4662 A pattern variable may optionally have a type signature.
4663 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4664 For example, here is the <literal>foldr/build</literal> rule:
4667 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4668 foldr k z (build g) = g k z
4671 Since <function>g</function> has a polymorphic type, it must have a type signature.
4678 The left hand side of a rule must consist of a top-level variable applied
4679 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4682 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4683 "wrong2" forall f. f True = True
4686 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4693 A rule does not need to be in the same module as (any of) the
4694 variables it mentions, though of course they need to be in scope.
4700 Rules are automatically exported from a module, just as instance declarations are.
4711 <title>Semantics</title>
4714 From a semantic point of view:
4720 Rules are only applied if you use the <option>-O</option> flag.
4726 Rules are regarded as left-to-right rewrite rules.
4727 When GHC finds an expression that is a substitution instance of the LHS
4728 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4729 By "a substitution instance" we mean that the LHS can be made equal to the
4730 expression by substituting for the pattern variables.
4737 The LHS and RHS of a rule are typechecked, and must have the
4745 GHC makes absolutely no attempt to verify that the LHS and RHS
4746 of a rule have the same meaning. That is undecidable in general, and
4747 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4754 GHC makes no attempt to make sure that the rules are confluent or
4755 terminating. For example:
4758 "loop" forall x,y. f x y = f y x
4761 This rule will cause the compiler to go into an infinite loop.
4768 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4774 GHC currently uses a very simple, syntactic, matching algorithm
4775 for matching a rule LHS with an expression. It seeks a substitution
4776 which makes the LHS and expression syntactically equal modulo alpha
4777 conversion. The pattern (rule), but not the expression, is eta-expanded if
4778 necessary. (Eta-expanding the expression can lead to laziness bugs.)
4779 But not beta conversion (that's called higher-order matching).
4783 Matching is carried out on GHC's intermediate language, which includes
4784 type abstractions and applications. So a rule only matches if the
4785 types match too. See <xref linkend="rule-spec"/> below.
4791 GHC keeps trying to apply the rules as it optimises the program.
4792 For example, consider:
4801 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4802 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
4803 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
4804 not be substituted, and the rule would not fire.
4811 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4812 that appears on the LHS of a rule</emphasis>, because once you have substituted
4813 for something you can't match against it (given the simple minded
4814 matching). So if you write the rule
4817 "map/map" forall f,g. map f . map g = map (f.g)
4820 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4821 It will only match something written with explicit use of ".".
4822 Well, not quite. It <emphasis>will</emphasis> match the expression
4828 where <function>wibble</function> is defined:
4831 wibble f g = map f . map g
4834 because <function>wibble</function> will be inlined (it's small).
4836 Later on in compilation, GHC starts inlining even things on the
4837 LHS of rules, but still leaves the rules enabled. This inlining
4838 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4845 All rules are implicitly exported from the module, and are therefore
4846 in force in any module that imports the module that defined the rule, directly
4847 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4848 in force when compiling A.) The situation is very similar to that for instance
4860 <title>List fusion</title>
4863 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4864 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4865 intermediate list should be eliminated entirely.
4869 The following are good producers:
4881 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4887 Explicit lists (e.g. <literal>[True, False]</literal>)
4893 The cons constructor (e.g <literal>3:4:[]</literal>)
4899 <function>++</function>
4905 <function>map</function>
4911 <function>filter</function>
4917 <function>iterate</function>, <function>repeat</function>
4923 <function>zip</function>, <function>zipWith</function>
4932 The following are good consumers:
4944 <function>array</function> (on its second argument)
4950 <function>length</function>
4956 <function>++</function> (on its first argument)
4962 <function>foldr</function>
4968 <function>map</function>
4974 <function>filter</function>
4980 <function>concat</function>
4986 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4992 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4993 will fuse with one but not the other)
4999 <function>partition</function>
5005 <function>head</function>
5011 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5017 <function>sequence_</function>
5023 <function>msum</function>
5029 <function>sortBy</function>
5038 So, for example, the following should generate no intermediate lists:
5041 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5047 This list could readily be extended; if there are Prelude functions that you use
5048 a lot which are not included, please tell us.
5052 If you want to write your own good consumers or producers, look at the
5053 Prelude definitions of the above functions to see how to do so.
5058 <sect2 id="rule-spec">
5059 <title>Specialisation
5063 Rewrite rules can be used to get the same effect as a feature
5064 present in earlier versions of GHC.
5065 For example, suppose that:
5068 genericLookup :: Ord a => Table a b -> a -> b
5069 intLookup :: Table Int b -> Int -> b
5072 where <function>intLookup</function> is an implementation of
5073 <function>genericLookup</function> that works very fast for
5074 keys of type <literal>Int</literal>. You might wish
5075 to tell GHC to use <function>intLookup</function> instead of
5076 <function>genericLookup</function> whenever the latter was called with
5077 type <literal>Table Int b -> Int -> b</literal>.
5078 It used to be possible to write
5081 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5084 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5087 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5090 This slightly odd-looking rule instructs GHC to replace
5091 <function>genericLookup</function> by <function>intLookup</function>
5092 <emphasis>whenever the types match</emphasis>.
5093 What is more, this rule does not need to be in the same
5094 file as <function>genericLookup</function>, unlike the
5095 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5096 have an original definition available to specialise).
5099 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5100 <function>intLookup</function> really behaves as a specialised version
5101 of <function>genericLookup</function>!!!</para>
5103 <para>An example in which using <literal>RULES</literal> for
5104 specialisation will Win Big:
5107 toDouble :: Real a => a -> Double
5108 toDouble = fromRational . toRational
5110 {-# RULES "toDouble/Int" toDouble = i2d #-}
5111 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5114 The <function>i2d</function> function is virtually one machine
5115 instruction; the default conversion—via an intermediate
5116 <literal>Rational</literal>—is obscenely expensive by
5123 <title>Controlling what's going on</title>
5131 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5137 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5138 If you add <option>-dppr-debug</option> you get a more detailed listing.
5144 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5147 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5148 {-# INLINE build #-}
5152 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5153 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5154 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5155 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5162 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5163 see how to write rules that will do fusion and yet give an efficient
5164 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5174 <sect2 id="core-pragma">
5175 <title>CORE pragma</title>
5177 <indexterm><primary>CORE pragma</primary></indexterm>
5178 <indexterm><primary>pragma, CORE</primary></indexterm>
5179 <indexterm><primary>core, annotation</primary></indexterm>
5182 The external core format supports <quote>Note</quote> annotations;
5183 the <literal>CORE</literal> pragma gives a way to specify what these
5184 should be in your Haskell source code. Syntactically, core
5185 annotations are attached to expressions and take a Haskell string
5186 literal as an argument. The following function definition shows an
5190 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5193 Semantically, this is equivalent to:
5201 However, when external for is generated (via
5202 <option>-fext-core</option>), there will be Notes attached to the
5203 expressions <function>show</function> and <varname>x</varname>.
5204 The core function declaration for <function>f</function> is:
5208 f :: %forall a . GHCziShow.ZCTShow a ->
5209 a -> GHCziBase.ZMZN GHCziBase.Char =
5210 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
5212 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
5214 (tpl1::GHCziBase.Int ->
5216 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5218 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
5219 (tpl3::GHCziBase.ZMZN a ->
5220 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
5228 Here, we can see that the function <function>show</function> (which
5229 has been expanded out to a case expression over the Show dictionary)
5230 has a <literal>%note</literal> attached to it, as does the
5231 expression <varname>eta</varname> (which used to be called
5232 <varname>x</varname>).
5239 <sect1 id="generic-classes">
5240 <title>Generic classes</title>
5242 <para>(Note: support for generic classes is currently broken in
5246 The ideas behind this extension are described in detail in "Derivable type classes",
5247 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
5248 An example will give the idea:
5256 fromBin :: [Int] -> (a, [Int])
5258 toBin {| Unit |} Unit = []
5259 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5260 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5261 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5263 fromBin {| Unit |} bs = (Unit, bs)
5264 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5265 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5266 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5267 (y,bs'') = fromBin bs'
5270 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5271 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5272 which are defined thus in the library module <literal>Generics</literal>:
5276 data a :+: b = Inl a | Inr b
5277 data a :*: b = a :*: b
5280 Now you can make a data type into an instance of Bin like this:
5282 instance (Bin a, Bin b) => Bin (a,b)
5283 instance Bin a => Bin [a]
5285 That is, just leave off the "where" clause. Of course, you can put in the
5286 where clause and over-ride whichever methods you please.
5290 <title> Using generics </title>
5291 <para>To use generics you need to</para>
5294 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5295 <option>-fgenerics</option> (to generate extra per-data-type code),
5296 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5300 <para>Import the module <literal>Generics</literal> from the
5301 <literal>lang</literal> package. This import brings into
5302 scope the data types <literal>Unit</literal>,
5303 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5304 don't need this import if you don't mention these types
5305 explicitly; for example, if you are simply giving instance
5306 declarations.)</para>
5311 <sect2> <title> Changes wrt the paper </title>
5313 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5314 can be written infix (indeed, you can now use
5315 any operator starting in a colon as an infix type constructor). Also note that
5316 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5317 Finally, note that the syntax of the type patterns in the class declaration
5318 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5319 alone would ambiguous when they appear on right hand sides (an extension we
5320 anticipate wanting).
5324 <sect2> <title>Terminology and restrictions</title>
5326 Terminology. A "generic default method" in a class declaration
5327 is one that is defined using type patterns as above.
5328 A "polymorphic default method" is a default method defined as in Haskell 98.
5329 A "generic class declaration" is a class declaration with at least one
5330 generic default method.
5338 Alas, we do not yet implement the stuff about constructor names and
5345 A generic class can have only one parameter; you can't have a generic
5346 multi-parameter class.
5352 A default method must be defined entirely using type patterns, or entirely
5353 without. So this is illegal:
5356 op :: a -> (a, Bool)
5357 op {| Unit |} Unit = (Unit, True)
5360 However it is perfectly OK for some methods of a generic class to have
5361 generic default methods and others to have polymorphic default methods.
5367 The type variable(s) in the type pattern for a generic method declaration
5368 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:
5372 op {| p :*: q |} (x :*: y) = op (x :: p)
5380 The type patterns in a generic default method must take one of the forms:
5386 where "a" and "b" are type variables. Furthermore, all the type patterns for
5387 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5388 must use the same type variables. So this is illegal:
5392 op {| a :+: b |} (Inl x) = True
5393 op {| p :+: q |} (Inr y) = False
5395 The type patterns must be identical, even in equations for different methods of the class.
5396 So this too is illegal:
5400 op1 {| a :*: b |} (x :*: y) = True
5403 op2 {| p :*: q |} (x :*: y) = False
5405 (The reason for this restriction is that we gather all the equations for a particular type consructor
5406 into a single generic instance declaration.)
5412 A generic method declaration must give a case for each of the three type constructors.
5418 The type for a generic method can be built only from:
5420 <listitem> <para> Function arrows </para> </listitem>
5421 <listitem> <para> Type variables </para> </listitem>
5422 <listitem> <para> Tuples </para> </listitem>
5423 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5425 Here are some example type signatures for generic methods:
5428 op2 :: Bool -> (a,Bool)
5429 op3 :: [Int] -> a -> a
5432 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5436 This restriction is an implementation restriction: we just havn't got around to
5437 implementing the necessary bidirectional maps over arbitrary type constructors.
5438 It would be relatively easy to add specific type constructors, such as Maybe and list,
5439 to the ones that are allowed.</para>
5444 In an instance declaration for a generic class, the idea is that the compiler
5445 will fill in the methods for you, based on the generic templates. However it can only
5450 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5455 No constructor of the instance type has unboxed fields.
5459 (Of course, these things can only arise if you are already using GHC extensions.)
5460 However, you can still give an instance declarations for types which break these rules,
5461 provided you give explicit code to override any generic default methods.
5469 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5470 what the compiler does with generic declarations.
5475 <sect2> <title> Another example </title>
5477 Just to finish with, here's another example I rather like:
5481 nCons {| Unit |} _ = 1
5482 nCons {| a :*: b |} _ = 1
5483 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5486 tag {| Unit |} _ = 1
5487 tag {| a :*: b |} _ = 1
5488 tag {| a :+: b |} (Inl x) = tag x
5489 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5498 ;;; Local Variables: ***
5500 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
projects / ghc-hetmet.git / blob