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"/>). This flag must
248 be given explicitly; it is no longer implied by
249 <option>-fglasgow-exts</option>.</para>
251 <para>Syntax stolen: <literal>[|</literal>,
252 <literal>[e|</literal>, <literal>[p|</literal>,
253 <literal>[d|</literal>, <literal>[t|</literal>,
254 <literal>$(</literal>,
255 <literal>$<replaceable>varid</replaceable></literal>.</para>
262 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
263 <!-- included from primitives.sgml -->
264 <!-- &primitives; -->
265 <sect1 id="primitives">
266 <title>Unboxed types and primitive operations</title>
268 <para>GHC is built on a raft of primitive data types and operations.
269 While you really can use this stuff to write fast code,
270 we generally find it a lot less painful, and more satisfying in the
271 long run, to use higher-level language features and libraries. With
272 any luck, the code you write will be optimised to the efficient
273 unboxed version in any case. And if it isn't, we'd like to know
276 <para>We do not currently have good, up-to-date documentation about the
277 primitives, perhaps because they are mainly intended for internal use.
278 There used to be a long section about them here in the User Guide, but it
279 became out of date, and wrong information is worse than none.</para>
281 <para>The Real Truth about what primitive types there are, and what operations
282 work over those types, is held in the file
283 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
284 This file is used directly to generate GHC's primitive-operation definitions, so
285 it is always correct! It is also intended for processing into text.</para>
288 the result of such processing is part of the description of the
290 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
291 Core language</ulink>.
292 So that document is a good place to look for a type-set version.
293 We would be very happy if someone wanted to volunteer to produce an SGML
294 back end to the program that processes <filename>primops.txt</filename> so that
295 we could include the results here in the User Guide.</para>
297 <para>What follows here is a brief summary of some main points.</para>
299 <sect2 id="glasgow-unboxed">
304 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
307 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
308 that values of that type are represented by a pointer to a heap
309 object. The representation of a Haskell <literal>Int</literal>, for
310 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
311 type, however, is represented by the value itself, no pointers or heap
312 allocation are involved.
316 Unboxed types correspond to the “raw machine” types you
317 would use in C: <literal>Int#</literal> (long int),
318 <literal>Double#</literal> (double), <literal>Addr#</literal>
319 (void *), etc. The <emphasis>primitive operations</emphasis>
320 (PrimOps) on these types are what you might expect; e.g.,
321 <literal>(+#)</literal> is addition on
322 <literal>Int#</literal>s, and is the machine-addition that we all
323 know and love—usually one instruction.
327 Primitive (unboxed) types cannot be defined in Haskell, and are
328 therefore built into the language and compiler. Primitive types are
329 always unlifted; that is, a value of a primitive type cannot be
330 bottom. We use the convention that primitive types, values, and
331 operations have a <literal>#</literal> suffix.
335 Primitive values are often represented by a simple bit-pattern, such
336 as <literal>Int#</literal>, <literal>Float#</literal>,
337 <literal>Double#</literal>. But this is not necessarily the case:
338 a primitive value might be represented by a pointer to a
339 heap-allocated object. Examples include
340 <literal>Array#</literal>, the type of primitive arrays. A
341 primitive array is heap-allocated because it is too big a value to fit
342 in a register, and would be too expensive to copy around; in a sense,
343 it is accidental that it is represented by a pointer. If a pointer
344 represents a primitive value, then it really does point to that value:
345 no unevaluated thunks, no indirections…nothing can be at the
346 other end of the pointer than the primitive value.
347 A numerically-intensive program using unboxed types can
348 go a <emphasis>lot</emphasis> faster than its “standard”
349 counterpart—we saw a threefold speedup on one example.
353 There are some restrictions on the use of primitive types:
355 <listitem><para>The main restriction
356 is that you can't pass a primitive value to a polymorphic
357 function or store one in a polymorphic data type. This rules out
358 things like <literal>[Int#]</literal> (i.e. lists of primitive
359 integers). The reason for this restriction is that polymorphic
360 arguments and constructor fields are assumed to be pointers: if an
361 unboxed integer is stored in one of these, the garbage collector would
362 attempt to follow it, leading to unpredictable space leaks. Or a
363 <function>seq</function> operation on the polymorphic component may
364 attempt to dereference the pointer, with disastrous results. Even
365 worse, the unboxed value might be larger than a pointer
366 (<literal>Double#</literal> for instance).
369 <listitem><para> You cannot bind a variable with an unboxed type
370 in a <emphasis>top-level</emphasis> binding.
372 <listitem><para> You cannot bind a variable with an unboxed type
373 in a <emphasis>recursive</emphasis> binding.
375 <listitem><para> You may bind unboxed variables in a (non-recursive,
376 non-top-level) pattern binding, but any such variable causes the entire
378 to become strict. For example:
380 data Foo = Foo Int Int#
382 f x = let (Foo a b, w) = ..rhs.. in ..body..
384 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
386 is strict, and the program behaves as if you had written
388 data Foo = Foo Int Int#
390 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
399 <sect2 id="unboxed-tuples">
400 <title>Unboxed Tuples
404 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
405 they're available by default with <option>-fglasgow-exts</option>. An
406 unboxed tuple looks like this:
418 where <literal>e_1..e_n</literal> are expressions of any
419 type (primitive or non-primitive). The type of an unboxed tuple looks
424 Unboxed tuples are used for functions that need to return multiple
425 values, but they avoid the heap allocation normally associated with
426 using fully-fledged tuples. When an unboxed tuple is returned, the
427 components are put directly into registers or on the stack; the
428 unboxed tuple itself does not have a composite representation. Many
429 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
431 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
432 tuples to avoid unnecessary allocation during sequences of operations.
436 There are some pretty stringent restrictions on the use of unboxed tuples:
441 Values of unboxed tuple types are subject to the same restrictions as
442 other unboxed types; i.e. they may not be stored in polymorphic data
443 structures or passed to polymorphic functions.
450 No variable can have an unboxed tuple type, nor may a constructor or function
451 argument have an unboxed tuple type. The following are all illegal:
455 data Foo = Foo (# Int, Int #)
457 f :: (# Int, Int #) -> (# Int, Int #)
460 g :: (# Int, Int #) -> Int
463 h x = let y = (# x,x #) in ...
470 The typical use of unboxed tuples is simply to return multiple values,
471 binding those multiple results with a <literal>case</literal> expression, thus:
473 f x y = (# x+1, y-1 #)
474 g x = case f x x of { (# a, b #) -> a + b }
476 You can have an unboxed tuple in a pattern binding, thus
478 f x = let (# p,q #) = h x in ..body..
480 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
481 the resulting binding is lazy like any other Haskell pattern binding. The
482 above example desugars like this:
484 f x = let t = case h x o f{ (# p,q #) -> (p,q)
489 Indeed, the bindings can even be recursive.
496 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
498 <sect1 id="syntax-extns">
499 <title>Syntactic extensions</title>
501 <!-- ====================== HIERARCHICAL MODULES ======================= -->
503 <sect2 id="hierarchical-modules">
504 <title>Hierarchical Modules</title>
506 <para>GHC supports a small extension to the syntax of module
507 names: a module name is allowed to contain a dot
508 <literal>‘.’</literal>. This is also known as the
509 “hierarchical module namespace” extension, because
510 it extends the normally flat Haskell module namespace into a
511 more flexible hierarchy of modules.</para>
513 <para>This extension has very little impact on the language
514 itself; modules names are <emphasis>always</emphasis> fully
515 qualified, so you can just think of the fully qualified module
516 name as <quote>the module name</quote>. In particular, this
517 means that the full module name must be given after the
518 <literal>module</literal> keyword at the beginning of the
519 module; for example, the module <literal>A.B.C</literal> must
522 <programlisting>module A.B.C</programlisting>
525 <para>It is a common strategy to use the <literal>as</literal>
526 keyword to save some typing when using qualified names with
527 hierarchical modules. For example:</para>
530 import qualified Control.Monad.ST.Strict as ST
533 <para>For details on how GHC searches for source and interface
534 files in the presence of hierarchical modules, see <xref
535 linkend="search-path"/>.</para>
537 <para>GHC comes with a large collection of libraries arranged
538 hierarchically; see the accompanying library documentation.
539 There is an ongoing project to create and maintain a stable set
540 of <quote>core</quote> libraries used by several Haskell
541 compilers, and the libraries that GHC comes with represent the
542 current status of that project. For more details, see <ulink
543 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
544 Libraries</ulink>.</para>
548 <!-- ====================== PATTERN GUARDS ======================= -->
550 <sect2 id="pattern-guards">
551 <title>Pattern guards</title>
554 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
555 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.)
559 Suppose we have an abstract data type of finite maps, with a
563 lookup :: FiniteMap -> Int -> Maybe Int
566 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
567 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
571 clunky env var1 var2 | ok1 && ok2 = val1 + val2
572 | otherwise = var1 + var2
583 The auxiliary functions are
587 maybeToBool :: Maybe a -> Bool
588 maybeToBool (Just x) = True
589 maybeToBool Nothing = False
591 expectJust :: Maybe a -> a
592 expectJust (Just x) = x
593 expectJust Nothing = error "Unexpected Nothing"
597 What is <function>clunky</function> doing? The guard <literal>ok1 &&
598 ok2</literal> checks that both lookups succeed, using
599 <function>maybeToBool</function> to convert the <function>Maybe</function>
600 types to booleans. The (lazily evaluated) <function>expectJust</function>
601 calls extract the values from the results of the lookups, and binds the
602 returned values to <varname>val1</varname> and <varname>val2</varname>
603 respectively. If either lookup fails, then clunky takes the
604 <literal>otherwise</literal> case and returns the sum of its arguments.
608 This is certainly legal Haskell, but it is a tremendously verbose and
609 un-obvious way to achieve the desired effect. Arguably, a more direct way
610 to write clunky would be to use case expressions:
614 clunky env var1 var1 = case lookup env var1 of
616 Just val1 -> case lookup env var2 of
618 Just val2 -> val1 + val2
624 This is a bit shorter, but hardly better. Of course, we can rewrite any set
625 of pattern-matching, guarded equations as case expressions; that is
626 precisely what the compiler does when compiling equations! The reason that
627 Haskell provides guarded equations is because they allow us to write down
628 the cases we want to consider, one at a time, independently of each other.
629 This structure is hidden in the case version. Two of the right-hand sides
630 are really the same (<function>fail</function>), and the whole expression
631 tends to become more and more indented.
635 Here is how I would write clunky:
640 | Just val1 <- lookup env var1
641 , Just val2 <- lookup env var2
643 ...other equations for clunky...
647 The semantics should be clear enough. The qualifiers are matched in order.
648 For a <literal><-</literal> qualifier, which I call a pattern guard, the
649 right hand side is evaluated and matched against the pattern on the left.
650 If the match fails then the whole guard fails and the next equation is
651 tried. If it succeeds, then the appropriate binding takes place, and the
652 next qualifier is matched, in the augmented environment. Unlike list
653 comprehensions, however, the type of the expression to the right of the
654 <literal><-</literal> is the same as the type of the pattern to its
655 left. The bindings introduced by pattern guards scope over all the
656 remaining guard qualifiers, and over the right hand side of the equation.
660 Just as with list comprehensions, boolean expressions can be freely mixed
661 with among the pattern guards. For example:
672 Haskell's current guards therefore emerge as a special case, in which the
673 qualifier list has just one element, a boolean expression.
677 <!-- ===================== Recursive do-notation =================== -->
679 <sect2 id="mdo-notation">
680 <title>The recursive do-notation
683 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
684 "A recursive do for Haskell",
685 Levent Erkok, John Launchbury",
686 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
689 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
690 that is, the variables bound in a do-expression are visible only in the textually following
691 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
692 group. It turns out that several applications can benefit from recursive bindings in
693 the do-notation, and this extension provides the necessary syntactic support.
696 Here is a simple (yet contrived) example:
699 import Control.Monad.Fix
701 justOnes = mdo xs <- Just (1:xs)
705 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
709 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
712 class Monad m => MonadFix m where
713 mfix :: (a -> m a) -> m a
716 The function <literal>mfix</literal>
717 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
718 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
719 For details, see the above mentioned reference.
722 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
723 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
724 for Haskell's internal state monad (strict and lazy, respectively).
727 There are three important points in using the recursive-do notation:
730 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
731 than <literal>do</literal>).
735 You should <literal>import Control.Monad.Fix</literal>.
736 (Note: Strictly speaking, this import is required only when you need to refer to the name
737 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
738 are encouraged to always import this module when using the mdo-notation.)
742 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
748 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
749 contains up to date information on recursive monadic bindings.
753 Historical note: The old implementation of the mdo-notation (and most
754 of the existing documents) used the name
755 <literal>MonadRec</literal> for the class and the corresponding library.
756 This name is not supported by GHC.
762 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
764 <sect2 id="parallel-list-comprehensions">
765 <title>Parallel List Comprehensions</title>
766 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
768 <indexterm><primary>parallel list comprehensions</primary>
771 <para>Parallel list comprehensions are a natural extension to list
772 comprehensions. List comprehensions can be thought of as a nice
773 syntax for writing maps and filters. Parallel comprehensions
774 extend this to include the zipWith family.</para>
776 <para>A parallel list comprehension has multiple independent
777 branches of qualifier lists, each separated by a `|' symbol. For
778 example, the following zips together two lists:</para>
781 [ (x, y) | x <- xs | y <- ys ]
784 <para>The behavior of parallel list comprehensions follows that of
785 zip, in that the resulting list will have the same length as the
786 shortest branch.</para>
788 <para>We can define parallel list comprehensions by translation to
789 regular comprehensions. Here's the basic idea:</para>
791 <para>Given a parallel comprehension of the form: </para>
794 [ e | p1 <- e11, p2 <- e12, ...
795 | q1 <- e21, q2 <- e22, ...
800 <para>This will be translated to: </para>
803 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
804 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
809 <para>where `zipN' is the appropriate zip for the given number of
814 <sect2 id="rebindable-syntax">
815 <title>Rebindable syntax</title>
818 <para>GHC allows most kinds of built-in syntax to be rebound by
819 the user, to facilitate replacing the <literal>Prelude</literal>
820 with a home-grown version, for example.</para>
822 <para>You may want to define your own numeric class
823 hierarchy. It completely defeats that purpose if the
824 literal "1" means "<literal>Prelude.fromInteger
825 1</literal>", which is what the Haskell Report specifies.
826 So the <option>-fno-implicit-prelude</option> flag causes
827 the following pieces of built-in syntax to refer to
828 <emphasis>whatever is in scope</emphasis>, not the Prelude
833 <para>An integer literal <literal>368</literal> means
834 "<literal>fromInteger (368::Integer)</literal>", rather than
835 "<literal>Prelude.fromInteger (368::Integer)</literal>".
838 <listitem><para>Fractional literals are handed in just the same way,
839 except that the translation is
840 <literal>fromRational (3.68::Rational)</literal>.
843 <listitem><para>The equality test in an overloaded numeric pattern
844 uses whatever <literal>(==)</literal> is in scope.
847 <listitem><para>The subtraction operation, and the
848 greater-than-or-equal test, in <literal>n+k</literal> patterns
849 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
853 <para>Negation (e.g. "<literal>- (f x)</literal>")
854 means "<literal>negate (f x)</literal>", both in numeric
855 patterns, and expressions.
859 <para>"Do" notation is translated using whatever
860 functions <literal>(>>=)</literal>,
861 <literal>(>>)</literal>, and <literal>fail</literal>,
862 are in scope (not the Prelude
863 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
864 comprehensions, are unaffected. </para></listitem>
868 notation (see <xref linkend="arrow-notation"/>)
869 uses whatever <literal>arr</literal>,
870 <literal>(>>>)</literal>, <literal>first</literal>,
871 <literal>app</literal>, <literal>(|||)</literal> and
872 <literal>loop</literal> functions are in scope. But unlike the
873 other constructs, the types of these functions must match the
874 Prelude types very closely. Details are in flux; if you want
878 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
879 even if that is a little unexpected. For emample, the
880 static semantics of the literal <literal>368</literal>
881 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
882 <literal>fromInteger</literal> to have any of the types:
884 fromInteger :: Integer -> Integer
885 fromInteger :: forall a. Foo a => Integer -> a
886 fromInteger :: Num a => a -> Integer
887 fromInteger :: Integer -> Bool -> Bool
891 <para>Be warned: this is an experimental facility, with
892 fewer checks than usual. Use <literal>-dcore-lint</literal>
893 to typecheck the desugared program. If Core Lint is happy
894 you should be all right.</para>
900 <!-- TYPE SYSTEM EXTENSIONS -->
901 <sect1 id="type-extensions">
902 <title>Type system extensions</title>
906 <title>Data types and type synonyms</title>
908 <sect3 id="nullary-types">
909 <title>Data types with no constructors</title>
911 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
912 a data type with no constructors. For example:</para>
916 data T a -- T :: * -> *
919 <para>Syntactically, the declaration lacks the "= constrs" part. The
920 type can be parameterised over types of any kind, but if the kind is
921 not <literal>*</literal> then an explicit kind annotation must be used
922 (see <xref linkend="sec-kinding"/>).</para>
924 <para>Such data types have only one value, namely bottom.
925 Nevertheless, they can be useful when defining "phantom types".</para>
928 <sect3 id="infix-tycons">
929 <title>Infix type constructors, classes, and type variables</title>
932 GHC allows type constructors, classes, and type variables to be operators, and
933 to be written infix, very much like expressions. More specifically:
936 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
937 The lexical syntax is the same as that for data constructors.
940 Data type and type-synonym declarations can be written infix, parenthesised
941 if you want further arguments. E.g.
943 data a :*: b = Foo a b
944 type a :+: b = Either a b
945 class a :=: b where ...
947 data (a :**: b) x = Baz a b x
948 type (a :++: b) y = Either (a,b) y
952 Types, and class constraints, can be written infix. For example
955 f :: (a :=: b) => a -> b
959 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
960 The lexical syntax is the same as that for variable operators, excluding "(.)",
961 "(!)", and "(*)". In a binding position, the operator must be
962 parenthesised. For example:
964 type T (+) = Int + Int
969 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
975 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
976 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
979 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
980 one cannot distinguish between the two in a fixity declaration; a fixity declaration
981 sets the fixity for a data constructor and the corresponding type constructor. For example:
985 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
986 and similarly for <literal>:*:</literal>.
987 <literal>Int `a` Bool</literal>.
990 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
997 <sect3 id="type-synonyms">
998 <title>Liberalised type synonyms</title>
1001 Type synonyms are like macros at the type level, and
1002 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1003 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1005 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1006 in a type synonym, thus:
1008 type Discard a = forall b. Show b => a -> b -> (a, String)
1013 g :: Discard Int -> (Int,String) -- A rank-2 type
1020 You can write an unboxed tuple in a type synonym:
1022 type Pr = (# Int, Int #)
1030 You can apply a type synonym to a forall type:
1032 type Foo a = a -> a -> Bool
1034 f :: Foo (forall b. b->b)
1036 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1038 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1043 You can apply a type synonym to a partially applied type synonym:
1045 type Generic i o = forall x. i x -> o x
1048 foo :: Generic Id []
1050 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1052 foo :: forall x. x -> [x]
1060 GHC currently does kind checking before expanding synonyms (though even that
1064 After expanding type synonyms, GHC does validity checking on types, looking for
1065 the following mal-formedness which isn't detected simply by kind checking:
1068 Type constructor applied to a type involving for-alls.
1071 Unboxed tuple on left of an arrow.
1074 Partially-applied type synonym.
1078 this will be rejected:
1080 type Pr = (# Int, Int #)
1085 because GHC does not allow unboxed tuples on the left of a function arrow.
1090 <sect3 id="existential-quantification">
1091 <title>Existentially quantified data constructors
1095 The idea of using existential quantification in data type declarations
1096 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1097 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1098 London, 1991). It was later formalised by Laufer and Odersky
1099 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1100 TOPLAS, 16(5), pp1411-1430, 1994).
1101 It's been in Lennart
1102 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1103 proved very useful. Here's the idea. Consider the declaration:
1109 data Foo = forall a. MkFoo a (a -> Bool)
1116 The data type <literal>Foo</literal> has two constructors with types:
1122 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1129 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1130 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1131 For example, the following expression is fine:
1137 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1143 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1144 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1145 isUpper</function> packages a character with a compatible function. These
1146 two things are each of type <literal>Foo</literal> and can be put in a list.
1150 What can we do with a value of type <literal>Foo</literal>?. In particular,
1151 what happens when we pattern-match on <function>MkFoo</function>?
1157 f (MkFoo val fn) = ???
1163 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1164 are compatible, the only (useful) thing we can do with them is to
1165 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1172 f (MkFoo val fn) = fn val
1178 What this allows us to do is to package heterogenous values
1179 together with a bunch of functions that manipulate them, and then treat
1180 that collection of packages in a uniform manner. You can express
1181 quite a bit of object-oriented-like programming this way.
1184 <sect4 id="existential">
1185 <title>Why existential?
1189 What has this to do with <emphasis>existential</emphasis> quantification?
1190 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1196 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1202 But Haskell programmers can safely think of the ordinary
1203 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1204 adding a new existential quantification construct.
1210 <title>Type classes</title>
1213 An easy extension is to allow
1214 arbitrary contexts before the constructor. For example:
1220 data Baz = forall a. Eq a => Baz1 a a
1221 | forall b. Show b => Baz2 b (b -> b)
1227 The two constructors have the types you'd expect:
1233 Baz1 :: forall a. Eq a => a -> a -> Baz
1234 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1240 But when pattern matching on <function>Baz1</function> the matched values can be compared
1241 for equality, and when pattern matching on <function>Baz2</function> the first matched
1242 value can be converted to a string (as well as applying the function to it).
1243 So this program is legal:
1250 f (Baz1 p q) | p == q = "Yes"
1252 f (Baz2 v fn) = show (fn v)
1258 Operationally, in a dictionary-passing implementation, the
1259 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1260 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1261 extract it on pattern matching.
1265 Notice the way that the syntax fits smoothly with that used for
1266 universal quantification earlier.
1272 <title>Record Constructors</title>
1275 GHC allows existentials to be used with records syntax as well. For example:
1278 data Counter a = forall self. NewCounter
1280 , _inc :: self -> self
1281 , _display :: self -> IO ()
1285 Here <literal>tag</literal> is a public field, with a well-typed selector
1286 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1287 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1288 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1289 compile-time error. In other words, <emphasis>GHC defines a record selector function
1290 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1291 (This example used an underscore in the fields for which record selectors
1292 will not be defined, but that is only programming style; GHC ignores them.)
1296 To make use of these hidden fields, we need to create some helper functions:
1299 inc :: Counter a -> Counter a
1300 inc (NewCounter x i d t) = NewCounter
1301 { _this = i x, _inc = i, _display = d, tag = t }
1303 display :: Counter a -> IO ()
1304 display NewCounter{ _this = x, _display = d } = d x
1307 Now we can define counters with different underlying implementations:
1310 counterA :: Counter String
1311 counterA = NewCounter
1312 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1314 counterB :: Counter String
1315 counterB = NewCounter
1316 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1319 display (inc counterA) -- prints "1"
1320 display (inc (inc counterB)) -- prints "##"
1323 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1324 <literal>forall</literal> may be omitted. For example, we can express
1325 the same <literal>Counter a</literal> using GADT:
1328 data Counter a where
1329 NewCounter { _this :: self
1330 , _inc :: self -> self
1331 , _display :: self -> IO ()
1337 At the moment, record update syntax is only supported for Haskell 98 data types,
1338 so the following function does <emphasis>not</emphasis> work:
1341 -- This is invalid; use explicit NewCounter instead for now
1342 setTag :: Counter a -> a -> Counter a
1343 setTag obj t = obj{ tag = t }
1352 <title>Restrictions</title>
1355 There are several restrictions on the ways in which existentially-quantified
1356 constructors can be use.
1365 When pattern matching, each pattern match introduces a new,
1366 distinct, type for each existential type variable. These types cannot
1367 be unified with any other type, nor can they escape from the scope of
1368 the pattern match. For example, these fragments are incorrect:
1376 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1377 is the result of <function>f1</function>. One way to see why this is wrong is to
1378 ask what type <function>f1</function> has:
1382 f1 :: Foo -> a -- Weird!
1386 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1391 f1 :: forall a. Foo -> a -- Wrong!
1395 The original program is just plain wrong. Here's another sort of error
1399 f2 (Baz1 a b) (Baz1 p q) = a==q
1403 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1404 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1405 from the two <function>Baz1</function> constructors.
1413 You can't pattern-match on an existentially quantified
1414 constructor in a <literal>let</literal> or <literal>where</literal> group of
1415 bindings. So this is illegal:
1419 f3 x = a==b where { Baz1 a b = x }
1422 Instead, use a <literal>case</literal> expression:
1425 f3 x = case x of Baz1 a b -> a==b
1428 In general, you can only pattern-match
1429 on an existentially-quantified constructor in a <literal>case</literal> expression or
1430 in the patterns of a function definition.
1432 The reason for this restriction is really an implementation one.
1433 Type-checking binding groups is already a nightmare without
1434 existentials complicating the picture. Also an existential pattern
1435 binding at the top level of a module doesn't make sense, because it's
1436 not clear how to prevent the existentially-quantified type "escaping".
1437 So for now, there's a simple-to-state restriction. We'll see how
1445 You can't use existential quantification for <literal>newtype</literal>
1446 declarations. So this is illegal:
1450 newtype T = forall a. Ord a => MkT a
1454 Reason: a value of type <literal>T</literal> must be represented as a
1455 pair of a dictionary for <literal>Ord t</literal> and a value of type
1456 <literal>t</literal>. That contradicts the idea that
1457 <literal>newtype</literal> should have no concrete representation.
1458 You can get just the same efficiency and effect by using
1459 <literal>data</literal> instead of <literal>newtype</literal>. If
1460 there is no overloading involved, then there is more of a case for
1461 allowing an existentially-quantified <literal>newtype</literal>,
1462 because the <literal>data</literal> version does carry an
1463 implementation cost, but single-field existentially quantified
1464 constructors aren't much use. So the simple restriction (no
1465 existential stuff on <literal>newtype</literal>) stands, unless there
1466 are convincing reasons to change it.
1474 You can't use <literal>deriving</literal> to define instances of a
1475 data type with existentially quantified data constructors.
1477 Reason: in most cases it would not make sense. For example:#
1480 data T = forall a. MkT [a] deriving( Eq )
1483 To derive <literal>Eq</literal> in the standard way we would need to have equality
1484 between the single component of two <function>MkT</function> constructors:
1488 (MkT a) == (MkT b) = ???
1491 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1492 It's just about possible to imagine examples in which the derived instance
1493 would make sense, but it seems altogether simpler simply to prohibit such
1494 declarations. Define your own instances!
1509 <sect2 id="multi-param-type-classes">
1510 <title>Class declarations</title>
1513 This section, and the next one, documents GHC's type-class extensions.
1514 There's lots of background in the paper <ulink
1515 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1516 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1517 Jones, Erik Meijer).
1520 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1524 <title>Multi-parameter type classes</title>
1526 Multi-parameter type classes are permitted. For example:
1530 class Collection c a where
1531 union :: c a -> c a -> c a
1539 <title>The superclasses of a class declaration</title>
1542 There are no restrictions on the context in a class declaration
1543 (which introduces superclasses), except that the class hierarchy must
1544 be acyclic. So these class declarations are OK:
1548 class Functor (m k) => FiniteMap m k where
1551 class (Monad m, Monad (t m)) => Transform t m where
1552 lift :: m a -> (t m) a
1558 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1559 of "acyclic" involves only the superclass relationships. For example,
1565 op :: D b => a -> b -> b
1568 class C a => D a where { ... }
1572 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1573 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1574 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1581 <sect3 id="class-method-types">
1582 <title>Class method types</title>
1585 Haskell 98 prohibits class method types to mention constraints on the
1586 class type variable, thus:
1589 fromList :: [a] -> s a
1590 elem :: Eq a => a -> s a -> Bool
1592 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1593 contains the constraint <literal>Eq a</literal>, constrains only the
1594 class type variable (in this case <literal>a</literal>).
1595 GHC lifts this restriction.
1602 <sect2 id="functional-dependencies">
1603 <title>Functional dependencies
1606 <para> Functional dependencies are implemented as described by Mark Jones
1607 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1608 In Proceedings of the 9th European Symposium on Programming,
1609 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1613 Functional dependencies are introduced by a vertical bar in the syntax of a
1614 class declaration; e.g.
1616 class (Monad m) => MonadState s m | m -> s where ...
1618 class Foo a b c | a b -> c where ...
1620 There should be more documentation, but there isn't (yet). Yell if you need it.
1623 <sect3><title>Rules for functional dependencies </title>
1625 In a class declaration, all of the class type variables must be reachable (in the sense
1626 mentioned in <xref linkend="type-restrictions"/>)
1627 from the free variables of each method type.
1631 class Coll s a where
1633 insert :: s -> a -> s
1636 is not OK, because the type of <literal>empty</literal> doesn't mention
1637 <literal>a</literal>. Functional dependencies can make the type variable
1640 class Coll s a | s -> a where
1642 insert :: s -> a -> s
1645 Alternatively <literal>Coll</literal> might be rewritten
1648 class Coll s a where
1650 insert :: s a -> a -> s a
1654 which makes the connection between the type of a collection of
1655 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1656 Occasionally this really doesn't work, in which case you can split the
1664 class CollE s => Coll s a where
1665 insert :: s -> a -> s
1672 <title>Background on functional dependencies</title>
1674 <para>The following description of the motivation and use of functional dependencies is taken
1675 from the Hugs user manual, reproduced here (with minor changes) by kind
1676 permission of Mark Jones.
1679 Consider the following class, intended as part of a
1680 library for collection types:
1682 class Collects e ce where
1684 insert :: e -> ce -> ce
1685 member :: e -> ce -> Bool
1687 The type variable e used here represents the element type, while ce is the type
1688 of the container itself. Within this framework, we might want to define
1689 instances of this class for lists or characteristic functions (both of which
1690 can be used to represent collections of any equality type), bit sets (which can
1691 be used to represent collections of characters), or hash tables (which can be
1692 used to represent any collection whose elements have a hash function). Omitting
1693 standard implementation details, this would lead to the following declarations:
1695 instance Eq e => Collects e [e] where ...
1696 instance Eq e => Collects e (e -> Bool) where ...
1697 instance Collects Char BitSet where ...
1698 instance (Hashable e, Collects a ce)
1699 => Collects e (Array Int ce) where ...
1701 All this looks quite promising; we have a class and a range of interesting
1702 implementations. Unfortunately, there are some serious problems with the class
1703 declaration. First, the empty function has an ambiguous type:
1705 empty :: Collects e ce => ce
1707 By "ambiguous" we mean that there is a type variable e that appears on the left
1708 of the <literal>=></literal> symbol, but not on the right. The problem with
1709 this is that, according to the theoretical foundations of Haskell overloading,
1710 we cannot guarantee a well-defined semantics for any term with an ambiguous
1714 We can sidestep this specific problem by removing the empty member from the
1715 class declaration. However, although the remaining members, insert and member,
1716 do not have ambiguous types, we still run into problems when we try to use
1717 them. For example, consider the following two functions:
1719 f x y = insert x . insert y
1722 for which GHC infers the following types:
1724 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1725 g :: (Collects Bool c, Collects Char c) => c -> c
1727 Notice that the type for f allows the two parameters x and y to be assigned
1728 different types, even though it attempts to insert each of the two values, one
1729 after the other, into the same collection. If we're trying to model collections
1730 that contain only one type of value, then this is clearly an inaccurate
1731 type. Worse still, the definition for g is accepted, without causing a type
1732 error. As a result, the error in this code will not be flagged at the point
1733 where it appears. Instead, it will show up only when we try to use g, which
1734 might even be in a different module.
1737 <sect4><title>An attempt to use constructor classes</title>
1740 Faced with the problems described above, some Haskell programmers might be
1741 tempted to use something like the following version of the class declaration:
1743 class Collects e c where
1745 insert :: e -> c e -> c e
1746 member :: e -> c e -> Bool
1748 The key difference here is that we abstract over the type constructor c that is
1749 used to form the collection type c e, and not over that collection type itself,
1750 represented by ce in the original class declaration. This avoids the immediate
1751 problems that we mentioned above: empty has type <literal>Collects e c => c
1752 e</literal>, which is not ambiguous.
1755 The function f from the previous section has a more accurate type:
1757 f :: (Collects e c) => e -> e -> c e -> c e
1759 The function g from the previous section is now rejected with a type error as
1760 we would hope because the type of f does not allow the two arguments to have
1762 This, then, is an example of a multiple parameter class that does actually work
1763 quite well in practice, without ambiguity problems.
1764 There is, however, a catch. This version of the Collects class is nowhere near
1765 as general as the original class seemed to be: only one of the four instances
1766 for <literal>Collects</literal>
1767 given above can be used with this version of Collects because only one of
1768 them---the instance for lists---has a collection type that can be written in
1769 the form c e, for some type constructor c, and element type e.
1773 <sect4><title>Adding functional dependencies</title>
1776 To get a more useful version of the Collects class, Hugs provides a mechanism
1777 that allows programmers to specify dependencies between the parameters of a
1778 multiple parameter class (For readers with an interest in theoretical
1779 foundations and previous work: The use of dependency information can be seen
1780 both as a generalization of the proposal for `parametric type classes' that was
1781 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1782 later framework for "improvement" of qualified types. The
1783 underlying ideas are also discussed in a more theoretical and abstract setting
1784 in a manuscript [implparam], where they are identified as one point in a
1785 general design space for systems of implicit parameterization.).
1787 To start with an abstract example, consider a declaration such as:
1789 class C a b where ...
1791 which tells us simply that C can be thought of as a binary relation on types
1792 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1793 included in the definition of classes to add information about dependencies
1794 between parameters, as in the following examples:
1796 class D a b | a -> b where ...
1797 class E a b | a -> b, b -> a where ...
1799 The notation <literal>a -> b</literal> used here between the | and where
1800 symbols --- not to be
1801 confused with a function type --- indicates that the a parameter uniquely
1802 determines the b parameter, and might be read as "a determines b." Thus D is
1803 not just a relation, but actually a (partial) function. Similarly, from the two
1804 dependencies that are included in the definition of E, we can see that E
1805 represents a (partial) one-one mapping between types.
1808 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1809 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1810 m>=0, meaning that the y parameters are uniquely determined by the x
1811 parameters. Spaces can be used as separators if more than one variable appears
1812 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1813 annotated with multiple dependencies using commas as separators, as in the
1814 definition of E above. Some dependencies that we can write in this notation are
1815 redundant, and will be rejected because they don't serve any useful
1816 purpose, and may instead indicate an error in the program. Examples of
1817 dependencies like this include <literal>a -> a </literal>,
1818 <literal>a -> a a </literal>,
1819 <literal>a -> </literal>, etc. There can also be
1820 some redundancy if multiple dependencies are given, as in
1821 <literal>a->b</literal>,
1822 <literal>b->c </literal>, <literal>a->c </literal>, and
1823 in which some subset implies the remaining dependencies. Examples like this are
1824 not treated as errors. Note that dependencies appear only in class
1825 declarations, and not in any other part of the language. In particular, the
1826 syntax for instance declarations, class constraints, and types is completely
1830 By including dependencies in a class declaration, we provide a mechanism for
1831 the programmer to specify each multiple parameter class more precisely. The
1832 compiler, on the other hand, is responsible for ensuring that the set of
1833 instances that are in scope at any given point in the program is consistent
1834 with any declared dependencies. For example, the following pair of instance
1835 declarations cannot appear together in the same scope because they violate the
1836 dependency for D, even though either one on its own would be acceptable:
1838 instance D Bool Int where ...
1839 instance D Bool Char where ...
1841 Note also that the following declaration is not allowed, even by itself:
1843 instance D [a] b where ...
1845 The problem here is that this instance would allow one particular choice of [a]
1846 to be associated with more than one choice for b, which contradicts the
1847 dependency specified in the definition of D. More generally, this means that,
1848 in any instance of the form:
1850 instance D t s where ...
1852 for some particular types t and s, the only variables that can appear in s are
1853 the ones that appear in t, and hence, if the type t is known, then s will be
1854 uniquely determined.
1857 The benefit of including dependency information is that it allows us to define
1858 more general multiple parameter classes, without ambiguity problems, and with
1859 the benefit of more accurate types. To illustrate this, we return to the
1860 collection class example, and annotate the original definition of <literal>Collects</literal>
1861 with a simple dependency:
1863 class Collects e ce | ce -> e where
1865 insert :: e -> ce -> ce
1866 member :: e -> ce -> Bool
1868 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1869 determined by the type of the collection ce. Note that both parameters of
1870 Collects are of kind *; there are no constructor classes here. Note too that
1871 all of the instances of Collects that we gave earlier can be used
1872 together with this new definition.
1875 What about the ambiguity problems that we encountered with the original
1876 definition? The empty function still has type Collects e ce => ce, but it is no
1877 longer necessary to regard that as an ambiguous type: Although the variable e
1878 does not appear on the right of the => symbol, the dependency for class
1879 Collects tells us that it is uniquely determined by ce, which does appear on
1880 the right of the => symbol. Hence the context in which empty is used can still
1881 give enough information to determine types for both ce and e, without
1882 ambiguity. More generally, we need only regard a type as ambiguous if it
1883 contains a variable on the left of the => that is not uniquely determined
1884 (either directly or indirectly) by the variables on the right.
1887 Dependencies also help to produce more accurate types for user defined
1888 functions, and hence to provide earlier detection of errors, and less cluttered
1889 types for programmers to work with. Recall the previous definition for a
1892 f x y = insert x y = insert x . insert y
1894 for which we originally obtained a type:
1896 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1898 Given the dependency information that we have for Collects, however, we can
1899 deduce that a and b must be equal because they both appear as the second
1900 parameter in a Collects constraint with the same first parameter c. Hence we
1901 can infer a shorter and more accurate type for f:
1903 f :: (Collects a c) => a -> a -> c -> c
1905 In a similar way, the earlier definition of g will now be flagged as a type error.
1908 Although we have given only a few examples here, it should be clear that the
1909 addition of dependency information can help to make multiple parameter classes
1910 more useful in practice, avoiding ambiguity problems, and allowing more general
1911 sets of instance declarations.
1917 <sect2 id="instance-decls">
1918 <title>Instance declarations</title>
1920 <sect3 id="instance-rules">
1921 <title>Relaxed rules for instance declarations</title>
1923 <para>An instance declaration has the form
1925 instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
1927 The part before the "<literal>=></literal>" is the
1928 <emphasis>context</emphasis>, while the part after the
1929 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1933 In Haskell 98 the head of an instance declaration
1934 must be of the form <literal>C (T a1 ... an)</literal>, where
1935 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1936 and the <literal>a1 ... an</literal> are distinct type variables.
1937 Furthermore, the assertions in the context of the instance declaration
1938 must be of the form <literal>C a</literal> where <literal>a</literal>
1939 is a type variable that occurs in the head.
1942 The <option>-fglasgow-exts</option> flag loosens these restrictions
1943 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1944 the context and head of the instance declaration can each consist of arbitrary
1945 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1949 For each assertion in the context:
1951 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1952 <listitem><para>The assertion has fewer constructors and variables (taken together
1953 and counting repetitions) than the head</para></listitem>
1957 <listitem><para>The coverage condition. For each functional dependency,
1958 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
1959 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
1960 every type variable in
1961 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
1962 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
1963 substitution mapping each type variable in the class declaration to the
1964 corresponding type in the instance declaration.
1967 These restrictions ensure that context reduction terminates: each reduction
1968 step makes the problem smaller by at least one
1969 constructor. For example, the following would make the type checker
1970 loop if it wasn't excluded:
1972 instance C a => C a where ...
1974 For example, these are OK:
1976 instance C Int [a] -- Multiple parameters
1977 instance Eq (S [a]) -- Structured type in head
1979 -- Repeated type variable in head
1980 instance C4 a a => C4 [a] [a]
1981 instance Stateful (ST s) (MutVar s)
1983 -- Head can consist of type variables only
1985 instance (Eq a, Show b) => C2 a b
1987 -- Non-type variables in context
1988 instance Show (s a) => Show (Sized s a)
1989 instance C2 Int a => C3 Bool [a]
1990 instance C2 Int a => C3 [a] b
1994 -- Context assertion no smaller than head
1995 instance C a => C a where ...
1996 -- (C b b) has more more occurrences of b than the head
1997 instance C b b => Foo [b] where ...
2002 The same restrictions apply to instances generated by
2003 <literal>deriving</literal> clauses. Thus the following is accepted:
2005 data MinHeap h a = H a (h a)
2008 because the derived instance
2010 instance (Show a, Show (h a)) => Show (MinHeap h a)
2012 conforms to the above rules.
2016 A useful idiom permitted by the above rules is as follows.
2017 If one allows overlapping instance declarations then it's quite
2018 convenient to have a "default instance" declaration that applies if
2019 something more specific does not:
2027 <sect3 id="undecidable-instances">
2028 <title>Undecidable instances</title>
2031 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2032 For example, sometimes you might want to use the following to get the
2033 effect of a "class synonym":
2035 class (C1 a, C2 a, C3 a) => C a where { }
2037 instance (C1 a, C2 a, C3 a) => C a where { }
2039 This allows you to write shorter signatures:
2045 f :: (C1 a, C2 a, C3 a) => ...
2047 The restrictions on functional dependencies (<xref
2048 linkend="functional-dependencies"/>) are particularly troublesome.
2049 It is tempting to introduce type variables in the context that do not appear in
2050 the head, something that is excluded by the normal rules. For example:
2052 class HasConverter a b | a -> b where
2055 data Foo a = MkFoo a
2057 instance (HasConverter a b,Show b) => Show (Foo a) where
2058 show (MkFoo value) = show (convert value)
2060 This is dangerous territory, however. Here, for example, is a program that would make the
2065 instance F [a] [[a]]
2066 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2068 Similarly, it can be tempting to lift the coverage condition:
2070 class Mul a b c | a b -> c where
2071 (.*.) :: a -> b -> c
2073 instance Mul Int Int Int where (.*.) = (*)
2074 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2075 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2077 The third instance declaration does not obey the coverage condition;
2078 and indeed the (somewhat strange) definition:
2080 f = \ b x y -> if b then x .*. [y] else y
2082 makes instance inference go into a loop, because it requires the constraint
2083 <literal>(Mul a [b] b)</literal>.
2086 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2087 the experimental flag <option>-fallow-undecidable-instances</option>
2088 <indexterm><primary>-fallow-undecidable-instances
2089 option</primary></indexterm>, you can use arbitrary
2090 types in both an instance context and instance head. Termination is ensured by having a
2091 fixed-depth recursion stack. If you exceed the stack depth you get a
2092 sort of backtrace, and the opportunity to increase the stack depth
2093 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
2099 <sect3 id="instance-overlap">
2100 <title>Overlapping instances</title>
2102 In general, <emphasis>GHC requires that that it be unambiguous which instance
2104 should be used to resolve a type-class constraint</emphasis>. This behaviour
2105 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2106 <indexterm><primary>-fallow-overlapping-instances
2107 </primary></indexterm>
2108 and <option>-fallow-incoherent-instances</option>
2109 <indexterm><primary>-fallow-incoherent-instances
2110 </primary></indexterm>, as this section discusses.</para>
2112 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2113 it tries to match every instance declaration against the
2115 by instantiating the head of the instance declaration. For example, consider
2118 instance context1 => C Int a where ... -- (A)
2119 instance context2 => C a Bool where ... -- (B)
2120 instance context3 => C Int [a] where ... -- (C)
2121 instance context4 => C Int [Int] where ... -- (D)
2123 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2124 but (C) and (D) do not. When matching, GHC takes
2125 no account of the context of the instance declaration
2126 (<literal>context1</literal> etc).
2127 GHC's default behaviour is that <emphasis>exactly one instance must match the
2128 constraint it is trying to resolve</emphasis>.
2129 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2130 including both declarations (A) and (B), say); an error is only reported if a
2131 particular constraint matches more than one.
2135 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2136 more than one instance to match, provided there is a most specific one. For
2137 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2138 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2139 most-specific match, the program is rejected.
2142 However, GHC is conservative about committing to an overlapping instance. For example:
2147 Suppose that from the RHS of <literal>f</literal> we get the constraint
2148 <literal>C Int [b]</literal>. But
2149 GHC does not commit to instance (C), because in a particular
2150 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2151 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2152 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2153 GHC will instead pick (C), without complaining about
2154 the problem of subsequent instantiations.
2157 The willingness to be overlapped or incoherent is a property of
2158 the <emphasis>instance declaration</emphasis> itself, controlled by the
2159 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2160 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2161 being defined. Neither flag is required in a module that imports and uses the
2162 instance declaration. Specifically, during the lookup process:
2165 An instance declaration is ignored during the lookup process if (a) a more specific
2166 match is found, and (b) the instance declaration was compiled with
2167 <option>-fallow-overlapping-instances</option>. The flag setting for the
2168 more-specific instance does not matter.
2171 Suppose an instance declaration does not matche the constraint being looked up, but
2172 does unify with it, so that it might match when the constraint is further
2173 instantiated. Usually GHC will regard this as a reason for not committing to
2174 some other constraint. But if the instance declaration was compiled with
2175 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2176 check for that declaration.
2179 All this makes it possible for a library author to design a library that relies on
2180 overlapping instances without the library client having to know.
2182 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2183 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2188 <title>Type synonyms in the instance head</title>
2191 <emphasis>Unlike Haskell 98, instance heads may use type
2192 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2193 As always, using a type synonym is just shorthand for
2194 writing the RHS of the type synonym definition. For example:
2198 type Point = (Int,Int)
2199 instance C Point where ...
2200 instance C [Point] where ...
2204 is legal. However, if you added
2208 instance C (Int,Int) where ...
2212 as well, then the compiler will complain about the overlapping
2213 (actually, identical) instance declarations. As always, type synonyms
2214 must be fully applied. You cannot, for example, write:
2219 instance Monad P where ...
2223 This design decision is independent of all the others, and easily
2224 reversed, but it makes sense to me.
2232 <sect2 id="type-restrictions">
2233 <title>Type signatures</title>
2235 <sect3><title>The context of a type signature</title>
2237 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2238 the form <emphasis>(class type-variable)</emphasis> or
2239 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2240 these type signatures are perfectly OK
2243 g :: Ord (T a ()) => ...
2247 GHC imposes the following restrictions on the constraints in a type signature.
2251 forall tv1..tvn (c1, ...,cn) => type
2254 (Here, we write the "foralls" explicitly, although the Haskell source
2255 language omits them; in Haskell 98, all the free type variables of an
2256 explicit source-language type signature are universally quantified,
2257 except for the class type variables in a class declaration. However,
2258 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2267 <emphasis>Each universally quantified type variable
2268 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2270 A type variable <literal>a</literal> is "reachable" if it it appears
2271 in the same constraint as either a type variable free in in
2272 <literal>type</literal>, or another reachable type variable.
2273 A value with a type that does not obey
2274 this reachability restriction cannot be used without introducing
2275 ambiguity; that is why the type is rejected.
2276 Here, for example, is an illegal type:
2280 forall a. Eq a => Int
2284 When a value with this type was used, the constraint <literal>Eq tv</literal>
2285 would be introduced where <literal>tv</literal> is a fresh type variable, and
2286 (in the dictionary-translation implementation) the value would be
2287 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2288 can never know which instance of <literal>Eq</literal> to use because we never
2289 get any more information about <literal>tv</literal>.
2293 that the reachability condition is weaker than saying that <literal>a</literal> is
2294 functionally dependent on a type variable free in
2295 <literal>type</literal> (see <xref
2296 linkend="functional-dependencies"/>). The reason for this is there
2297 might be a "hidden" dependency, in a superclass perhaps. So
2298 "reachable" is a conservative approximation to "functionally dependent".
2299 For example, consider:
2301 class C a b | a -> b where ...
2302 class C a b => D a b where ...
2303 f :: forall a b. D a b => a -> a
2305 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2306 but that is not immediately apparent from <literal>f</literal>'s type.
2312 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2313 universally quantified type variables <literal>tvi</literal></emphasis>.
2315 For example, this type is OK because <literal>C a b</literal> mentions the
2316 universally quantified type variable <literal>b</literal>:
2320 forall a. C a b => burble
2324 The next type is illegal because the constraint <literal>Eq b</literal> does not
2325 mention <literal>a</literal>:
2329 forall a. Eq b => burble
2333 The reason for this restriction is milder than the other one. The
2334 excluded types are never useful or necessary (because the offending
2335 context doesn't need to be witnessed at this point; it can be floated
2336 out). Furthermore, floating them out increases sharing. Lastly,
2337 excluding them is a conservative choice; it leaves a patch of
2338 territory free in case we need it later.
2349 <title>For-all hoisting</title>
2351 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2352 end of an arrow, thus:
2354 type Discard a = forall b. a -> b -> a
2356 g :: Int -> Discard Int
2359 Simply expanding the type synonym would give
2361 g :: Int -> (forall b. Int -> b -> Int)
2363 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2365 g :: forall b. Int -> Int -> b -> Int
2367 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2368 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2369 performs the transformation:</emphasis>
2371 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2373 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2375 (In fact, GHC tries to retain as much synonym information as possible for use in
2376 error messages, but that is a usability issue.) This rule applies, of course, whether
2377 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2378 valid way to write <literal>g</literal>'s type signature:
2380 g :: Int -> Int -> forall b. b -> Int
2384 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2387 type Foo a = (?x::Int) => Bool -> a
2392 g :: (?x::Int) => Bool -> Bool -> Int
2400 <sect2 id="implicit-parameters">
2401 <title>Implicit parameters</title>
2403 <para> Implicit parameters are implemented as described in
2404 "Implicit parameters: dynamic scoping with static types",
2405 J Lewis, MB Shields, E Meijer, J Launchbury,
2406 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2410 <para>(Most of the following, stil rather incomplete, documentation is
2411 due to Jeff Lewis.)</para>
2413 <para>Implicit parameter support is enabled with the option
2414 <option>-fimplicit-params</option>.</para>
2417 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2418 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2419 context. In Haskell, all variables are statically bound. Dynamic
2420 binding of variables is a notion that goes back to Lisp, but was later
2421 discarded in more modern incarnations, such as Scheme. Dynamic binding
2422 can be very confusing in an untyped language, and unfortunately, typed
2423 languages, in particular Hindley-Milner typed languages like Haskell,
2424 only support static scoping of variables.
2427 However, by a simple extension to the type class system of Haskell, we
2428 can support dynamic binding. Basically, we express the use of a
2429 dynamically bound variable as a constraint on the type. These
2430 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2431 function uses a dynamically-bound variable <literal>?x</literal>
2432 of type <literal>t'</literal>". For
2433 example, the following expresses the type of a sort function,
2434 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2436 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2438 The dynamic binding constraints are just a new form of predicate in the type class system.
2441 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2442 where <literal>x</literal> is
2443 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2444 Use of this construct also introduces a new
2445 dynamic-binding constraint in the type of the expression.
2446 For example, the following definition
2447 shows how we can define an implicitly parameterized sort function in
2448 terms of an explicitly parameterized <literal>sortBy</literal> function:
2450 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2452 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2458 <title>Implicit-parameter type constraints</title>
2460 Dynamic binding constraints behave just like other type class
2461 constraints in that they are automatically propagated. Thus, when a
2462 function is used, its implicit parameters are inherited by the
2463 function that called it. For example, our <literal>sort</literal> function might be used
2464 to pick out the least value in a list:
2466 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2467 least xs = fst (sort xs)
2469 Without lifting a finger, the <literal>?cmp</literal> parameter is
2470 propagated to become a parameter of <literal>least</literal> as well. With explicit
2471 parameters, the default is that parameters must always be explicit
2472 propagated. With implicit parameters, the default is to always
2476 An implicit-parameter type constraint differs from other type class constraints in the
2477 following way: All uses of a particular implicit parameter must have
2478 the same type. This means that the type of <literal>(?x, ?x)</literal>
2479 is <literal>(?x::a) => (a,a)</literal>, and not
2480 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2484 <para> You can't have an implicit parameter in the context of a class or instance
2485 declaration. For example, both these declarations are illegal:
2487 class (?x::Int) => C a where ...
2488 instance (?x::a) => Foo [a] where ...
2490 Reason: exactly which implicit parameter you pick up depends on exactly where
2491 you invoke a function. But the ``invocation'' of instance declarations is done
2492 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2493 Easiest thing is to outlaw the offending types.</para>
2495 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2497 f :: (?x :: [a]) => Int -> Int
2500 g :: (Read a, Show a) => String -> String
2503 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2504 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2505 quite unambiguous, and fixes the type <literal>a</literal>.
2510 <title>Implicit-parameter bindings</title>
2513 An implicit parameter is <emphasis>bound</emphasis> using the standard
2514 <literal>let</literal> or <literal>where</literal> binding forms.
2515 For example, we define the <literal>min</literal> function by binding
2516 <literal>cmp</literal>.
2519 min = let ?cmp = (<=) in least
2523 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2524 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2525 (including in a list comprehension, or do-notation, or pattern guards),
2526 or a <literal>where</literal> clause.
2527 Note the following points:
2530 An implicit-parameter binding group must be a
2531 collection of simple bindings to implicit-style variables (no
2532 function-style bindings, and no type signatures); these bindings are
2533 neither polymorphic or recursive.
2536 You may not mix implicit-parameter bindings with ordinary bindings in a
2537 single <literal>let</literal>
2538 expression; use two nested <literal>let</literal>s instead.
2539 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2543 You may put multiple implicit-parameter bindings in a
2544 single binding group; but they are <emphasis>not</emphasis> treated
2545 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2546 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2547 parameter. The bindings are not nested, and may be re-ordered without changing
2548 the meaning of the program.
2549 For example, consider:
2551 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2553 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2554 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2556 f :: (?x::Int) => Int -> Int
2564 <sect3><title>Implicit parameters and polymorphic recursion</title>
2567 Consider these two definitions:
2570 len1 xs = let ?acc = 0 in len_acc1 xs
2573 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2578 len2 xs = let ?acc = 0 in len_acc2 xs
2580 len_acc2 :: (?acc :: Int) => [a] -> Int
2582 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2584 The only difference between the two groups is that in the second group
2585 <literal>len_acc</literal> is given a type signature.
2586 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2587 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2588 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2589 has a type signature, the recursive call is made to the
2590 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2591 as an implicit parameter. So we get the following results in GHCi:
2598 Adding a type signature dramatically changes the result! This is a rather
2599 counter-intuitive phenomenon, worth watching out for.
2603 <sect3><title>Implicit parameters and monomorphism</title>
2605 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2606 Haskell Report) to implicit parameters. For example, consider:
2614 Since the binding for <literal>y</literal> falls under the Monomorphism
2615 Restriction it is not generalised, so the type of <literal>y</literal> is
2616 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2617 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2618 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2619 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2620 <literal>y</literal> in the body of the <literal>let</literal> will see the
2621 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2622 <literal>14</literal>.
2627 <sect2 id="linear-implicit-parameters">
2628 <title>Linear implicit parameters</title>
2630 Linear implicit parameters are an idea developed by Koen Claessen,
2631 Mark Shields, and Simon PJ. They address the long-standing
2632 problem that monads seem over-kill for certain sorts of problem, notably:
2635 <listitem> <para> distributing a supply of unique names </para> </listitem>
2636 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2637 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2641 Linear implicit parameters are just like ordinary implicit parameters,
2642 except that they are "linear" -- that is, they cannot be copied, and
2643 must be explicitly "split" instead. Linear implicit parameters are
2644 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2645 (The '/' in the '%' suggests the split!)
2650 import GHC.Exts( Splittable )
2652 data NameSupply = ...
2654 splitNS :: NameSupply -> (NameSupply, NameSupply)
2655 newName :: NameSupply -> Name
2657 instance Splittable NameSupply where
2661 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2662 f env (Lam x e) = Lam x' (f env e)
2665 env' = extend env x x'
2666 ...more equations for f...
2668 Notice that the implicit parameter %ns is consumed
2670 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2671 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2675 So the translation done by the type checker makes
2676 the parameter explicit:
2678 f :: NameSupply -> Env -> Expr -> Expr
2679 f ns env (Lam x e) = Lam x' (f ns1 env e)
2681 (ns1,ns2) = splitNS ns
2683 env = extend env x x'
2685 Notice the call to 'split' introduced by the type checker.
2686 How did it know to use 'splitNS'? Because what it really did
2687 was to introduce a call to the overloaded function 'split',
2688 defined by the class <literal>Splittable</literal>:
2690 class Splittable a where
2693 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2694 split for name supplies. But we can simply write
2700 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2702 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2703 <literal>GHC.Exts</literal>.
2708 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2709 are entirely distinct implicit parameters: you
2710 can use them together and they won't intefere with each other. </para>
2713 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2715 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2716 in the context of a class or instance declaration. </para></listitem>
2720 <sect3><title>Warnings</title>
2723 The monomorphism restriction is even more important than usual.
2724 Consider the example above:
2726 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2727 f env (Lam x e) = Lam x' (f env e)
2730 env' = extend env x x'
2732 If we replaced the two occurrences of x' by (newName %ns), which is
2733 usually a harmless thing to do, we get:
2735 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2736 f env (Lam x e) = Lam (newName %ns) (f env e)
2738 env' = extend env x (newName %ns)
2740 But now the name supply is consumed in <emphasis>three</emphasis> places
2741 (the two calls to newName,and the recursive call to f), so
2742 the result is utterly different. Urk! We don't even have
2746 Well, this is an experimental change. With implicit
2747 parameters we have already lost beta reduction anyway, and
2748 (as John Launchbury puts it) we can't sensibly reason about
2749 Haskell programs without knowing their typing.
2754 <sect3><title>Recursive functions</title>
2755 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2758 foo :: %x::T => Int -> [Int]
2760 foo n = %x : foo (n-1)
2762 where T is some type in class Splittable.</para>
2764 Do you get a list of all the same T's or all different T's
2765 (assuming that split gives two distinct T's back)?
2767 If you supply the type signature, taking advantage of polymorphic
2768 recursion, you get what you'd probably expect. Here's the
2769 translated term, where the implicit param is made explicit:
2772 foo x n = let (x1,x2) = split x
2773 in x1 : foo x2 (n-1)
2775 But if you don't supply a type signature, GHC uses the Hindley
2776 Milner trick of using a single monomorphic instance of the function
2777 for the recursive calls. That is what makes Hindley Milner type inference
2778 work. So the translation becomes
2782 foom n = x : foom (n-1)
2786 Result: 'x' is not split, and you get a list of identical T's. So the
2787 semantics of the program depends on whether or not foo has a type signature.
2790 You may say that this is a good reason to dislike linear implicit parameters
2791 and you'd be right. That is why they are an experimental feature.
2797 <sect2 id="sec-kinding">
2798 <title>Explicitly-kinded quantification</title>
2801 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2802 to give the kind explicitly as (machine-checked) documentation,
2803 just as it is nice to give a type signature for a function. On some occasions,
2804 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2805 John Hughes had to define the data type:
2807 data Set cxt a = Set [a]
2808 | Unused (cxt a -> ())
2810 The only use for the <literal>Unused</literal> constructor was to force the correct
2811 kind for the type variable <literal>cxt</literal>.
2814 GHC now instead allows you to specify the kind of a type variable directly, wherever
2815 a type variable is explicitly bound. Namely:
2817 <listitem><para><literal>data</literal> declarations:
2819 data Set (cxt :: * -> *) a = Set [a]
2820 </screen></para></listitem>
2821 <listitem><para><literal>type</literal> declarations:
2823 type T (f :: * -> *) = f Int
2824 </screen></para></listitem>
2825 <listitem><para><literal>class</literal> declarations:
2827 class (Eq a) => C (f :: * -> *) a where ...
2828 </screen></para></listitem>
2829 <listitem><para><literal>forall</literal>'s in type signatures:
2831 f :: forall (cxt :: * -> *). Set cxt Int
2832 </screen></para></listitem>
2837 The parentheses are required. Some of the spaces are required too, to
2838 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2839 will get a parse error, because "<literal>::*->*</literal>" is a
2840 single lexeme in Haskell.
2844 As part of the same extension, you can put kind annotations in types
2847 f :: (Int :: *) -> Int
2848 g :: forall a. a -> (a :: *)
2852 atype ::= '(' ctype '::' kind ')
2854 The parentheses are required.
2859 <sect2 id="universal-quantification">
2860 <title>Arbitrary-rank polymorphism
2864 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2865 allows us to say exactly what this means. For example:
2873 g :: forall b. (b -> b)
2875 The two are treated identically.
2879 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2880 explicit universal quantification in
2882 For example, all the following types are legal:
2884 f1 :: forall a b. a -> b -> a
2885 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2887 f2 :: (forall a. a->a) -> Int -> Int
2888 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2890 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2892 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2893 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2894 The <literal>forall</literal> makes explicit the universal quantification that
2895 is implicitly added by Haskell.
2898 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2899 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2900 shows, the polymorphic type on the left of the function arrow can be overloaded.
2903 The function <literal>f3</literal> has a rank-3 type;
2904 it has rank-2 types on the left of a function arrow.
2907 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2908 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2909 that restriction has now been lifted.)
2910 In particular, a forall-type (also called a "type scheme"),
2911 including an operational type class context, is legal:
2913 <listitem> <para> On the left of a function arrow </para> </listitem>
2914 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2915 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2916 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2917 field type signatures.</para> </listitem>
2918 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2919 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2921 There is one place you cannot put a <literal>forall</literal>:
2922 you cannot instantiate a type variable with a forall-type. So you cannot
2923 make a forall-type the argument of a type constructor. So these types are illegal:
2925 x1 :: [forall a. a->a]
2926 x2 :: (forall a. a->a, Int)
2927 x3 :: Maybe (forall a. a->a)
2929 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2930 a type variable any more!
2939 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2940 the types of the constructor arguments. Here are several examples:
2946 data T a = T1 (forall b. b -> b -> b) a
2948 data MonadT m = MkMonad { return :: forall a. a -> m a,
2949 bind :: forall a b. m a -> (a -> m b) -> m b
2952 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2958 The constructors have rank-2 types:
2964 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2965 MkMonad :: forall m. (forall a. a -> m a)
2966 -> (forall a b. m a -> (a -> m b) -> m b)
2968 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2974 Notice that you don't need to use a <literal>forall</literal> if there's an
2975 explicit context. For example in the first argument of the
2976 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2977 prefixed to the argument type. The implicit <literal>forall</literal>
2978 quantifies all type variables that are not already in scope, and are
2979 mentioned in the type quantified over.
2983 As for type signatures, implicit quantification happens for non-overloaded
2984 types too. So if you write this:
2987 data T a = MkT (Either a b) (b -> b)
2990 it's just as if you had written this:
2993 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2996 That is, since the type variable <literal>b</literal> isn't in scope, it's
2997 implicitly universally quantified. (Arguably, it would be better
2998 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2999 where that is what is wanted. Feedback welcomed.)
3003 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3004 the constructor to suitable values, just as usual. For example,
3015 a3 = MkSwizzle reverse
3018 a4 = let r x = Just x
3025 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3026 mkTs f x y = [T1 f x, T1 f y]
3032 The type of the argument can, as usual, be more general than the type
3033 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3034 does not need the <literal>Ord</literal> constraint.)
3038 When you use pattern matching, the bound variables may now have
3039 polymorphic types. For example:
3045 f :: T a -> a -> (a, Char)
3046 f (T1 w k) x = (w k x, w 'c' 'd')
3048 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3049 g (MkSwizzle s) xs f = s (map f (s xs))
3051 h :: MonadT m -> [m a] -> m [a]
3052 h m [] = return m []
3053 h m (x:xs) = bind m x $ \y ->
3054 bind m (h m xs) $ \ys ->
3061 In the function <function>h</function> we use the record selectors <literal>return</literal>
3062 and <literal>bind</literal> to extract the polymorphic bind and return functions
3063 from the <literal>MonadT</literal> data structure, rather than using pattern
3069 <title>Type inference</title>
3072 In general, type inference for arbitrary-rank types is undecidable.
3073 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3074 to get a decidable algorithm by requiring some help from the programmer.
3075 We do not yet have a formal specification of "some help" but the rule is this:
3078 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3079 provides an explicit polymorphic type for x, or GHC's type inference will assume
3080 that x's type has no foralls in it</emphasis>.
3083 What does it mean to "provide" an explicit type for x? You can do that by
3084 giving a type signature for x directly, using a pattern type signature
3085 (<xref linkend="scoped-type-variables"/>), thus:
3087 \ f :: (forall a. a->a) -> (f True, f 'c')
3089 Alternatively, you can give a type signature to the enclosing
3090 context, which GHC can "push down" to find the type for the variable:
3092 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3094 Here the type signature on the expression can be pushed inwards
3095 to give a type signature for f. Similarly, and more commonly,
3096 one can give a type signature for the function itself:
3098 h :: (forall a. a->a) -> (Bool,Char)
3099 h f = (f True, f 'c')
3101 You don't need to give a type signature if the lambda bound variable
3102 is a constructor argument. Here is an example we saw earlier:
3104 f :: T a -> a -> (a, Char)
3105 f (T1 w k) x = (w k x, w 'c' 'd')
3107 Here we do not need to give a type signature to <literal>w</literal>, because
3108 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3115 <sect3 id="implicit-quant">
3116 <title>Implicit quantification</title>
3119 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3120 user-written types, if and only if there is no explicit <literal>forall</literal>,
3121 GHC finds all the type variables mentioned in the type that are not already
3122 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3126 f :: forall a. a -> a
3133 h :: forall b. a -> b -> b
3139 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3142 f :: (a -> a) -> Int
3144 f :: forall a. (a -> a) -> Int
3146 f :: (forall a. a -> a) -> Int
3149 g :: (Ord a => a -> a) -> Int
3150 -- MEANS the illegal type
3151 g :: forall a. (Ord a => a -> a) -> Int
3153 g :: (forall a. Ord a => a -> a) -> Int
3155 The latter produces an illegal type, which you might think is silly,
3156 but at least the rule is simple. If you want the latter type, you
3157 can write your for-alls explicitly. Indeed, doing so is strongly advised
3166 <sect2 id="scoped-type-variables">
3167 <title>Scoped type variables
3171 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3173 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3174 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3175 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
3179 f (xs::[a]) = ys ++ ys
3184 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
3185 This brings the type variable <literal>a</literal> into scope; it scopes over
3186 all the patterns and right hand sides for this equation for <function>f</function>.
3187 In particular, it is in scope at the type signature for <varname>y</varname>.
3191 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
3192 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
3193 implicitly universally quantified. (If there are no type variables in
3194 scope, all type variables mentioned in the signature are universally
3195 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
3196 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
3197 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
3198 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3199 it becomes possible to do so.
3203 Scoped type variables are implemented in both GHC and Hugs. Where the
3204 implementations differ from the specification below, those differences
3209 So much for the basic idea. Here are the details.
3213 <title>What a scoped type variable means</title>
3215 A lexically-scoped type variable is simply
3216 the name for a type. The restriction it expresses is that all occurrences
3217 of the same name mean the same type. For example:
3219 f :: [Int] -> Int -> Int
3220 f (xs::[a]) (y::a) = (head xs + y) :: a
3222 The pattern type signatures on the left hand side of
3223 <literal>f</literal> express the fact that <literal>xs</literal>
3224 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
3225 must have this same type. The type signature on the expression <literal>(head xs)</literal>
3226 specifies that this expression must have the same type <literal>a</literal>.
3227 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
3228 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
3229 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
3230 rules, which specified that a pattern-bound type variable should be universally quantified.)
3231 For example, all of these are legal:</para>
3234 t (x::a) (y::a) = x+y*2
3236 f (x::a) (y::b) = [x,y] -- a unifies with b
3238 g (x::a) = x + 1::Int -- a unifies with Int
3240 h x = let k (y::a) = [x,y] -- a is free in the
3241 in k x -- environment
3243 k (x::a) True = ... -- a unifies with Int
3244 k (x::Int) False = ...
3247 w (x::a) = x -- a unifies with [b]
3253 <title>Scope and implicit quantification</title>
3261 All the type variables mentioned in a pattern,
3262 that are not already in scope,
3263 are brought into scope by the pattern. We describe this set as
3264 the <emphasis>type variables bound by the pattern</emphasis>.
3267 f (x::a) = let g (y::(a,b)) = fst y
3271 The pattern <literal>(x::a)</literal> brings the type variable
3272 <literal>a</literal> into scope, as well as the term
3273 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
3274 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
3275 and brings into scope the type variable <literal>b</literal>.
3281 The type variable(s) bound by the pattern have the same scope
3282 as the term variable(s) bound by the pattern. For example:
3285 f (x::a) = <...rhs of f...>
3286 (p::b, q::b) = (1,2)
3287 in <...body of let...>
3289 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3290 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3291 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3292 just like <literal>p</literal> and <literal>q</literal> do.
3293 Indeed, the newly bound type variables also scope over any ordinary, separate
3294 type signatures in the <literal>let</literal> group.
3301 The type variables bound by the pattern may be
3302 mentioned in ordinary type signatures or pattern
3303 type signatures anywhere within their scope.
3310 In ordinary type signatures, any type variable mentioned in the
3311 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3319 Ordinary type signatures do not bring any new type variables
3320 into scope (except in the type signature itself!). So this is illegal:
3327 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3328 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3329 and that is an incorrect typing.
3336 The pattern type signature is a monotype:
3341 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3345 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3346 not to type schemes.
3350 There is no implicit universal quantification on pattern type signatures (in contrast to
3351 ordinary type signatures).
3361 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3362 scope over the methods defined in the <literal>where</literal> part. For example:
3376 (Not implemented in Hugs yet, Dec 98).
3386 <sect3 id="decl-type-sigs">
3387 <title>Declaration type signatures</title>
3388 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3389 quantification (using <literal>forall</literal>) brings into scope the
3390 explicitly-quantified
3391 type variables, in the definition of the named function(s). For example:
3393 f :: forall a. [a] -> [a]
3394 f (x:xs) = xs ++ [ x :: a ]
3396 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3397 the definition of "<literal>f</literal>".
3399 <para>This only happens if the quantification in <literal>f</literal>'s type
3400 signature is explicit. For example:
3403 g (x:xs) = xs ++ [ x :: a ]
3405 This program will be rejected, because "<literal>a</literal>" does not scope
3406 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3407 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3408 quantification rules.
3412 <sect3 id="pattern-type-sigs">
3413 <title>Where a pattern type signature can occur</title>
3416 A pattern type signature can occur in any pattern. For example:
3421 A pattern type signature can be on an arbitrary sub-pattern, not
3426 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3435 Pattern type signatures, including the result part, can be used
3436 in lambda abstractions:
3439 (\ (x::a, y) :: a -> x)
3446 Pattern type signatures, including the result part, can be used
3447 in <literal>case</literal> expressions:
3450 case e of { ((x::a, y) :: (a,b)) -> x }
3453 Note that the <literal>-></literal> symbol in a case alternative
3454 leads to difficulties when parsing a type signature in the pattern: in
3455 the absence of the extra parentheses in the example above, the parser
3456 would try to interpret the <literal>-></literal> as a function
3457 arrow and give a parse error later.
3465 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3466 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3467 token or a parenthesised type of some sort). To see why,
3468 consider how one would parse this:
3482 Pattern type signatures can bind existential type variables.
3487 data T = forall a. MkT [a]
3490 f (MkT [t::a]) = MkT t3
3503 Pattern type signatures
3504 can be used in pattern bindings:
3507 f x = let (y, z::a) = x in ...
3508 f1 x = let (y, z::Int) = x in ...
3509 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3510 f3 :: (b->b) = \x -> x
3513 In all such cases, the binding is not generalised over the pattern-bound
3514 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3515 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3516 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3517 In contrast, the binding
3522 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3523 in <literal>f4</literal>'s scope.
3529 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3530 type signatures. The two can be used independently or together.</para>
3534 <sect3 id="result-type-sigs">
3535 <title>Result type signatures</title>
3538 The result type of a function can be given a signature, thus:
3542 f (x::a) :: [a] = [x,x,x]
3546 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3547 result type. Sometimes this is the only way of naming the type variable
3552 f :: Int -> [a] -> [a]
3553 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3554 in \xs -> map g (reverse xs `zip` xs)
3559 The type variables bound in a result type signature scope over the right hand side
3560 of the definition. However, consider this corner-case:
3562 rev1 :: [a] -> [a] = \xs -> reverse xs
3564 foo ys = rev (ys::[a])
3566 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3567 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3568 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3569 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3570 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3573 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3574 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3578 rev1 :: [a] -> [a] = \xs -> reverse xs
3583 Result type signatures are not yet implemented in Hugs.
3590 <sect2 id="deriving-typeable">
3591 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3594 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3595 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3596 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3597 classes <literal>Eq</literal>, <literal>Ord</literal>,
3598 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3601 GHC extends this list with two more classes that may be automatically derived
3602 (provided the <option>-fglasgow-exts</option> flag is specified):
3603 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3604 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3605 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3607 <para>An instance of <literal>Typeable</literal> can only be derived if the
3608 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3609 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3611 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3612 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3614 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3615 are used, and only <literal>Typeable1</literal> up to
3616 <literal>Typeable7</literal> are provided in the library.)
3617 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3618 class, whose kind suits that of the data type constructor, and
3619 then writing the data type instance by hand.
3623 <sect2 id="newtype-deriving">
3624 <title>Generalised derived instances for newtypes</title>
3627 When you define an abstract type using <literal>newtype</literal>, you may want
3628 the new type to inherit some instances from its representation. In
3629 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3630 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3631 other classes you have to write an explicit instance declaration. For
3632 example, if you define
3635 newtype Dollars = Dollars Int
3638 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3639 explicitly define an instance of <literal>Num</literal>:
3642 instance Num Dollars where
3643 Dollars a + Dollars b = Dollars (a+b)
3646 All the instance does is apply and remove the <literal>newtype</literal>
3647 constructor. It is particularly galling that, since the constructor
3648 doesn't appear at run-time, this instance declaration defines a
3649 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3650 dictionary, only slower!
3654 <sect3> <title> Generalising the deriving clause </title>
3656 GHC now permits such instances to be derived instead, so one can write
3658 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3661 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3662 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3663 derives an instance declaration of the form
3666 instance Num Int => Num Dollars
3669 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3673 We can also derive instances of constructor classes in a similar
3674 way. For example, suppose we have implemented state and failure monad
3675 transformers, such that
3678 instance Monad m => Monad (State s m)
3679 instance Monad m => Monad (Failure m)
3681 In Haskell 98, we can define a parsing monad by
3683 type Parser tok m a = State [tok] (Failure m) a
3686 which is automatically a monad thanks to the instance declarations
3687 above. With the extension, we can make the parser type abstract,
3688 without needing to write an instance of class <literal>Monad</literal>, via
3691 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3694 In this case the derived instance declaration is of the form
3696 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3699 Notice that, since <literal>Monad</literal> is a constructor class, the
3700 instance is a <emphasis>partial application</emphasis> of the new type, not the
3701 entire left hand side. We can imagine that the type declaration is
3702 ``eta-converted'' to generate the context of the instance
3707 We can even derive instances of multi-parameter classes, provided the
3708 newtype is the last class parameter. In this case, a ``partial
3709 application'' of the class appears in the <literal>deriving</literal>
3710 clause. For example, given the class
3713 class StateMonad s m | m -> s where ...
3714 instance Monad m => StateMonad s (State s m) where ...
3716 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3718 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3719 deriving (Monad, StateMonad [tok])
3722 The derived instance is obtained by completing the application of the
3723 class to the new type:
3726 instance StateMonad [tok] (State [tok] (Failure m)) =>
3727 StateMonad [tok] (Parser tok m)
3732 As a result of this extension, all derived instances in newtype
3733 declarations are treated uniformly (and implemented just by reusing
3734 the dictionary for the representation type), <emphasis>except</emphasis>
3735 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3736 the newtype and its representation.
3740 <sect3> <title> A more precise specification </title>
3742 Derived instance declarations are constructed as follows. Consider the
3743 declaration (after expansion of any type synonyms)
3746 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3752 The type <literal>t</literal> is an arbitrary type
3755 The <literal>vk+1...vn</literal> are type variables which do not occur in
3756 <literal>t</literal>, and
3759 The <literal>ci</literal> are partial applications of
3760 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3761 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3764 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3765 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3766 should not "look through" the type or its constructor. You can still
3767 derive these classes for a newtype, but it happens in the usual way, not
3768 via this new mechanism.
3771 Then, for each <literal>ci</literal>, the derived instance
3774 instance ci (t vk+1...v) => ci (T v1...vp)
3776 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3777 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3781 As an example which does <emphasis>not</emphasis> work, consider
3783 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3785 Here we cannot derive the instance
3787 instance Monad (State s m) => Monad (NonMonad m)
3790 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3791 and so cannot be "eta-converted" away. It is a good thing that this
3792 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3793 not, in fact, a monad --- for the same reason. Try defining
3794 <literal>>>=</literal> with the correct type: you won't be able to.
3798 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3799 important, since we can only derive instances for the last one. If the
3800 <literal>StateMonad</literal> class above were instead defined as
3803 class StateMonad m s | m -> s where ...
3806 then we would not have been able to derive an instance for the
3807 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3808 classes usually have one "main" parameter for which deriving new
3809 instances is most interesting.
3811 <para>Lastly, all of this applies only for classes other than
3812 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3813 and <literal>Data</literal>, for which the built-in derivation applies (section
3814 4.3.3. of the Haskell Report).
3815 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3816 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3817 the standard method is used or the one described here.)
3823 <sect2 id="typing-binds">
3824 <title>Generalised typing of mutually recursive bindings</title>
3827 The Haskell Report specifies that a group of bindings (at top level, or in a
3828 <literal>let</literal> or <literal>where</literal>) should be sorted into
3829 strongly-connected components, and then type-checked in dependency order
3830 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3831 Report, Section 4.5.1</ulink>).
3832 As each group is type-checked, any binders of the group that
3834 an explicit type signature are put in the type environment with the specified
3836 and all others are monomorphic until the group is generalised
3837 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3840 <para>Following a suggestion of Mark Jones, in his paper
3841 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3843 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3845 <emphasis>the dependency analysis ignores references to variables that have an explicit
3846 type signature</emphasis>.
3847 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3848 typecheck. For example, consider:
3850 f :: Eq a => a -> Bool
3851 f x = (x == x) || g True || g "Yes"
3853 g y = (y <= y) || f True
3855 This is rejected by Haskell 98, but under Jones's scheme the definition for
3856 <literal>g</literal> is typechecked first, separately from that for
3857 <literal>f</literal>,
3858 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3859 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3860 type is generalised, to get
3862 g :: Ord a => a -> Bool
3864 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3865 <literal>g</literal> in the type environment.
3869 The same refined dependency analysis also allows the type signatures of
3870 mutually-recursive functions to have different contexts, something that is illegal in
3871 Haskell 98 (Section 4.5.2, last sentence). With
3872 <option>-fglasgow-exts</option>
3873 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3874 type signatures; in practice this means that only variables bound by the same
3875 pattern binding must have the same context. For example, this is fine:
3877 f :: Eq a => a -> Bool
3878 f x = (x == x) || g True
3880 g :: Ord a => a -> Bool
3881 g y = (y <= y) || f True
3887 <!-- ==================== End of type system extensions ================= -->
3889 <!-- ====================== Generalised algebraic data types ======================= -->
3892 <title>Generalised Algebraic Data Types</title>
3894 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3895 to give the type signatures of constructors explicitly. For example:
3898 Lit :: Int -> Term Int
3899 Succ :: Term Int -> Term Int
3900 IsZero :: Term Int -> Term Bool
3901 If :: Term Bool -> Term a -> Term a -> Term a
3902 Pair :: Term a -> Term b -> Term (a,b)
3904 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3905 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3906 for these <literal>Terms</literal>:
3910 eval (Succ t) = 1 + eval t
3911 eval (IsZero t) = eval t == 0
3912 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3913 eval (Pair e1 e2) = (eval e1, eval e2)
3915 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3917 <para> The extensions to GHC are these:
3920 Data type declarations have a 'where' form, as exemplified above. The type signature of
3921 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3922 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3923 have no scope. Indeed, one can write a kind signature instead:
3925 data Term :: * -> * where ...
3927 or even a mixture of the two:
3929 data Foo a :: (* -> *) -> * where ...
3931 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3934 data Foo a (b :: * -> *) where ...
3939 There are no restrictions on the type of the data constructor, except that the result
3940 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3941 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3945 You can use record syntax on a GADT-style data type declaration:
3949 Lit { val :: Int } :: Term Int
3950 Succ { num :: Term Int } :: Term Int
3951 Pred { num :: Term Int } :: Term Int
3952 IsZero { arg :: Term Int } :: Term Bool
3953 Pair { arg1 :: Term a
3956 If { cnd :: Term Bool
3961 For every constructor that has a field <literal>f</literal>, (a) the type of
3962 field <literal>f</literal> must be the same; and (b) the
3963 result type of the constructor must be the same; both modulo alpha conversion.
3964 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3966 single name. Although their field types are both <literal>Term Int</literal>,
3967 their selector functions actually have different types:
3970 num :: Term Int -> Term Int
3971 arg :: Term Bool -> Term Int
3974 At the moment, record updates are not yet possible with GADT, so support is
3975 limited to record construction, selection and pattern matching:
3978 someTerm :: Term Bool
3979 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3982 eval Lit { val = i } = i
3983 eval Succ { num = t } = eval t + 1
3984 eval Pred { num = t } = eval t - 1
3985 eval IsZero { arg = t } = eval t == 0
3986 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3987 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3993 You can use strictness annotations, in the obvious places
3994 in the constructor type:
3997 Lit :: !Int -> Term Int
3998 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3999 Pair :: Term a -> Term b -> Term (a,b)
4004 You can use a <literal>deriving</literal> clause on a GADT-style data type
4005 declaration, but only if the data type could also have been declared in
4006 Haskell-98 syntax. For example, these two declarations are equivalent
4008 data Maybe1 a where {
4009 Nothing1 :: Maybe a ;
4010 Just1 :: a -> Maybe a
4011 } deriving( Eq, Ord )
4013 data Maybe2 a = Nothing2 | Just2 a
4016 This simply allows you to declare a vanilla Haskell-98 data type using the
4017 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
4021 Pattern matching causes type refinement. For example, in the right hand side of the equation
4026 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
4027 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
4028 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
4030 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
4031 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
4032 occur. However, the refinement is quite general. For example, if we had:
4034 eval :: Term a -> a -> a
4035 eval (Lit i) j = i+j
4037 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
4038 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
4039 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
4045 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
4047 data T a = forall b. MkT b (b->a)
4048 data T' a where { MKT :: b -> (b->a) -> T' a }
4053 <!-- ====================== End of Generalised algebraic data types ======================= -->
4055 <!-- ====================== TEMPLATE HASKELL ======================= -->
4057 <sect1 id="template-haskell">
4058 <title>Template Haskell</title>
4060 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
4061 Template Haskell at <ulink url="http://www.haskell.org/th/">
4062 http://www.haskell.org/th/</ulink>, while
4064 the main technical innovations is discussed in "<ulink
4065 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4066 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4067 The details of the Template Haskell design are still in flux. Make sure you
4068 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
4069 (search for the type ExpQ).
4070 [Temporary: many changes to the original design are described in
4071 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4072 Not all of these changes are in GHC 6.2.]
4075 <para> The first example from that paper is set out below as a worked example to help get you started.
4079 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4080 Tim Sheard is going to expand it.)
4084 <title>Syntax</title>
4086 <para> Template Haskell has the following new syntactic
4087 constructions. You need to use the flag
4088 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4089 </indexterm>to switch these syntactic extensions on
4090 (<option>-fth</option> is no longer implied by
4091 <option>-fglasgow-exts</option>).</para>
4095 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4096 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4097 There must be no space between the "$" and the identifier or parenthesis. This use
4098 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4099 of "." as an infix operator. If you want the infix operator, put spaces around it.
4101 <para> A splice can occur in place of
4103 <listitem><para> an expression; the spliced expression must
4104 have type <literal>Q Exp</literal></para></listitem>
4105 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4106 <listitem><para> [Planned, but not implemented yet.] a
4107 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4109 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4110 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4116 A expression quotation is written in Oxford brackets, thus:
4118 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4119 the quotation has type <literal>Expr</literal>.</para></listitem>
4120 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4121 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4122 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4123 the quotation has type <literal>Type</literal>.</para></listitem>
4124 </itemizedlist></para></listitem>
4127 Reification is written thus:
4129 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4130 has type <literal>Dec</literal>. </para></listitem>
4131 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4132 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4133 <listitem><para> Still to come: fixities </para></listitem>
4135 </itemizedlist></para>
4142 <sect2> <title> Using Template Haskell </title>
4146 The data types and monadic constructor functions for Template Haskell are in the library
4147 <literal>Language.Haskell.THSyntax</literal>.
4151 You can only run a function at compile time if it is imported from another module. That is,
4152 you can't define a function in a module, and call it from within a splice in the same module.
4153 (It would make sense to do so, but it's hard to implement.)
4157 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4160 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4161 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4162 compiles and runs a program, and then looks at the result. So it's important that
4163 the program it compiles produces results whose representations are identical to
4164 those of the compiler itself.
4168 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4169 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4174 <sect2> <title> A Template Haskell Worked Example </title>
4175 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4176 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4183 -- Import our template "pr"
4184 import Printf ( pr )
4186 -- The splice operator $ takes the Haskell source code
4187 -- generated at compile time by "pr" and splices it into
4188 -- the argument of "putStrLn".
4189 main = putStrLn ( $(pr "Hello") )
4195 -- Skeletal printf from the paper.
4196 -- It needs to be in a separate module to the one where
4197 -- you intend to use it.
4199 -- Import some Template Haskell syntax
4200 import Language.Haskell.TH
4202 -- Describe a format string
4203 data Format = D | S | L String
4205 -- Parse a format string. This is left largely to you
4206 -- as we are here interested in building our first ever
4207 -- Template Haskell program and not in building printf.
4208 parse :: String -> [Format]
4211 -- Generate Haskell source code from a parsed representation
4212 -- of the format string. This code will be spliced into
4213 -- the module which calls "pr", at compile time.
4214 gen :: [Format] -> ExpQ
4215 gen [D] = [| \n -> show n |]
4216 gen [S] = [| \s -> s |]
4217 gen [L s] = stringE s
4219 -- Here we generate the Haskell code for the splice
4220 -- from an input format string.
4221 pr :: String -> ExpQ
4222 pr s = gen (parse s)
4225 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4228 $ ghc --make -fth main.hs -o main.exe
4231 <para>Run "main.exe" and here is your output:</para>
4241 <title>Using Template Haskell with Profiling</title>
4242 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4244 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4245 interpreter to run the splice expressions. The bytecode interpreter
4246 runs the compiled expression on top of the same runtime on which GHC
4247 itself is running; this means that the compiled code referred to by
4248 the interpreted expression must be compatible with this runtime, and
4249 in particular this means that object code that is compiled for
4250 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4251 expression, because profiled object code is only compatible with the
4252 profiling version of the runtime.</para>
4254 <para>This causes difficulties if you have a multi-module program
4255 containing Template Haskell code and you need to compile it for
4256 profiling, because GHC cannot load the profiled object code and use it
4257 when executing the splices. Fortunately GHC provides a workaround.
4258 The basic idea is to compile the program twice:</para>
4262 <para>Compile the program or library first the normal way, without
4263 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4266 <para>Then compile it again with <option>-prof</option>, and
4267 additionally use <option>-osuf
4268 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4269 to name the object files differentliy (you can choose any suffix
4270 that isn't the normal object suffix here). GHC will automatically
4271 load the object files built in the first step when executing splice
4272 expressions. If you omit the <option>-osuf</option> flag when
4273 building with <option>-prof</option> and Template Haskell is used,
4274 GHC will emit an error message. </para>
4281 <!-- ===================== Arrow notation =================== -->
4283 <sect1 id="arrow-notation">
4284 <title>Arrow notation
4287 <para>Arrows are a generalization of monads introduced by John Hughes.
4288 For more details, see
4293 “Generalising Monads to Arrows”,
4294 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4295 pp67–111, May 2000.
4301 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4302 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4308 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4309 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4315 and the arrows web page at
4316 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4317 With the <option>-farrows</option> flag, GHC supports the arrow
4318 notation described in the second of these papers.
4319 What follows is a brief introduction to the notation;
4320 it won't make much sense unless you've read Hughes's paper.
4321 This notation is translated to ordinary Haskell,
4322 using combinators from the
4323 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4327 <para>The extension adds a new kind of expression for defining arrows:
4329 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4330 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4332 where <literal>proc</literal> is a new keyword.
4333 The variables of the pattern are bound in the body of the
4334 <literal>proc</literal>-expression,
4335 which is a new sort of thing called a <firstterm>command</firstterm>.
4336 The syntax of commands is as follows:
4338 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4339 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4340 | <replaceable>cmd</replaceable><superscript>0</superscript>
4342 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4343 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4344 infix operators as for expressions, and
4346 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4347 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4348 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4349 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4350 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4351 | <replaceable>fcmd</replaceable>
4353 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4354 | ( <replaceable>cmd</replaceable> )
4355 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4357 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4358 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4359 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4360 | <replaceable>cmd</replaceable>
4362 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4363 except that the bodies are commands instead of expressions.
4367 Commands produce values, but (like monadic computations)
4368 may yield more than one value,
4369 or none, and may do other things as well.
4370 For the most part, familiarity with monadic notation is a good guide to
4372 However the values of expressions, even monadic ones,
4373 are determined by the values of the variables they contain;
4374 this is not necessarily the case for commands.
4378 A simple example of the new notation is the expression
4380 proc x -> f -< x+1
4382 We call this a <firstterm>procedure</firstterm> or
4383 <firstterm>arrow abstraction</firstterm>.
4384 As with a lambda expression, the variable <literal>x</literal>
4385 is a new variable bound within the <literal>proc</literal>-expression.
4386 It refers to the input to the arrow.
4387 In the above example, <literal>-<</literal> is not an identifier but an
4388 new reserved symbol used for building commands from an expression of arrow
4389 type and an expression to be fed as input to that arrow.
4390 (The weird look will make more sense later.)
4391 It may be read as analogue of application for arrows.
4392 The above example is equivalent to the Haskell expression
4394 arr (\ x -> x+1) >>> f
4396 That would make no sense if the expression to the left of
4397 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4398 More generally, the expression to the left of <literal>-<</literal>
4399 may not involve any <firstterm>local variable</firstterm>,
4400 i.e. a variable bound in the current arrow abstraction.
4401 For such a situation there is a variant <literal>-<<</literal>, as in
4403 proc x -> f x -<< x+1
4405 which is equivalent to
4407 arr (\ x -> (f x, x+1)) >>> app
4409 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4411 Such an arrow is equivalent to a monad, so if you're using this form
4412 you may find a monadic formulation more convenient.
4416 <title>do-notation for commands</title>
4419 Another form of command is a form of <literal>do</literal>-notation.
4420 For example, you can write
4429 You can read this much like ordinary <literal>do</literal>-notation,
4430 but with commands in place of monadic expressions.
4431 The first line sends the value of <literal>x+1</literal> as an input to
4432 the arrow <literal>f</literal>, and matches its output against
4433 <literal>y</literal>.
4434 In the next line, the output is discarded.
4435 The arrow <function>returnA</function> is defined in the
4436 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4437 module as <literal>arr id</literal>.
4438 The above example is treated as an abbreviation for
4440 arr (\ x -> (x, x)) >>>
4441 first (arr (\ x -> x+1) >>> f) >>>
4442 arr (\ (y, x) -> (y, (x, y))) >>>
4443 first (arr (\ y -> 2*y) >>> g) >>>
4445 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4446 first (arr (\ (x, z) -> x*z) >>> h) >>>
4447 arr (\ (t, z) -> t+z) >>>
4450 Note that variables not used later in the composition are projected out.
4451 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4453 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4454 module, this reduces to
4456 arr (\ x -> (x+1, x)) >>>
4458 arr (\ (y, x) -> (2*y, (x, y))) >>>
4460 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4462 arr (\ (t, z) -> t+z)
4464 which is what you might have written by hand.
4465 With arrow notation, GHC keeps track of all those tuples of variables for you.
4469 Note that although the above translation suggests that
4470 <literal>let</literal>-bound variables like <literal>z</literal> must be
4471 monomorphic, the actual translation produces Core,
4472 so polymorphic variables are allowed.
4476 It's also possible to have mutually recursive bindings,
4477 using the new <literal>rec</literal> keyword, as in the following example:
4479 counter :: ArrowCircuit a => a Bool Int
4480 counter = proc reset -> do
4481 rec output <- returnA -< if reset then 0 else next
4482 next <- delay 0 -< output+1
4483 returnA -< output
4485 The translation of such forms uses the <function>loop</function> combinator,
4486 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4492 <title>Conditional commands</title>
4495 In the previous example, we used a conditional expression to construct the
4497 Sometimes we want to conditionally execute different commands, as in
4504 which is translated to
4506 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4507 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4509 Since the translation uses <function>|||</function>,
4510 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4514 There are also <literal>case</literal> commands, like
4520 y <- h -< (x1, x2)
4524 The syntax is the same as for <literal>case</literal> expressions,
4525 except that the bodies of the alternatives are commands rather than expressions.
4526 The translation is similar to that of <literal>if</literal> commands.
4532 <title>Defining your own control structures</title>
4535 As we're seen, arrow notation provides constructs,
4536 modelled on those for expressions,
4537 for sequencing, value recursion and conditionals.
4538 But suitable combinators,
4539 which you can define in ordinary Haskell,
4540 may also be used to build new commands out of existing ones.
4541 The basic idea is that a command defines an arrow from environments to values.
4542 These environments assign values to the free local variables of the command.
4543 Thus combinators that produce arrows from arrows
4544 may also be used to build commands from commands.
4545 For example, the <literal>ArrowChoice</literal> class includes a combinator
4547 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4549 so we can use it to build commands:
4551 expr' = proc x -> do
4554 symbol Plus -< ()
4555 y <- term -< ()
4558 symbol Minus -< ()
4559 y <- term -< ()
4562 (The <literal>do</literal> on the first line is needed to prevent the first
4563 <literal><+> ...</literal> from being interpreted as part of the
4564 expression on the previous line.)
4565 This is equivalent to
4567 expr' = (proc x -> returnA -< x)
4568 <+> (proc x -> do
4569 symbol Plus -< ()
4570 y <- term -< ()
4572 <+> (proc x -> do
4573 symbol Minus -< ()
4574 y <- term -< ()
4577 It is essential that this operator be polymorphic in <literal>e</literal>
4578 (representing the environment input to the command
4579 and thence to its subcommands)
4580 and satisfy the corresponding naturality property
4582 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4584 at least for strict <literal>k</literal>.
4585 (This should be automatic if you're not using <function>seq</function>.)
4586 This ensures that environments seen by the subcommands are environments
4587 of the whole command,
4588 and also allows the translation to safely trim these environments.
4589 The operator must also not use any variable defined within the current
4594 We could define our own operator
4596 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4597 untilA body cond = proc x ->
4598 if cond x then returnA -< ()
4601 untilA body cond -< x
4603 and use it in the same way.
4604 Of course this infix syntax only makes sense for binary operators;
4605 there is also a more general syntax involving special brackets:
4609 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4616 <title>Primitive constructs</title>
4619 Some operators will need to pass additional inputs to their subcommands.
4620 For example, in an arrow type supporting exceptions,
4621 the operator that attaches an exception handler will wish to pass the
4622 exception that occurred to the handler.
4623 Such an operator might have a type
4625 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4627 where <literal>Ex</literal> is the type of exceptions handled.
4628 You could then use this with arrow notation by writing a command
4630 body `handleA` \ ex -> handler
4632 so that if an exception is raised in the command <literal>body</literal>,
4633 the variable <literal>ex</literal> is bound to the value of the exception
4634 and the command <literal>handler</literal>,
4635 which typically refers to <literal>ex</literal>, is entered.
4636 Though the syntax here looks like a functional lambda,
4637 we are talking about commands, and something different is going on.
4638 The input to the arrow represented by a command consists of values for
4639 the free local variables in the command, plus a stack of anonymous values.
4640 In all the prior examples, this stack was empty.
4641 In the second argument to <function>handleA</function>,
4642 this stack consists of one value, the value of the exception.
4643 The command form of lambda merely gives this value a name.
4648 the values on the stack are paired to the right of the environment.
4649 So operators like <function>handleA</function> that pass
4650 extra inputs to their subcommands can be designed for use with the notation
4651 by pairing the values with the environment in this way.
4652 More precisely, the type of each argument of the operator (and its result)
4653 should have the form
4655 a (...(e,t1), ... tn) t
4657 where <replaceable>e</replaceable> is a polymorphic variable
4658 (representing the environment)
4659 and <replaceable>ti</replaceable> are the types of the values on the stack,
4660 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4661 The polymorphic variable <replaceable>e</replaceable> must not occur in
4662 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4663 <replaceable>t</replaceable>.
4664 However the arrows involved need not be the same.
4665 Here are some more examples of suitable operators:
4667 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4668 runReader :: ... => a e c -> a' (e,State) c
4669 runState :: ... => a e c -> a' (e,State) (c,State)
4671 We can supply the extra input required by commands built with the last two
4672 by applying them to ordinary expressions, as in
4676 (|runReader (do { ... })|) s
4678 which adds <literal>s</literal> to the stack of inputs to the command
4679 built using <function>runReader</function>.
4683 The command versions of lambda abstraction and application are analogous to
4684 the expression versions.
4685 In particular, the beta and eta rules describe equivalences of commands.
4686 These three features (operators, lambda abstraction and application)
4687 are the core of the notation; everything else can be built using them,
4688 though the results would be somewhat clumsy.
4689 For example, we could simulate <literal>do</literal>-notation by defining
4691 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4692 u `bind` f = returnA &&& u >>> f
4694 bind_ :: Arrow a => a e b -> a e c -> a e c
4695 u `bind_` f = u `bind` (arr fst >>> f)
4697 We could simulate <literal>if</literal> by defining
4699 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4700 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4707 <title>Differences with the paper</title>
4712 <para>Instead of a single form of arrow application (arrow tail) with two
4713 translations, the implementation provides two forms
4714 <quote><literal>-<</literal></quote> (first-order)
4715 and <quote><literal>-<<</literal></quote> (higher-order).
4720 <para>User-defined operators are flagged with banana brackets instead of
4721 a new <literal>form</literal> keyword.
4730 <title>Portability</title>
4733 Although only GHC implements arrow notation directly,
4734 there is also a preprocessor
4736 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4737 that translates arrow notation into Haskell 98
4738 for use with other Haskell systems.
4739 You would still want to check arrow programs with GHC;
4740 tracing type errors in the preprocessor output is not easy.
4741 Modules intended for both GHC and the preprocessor must observe some
4742 additional restrictions:
4747 The module must import
4748 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4754 The preprocessor cannot cope with other Haskell extensions.
4755 These would have to go in separate modules.
4761 Because the preprocessor targets Haskell (rather than Core),
4762 <literal>let</literal>-bound variables are monomorphic.
4773 <!-- ==================== ASSERTIONS ================= -->
4775 <sect1 id="sec-assertions">
4777 <indexterm><primary>Assertions</primary></indexterm>
4781 If you want to make use of assertions in your standard Haskell code, you
4782 could define a function like the following:
4788 assert :: Bool -> a -> a
4789 assert False x = error "assertion failed!"
4796 which works, but gives you back a less than useful error message --
4797 an assertion failed, but which and where?
4801 One way out is to define an extended <function>assert</function> function which also
4802 takes a descriptive string to include in the error message and
4803 perhaps combine this with the use of a pre-processor which inserts
4804 the source location where <function>assert</function> was used.
4808 Ghc offers a helping hand here, doing all of this for you. For every
4809 use of <function>assert</function> in the user's source:
4815 kelvinToC :: Double -> Double
4816 kelvinToC k = assert (k >= 0.0) (k+273.15)
4822 Ghc will rewrite this to also include the source location where the
4829 assert pred val ==> assertError "Main.hs|15" pred val
4835 The rewrite is only performed by the compiler when it spots
4836 applications of <function>Control.Exception.assert</function>, so you
4837 can still define and use your own versions of
4838 <function>assert</function>, should you so wish. If not, import
4839 <literal>Control.Exception</literal> to make use
4840 <function>assert</function> in your code.
4844 GHC ignores assertions when optimisation is turned on with the
4845 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4846 <literal>assert pred e</literal> will be rewritten to
4847 <literal>e</literal>. You can also disable assertions using the
4848 <option>-fignore-asserts</option>
4849 option<indexterm><primary><option>-fignore-asserts</option></primary>
4850 </indexterm>.</para>
4853 Assertion failures can be caught, see the documentation for the
4854 <literal>Control.Exception</literal> library for the details.
4860 <!-- =============================== PRAGMAS =========================== -->
4862 <sect1 id="pragmas">
4863 <title>Pragmas</title>
4865 <indexterm><primary>pragma</primary></indexterm>
4867 <para>GHC supports several pragmas, or instructions to the
4868 compiler placed in the source code. Pragmas don't normally affect
4869 the meaning of the program, but they might affect the efficiency
4870 of the generated code.</para>
4872 <para>Pragmas all take the form
4874 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4876 where <replaceable>word</replaceable> indicates the type of
4877 pragma, and is followed optionally by information specific to that
4878 type of pragma. Case is ignored in
4879 <replaceable>word</replaceable>. The various values for
4880 <replaceable>word</replaceable> that GHC understands are described
4881 in the following sections; any pragma encountered with an
4882 unrecognised <replaceable>word</replaceable> is (silently)
4885 <sect2 id="deprecated-pragma">
4886 <title>DEPRECATED pragma</title>
4887 <indexterm><primary>DEPRECATED</primary>
4890 <para>The DEPRECATED pragma lets you specify that a particular
4891 function, class, or type, is deprecated. There are two
4896 <para>You can deprecate an entire module thus:</para>
4898 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4901 <para>When you compile any module that import
4902 <literal>Wibble</literal>, GHC will print the specified
4907 <para>You can deprecate a function, class, type, or data constructor, with the
4908 following top-level declaration:</para>
4910 {-# DEPRECATED f, C, T "Don't use these" #-}
4912 <para>When you compile any module that imports and uses any
4913 of the specified entities, GHC will print the specified
4915 <para> You can only depecate entities declared at top level in the module
4916 being compiled, and you can only use unqualified names in the list of
4917 entities being deprecated. A capitalised name, such as <literal>T</literal>
4918 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4919 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4920 both are in scope. If both are in scope, there is currently no way to deprecate
4921 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4924 Any use of the deprecated item, or of anything from a deprecated
4925 module, will be flagged with an appropriate message. However,
4926 deprecations are not reported for
4927 (a) uses of a deprecated function within its defining module, and
4928 (b) uses of a deprecated function in an export list.
4929 The latter reduces spurious complaints within a library
4930 in which one module gathers together and re-exports
4931 the exports of several others.
4933 <para>You can suppress the warnings with the flag
4934 <option>-fno-warn-deprecations</option>.</para>
4937 <sect2 id="include-pragma">
4938 <title>INCLUDE pragma</title>
4940 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
4941 of C header files that should be <literal>#include</literal>'d into
4942 the C source code generated by the compiler for the current module (if
4943 compiling via C). For example:</para>
4946 {-# INCLUDE "foo.h" #-}
4947 {-# INCLUDE <stdio.h> #-}</programlisting>
4949 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
4950 your source file with any <literal>OPTIONS_GHC</literal>
4953 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
4954 to the <option>-#include</option> option (<xref
4955 linkend="options-C-compiler" />), because the
4956 <literal>INCLUDE</literal> pragma is understood by other
4957 compilers. Yet another alternative is to add the include file to each
4958 <literal>foreign import</literal> declaration in your code, but we
4959 don't recommend using this approach with GHC.</para>
4962 <sect2 id="inline-noinline-pragma">
4963 <title>INLINE and NOINLINE pragmas</title>
4965 <para>These pragmas control the inlining of function
4968 <sect3 id="inline-pragma">
4969 <title>INLINE pragma</title>
4970 <indexterm><primary>INLINE</primary></indexterm>
4972 <para>GHC (with <option>-O</option>, as always) tries to
4973 inline (or “unfold”) functions/values that are
4974 “small enough,” thus avoiding the call overhead
4975 and possibly exposing other more-wonderful optimisations.
4976 Normally, if GHC decides a function is “too
4977 expensive” to inline, it will not do so, nor will it
4978 export that unfolding for other modules to use.</para>
4980 <para>The sledgehammer you can bring to bear is the
4981 <literal>INLINE</literal><indexterm><primary>INLINE
4982 pragma</primary></indexterm> pragma, used thusly:</para>
4985 key_function :: Int -> String -> (Bool, Double)
4987 #ifdef __GLASGOW_HASKELL__
4988 {-# INLINE key_function #-}
4992 <para>(You don't need to do the C pre-processor carry-on
4993 unless you're going to stick the code through HBC—it
4994 doesn't like <literal>INLINE</literal> pragmas.)</para>
4996 <para>The major effect of an <literal>INLINE</literal> pragma
4997 is to declare a function's “cost” to be very low.
4998 The normal unfolding machinery will then be very keen to
5001 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5002 function can be put anywhere its type signature could be
5005 <para><literal>INLINE</literal> pragmas are a particularly
5007 <literal>then</literal>/<literal>return</literal> (or
5008 <literal>bind</literal>/<literal>unit</literal>) functions in
5009 a monad. For example, in GHC's own
5010 <literal>UniqueSupply</literal> monad code, we have:</para>
5013 #ifdef __GLASGOW_HASKELL__
5014 {-# INLINE thenUs #-}
5015 {-# INLINE returnUs #-}
5019 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5020 linkend="noinline-pragma"/>).</para>
5023 <sect3 id="noinline-pragma">
5024 <title>NOINLINE pragma</title>
5026 <indexterm><primary>NOINLINE</primary></indexterm>
5027 <indexterm><primary>NOTINLINE</primary></indexterm>
5029 <para>The <literal>NOINLINE</literal> pragma does exactly what
5030 you'd expect: it stops the named function from being inlined
5031 by the compiler. You shouldn't ever need to do this, unless
5032 you're very cautious about code size.</para>
5034 <para><literal>NOTINLINE</literal> is a synonym for
5035 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5036 specified by Haskell 98 as the standard way to disable
5037 inlining, so it should be used if you want your code to be
5041 <sect3 id="phase-control">
5042 <title>Phase control</title>
5044 <para> Sometimes you want to control exactly when in GHC's
5045 pipeline the INLINE pragma is switched on. Inlining happens
5046 only during runs of the <emphasis>simplifier</emphasis>. Each
5047 run of the simplifier has a different <emphasis>phase
5048 number</emphasis>; the phase number decreases towards zero.
5049 If you use <option>-dverbose-core2core</option> you'll see the
5050 sequence of phase numbers for successive runs of the
5051 simplifier. In an INLINE pragma you can optionally specify a
5055 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5056 <literal>f</literal>
5057 until phase <literal>k</literal>, but from phase
5058 <literal>k</literal> onwards be very keen to inline it.
5061 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5062 <literal>f</literal>
5063 until phase <literal>k</literal>, but from phase
5064 <literal>k</literal> onwards do not inline it.
5067 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5068 <literal>f</literal>
5069 until phase <literal>k</literal>, but from phase
5070 <literal>k</literal> onwards be willing to inline it (as if
5071 there was no pragma).
5074 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5075 <literal>f</literal>
5076 until phase <literal>k</literal>, but from phase
5077 <literal>k</literal> onwards do not inline it.
5080 The same information is summarised here:
5082 -- Before phase 2 Phase 2 and later
5083 {-# INLINE [2] f #-} -- No Yes
5084 {-# INLINE [~2] f #-} -- Yes No
5085 {-# NOINLINE [2] f #-} -- No Maybe
5086 {-# NOINLINE [~2] f #-} -- Maybe No
5088 {-# INLINE f #-} -- Yes Yes
5089 {-# NOINLINE f #-} -- No No
5091 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5092 function body is small, or it is applied to interesting-looking arguments etc).
5093 Another way to understand the semantics is this:
5095 <listitem><para>For both INLINE and NOINLINE, the phase number says
5096 when inlining is allowed at all.</para></listitem>
5097 <listitem><para>The INLINE pragma has the additional effect of making the
5098 function body look small, so that when inlining is allowed it is very likely to
5103 <para>The same phase-numbering control is available for RULES
5104 (<xref linkend="rewrite-rules"/>).</para>
5108 <sect2 id="language-pragma">
5109 <title>LANGUAGE pragma</title>
5111 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5112 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5114 <para>This allows language extensions to be enabled in a portable way.
5115 It is the intention that all Haskell compilers support the
5116 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5117 all extensions are supported by all compilers, of
5118 course. The <literal>LANGUAGE</literal> pragma should be used instead
5119 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5121 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5123 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5125 <para>Any extension from the <literal>Extension</literal> type defined in
5127 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink> may be used. GHC will report an error if any of the requested extensions are not supported.</para>
5131 <sect2 id="line-pragma">
5132 <title>LINE pragma</title>
5134 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5135 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5136 <para>This pragma is similar to C's <literal>#line</literal>
5137 pragma, and is mainly for use in automatically generated Haskell
5138 code. It lets you specify the line number and filename of the
5139 original code; for example</para>
5141 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5143 <para>if you'd generated the current file from something called
5144 <filename>Foo.vhs</filename> and this line corresponds to line
5145 42 in the original. GHC will adjust its error messages to refer
5146 to the line/file named in the <literal>LINE</literal>
5150 <sect2 id="options-pragma">
5151 <title>OPTIONS_GHC pragma</title>
5152 <indexterm><primary>OPTIONS_GHC</primary>
5154 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5157 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5158 additional options that are given to the compiler when compiling
5159 this source file. See <xref linkend="source-file-options"/> for
5162 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5163 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5167 <title>RULES pragma</title>
5169 <para>The RULES pragma lets you specify rewrite rules. It is
5170 described in <xref linkend="rewrite-rules"/>.</para>
5173 <sect2 id="specialize-pragma">
5174 <title>SPECIALIZE pragma</title>
5176 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5177 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5178 <indexterm><primary>overloading, death to</primary></indexterm>
5180 <para>(UK spelling also accepted.) For key overloaded
5181 functions, you can create extra versions (NB: more code space)
5182 specialised to particular types. Thus, if you have an
5183 overloaded function:</para>
5186 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5189 <para>If it is heavily used on lists with
5190 <literal>Widget</literal> keys, you could specialise it as
5194 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5197 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5198 be put anywhere its type signature could be put.</para>
5200 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5201 (a) a specialised version of the function and (b) a rewrite rule
5202 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5203 un-specialised function into a call to the specialised one.</para>
5205 <para>The type in a SPECIALIZE pragma can be any type that is less
5206 polymorphic than the type of the original function. In concrete terms,
5207 if the original function is <literal>f</literal> then the pragma
5209 {-# SPECIALIZE f :: <type> #-}
5211 is valid if and only if the defintion
5213 f_spec :: <type>
5216 is valid. Here are some examples (where we only give the type signature
5217 for the original function, not its code):
5219 f :: Eq a => a -> b -> b
5220 {-# SPECIALISE f :: Int -> b -> b #-}
5222 g :: (Eq a, Ix b) => a -> b -> b
5223 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5225 h :: Eq a => a -> a -> a
5226 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5228 The last of these examples will generate a
5229 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5230 well. If you use this kind of specialisation, let us know how well it works.
5233 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5234 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5235 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5236 The <literal>INLINE</literal> pragma affects the specialised verison of the
5237 function (only), and applies even if the function is recursive. The motivating
5240 -- A GADT for arrays with type-indexed representation
5242 ArrInt :: !Int -> ByteArray# -> Arr Int
5243 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5245 (!:) :: Arr e -> Int -> e
5246 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5247 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5248 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5249 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5251 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5252 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5253 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5254 the specialised function will be inlined. It has two calls to
5255 <literal>(!:)</literal>,
5256 both at type <literal>Int</literal>. Both these calls fire the first
5257 specialisation, whose body is also inlined. The result is a type-based
5258 unrolling of the indexing function.</para>
5259 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5260 on an ordinarily-recursive function.</para>
5262 <para>Note: In earlier versions of GHC, it was possible to provide your own
5263 specialised function for a given type:
5266 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5269 This feature has been removed, as it is now subsumed by the
5270 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5274 <sect2 id="specialize-instance-pragma">
5275 <title>SPECIALIZE instance pragma
5279 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5280 <indexterm><primary>overloading, death to</primary></indexterm>
5281 Same idea, except for instance declarations. For example:
5284 instance (Eq a) => Eq (Foo a) where {
5285 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5289 The pragma must occur inside the <literal>where</literal> part
5290 of the instance declaration.
5293 Compatible with HBC, by the way, except perhaps in the placement
5299 <sect2 id="unpack-pragma">
5300 <title>UNPACK pragma</title>
5302 <indexterm><primary>UNPACK</primary></indexterm>
5304 <para>The <literal>UNPACK</literal> indicates to the compiler
5305 that it should unpack the contents of a constructor field into
5306 the constructor itself, removing a level of indirection. For
5310 data T = T {-# UNPACK #-} !Float
5311 {-# UNPACK #-} !Float
5314 <para>will create a constructor <literal>T</literal> containing
5315 two unboxed floats. This may not always be an optimisation: if
5316 the <function>T</function> constructor is scrutinised and the
5317 floats passed to a non-strict function for example, they will
5318 have to be reboxed (this is done automatically by the
5321 <para>Unpacking constructor fields should only be used in
5322 conjunction with <option>-O</option>, in order to expose
5323 unfoldings to the compiler so the reboxing can be removed as
5324 often as possible. For example:</para>
5328 f (T f1 f2) = f1 + f2
5331 <para>The compiler will avoid reboxing <function>f1</function>
5332 and <function>f2</function> by inlining <function>+</function>
5333 on floats, but only when <option>-O</option> is on.</para>
5335 <para>Any single-constructor data is eligible for unpacking; for
5339 data T = T {-# UNPACK #-} !(Int,Int)
5342 <para>will store the two <literal>Int</literal>s directly in the
5343 <function>T</function> constructor, by flattening the pair.
5344 Multi-level unpacking is also supported:</para>
5347 data T = T {-# UNPACK #-} !S
5348 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5351 <para>will store two unboxed <literal>Int#</literal>s
5352 directly in the <function>T</function> constructor. The
5353 unpacker can see through newtypes, too.</para>
5355 <para>If a field cannot be unpacked, you will not get a warning,
5356 so it might be an idea to check the generated code with
5357 <option>-ddump-simpl</option>.</para>
5359 <para>See also the <option>-funbox-strict-fields</option> flag,
5360 which essentially has the effect of adding
5361 <literal>{-# UNPACK #-}</literal> to every strict
5362 constructor field.</para>
5367 <!-- ======================= REWRITE RULES ======================== -->
5369 <sect1 id="rewrite-rules">
5370 <title>Rewrite rules
5372 <indexterm><primary>RULES pragma</primary></indexterm>
5373 <indexterm><primary>pragma, RULES</primary></indexterm>
5374 <indexterm><primary>rewrite rules</primary></indexterm></title>
5377 The programmer can specify rewrite rules as part of the source program
5378 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5379 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5380 and (b) the <option>-frules-off</option> flag
5381 (<xref linkend="options-f"/>) is not specified, and (c) the
5382 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5391 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5398 <title>Syntax</title>
5401 From a syntactic point of view:
5407 There may be zero or more rules in a <literal>RULES</literal> pragma.
5414 Each rule has a name, enclosed in double quotes. The name itself has
5415 no significance at all. It is only used when reporting how many times the rule fired.
5421 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5422 immediately after the name of the rule. Thus:
5425 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5428 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5429 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5438 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5439 is set, so you must lay out your rules starting in the same column as the
5440 enclosing definitions.
5447 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5448 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5449 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5450 by spaces, just like in a type <literal>forall</literal>.
5456 A pattern variable may optionally have a type signature.
5457 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5458 For example, here is the <literal>foldr/build</literal> rule:
5461 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5462 foldr k z (build g) = g k z
5465 Since <function>g</function> has a polymorphic type, it must have a type signature.
5472 The left hand side of a rule must consist of a top-level variable applied
5473 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5476 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5477 "wrong2" forall f. f True = True
5480 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5487 A rule does not need to be in the same module as (any of) the
5488 variables it mentions, though of course they need to be in scope.
5494 Rules are automatically exported from a module, just as instance declarations are.
5505 <title>Semantics</title>
5508 From a semantic point of view:
5514 Rules are only applied if you use the <option>-O</option> flag.
5520 Rules are regarded as left-to-right rewrite rules.
5521 When GHC finds an expression that is a substitution instance of the LHS
5522 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5523 By "a substitution instance" we mean that the LHS can be made equal to the
5524 expression by substituting for the pattern variables.
5531 The LHS and RHS of a rule are typechecked, and must have the
5539 GHC makes absolutely no attempt to verify that the LHS and RHS
5540 of a rule have the same meaning. That is undecidable in general, and
5541 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5548 GHC makes no attempt to make sure that the rules are confluent or
5549 terminating. For example:
5552 "loop" forall x,y. f x y = f y x
5555 This rule will cause the compiler to go into an infinite loop.
5562 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5568 GHC currently uses a very simple, syntactic, matching algorithm
5569 for matching a rule LHS with an expression. It seeks a substitution
5570 which makes the LHS and expression syntactically equal modulo alpha
5571 conversion. The pattern (rule), but not the expression, is eta-expanded if
5572 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5573 But not beta conversion (that's called higher-order matching).
5577 Matching is carried out on GHC's intermediate language, which includes
5578 type abstractions and applications. So a rule only matches if the
5579 types match too. See <xref linkend="rule-spec"/> below.
5585 GHC keeps trying to apply the rules as it optimises the program.
5586 For example, consider:
5595 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5596 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5597 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5598 not be substituted, and the rule would not fire.
5605 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5606 that appears on the LHS of a rule</emphasis>, because once you have substituted
5607 for something you can't match against it (given the simple minded
5608 matching). So if you write the rule
5611 "map/map" forall f,g. map f . map g = map (f.g)
5614 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5615 It will only match something written with explicit use of ".".
5616 Well, not quite. It <emphasis>will</emphasis> match the expression
5622 where <function>wibble</function> is defined:
5625 wibble f g = map f . map g
5628 because <function>wibble</function> will be inlined (it's small).
5630 Later on in compilation, GHC starts inlining even things on the
5631 LHS of rules, but still leaves the rules enabled. This inlining
5632 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5639 All rules are implicitly exported from the module, and are therefore
5640 in force in any module that imports the module that defined the rule, directly
5641 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5642 in force when compiling A.) The situation is very similar to that for instance
5654 <title>List fusion</title>
5657 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5658 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5659 intermediate list should be eliminated entirely.
5663 The following are good producers:
5675 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5681 Explicit lists (e.g. <literal>[True, False]</literal>)
5687 The cons constructor (e.g <literal>3:4:[]</literal>)
5693 <function>++</function>
5699 <function>map</function>
5705 <function>take</function>, <function>filter</function>
5711 <function>iterate</function>, <function>repeat</function>
5717 <function>zip</function>, <function>zipWith</function>
5726 The following are good consumers:
5738 <function>array</function> (on its second argument)
5744 <function>length</function>
5750 <function>++</function> (on its first argument)
5756 <function>foldr</function>
5762 <function>map</function>
5768 <function>take</function>, <function>filter</function>
5774 <function>concat</function>
5780 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5786 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5787 will fuse with one but not the other)
5793 <function>partition</function>
5799 <function>head</function>
5805 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5811 <function>sequence_</function>
5817 <function>msum</function>
5823 <function>sortBy</function>
5832 So, for example, the following should generate no intermediate lists:
5835 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5841 This list could readily be extended; if there are Prelude functions that you use
5842 a lot which are not included, please tell us.
5846 If you want to write your own good consumers or producers, look at the
5847 Prelude definitions of the above functions to see how to do so.
5852 <sect2 id="rule-spec">
5853 <title>Specialisation
5857 Rewrite rules can be used to get the same effect as a feature
5858 present in earlier versions of GHC.
5859 For example, suppose that:
5862 genericLookup :: Ord a => Table a b -> a -> b
5863 intLookup :: Table Int b -> Int -> b
5866 where <function>intLookup</function> is an implementation of
5867 <function>genericLookup</function> that works very fast for
5868 keys of type <literal>Int</literal>. You might wish
5869 to tell GHC to use <function>intLookup</function> instead of
5870 <function>genericLookup</function> whenever the latter was called with
5871 type <literal>Table Int b -> Int -> b</literal>.
5872 It used to be possible to write
5875 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5878 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5881 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5884 This slightly odd-looking rule instructs GHC to replace
5885 <function>genericLookup</function> by <function>intLookup</function>
5886 <emphasis>whenever the types match</emphasis>.
5887 What is more, this rule does not need to be in the same
5888 file as <function>genericLookup</function>, unlike the
5889 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5890 have an original definition available to specialise).
5893 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5894 <function>intLookup</function> really behaves as a specialised version
5895 of <function>genericLookup</function>!!!</para>
5897 <para>An example in which using <literal>RULES</literal> for
5898 specialisation will Win Big:
5901 toDouble :: Real a => a -> Double
5902 toDouble = fromRational . toRational
5904 {-# RULES "toDouble/Int" toDouble = i2d #-}
5905 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5908 The <function>i2d</function> function is virtually one machine
5909 instruction; the default conversion—via an intermediate
5910 <literal>Rational</literal>—is obscenely expensive by
5917 <title>Controlling what's going on</title>
5925 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
5931 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
5932 If you add <option>-dppr-debug</option> you get a more detailed listing.
5938 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
5941 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
5942 {-# INLINE build #-}
5946 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
5947 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
5948 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
5949 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
5956 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
5957 see how to write rules that will do fusion and yet give an efficient
5958 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
5968 <sect2 id="core-pragma">
5969 <title>CORE pragma</title>
5971 <indexterm><primary>CORE pragma</primary></indexterm>
5972 <indexterm><primary>pragma, CORE</primary></indexterm>
5973 <indexterm><primary>core, annotation</primary></indexterm>
5976 The external core format supports <quote>Note</quote> annotations;
5977 the <literal>CORE</literal> pragma gives a way to specify what these
5978 should be in your Haskell source code. Syntactically, core
5979 annotations are attached to expressions and take a Haskell string
5980 literal as an argument. The following function definition shows an
5984 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
5987 Semantically, this is equivalent to:
5995 However, when external for is generated (via
5996 <option>-fext-core</option>), there will be Notes attached to the
5997 expressions <function>show</function> and <varname>x</varname>.
5998 The core function declaration for <function>f</function> is:
6002 f :: %forall a . GHCziShow.ZCTShow a ->
6003 a -> GHCziBase.ZMZN GHCziBase.Char =
6004 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6006 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6008 (tpl1::GHCziBase.Int ->
6010 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6012 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6013 (tpl3::GHCziBase.ZMZN a ->
6014 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6022 Here, we can see that the function <function>show</function> (which
6023 has been expanded out to a case expression over the Show dictionary)
6024 has a <literal>%note</literal> attached to it, as does the
6025 expression <varname>eta</varname> (which used to be called
6026 <varname>x</varname>).
6033 <sect1 id="special-ids">
6034 <title>Special built-in functions</title>
6035 <para>GHC has a few built-in funcions with special behaviour,
6036 described in this section. All are exported by
6037 <literal>GHC.Exts</literal>.</para>
6039 <sect2> <title>The <literal>inline</literal> function </title>
6041 The <literal>inline</literal> function is somewhat experimental.
6045 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6046 is inlined, regardless of its size. More precisely, the call
6047 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6049 This allows the programmer to control inlining from
6050 a particular <emphasis>call site</emphasis>
6051 rather than the <emphasis>definition site</emphasis> of the function
6052 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6055 This inlining occurs regardless of the argument to the call
6056 or the size of <literal>f</literal>'s definition; it is unconditional.
6057 The main caveat is that <literal>f</literal>'s definition must be
6058 visible to the compiler. That is, <literal>f</literal> must be
6059 let-bound in the current scope.
6060 If no inlining takes place, the <literal>inline</literal> function
6061 expands to the identity function in Phase zero; so its use imposes
6064 <para> If the function is defined in another
6065 module, GHC only exposes its inlining in the interface file if the
6066 function is sufficiently small that it <emphasis>might</emphasis> be
6067 inlined by the automatic mechanism. There is currently no way to tell
6068 GHC to expose arbitrarily-large functions in the interface file. (This
6069 shortcoming is something that could be fixed, with some kind of pragma.)
6073 <sect2> <title>The <literal>inline</literal> function </title>
6075 The <literal>lazy</literal> function restrains strictness analysis a little:
6079 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6080 but <literal>lazy</literal> has a magical property so far as strictness
6081 analysis is concerned: it is lazy in its first argument,
6082 even though its semantics is strict. After strictness analysis has run,
6083 calls to <literal>lazy</literal> are inlined to be the identity function.
6086 This behaviour is occasionally useful when controlling evaluation order.
6087 Notably, <literal>lazy</literal> is used in the library definition of
6088 <literal>Control.Parallel.par</literal>:
6091 par x y = case (par# x) of { _ -> lazy y }
6093 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6094 look strict in <literal>y</literal> which would defeat the whole
6095 purpose of <literal>par</literal>.
6101 <sect1 id="generic-classes">
6102 <title>Generic classes</title>
6104 <para>(Note: support for generic classes is currently broken in
6108 The ideas behind this extension are described in detail in "Derivable type classes",
6109 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6110 An example will give the idea:
6118 fromBin :: [Int] -> (a, [Int])
6120 toBin {| Unit |} Unit = []
6121 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6122 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6123 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6125 fromBin {| Unit |} bs = (Unit, bs)
6126 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6127 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6128 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6129 (y,bs'') = fromBin bs'
6132 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6133 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6134 which are defined thus in the library module <literal>Generics</literal>:
6138 data a :+: b = Inl a | Inr b
6139 data a :*: b = a :*: b
6142 Now you can make a data type into an instance of Bin like this:
6144 instance (Bin a, Bin b) => Bin (a,b)
6145 instance Bin a => Bin [a]
6147 That is, just leave off the "where" clause. Of course, you can put in the
6148 where clause and over-ride whichever methods you please.
6152 <title> Using generics </title>
6153 <para>To use generics you need to</para>
6156 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6157 <option>-fgenerics</option> (to generate extra per-data-type code),
6158 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6162 <para>Import the module <literal>Generics</literal> from the
6163 <literal>lang</literal> package. This import brings into
6164 scope the data types <literal>Unit</literal>,
6165 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6166 don't need this import if you don't mention these types
6167 explicitly; for example, if you are simply giving instance
6168 declarations.)</para>
6173 <sect2> <title> Changes wrt the paper </title>
6175 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6176 can be written infix (indeed, you can now use
6177 any operator starting in a colon as an infix type constructor). Also note that
6178 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6179 Finally, note that the syntax of the type patterns in the class declaration
6180 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6181 alone would ambiguous when they appear on right hand sides (an extension we
6182 anticipate wanting).
6186 <sect2> <title>Terminology and restrictions</title>
6188 Terminology. A "generic default method" in a class declaration
6189 is one that is defined using type patterns as above.
6190 A "polymorphic default method" is a default method defined as in Haskell 98.
6191 A "generic class declaration" is a class declaration with at least one
6192 generic default method.
6200 Alas, we do not yet implement the stuff about constructor names and
6207 A generic class can have only one parameter; you can't have a generic
6208 multi-parameter class.
6214 A default method must be defined entirely using type patterns, or entirely
6215 without. So this is illegal:
6218 op :: a -> (a, Bool)
6219 op {| Unit |} Unit = (Unit, True)
6222 However it is perfectly OK for some methods of a generic class to have
6223 generic default methods and others to have polymorphic default methods.
6229 The type variable(s) in the type pattern for a generic method declaration
6230 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:
6234 op {| p :*: q |} (x :*: y) = op (x :: p)
6242 The type patterns in a generic default method must take one of the forms:
6248 where "a" and "b" are type variables. Furthermore, all the type patterns for
6249 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6250 must use the same type variables. So this is illegal:
6254 op {| a :+: b |} (Inl x) = True
6255 op {| p :+: q |} (Inr y) = False
6257 The type patterns must be identical, even in equations for different methods of the class.
6258 So this too is illegal:
6262 op1 {| a :*: b |} (x :*: y) = True
6265 op2 {| p :*: q |} (x :*: y) = False
6267 (The reason for this restriction is that we gather all the equations for a particular type consructor
6268 into a single generic instance declaration.)
6274 A generic method declaration must give a case for each of the three type constructors.
6280 The type for a generic method can be built only from:
6282 <listitem> <para> Function arrows </para> </listitem>
6283 <listitem> <para> Type variables </para> </listitem>
6284 <listitem> <para> Tuples </para> </listitem>
6285 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6287 Here are some example type signatures for generic methods:
6290 op2 :: Bool -> (a,Bool)
6291 op3 :: [Int] -> a -> a
6294 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6298 This restriction is an implementation restriction: we just havn't got around to
6299 implementing the necessary bidirectional maps over arbitrary type constructors.
6300 It would be relatively easy to add specific type constructors, such as Maybe and list,
6301 to the ones that are allowed.</para>
6306 In an instance declaration for a generic class, the idea is that the compiler
6307 will fill in the methods for you, based on the generic templates. However it can only
6312 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6317 No constructor of the instance type has unboxed fields.
6321 (Of course, these things can only arise if you are already using GHC extensions.)
6322 However, you can still give an instance declarations for types which break these rules,
6323 provided you give explicit code to override any generic default methods.
6331 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6332 what the compiler does with generic declarations.
6337 <sect2> <title> Another example </title>
6339 Just to finish with, here's another example I rather like:
6343 nCons {| Unit |} _ = 1
6344 nCons {| a :*: b |} _ = 1
6345 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6348 tag {| Unit |} _ = 1
6349 tag {| a :*: b |} _ = 1
6350 tag {| a :+: b |} (Inl x) = tag x
6351 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6360 ;;; Local Variables: ***
6362 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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