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>,<option>-fno-monomorphism-restriction</option>:
122 <para> These two flags control how generalisation is done.
123 See <xref linkend="monomorphism"/>.
130 <option>-fextended-default-rules</option>:
131 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
134 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
135 Independent of the <option>-fglasgow-exts</option>
142 <option>-fallow-overlapping-instances</option>
143 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
146 <option>-fallow-undecidable-instances</option>
147 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
150 <option>-fallow-incoherent-instances</option>
151 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
154 <option>-fcontext-stack=N</option>
155 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
158 <para> See <xref linkend="instance-decls"/>. Only relevant
159 if you also use <option>-fglasgow-exts</option>.</para>
165 <option>-finline-phase</option>
166 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
169 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
170 you also use <option>-fglasgow-exts</option>.</para>
176 <option>-farrows</option>
177 <indexterm><primary><option>-farrows</option></primary></indexterm>
180 <para>See <xref linkend="arrow-notation"/>. Independent of
181 <option>-fglasgow-exts</option>.</para>
183 <para>New reserved words/symbols: <literal>rec</literal>,
184 <literal>proc</literal>, <literal>-<</literal>,
185 <literal>>-</literal>, <literal>-<<</literal>,
186 <literal>>>-</literal>.</para>
188 <para>Other syntax stolen: <literal>(|</literal>,
189 <literal>|)</literal>.</para>
195 <option>-fgenerics</option>
196 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
199 <para>See <xref linkend="generic-classes"/>. Independent of
200 <option>-fglasgow-exts</option>.</para>
205 <term><option>-fno-implicit-prelude</option></term>
207 <para><indexterm><primary>-fno-implicit-prelude
208 option</primary></indexterm> GHC normally imports
209 <filename>Prelude.hi</filename> files for you. If you'd
210 rather it didn't, then give it a
211 <option>-fno-implicit-prelude</option> option. The idea is
212 that you can then import a Prelude of your own. (But don't
213 call it <literal>Prelude</literal>; the Haskell module
214 namespace is flat, and you must not conflict with any
215 Prelude module.)</para>
217 <para>Even though you have not imported the Prelude, most of
218 the built-in syntax still refers to the built-in Haskell
219 Prelude types and values, as specified by the Haskell
220 Report. For example, the type <literal>[Int]</literal>
221 still means <literal>Prelude.[] Int</literal>; tuples
222 continue to refer to the standard Prelude tuples; the
223 translation for list comprehensions continues to use
224 <literal>Prelude.map</literal> etc.</para>
226 <para>However, <option>-fno-implicit-prelude</option> does
227 change the handling of certain built-in syntax: see <xref
228 linkend="rebindable-syntax"/>.</para>
233 <term><option>-fimplicit-params</option></term>
235 <para>Enables implicit parameters (see <xref
236 linkend="implicit-parameters"/>). Currently also implied by
237 <option>-fglasgow-exts</option>.</para>
240 <literal>?<replaceable>varid</replaceable></literal>,
241 <literal>%<replaceable>varid</replaceable></literal>.</para>
246 <term><option>-fscoped-type-variables</option></term>
248 <para>Enables lexically-scoped type variables (see <xref
249 linkend="scoped-type-variables"/>). Implied by
250 <option>-fglasgow-exts</option>.</para>
255 <term><option>-fth</option></term>
257 <para>Enables Template Haskell (see <xref
258 linkend="template-haskell"/>). This flag must
259 be given explicitly; it is no longer implied by
260 <option>-fglasgow-exts</option>.</para>
262 <para>Syntax stolen: <literal>[|</literal>,
263 <literal>[e|</literal>, <literal>[p|</literal>,
264 <literal>[d|</literal>, <literal>[t|</literal>,
265 <literal>$(</literal>,
266 <literal>$<replaceable>varid</replaceable></literal>.</para>
273 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
274 <!-- included from primitives.sgml -->
275 <!-- &primitives; -->
276 <sect1 id="primitives">
277 <title>Unboxed types and primitive operations</title>
279 <para>GHC is built on a raft of primitive data types and operations.
280 While you really can use this stuff to write fast code,
281 we generally find it a lot less painful, and more satisfying in the
282 long run, to use higher-level language features and libraries. With
283 any luck, the code you write will be optimised to the efficient
284 unboxed version in any case. And if it isn't, we'd like to know
287 <para>We do not currently have good, up-to-date documentation about the
288 primitives, perhaps because they are mainly intended for internal use.
289 There used to be a long section about them here in the User Guide, but it
290 became out of date, and wrong information is worse than none.</para>
292 <para>The Real Truth about what primitive types there are, and what operations
293 work over those types, is held in the file
294 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
295 This file is used directly to generate GHC's primitive-operation definitions, so
296 it is always correct! It is also intended for processing into text.</para>
299 the result of such processing is part of the description of the
301 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
302 Core language</ulink>.
303 So that document is a good place to look for a type-set version.
304 We would be very happy if someone wanted to volunteer to produce an SGML
305 back end to the program that processes <filename>primops.txt</filename> so that
306 we could include the results here in the User Guide.</para>
308 <para>What follows here is a brief summary of some main points.</para>
310 <sect2 id="glasgow-unboxed">
315 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
318 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
319 that values of that type are represented by a pointer to a heap
320 object. The representation of a Haskell <literal>Int</literal>, for
321 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
322 type, however, is represented by the value itself, no pointers or heap
323 allocation are involved.
327 Unboxed types correspond to the “raw machine” types you
328 would use in C: <literal>Int#</literal> (long int),
329 <literal>Double#</literal> (double), <literal>Addr#</literal>
330 (void *), etc. The <emphasis>primitive operations</emphasis>
331 (PrimOps) on these types are what you might expect; e.g.,
332 <literal>(+#)</literal> is addition on
333 <literal>Int#</literal>s, and is the machine-addition that we all
334 know and love—usually one instruction.
338 Primitive (unboxed) types cannot be defined in Haskell, and are
339 therefore built into the language and compiler. Primitive types are
340 always unlifted; that is, a value of a primitive type cannot be
341 bottom. We use the convention that primitive types, values, and
342 operations have a <literal>#</literal> suffix.
346 Primitive values are often represented by a simple bit-pattern, such
347 as <literal>Int#</literal>, <literal>Float#</literal>,
348 <literal>Double#</literal>. But this is not necessarily the case:
349 a primitive value might be represented by a pointer to a
350 heap-allocated object. Examples include
351 <literal>Array#</literal>, the type of primitive arrays. A
352 primitive array is heap-allocated because it is too big a value to fit
353 in a register, and would be too expensive to copy around; in a sense,
354 it is accidental that it is represented by a pointer. If a pointer
355 represents a primitive value, then it really does point to that value:
356 no unevaluated thunks, no indirections…nothing can be at the
357 other end of the pointer than the primitive value.
358 A numerically-intensive program using unboxed types can
359 go a <emphasis>lot</emphasis> faster than its “standard”
360 counterpart—we saw a threefold speedup on one example.
364 There are some restrictions on the use of primitive types:
366 <listitem><para>The main restriction
367 is that you can't pass a primitive value to a polymorphic
368 function or store one in a polymorphic data type. This rules out
369 things like <literal>[Int#]</literal> (i.e. lists of primitive
370 integers). The reason for this restriction is that polymorphic
371 arguments and constructor fields are assumed to be pointers: if an
372 unboxed integer is stored in one of these, the garbage collector would
373 attempt to follow it, leading to unpredictable space leaks. Or a
374 <function>seq</function> operation on the polymorphic component may
375 attempt to dereference the pointer, with disastrous results. Even
376 worse, the unboxed value might be larger than a pointer
377 (<literal>Double#</literal> for instance).
380 <listitem><para> You cannot bind a variable with an unboxed type
381 in a <emphasis>top-level</emphasis> binding.
383 <listitem><para> You cannot bind a variable with an unboxed type
384 in a <emphasis>recursive</emphasis> binding.
386 <listitem><para> You may bind unboxed variables in a (non-recursive,
387 non-top-level) pattern binding, but any such variable causes the entire
389 to become strict. For example:
391 data Foo = Foo Int Int#
393 f x = let (Foo a b, w) = ..rhs.. in ..body..
395 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
397 is strict, and the program behaves as if you had written
399 data Foo = Foo Int Int#
401 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
410 <sect2 id="unboxed-tuples">
411 <title>Unboxed Tuples
415 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
416 they're available by default with <option>-fglasgow-exts</option>. An
417 unboxed tuple looks like this:
429 where <literal>e_1..e_n</literal> are expressions of any
430 type (primitive or non-primitive). The type of an unboxed tuple looks
435 Unboxed tuples are used for functions that need to return multiple
436 values, but they avoid the heap allocation normally associated with
437 using fully-fledged tuples. When an unboxed tuple is returned, the
438 components are put directly into registers or on the stack; the
439 unboxed tuple itself does not have a composite representation. Many
440 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
442 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
443 tuples to avoid unnecessary allocation during sequences of operations.
447 There are some pretty stringent restrictions on the use of unboxed tuples:
452 Values of unboxed tuple types are subject to the same restrictions as
453 other unboxed types; i.e. they may not be stored in polymorphic data
454 structures or passed to polymorphic functions.
461 No variable can have an unboxed tuple type, nor may a constructor or function
462 argument have an unboxed tuple type. The following are all illegal:
466 data Foo = Foo (# Int, Int #)
468 f :: (# Int, Int #) -> (# Int, Int #)
471 g :: (# Int, Int #) -> Int
474 h x = let y = (# x,x #) in ...
481 The typical use of unboxed tuples is simply to return multiple values,
482 binding those multiple results with a <literal>case</literal> expression, thus:
484 f x y = (# x+1, y-1 #)
485 g x = case f x x of { (# a, b #) -> a + b }
487 You can have an unboxed tuple in a pattern binding, thus
489 f x = let (# p,q #) = h x in ..body..
491 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
492 the resulting binding is lazy like any other Haskell pattern binding. The
493 above example desugars like this:
495 f x = let t = case h x o f{ (# p,q #) -> (p,q)
500 Indeed, the bindings can even be recursive.
507 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
509 <sect1 id="syntax-extns">
510 <title>Syntactic extensions</title>
512 <!-- ====================== HIERARCHICAL MODULES ======================= -->
514 <sect2 id="hierarchical-modules">
515 <title>Hierarchical Modules</title>
517 <para>GHC supports a small extension to the syntax of module
518 names: a module name is allowed to contain a dot
519 <literal>‘.’</literal>. This is also known as the
520 “hierarchical module namespace” extension, because
521 it extends the normally flat Haskell module namespace into a
522 more flexible hierarchy of modules.</para>
524 <para>This extension has very little impact on the language
525 itself; modules names are <emphasis>always</emphasis> fully
526 qualified, so you can just think of the fully qualified module
527 name as <quote>the module name</quote>. In particular, this
528 means that the full module name must be given after the
529 <literal>module</literal> keyword at the beginning of the
530 module; for example, the module <literal>A.B.C</literal> must
533 <programlisting>module A.B.C</programlisting>
536 <para>It is a common strategy to use the <literal>as</literal>
537 keyword to save some typing when using qualified names with
538 hierarchical modules. For example:</para>
541 import qualified Control.Monad.ST.Strict as ST
544 <para>For details on how GHC searches for source and interface
545 files in the presence of hierarchical modules, see <xref
546 linkend="search-path"/>.</para>
548 <para>GHC comes with a large collection of libraries arranged
549 hierarchically; see the accompanying library documentation.
550 There is an ongoing project to create and maintain a stable set
551 of <quote>core</quote> libraries used by several Haskell
552 compilers, and the libraries that GHC comes with represent the
553 current status of that project. For more details, see <ulink
554 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
555 Libraries</ulink>.</para>
559 <!-- ====================== PATTERN GUARDS ======================= -->
561 <sect2 id="pattern-guards">
562 <title>Pattern guards</title>
565 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
566 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.)
570 Suppose we have an abstract data type of finite maps, with a
574 lookup :: FiniteMap -> Int -> Maybe Int
577 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
578 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
582 clunky env var1 var2 | ok1 && ok2 = val1 + val2
583 | otherwise = var1 + var2
594 The auxiliary functions are
598 maybeToBool :: Maybe a -> Bool
599 maybeToBool (Just x) = True
600 maybeToBool Nothing = False
602 expectJust :: Maybe a -> a
603 expectJust (Just x) = x
604 expectJust Nothing = error "Unexpected Nothing"
608 What is <function>clunky</function> doing? The guard <literal>ok1 &&
609 ok2</literal> checks that both lookups succeed, using
610 <function>maybeToBool</function> to convert the <function>Maybe</function>
611 types to booleans. The (lazily evaluated) <function>expectJust</function>
612 calls extract the values from the results of the lookups, and binds the
613 returned values to <varname>val1</varname> and <varname>val2</varname>
614 respectively. If either lookup fails, then clunky takes the
615 <literal>otherwise</literal> case and returns the sum of its arguments.
619 This is certainly legal Haskell, but it is a tremendously verbose and
620 un-obvious way to achieve the desired effect. Arguably, a more direct way
621 to write clunky would be to use case expressions:
625 clunky env var1 var1 = case lookup env var1 of
627 Just val1 -> case lookup env var2 of
629 Just val2 -> val1 + val2
635 This is a bit shorter, but hardly better. Of course, we can rewrite any set
636 of pattern-matching, guarded equations as case expressions; that is
637 precisely what the compiler does when compiling equations! The reason that
638 Haskell provides guarded equations is because they allow us to write down
639 the cases we want to consider, one at a time, independently of each other.
640 This structure is hidden in the case version. Two of the right-hand sides
641 are really the same (<function>fail</function>), and the whole expression
642 tends to become more and more indented.
646 Here is how I would write clunky:
651 | Just val1 <- lookup env var1
652 , Just val2 <- lookup env var2
654 ...other equations for clunky...
658 The semantics should be clear enough. The qualifiers are matched in order.
659 For a <literal><-</literal> qualifier, which I call a pattern guard, the
660 right hand side is evaluated and matched against the pattern on the left.
661 If the match fails then the whole guard fails and the next equation is
662 tried. If it succeeds, then the appropriate binding takes place, and the
663 next qualifier is matched, in the augmented environment. Unlike list
664 comprehensions, however, the type of the expression to the right of the
665 <literal><-</literal> is the same as the type of the pattern to its
666 left. The bindings introduced by pattern guards scope over all the
667 remaining guard qualifiers, and over the right hand side of the equation.
671 Just as with list comprehensions, boolean expressions can be freely mixed
672 with among the pattern guards. For example:
683 Haskell's current guards therefore emerge as a special case, in which the
684 qualifier list has just one element, a boolean expression.
688 <!-- ===================== Recursive do-notation =================== -->
690 <sect2 id="mdo-notation">
691 <title>The recursive do-notation
694 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
695 "A recursive do for Haskell",
696 Levent Erkok, John Launchbury",
697 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
700 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
701 that is, the variables bound in a do-expression are visible only in the textually following
702 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
703 group. It turns out that several applications can benefit from recursive bindings in
704 the do-notation, and this extension provides the necessary syntactic support.
707 Here is a simple (yet contrived) example:
710 import Control.Monad.Fix
712 justOnes = mdo xs <- Just (1:xs)
716 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
720 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
723 class Monad m => MonadFix m where
724 mfix :: (a -> m a) -> m a
727 The function <literal>mfix</literal>
728 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
729 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
730 For details, see the above mentioned reference.
733 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
734 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
735 for Haskell's internal state monad (strict and lazy, respectively).
738 There are three important points in using the recursive-do notation:
741 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
742 than <literal>do</literal>).
746 You should <literal>import Control.Monad.Fix</literal>.
747 (Note: Strictly speaking, this import is required only when you need to refer to the name
748 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
749 are encouraged to always import this module when using the mdo-notation.)
753 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
759 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
760 contains up to date information on recursive monadic bindings.
764 Historical note: The old implementation of the mdo-notation (and most
765 of the existing documents) used the name
766 <literal>MonadRec</literal> for the class and the corresponding library.
767 This name is not supported by GHC.
773 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
775 <sect2 id="parallel-list-comprehensions">
776 <title>Parallel List Comprehensions</title>
777 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
779 <indexterm><primary>parallel list comprehensions</primary>
782 <para>Parallel list comprehensions are a natural extension to list
783 comprehensions. List comprehensions can be thought of as a nice
784 syntax for writing maps and filters. Parallel comprehensions
785 extend this to include the zipWith family.</para>
787 <para>A parallel list comprehension has multiple independent
788 branches of qualifier lists, each separated by a `|' symbol. For
789 example, the following zips together two lists:</para>
792 [ (x, y) | x <- xs | y <- ys ]
795 <para>The behavior of parallel list comprehensions follows that of
796 zip, in that the resulting list will have the same length as the
797 shortest branch.</para>
799 <para>We can define parallel list comprehensions by translation to
800 regular comprehensions. Here's the basic idea:</para>
802 <para>Given a parallel comprehension of the form: </para>
805 [ e | p1 <- e11, p2 <- e12, ...
806 | q1 <- e21, q2 <- e22, ...
811 <para>This will be translated to: </para>
814 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
815 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
820 <para>where `zipN' is the appropriate zip for the given number of
825 <sect2 id="rebindable-syntax">
826 <title>Rebindable syntax</title>
829 <para>GHC allows most kinds of built-in syntax to be rebound by
830 the user, to facilitate replacing the <literal>Prelude</literal>
831 with a home-grown version, for example.</para>
833 <para>You may want to define your own numeric class
834 hierarchy. It completely defeats that purpose if the
835 literal "1" means "<literal>Prelude.fromInteger
836 1</literal>", which is what the Haskell Report specifies.
837 So the <option>-fno-implicit-prelude</option> flag causes
838 the following pieces of built-in syntax to refer to
839 <emphasis>whatever is in scope</emphasis>, not the Prelude
844 <para>An integer literal <literal>368</literal> means
845 "<literal>fromInteger (368::Integer)</literal>", rather than
846 "<literal>Prelude.fromInteger (368::Integer)</literal>".
849 <listitem><para>Fractional literals are handed in just the same way,
850 except that the translation is
851 <literal>fromRational (3.68::Rational)</literal>.
854 <listitem><para>The equality test in an overloaded numeric pattern
855 uses whatever <literal>(==)</literal> is in scope.
858 <listitem><para>The subtraction operation, and the
859 greater-than-or-equal test, in <literal>n+k</literal> patterns
860 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
864 <para>Negation (e.g. "<literal>- (f x)</literal>")
865 means "<literal>negate (f x)</literal>", both in numeric
866 patterns, and expressions.
870 <para>"Do" notation is translated using whatever
871 functions <literal>(>>=)</literal>,
872 <literal>(>>)</literal>, and <literal>fail</literal>,
873 are in scope (not the Prelude
874 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
875 comprehensions, are unaffected. </para></listitem>
879 notation (see <xref linkend="arrow-notation"/>)
880 uses whatever <literal>arr</literal>,
881 <literal>(>>>)</literal>, <literal>first</literal>,
882 <literal>app</literal>, <literal>(|||)</literal> and
883 <literal>loop</literal> functions are in scope. But unlike the
884 other constructs, the types of these functions must match the
885 Prelude types very closely. Details are in flux; if you want
889 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
890 even if that is a little unexpected. For emample, the
891 static semantics of the literal <literal>368</literal>
892 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
893 <literal>fromInteger</literal> to have any of the types:
895 fromInteger :: Integer -> Integer
896 fromInteger :: forall a. Foo a => Integer -> a
897 fromInteger :: Num a => a -> Integer
898 fromInteger :: Integer -> Bool -> Bool
902 <para>Be warned: this is an experimental facility, with
903 fewer checks than usual. Use <literal>-dcore-lint</literal>
904 to typecheck the desugared program. If Core Lint is happy
905 you should be all right.</para>
909 <sect2 id="postfix-operators">
910 <title>Postfix operators</title>
913 GHC allows a small extension to the syntax of left operator sections, which
914 allows you to define postfix operators. The extension is this: the left section
918 is equivalent (from the point of view of both type checking and execution) to the expression
922 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
923 The strict Haskell 98 interpretation is that the section is equivalent to
927 That is, the operator must be a function of two arguments. GHC allows it to
928 take only one argument, and that in turn allows you to write the function
931 <para>Since this extension goes beyond Haskell 98, it should really be enabled
932 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
933 change their behaviour, of course.)
935 <para>The extension does not extend to the left-hand side of function
936 definitions; you must define such a function in prefix form.</para>
943 <!-- TYPE SYSTEM EXTENSIONS -->
944 <sect1 id="type-extensions">
945 <title>Type system extensions</title>
949 <title>Data types and type synonyms</title>
951 <sect3 id="nullary-types">
952 <title>Data types with no constructors</title>
954 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
955 a data type with no constructors. For example:</para>
959 data T a -- T :: * -> *
962 <para>Syntactically, the declaration lacks the "= constrs" part. The
963 type can be parameterised over types of any kind, but if the kind is
964 not <literal>*</literal> then an explicit kind annotation must be used
965 (see <xref linkend="sec-kinding"/>).</para>
967 <para>Such data types have only one value, namely bottom.
968 Nevertheless, they can be useful when defining "phantom types".</para>
971 <sect3 id="infix-tycons">
972 <title>Infix type constructors, classes, and type variables</title>
975 GHC allows type constructors, classes, and type variables to be operators, and
976 to be written infix, very much like expressions. More specifically:
979 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
980 The lexical syntax is the same as that for data constructors.
983 Data type and type-synonym declarations can be written infix, parenthesised
984 if you want further arguments. E.g.
986 data a :*: b = Foo a b
987 type a :+: b = Either a b
988 class a :=: b where ...
990 data (a :**: b) x = Baz a b x
991 type (a :++: b) y = Either (a,b) y
995 Types, and class constraints, can be written infix. For example
998 f :: (a :=: b) => a -> b
1002 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1003 The lexical syntax is the same as that for variable operators, excluding "(.)",
1004 "(!)", and "(*)". In a binding position, the operator must be
1005 parenthesised. For example:
1007 type T (+) = Int + Int
1011 liftA2 :: Arrow (~>)
1012 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1018 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1019 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1022 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1023 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1024 sets the fixity for a data constructor and the corresponding type constructor. For example:
1028 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1029 and similarly for <literal>:*:</literal>.
1030 <literal>Int `a` Bool</literal>.
1033 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1040 <sect3 id="type-synonyms">
1041 <title>Liberalised type synonyms</title>
1044 Type synonyms are like macros at the type level, and
1045 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1046 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1048 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1049 in a type synonym, thus:
1051 type Discard a = forall b. Show b => a -> b -> (a, String)
1056 g :: Discard Int -> (Int,String) -- A rank-2 type
1063 You can write an unboxed tuple in a type synonym:
1065 type Pr = (# Int, Int #)
1073 You can apply a type synonym to a forall type:
1075 type Foo a = a -> a -> Bool
1077 f :: Foo (forall b. b->b)
1079 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1081 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1086 You can apply a type synonym to a partially applied type synonym:
1088 type Generic i o = forall x. i x -> o x
1091 foo :: Generic Id []
1093 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1095 foo :: forall x. x -> [x]
1103 GHC currently does kind checking before expanding synonyms (though even that
1107 After expanding type synonyms, GHC does validity checking on types, looking for
1108 the following mal-formedness which isn't detected simply by kind checking:
1111 Type constructor applied to a type involving for-alls.
1114 Unboxed tuple on left of an arrow.
1117 Partially-applied type synonym.
1121 this will be rejected:
1123 type Pr = (# Int, Int #)
1128 because GHC does not allow unboxed tuples on the left of a function arrow.
1133 <sect3 id="existential-quantification">
1134 <title>Existentially quantified data constructors
1138 The idea of using existential quantification in data type declarations
1139 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1140 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1141 London, 1991). It was later formalised by Laufer and Odersky
1142 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1143 TOPLAS, 16(5), pp1411-1430, 1994).
1144 It's been in Lennart
1145 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1146 proved very useful. Here's the idea. Consider the declaration:
1152 data Foo = forall a. MkFoo a (a -> Bool)
1159 The data type <literal>Foo</literal> has two constructors with types:
1165 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1172 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1173 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1174 For example, the following expression is fine:
1180 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1186 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1187 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1188 isUpper</function> packages a character with a compatible function. These
1189 two things are each of type <literal>Foo</literal> and can be put in a list.
1193 What can we do with a value of type <literal>Foo</literal>?. In particular,
1194 what happens when we pattern-match on <function>MkFoo</function>?
1200 f (MkFoo val fn) = ???
1206 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1207 are compatible, the only (useful) thing we can do with them is to
1208 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1215 f (MkFoo val fn) = fn val
1221 What this allows us to do is to package heterogenous values
1222 together with a bunch of functions that manipulate them, and then treat
1223 that collection of packages in a uniform manner. You can express
1224 quite a bit of object-oriented-like programming this way.
1227 <sect4 id="existential">
1228 <title>Why existential?
1232 What has this to do with <emphasis>existential</emphasis> quantification?
1233 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1239 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1245 But Haskell programmers can safely think of the ordinary
1246 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1247 adding a new existential quantification construct.
1253 <title>Type classes</title>
1256 An easy extension is to allow
1257 arbitrary contexts before the constructor. For example:
1263 data Baz = forall a. Eq a => Baz1 a a
1264 | forall b. Show b => Baz2 b (b -> b)
1270 The two constructors have the types you'd expect:
1276 Baz1 :: forall a. Eq a => a -> a -> Baz
1277 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1283 But when pattern matching on <function>Baz1</function> the matched values can be compared
1284 for equality, and when pattern matching on <function>Baz2</function> the first matched
1285 value can be converted to a string (as well as applying the function to it).
1286 So this program is legal:
1293 f (Baz1 p q) | p == q = "Yes"
1295 f (Baz2 v fn) = show (fn v)
1301 Operationally, in a dictionary-passing implementation, the
1302 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1303 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1304 extract it on pattern matching.
1308 Notice the way that the syntax fits smoothly with that used for
1309 universal quantification earlier.
1315 <title>Record Constructors</title>
1318 GHC allows existentials to be used with records syntax as well. For example:
1321 data Counter a = forall self. NewCounter
1323 , _inc :: self -> self
1324 , _display :: self -> IO ()
1328 Here <literal>tag</literal> is a public field, with a well-typed selector
1329 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1330 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1331 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1332 compile-time error. In other words, <emphasis>GHC defines a record selector function
1333 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1334 (This example used an underscore in the fields for which record selectors
1335 will not be defined, but that is only programming style; GHC ignores them.)
1339 To make use of these hidden fields, we need to create some helper functions:
1342 inc :: Counter a -> Counter a
1343 inc (NewCounter x i d t) = NewCounter
1344 { _this = i x, _inc = i, _display = d, tag = t }
1346 display :: Counter a -> IO ()
1347 display NewCounter{ _this = x, _display = d } = d x
1350 Now we can define counters with different underlying implementations:
1353 counterA :: Counter String
1354 counterA = NewCounter
1355 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1357 counterB :: Counter String
1358 counterB = NewCounter
1359 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1362 display (inc counterA) -- prints "1"
1363 display (inc (inc counterB)) -- prints "##"
1366 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1367 <literal>forall</literal> may be omitted. For example, we can express
1368 the same <literal>Counter a</literal> using GADT:
1371 data Counter a where
1372 NewCounter { _this :: self
1373 , _inc :: self -> self
1374 , _display :: self -> IO ()
1380 At the moment, record update syntax is only supported for Haskell 98 data types,
1381 so the following function does <emphasis>not</emphasis> work:
1384 -- This is invalid; use explicit NewCounter instead for now
1385 setTag :: Counter a -> a -> Counter a
1386 setTag obj t = obj{ tag = t }
1395 <title>Restrictions</title>
1398 There are several restrictions on the ways in which existentially-quantified
1399 constructors can be use.
1408 When pattern matching, each pattern match introduces a new,
1409 distinct, type for each existential type variable. These types cannot
1410 be unified with any other type, nor can they escape from the scope of
1411 the pattern match. For example, these fragments are incorrect:
1419 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1420 is the result of <function>f1</function>. One way to see why this is wrong is to
1421 ask what type <function>f1</function> has:
1425 f1 :: Foo -> a -- Weird!
1429 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1434 f1 :: forall a. Foo -> a -- Wrong!
1438 The original program is just plain wrong. Here's another sort of error
1442 f2 (Baz1 a b) (Baz1 p q) = a==q
1446 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1447 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1448 from the two <function>Baz1</function> constructors.
1456 You can't pattern-match on an existentially quantified
1457 constructor in a <literal>let</literal> or <literal>where</literal> group of
1458 bindings. So this is illegal:
1462 f3 x = a==b where { Baz1 a b = x }
1465 Instead, use a <literal>case</literal> expression:
1468 f3 x = case x of Baz1 a b -> a==b
1471 In general, you can only pattern-match
1472 on an existentially-quantified constructor in a <literal>case</literal> expression or
1473 in the patterns of a function definition.
1475 The reason for this restriction is really an implementation one.
1476 Type-checking binding groups is already a nightmare without
1477 existentials complicating the picture. Also an existential pattern
1478 binding at the top level of a module doesn't make sense, because it's
1479 not clear how to prevent the existentially-quantified type "escaping".
1480 So for now, there's a simple-to-state restriction. We'll see how
1488 You can't use existential quantification for <literal>newtype</literal>
1489 declarations. So this is illegal:
1493 newtype T = forall a. Ord a => MkT a
1497 Reason: a value of type <literal>T</literal> must be represented as a
1498 pair of a dictionary for <literal>Ord t</literal> and a value of type
1499 <literal>t</literal>. That contradicts the idea that
1500 <literal>newtype</literal> should have no concrete representation.
1501 You can get just the same efficiency and effect by using
1502 <literal>data</literal> instead of <literal>newtype</literal>. If
1503 there is no overloading involved, then there is more of a case for
1504 allowing an existentially-quantified <literal>newtype</literal>,
1505 because the <literal>data</literal> version does carry an
1506 implementation cost, but single-field existentially quantified
1507 constructors aren't much use. So the simple restriction (no
1508 existential stuff on <literal>newtype</literal>) stands, unless there
1509 are convincing reasons to change it.
1517 You can't use <literal>deriving</literal> to define instances of a
1518 data type with existentially quantified data constructors.
1520 Reason: in most cases it would not make sense. For example:#
1523 data T = forall a. MkT [a] deriving( Eq )
1526 To derive <literal>Eq</literal> in the standard way we would need to have equality
1527 between the single component of two <function>MkT</function> constructors:
1531 (MkT a) == (MkT b) = ???
1534 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1535 It's just about possible to imagine examples in which the derived instance
1536 would make sense, but it seems altogether simpler simply to prohibit such
1537 declarations. Define your own instances!
1552 <sect2 id="multi-param-type-classes">
1553 <title>Class declarations</title>
1556 This section, and the next one, documents GHC's type-class extensions.
1557 There's lots of background in the paper <ulink
1558 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1559 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1560 Jones, Erik Meijer).
1563 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1567 <title>Multi-parameter type classes</title>
1569 Multi-parameter type classes are permitted. For example:
1573 class Collection c a where
1574 union :: c a -> c a -> c a
1582 <title>The superclasses of a class declaration</title>
1585 There are no restrictions on the context in a class declaration
1586 (which introduces superclasses), except that the class hierarchy must
1587 be acyclic. So these class declarations are OK:
1591 class Functor (m k) => FiniteMap m k where
1594 class (Monad m, Monad (t m)) => Transform t m where
1595 lift :: m a -> (t m) a
1601 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1602 of "acyclic" involves only the superclass relationships. For example,
1608 op :: D b => a -> b -> b
1611 class C a => D a where { ... }
1615 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1616 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1617 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1624 <sect3 id="class-method-types">
1625 <title>Class method types</title>
1628 Haskell 98 prohibits class method types to mention constraints on the
1629 class type variable, thus:
1632 fromList :: [a] -> s a
1633 elem :: Eq a => a -> s a -> Bool
1635 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1636 contains the constraint <literal>Eq a</literal>, constrains only the
1637 class type variable (in this case <literal>a</literal>).
1638 GHC lifts this restriction.
1645 <sect2 id="functional-dependencies">
1646 <title>Functional dependencies
1649 <para> Functional dependencies are implemented as described by Mark Jones
1650 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1651 In Proceedings of the 9th European Symposium on Programming,
1652 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1656 Functional dependencies are introduced by a vertical bar in the syntax of a
1657 class declaration; e.g.
1659 class (Monad m) => MonadState s m | m -> s where ...
1661 class Foo a b c | a b -> c where ...
1663 There should be more documentation, but there isn't (yet). Yell if you need it.
1666 <sect3><title>Rules for functional dependencies </title>
1668 In a class declaration, all of the class type variables must be reachable (in the sense
1669 mentioned in <xref linkend="type-restrictions"/>)
1670 from the free variables of each method type.
1674 class Coll s a where
1676 insert :: s -> a -> s
1679 is not OK, because the type of <literal>empty</literal> doesn't mention
1680 <literal>a</literal>. Functional dependencies can make the type variable
1683 class Coll s a | s -> a where
1685 insert :: s -> a -> s
1688 Alternatively <literal>Coll</literal> might be rewritten
1691 class Coll s a where
1693 insert :: s a -> a -> s a
1697 which makes the connection between the type of a collection of
1698 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1699 Occasionally this really doesn't work, in which case you can split the
1707 class CollE s => Coll s a where
1708 insert :: s -> a -> s
1715 <title>Background on functional dependencies</title>
1717 <para>The following description of the motivation and use of functional dependencies is taken
1718 from the Hugs user manual, reproduced here (with minor changes) by kind
1719 permission of Mark Jones.
1722 Consider the following class, intended as part of a
1723 library for collection types:
1725 class Collects e ce where
1727 insert :: e -> ce -> ce
1728 member :: e -> ce -> Bool
1730 The type variable e used here represents the element type, while ce is the type
1731 of the container itself. Within this framework, we might want to define
1732 instances of this class for lists or characteristic functions (both of which
1733 can be used to represent collections of any equality type), bit sets (which can
1734 be used to represent collections of characters), or hash tables (which can be
1735 used to represent any collection whose elements have a hash function). Omitting
1736 standard implementation details, this would lead to the following declarations:
1738 instance Eq e => Collects e [e] where ...
1739 instance Eq e => Collects e (e -> Bool) where ...
1740 instance Collects Char BitSet where ...
1741 instance (Hashable e, Collects a ce)
1742 => Collects e (Array Int ce) where ...
1744 All this looks quite promising; we have a class and a range of interesting
1745 implementations. Unfortunately, there are some serious problems with the class
1746 declaration. First, the empty function has an ambiguous type:
1748 empty :: Collects e ce => ce
1750 By "ambiguous" we mean that there is a type variable e that appears on the left
1751 of the <literal>=></literal> symbol, but not on the right. The problem with
1752 this is that, according to the theoretical foundations of Haskell overloading,
1753 we cannot guarantee a well-defined semantics for any term with an ambiguous
1757 We can sidestep this specific problem by removing the empty member from the
1758 class declaration. However, although the remaining members, insert and member,
1759 do not have ambiguous types, we still run into problems when we try to use
1760 them. For example, consider the following two functions:
1762 f x y = insert x . insert y
1765 for which GHC infers the following types:
1767 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1768 g :: (Collects Bool c, Collects Char c) => c -> c
1770 Notice that the type for f allows the two parameters x and y to be assigned
1771 different types, even though it attempts to insert each of the two values, one
1772 after the other, into the same collection. If we're trying to model collections
1773 that contain only one type of value, then this is clearly an inaccurate
1774 type. Worse still, the definition for g is accepted, without causing a type
1775 error. As a result, the error in this code will not be flagged at the point
1776 where it appears. Instead, it will show up only when we try to use g, which
1777 might even be in a different module.
1780 <sect4><title>An attempt to use constructor classes</title>
1783 Faced with the problems described above, some Haskell programmers might be
1784 tempted to use something like the following version of the class declaration:
1786 class Collects e c where
1788 insert :: e -> c e -> c e
1789 member :: e -> c e -> Bool
1791 The key difference here is that we abstract over the type constructor c that is
1792 used to form the collection type c e, and not over that collection type itself,
1793 represented by ce in the original class declaration. This avoids the immediate
1794 problems that we mentioned above: empty has type <literal>Collects e c => c
1795 e</literal>, which is not ambiguous.
1798 The function f from the previous section has a more accurate type:
1800 f :: (Collects e c) => e -> e -> c e -> c e
1802 The function g from the previous section is now rejected with a type error as
1803 we would hope because the type of f does not allow the two arguments to have
1805 This, then, is an example of a multiple parameter class that does actually work
1806 quite well in practice, without ambiguity problems.
1807 There is, however, a catch. This version of the Collects class is nowhere near
1808 as general as the original class seemed to be: only one of the four instances
1809 for <literal>Collects</literal>
1810 given above can be used with this version of Collects because only one of
1811 them---the instance for lists---has a collection type that can be written in
1812 the form c e, for some type constructor c, and element type e.
1816 <sect4><title>Adding functional dependencies</title>
1819 To get a more useful version of the Collects class, Hugs provides a mechanism
1820 that allows programmers to specify dependencies between the parameters of a
1821 multiple parameter class (For readers with an interest in theoretical
1822 foundations and previous work: The use of dependency information can be seen
1823 both as a generalization of the proposal for `parametric type classes' that was
1824 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1825 later framework for "improvement" of qualified types. The
1826 underlying ideas are also discussed in a more theoretical and abstract setting
1827 in a manuscript [implparam], where they are identified as one point in a
1828 general design space for systems of implicit parameterization.).
1830 To start with an abstract example, consider a declaration such as:
1832 class C a b where ...
1834 which tells us simply that C can be thought of as a binary relation on types
1835 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1836 included in the definition of classes to add information about dependencies
1837 between parameters, as in the following examples:
1839 class D a b | a -> b where ...
1840 class E a b | a -> b, b -> a where ...
1842 The notation <literal>a -> b</literal> used here between the | and where
1843 symbols --- not to be
1844 confused with a function type --- indicates that the a parameter uniquely
1845 determines the b parameter, and might be read as "a determines b." Thus D is
1846 not just a relation, but actually a (partial) function. Similarly, from the two
1847 dependencies that are included in the definition of E, we can see that E
1848 represents a (partial) one-one mapping between types.
1851 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1852 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1853 m>=0, meaning that the y parameters are uniquely determined by the x
1854 parameters. Spaces can be used as separators if more than one variable appears
1855 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1856 annotated with multiple dependencies using commas as separators, as in the
1857 definition of E above. Some dependencies that we can write in this notation are
1858 redundant, and will be rejected because they don't serve any useful
1859 purpose, and may instead indicate an error in the program. Examples of
1860 dependencies like this include <literal>a -> a </literal>,
1861 <literal>a -> a a </literal>,
1862 <literal>a -> </literal>, etc. There can also be
1863 some redundancy if multiple dependencies are given, as in
1864 <literal>a->b</literal>,
1865 <literal>b->c </literal>, <literal>a->c </literal>, and
1866 in which some subset implies the remaining dependencies. Examples like this are
1867 not treated as errors. Note that dependencies appear only in class
1868 declarations, and not in any other part of the language. In particular, the
1869 syntax for instance declarations, class constraints, and types is completely
1873 By including dependencies in a class declaration, we provide a mechanism for
1874 the programmer to specify each multiple parameter class more precisely. The
1875 compiler, on the other hand, is responsible for ensuring that the set of
1876 instances that are in scope at any given point in the program is consistent
1877 with any declared dependencies. For example, the following pair of instance
1878 declarations cannot appear together in the same scope because they violate the
1879 dependency for D, even though either one on its own would be acceptable:
1881 instance D Bool Int where ...
1882 instance D Bool Char where ...
1884 Note also that the following declaration is not allowed, even by itself:
1886 instance D [a] b where ...
1888 The problem here is that this instance would allow one particular choice of [a]
1889 to be associated with more than one choice for b, which contradicts the
1890 dependency specified in the definition of D. More generally, this means that,
1891 in any instance of the form:
1893 instance D t s where ...
1895 for some particular types t and s, the only variables that can appear in s are
1896 the ones that appear in t, and hence, if the type t is known, then s will be
1897 uniquely determined.
1900 The benefit of including dependency information is that it allows us to define
1901 more general multiple parameter classes, without ambiguity problems, and with
1902 the benefit of more accurate types. To illustrate this, we return to the
1903 collection class example, and annotate the original definition of <literal>Collects</literal>
1904 with a simple dependency:
1906 class Collects e ce | ce -> e where
1908 insert :: e -> ce -> ce
1909 member :: e -> ce -> Bool
1911 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1912 determined by the type of the collection ce. Note that both parameters of
1913 Collects are of kind *; there are no constructor classes here. Note too that
1914 all of the instances of Collects that we gave earlier can be used
1915 together with this new definition.
1918 What about the ambiguity problems that we encountered with the original
1919 definition? The empty function still has type Collects e ce => ce, but it is no
1920 longer necessary to regard that as an ambiguous type: Although the variable e
1921 does not appear on the right of the => symbol, the dependency for class
1922 Collects tells us that it is uniquely determined by ce, which does appear on
1923 the right of the => symbol. Hence the context in which empty is used can still
1924 give enough information to determine types for both ce and e, without
1925 ambiguity. More generally, we need only regard a type as ambiguous if it
1926 contains a variable on the left of the => that is not uniquely determined
1927 (either directly or indirectly) by the variables on the right.
1930 Dependencies also help to produce more accurate types for user defined
1931 functions, and hence to provide earlier detection of errors, and less cluttered
1932 types for programmers to work with. Recall the previous definition for a
1935 f x y = insert x y = insert x . insert y
1937 for which we originally obtained a type:
1939 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1941 Given the dependency information that we have for Collects, however, we can
1942 deduce that a and b must be equal because they both appear as the second
1943 parameter in a Collects constraint with the same first parameter c. Hence we
1944 can infer a shorter and more accurate type for f:
1946 f :: (Collects a c) => a -> a -> c -> c
1948 In a similar way, the earlier definition of g will now be flagged as a type error.
1951 Although we have given only a few examples here, it should be clear that the
1952 addition of dependency information can help to make multiple parameter classes
1953 more useful in practice, avoiding ambiguity problems, and allowing more general
1954 sets of instance declarations.
1960 <sect2 id="instance-decls">
1961 <title>Instance declarations</title>
1963 <sect3 id="instance-rules">
1964 <title>Relaxed rules for instance declarations</title>
1966 <para>An instance declaration has the form
1968 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 ...
1970 The part before the "<literal>=></literal>" is the
1971 <emphasis>context</emphasis>, while the part after the
1972 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1976 In Haskell 98 the head of an instance declaration
1977 must be of the form <literal>C (T a1 ... an)</literal>, where
1978 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1979 and the <literal>a1 ... an</literal> are distinct type variables.
1980 Furthermore, the assertions in the context of the instance declaration
1981 must be of the form <literal>C a</literal> where <literal>a</literal>
1982 is a type variable that occurs in the head.
1985 The <option>-fglasgow-exts</option> flag loosens these restrictions
1986 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1987 the context and head of the instance declaration can each consist of arbitrary
1988 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1992 For each assertion in the context:
1994 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1995 <listitem><para>The assertion has fewer constructors and variables (taken together
1996 and counting repetitions) than the head</para></listitem>
2000 <listitem><para>The coverage condition. For each functional dependency,
2001 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
2002 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2003 every type variable in
2004 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2005 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2006 substitution mapping each type variable in the class declaration to the
2007 corresponding type in the instance declaration.
2010 These restrictions ensure that context reduction terminates: each reduction
2011 step makes the problem smaller by at least one
2012 constructor. For example, the following would make the type checker
2013 loop if it wasn't excluded:
2015 instance C a => C a where ...
2017 For example, these are OK:
2019 instance C Int [a] -- Multiple parameters
2020 instance Eq (S [a]) -- Structured type in head
2022 -- Repeated type variable in head
2023 instance C4 a a => C4 [a] [a]
2024 instance Stateful (ST s) (MutVar s)
2026 -- Head can consist of type variables only
2028 instance (Eq a, Show b) => C2 a b
2030 -- Non-type variables in context
2031 instance Show (s a) => Show (Sized s a)
2032 instance C2 Int a => C3 Bool [a]
2033 instance C2 Int a => C3 [a] b
2037 -- Context assertion no smaller than head
2038 instance C a => C a where ...
2039 -- (C b b) has more more occurrences of b than the head
2040 instance C b b => Foo [b] where ...
2045 The same restrictions apply to instances generated by
2046 <literal>deriving</literal> clauses. Thus the following is accepted:
2048 data MinHeap h a = H a (h a)
2051 because the derived instance
2053 instance (Show a, Show (h a)) => Show (MinHeap h a)
2055 conforms to the above rules.
2059 A useful idiom permitted by the above rules is as follows.
2060 If one allows overlapping instance declarations then it's quite
2061 convenient to have a "default instance" declaration that applies if
2062 something more specific does not:
2068 <para>You can find lots of background material about the reason for these
2069 restrictions in the paper <ulink
2070 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2071 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2075 <sect3 id="undecidable-instances">
2076 <title>Undecidable instances</title>
2079 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2080 For example, sometimes you might want to use the following to get the
2081 effect of a "class synonym":
2083 class (C1 a, C2 a, C3 a) => C a where { }
2085 instance (C1 a, C2 a, C3 a) => C a where { }
2087 This allows you to write shorter signatures:
2093 f :: (C1 a, C2 a, C3 a) => ...
2095 The restrictions on functional dependencies (<xref
2096 linkend="functional-dependencies"/>) are particularly troublesome.
2097 It is tempting to introduce type variables in the context that do not appear in
2098 the head, something that is excluded by the normal rules. For example:
2100 class HasConverter a b | a -> b where
2103 data Foo a = MkFoo a
2105 instance (HasConverter a b,Show b) => Show (Foo a) where
2106 show (MkFoo value) = show (convert value)
2108 This is dangerous territory, however. Here, for example, is a program that would make the
2113 instance F [a] [[a]]
2114 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2116 Similarly, it can be tempting to lift the coverage condition:
2118 class Mul a b c | a b -> c where
2119 (.*.) :: a -> b -> c
2121 instance Mul Int Int Int where (.*.) = (*)
2122 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2123 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2125 The third instance declaration does not obey the coverage condition;
2126 and indeed the (somewhat strange) definition:
2128 f = \ b x y -> if b then x .*. [y] else y
2130 makes instance inference go into a loop, because it requires the constraint
2131 <literal>(Mul a [b] b)</literal>.
2134 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2135 the experimental flag <option>-fallow-undecidable-instances</option>
2136 <indexterm><primary>-fallow-undecidable-instances
2137 option</primary></indexterm>, you can use arbitrary
2138 types in both an instance context and instance head. Termination is ensured by having a
2139 fixed-depth recursion stack. If you exceed the stack depth you get a
2140 sort of backtrace, and the opportunity to increase the stack depth
2141 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2147 <sect3 id="instance-overlap">
2148 <title>Overlapping instances</title>
2150 In general, <emphasis>GHC requires that that it be unambiguous which instance
2152 should be used to resolve a type-class constraint</emphasis>. This behaviour
2153 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2154 <indexterm><primary>-fallow-overlapping-instances
2155 </primary></indexterm>
2156 and <option>-fallow-incoherent-instances</option>
2157 <indexterm><primary>-fallow-incoherent-instances
2158 </primary></indexterm>, as this section discusses. Both these
2159 flags are dynamic flags, and can be set on a per-module basis, using
2160 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2162 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2163 it tries to match every instance declaration against the
2165 by instantiating the head of the instance declaration. For example, consider
2168 instance context1 => C Int a where ... -- (A)
2169 instance context2 => C a Bool where ... -- (B)
2170 instance context3 => C Int [a] where ... -- (C)
2171 instance context4 => C Int [Int] where ... -- (D)
2173 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2174 but (C) and (D) do not. When matching, GHC takes
2175 no account of the context of the instance declaration
2176 (<literal>context1</literal> etc).
2177 GHC's default behaviour is that <emphasis>exactly one instance must match the
2178 constraint it is trying to resolve</emphasis>.
2179 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2180 including both declarations (A) and (B), say); an error is only reported if a
2181 particular constraint matches more than one.
2185 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2186 more than one instance to match, provided there is a most specific one. For
2187 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2188 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2189 most-specific match, the program is rejected.
2192 However, GHC is conservative about committing to an overlapping instance. For example:
2197 Suppose that from the RHS of <literal>f</literal> we get the constraint
2198 <literal>C Int [b]</literal>. But
2199 GHC does not commit to instance (C), because in a particular
2200 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2201 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2202 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2203 GHC will instead pick (C), without complaining about
2204 the problem of subsequent instantiations.
2207 The willingness to be overlapped or incoherent is a property of
2208 the <emphasis>instance declaration</emphasis> itself, controlled by the
2209 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2210 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2211 being defined. Neither flag is required in a module that imports and uses the
2212 instance declaration. Specifically, during the lookup process:
2215 An instance declaration is ignored during the lookup process if (a) a more specific
2216 match is found, and (b) the instance declaration was compiled with
2217 <option>-fallow-overlapping-instances</option>. The flag setting for the
2218 more-specific instance does not matter.
2221 Suppose an instance declaration does not matche the constraint being looked up, but
2222 does unify with it, so that it might match when the constraint is further
2223 instantiated. Usually GHC will regard this as a reason for not committing to
2224 some other constraint. But if the instance declaration was compiled with
2225 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2226 check for that declaration.
2229 These rules make it possible for a library author to design a library that relies on
2230 overlapping instances without the library client having to know.
2233 If an instance declaration is compiled without
2234 <option>-fallow-overlapping-instances</option>,
2235 then that instance can never be overlapped. This could perhaps be
2236 inconvenient. Perhaps the rule should instead say that the
2237 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2238 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2239 at a usage site should be permitted regardless of how the instance declarations
2240 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2241 used at the usage site. (Mind you, the exact usage site can occasionally be
2242 hard to pin down.) We are interested to receive feedback on these points.
2244 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2245 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2250 <title>Type synonyms in the instance head</title>
2253 <emphasis>Unlike Haskell 98, instance heads may use type
2254 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2255 As always, using a type synonym is just shorthand for
2256 writing the RHS of the type synonym definition. For example:
2260 type Point = (Int,Int)
2261 instance C Point where ...
2262 instance C [Point] where ...
2266 is legal. However, if you added
2270 instance C (Int,Int) where ...
2274 as well, then the compiler will complain about the overlapping
2275 (actually, identical) instance declarations. As always, type synonyms
2276 must be fully applied. You cannot, for example, write:
2281 instance Monad P where ...
2285 This design decision is independent of all the others, and easily
2286 reversed, but it makes sense to me.
2294 <sect2 id="type-restrictions">
2295 <title>Type signatures</title>
2297 <sect3><title>The context of a type signature</title>
2299 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2300 the form <emphasis>(class type-variable)</emphasis> or
2301 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2302 these type signatures are perfectly OK
2305 g :: Ord (T a ()) => ...
2309 GHC imposes the following restrictions on the constraints in a type signature.
2313 forall tv1..tvn (c1, ...,cn) => type
2316 (Here, we write the "foralls" explicitly, although the Haskell source
2317 language omits them; in Haskell 98, all the free type variables of an
2318 explicit source-language type signature are universally quantified,
2319 except for the class type variables in a class declaration. However,
2320 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2329 <emphasis>Each universally quantified type variable
2330 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2332 A type variable <literal>a</literal> is "reachable" if it it appears
2333 in the same constraint as either a type variable free in in
2334 <literal>type</literal>, or another reachable type variable.
2335 A value with a type that does not obey
2336 this reachability restriction cannot be used without introducing
2337 ambiguity; that is why the type is rejected.
2338 Here, for example, is an illegal type:
2342 forall a. Eq a => Int
2346 When a value with this type was used, the constraint <literal>Eq tv</literal>
2347 would be introduced where <literal>tv</literal> is a fresh type variable, and
2348 (in the dictionary-translation implementation) the value would be
2349 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2350 can never know which instance of <literal>Eq</literal> to use because we never
2351 get any more information about <literal>tv</literal>.
2355 that the reachability condition is weaker than saying that <literal>a</literal> is
2356 functionally dependent on a type variable free in
2357 <literal>type</literal> (see <xref
2358 linkend="functional-dependencies"/>). The reason for this is there
2359 might be a "hidden" dependency, in a superclass perhaps. So
2360 "reachable" is a conservative approximation to "functionally dependent".
2361 For example, consider:
2363 class C a b | a -> b where ...
2364 class C a b => D a b where ...
2365 f :: forall a b. D a b => a -> a
2367 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2368 but that is not immediately apparent from <literal>f</literal>'s type.
2374 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2375 universally quantified type variables <literal>tvi</literal></emphasis>.
2377 For example, this type is OK because <literal>C a b</literal> mentions the
2378 universally quantified type variable <literal>b</literal>:
2382 forall a. C a b => burble
2386 The next type is illegal because the constraint <literal>Eq b</literal> does not
2387 mention <literal>a</literal>:
2391 forall a. Eq b => burble
2395 The reason for this restriction is milder than the other one. The
2396 excluded types are never useful or necessary (because the offending
2397 context doesn't need to be witnessed at this point; it can be floated
2398 out). Furthermore, floating them out increases sharing. Lastly,
2399 excluding them is a conservative choice; it leaves a patch of
2400 territory free in case we need it later.
2411 <title>For-all hoisting</title>
2413 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2414 end of an arrow, thus:
2416 type Discard a = forall b. a -> b -> a
2418 g :: Int -> Discard Int
2421 Simply expanding the type synonym would give
2423 g :: Int -> (forall b. Int -> b -> Int)
2425 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2427 g :: forall b. Int -> Int -> b -> Int
2429 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2430 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2431 performs the transformation:</emphasis>
2433 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2435 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2437 (In fact, GHC tries to retain as much synonym information as possible for use in
2438 error messages, but that is a usability issue.) This rule applies, of course, whether
2439 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2440 valid way to write <literal>g</literal>'s type signature:
2442 g :: Int -> Int -> forall b. b -> Int
2446 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2449 type Foo a = (?x::Int) => Bool -> a
2454 g :: (?x::Int) => Bool -> Bool -> Int
2462 <sect2 id="implicit-parameters">
2463 <title>Implicit parameters</title>
2465 <para> Implicit parameters are implemented as described in
2466 "Implicit parameters: dynamic scoping with static types",
2467 J Lewis, MB Shields, E Meijer, J Launchbury,
2468 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2472 <para>(Most of the following, stil rather incomplete, documentation is
2473 due to Jeff Lewis.)</para>
2475 <para>Implicit parameter support is enabled with the option
2476 <option>-fimplicit-params</option>.</para>
2479 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2480 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2481 context. In Haskell, all variables are statically bound. Dynamic
2482 binding of variables is a notion that goes back to Lisp, but was later
2483 discarded in more modern incarnations, such as Scheme. Dynamic binding
2484 can be very confusing in an untyped language, and unfortunately, typed
2485 languages, in particular Hindley-Milner typed languages like Haskell,
2486 only support static scoping of variables.
2489 However, by a simple extension to the type class system of Haskell, we
2490 can support dynamic binding. Basically, we express the use of a
2491 dynamically bound variable as a constraint on the type. These
2492 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2493 function uses a dynamically-bound variable <literal>?x</literal>
2494 of type <literal>t'</literal>". For
2495 example, the following expresses the type of a sort function,
2496 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2498 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2500 The dynamic binding constraints are just a new form of predicate in the type class system.
2503 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2504 where <literal>x</literal> is
2505 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2506 Use of this construct also introduces a new
2507 dynamic-binding constraint in the type of the expression.
2508 For example, the following definition
2509 shows how we can define an implicitly parameterized sort function in
2510 terms of an explicitly parameterized <literal>sortBy</literal> function:
2512 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2514 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2520 <title>Implicit-parameter type constraints</title>
2522 Dynamic binding constraints behave just like other type class
2523 constraints in that they are automatically propagated. Thus, when a
2524 function is used, its implicit parameters are inherited by the
2525 function that called it. For example, our <literal>sort</literal> function might be used
2526 to pick out the least value in a list:
2528 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2529 least xs = head (sort xs)
2531 Without lifting a finger, the <literal>?cmp</literal> parameter is
2532 propagated to become a parameter of <literal>least</literal> as well. With explicit
2533 parameters, the default is that parameters must always be explicit
2534 propagated. With implicit parameters, the default is to always
2538 An implicit-parameter type constraint differs from other type class constraints in the
2539 following way: All uses of a particular implicit parameter must have
2540 the same type. This means that the type of <literal>(?x, ?x)</literal>
2541 is <literal>(?x::a) => (a,a)</literal>, and not
2542 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2546 <para> You can't have an implicit parameter in the context of a class or instance
2547 declaration. For example, both these declarations are illegal:
2549 class (?x::Int) => C a where ...
2550 instance (?x::a) => Foo [a] where ...
2552 Reason: exactly which implicit parameter you pick up depends on exactly where
2553 you invoke a function. But the ``invocation'' of instance declarations is done
2554 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2555 Easiest thing is to outlaw the offending types.</para>
2557 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2559 f :: (?x :: [a]) => Int -> Int
2562 g :: (Read a, Show a) => String -> String
2565 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2566 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2567 quite unambiguous, and fixes the type <literal>a</literal>.
2572 <title>Implicit-parameter bindings</title>
2575 An implicit parameter is <emphasis>bound</emphasis> using the standard
2576 <literal>let</literal> or <literal>where</literal> binding forms.
2577 For example, we define the <literal>min</literal> function by binding
2578 <literal>cmp</literal>.
2581 min = let ?cmp = (<=) in least
2585 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2586 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2587 (including in a list comprehension, or do-notation, or pattern guards),
2588 or a <literal>where</literal> clause.
2589 Note the following points:
2592 An implicit-parameter binding group must be a
2593 collection of simple bindings to implicit-style variables (no
2594 function-style bindings, and no type signatures); these bindings are
2595 neither polymorphic or recursive.
2598 You may not mix implicit-parameter bindings with ordinary bindings in a
2599 single <literal>let</literal>
2600 expression; use two nested <literal>let</literal>s instead.
2601 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2605 You may put multiple implicit-parameter bindings in a
2606 single binding group; but they are <emphasis>not</emphasis> treated
2607 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2608 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2609 parameter. The bindings are not nested, and may be re-ordered without changing
2610 the meaning of the program.
2611 For example, consider:
2613 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2615 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2616 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2618 f :: (?x::Int) => Int -> Int
2626 <sect3><title>Implicit parameters and polymorphic recursion</title>
2629 Consider these two definitions:
2632 len1 xs = let ?acc = 0 in len_acc1 xs
2635 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2640 len2 xs = let ?acc = 0 in len_acc2 xs
2642 len_acc2 :: (?acc :: Int) => [a] -> Int
2644 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2646 The only difference between the two groups is that in the second group
2647 <literal>len_acc</literal> is given a type signature.
2648 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2649 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2650 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2651 has a type signature, the recursive call is made to the
2652 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2653 as an implicit parameter. So we get the following results in GHCi:
2660 Adding a type signature dramatically changes the result! This is a rather
2661 counter-intuitive phenomenon, worth watching out for.
2665 <sect3><title>Implicit parameters and monomorphism</title>
2667 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2668 Haskell Report) to implicit parameters. For example, consider:
2676 Since the binding for <literal>y</literal> falls under the Monomorphism
2677 Restriction it is not generalised, so the type of <literal>y</literal> is
2678 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2679 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2680 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2681 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2682 <literal>y</literal> in the body of the <literal>let</literal> will see the
2683 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2684 <literal>14</literal>.
2689 <!-- ======================= COMMENTED OUT ========================
2691 We intend to remove linear implicit parameters, so I'm at least removing
2692 them from the 6.6 user manual
2694 <sect2 id="linear-implicit-parameters">
2695 <title>Linear implicit parameters</title>
2697 Linear implicit parameters are an idea developed by Koen Claessen,
2698 Mark Shields, and Simon PJ. They address the long-standing
2699 problem that monads seem over-kill for certain sorts of problem, notably:
2702 <listitem> <para> distributing a supply of unique names </para> </listitem>
2703 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2704 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2708 Linear implicit parameters are just like ordinary implicit parameters,
2709 except that they are "linear"; that is, they cannot be copied, and
2710 must be explicitly "split" instead. Linear implicit parameters are
2711 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2712 (The '/' in the '%' suggests the split!)
2717 import GHC.Exts( Splittable )
2719 data NameSupply = ...
2721 splitNS :: NameSupply -> (NameSupply, NameSupply)
2722 newName :: NameSupply -> Name
2724 instance Splittable NameSupply where
2728 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2729 f env (Lam x e) = Lam x' (f env e)
2732 env' = extend env x x'
2733 ...more equations for f...
2735 Notice that the implicit parameter %ns is consumed
2737 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2738 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2742 So the translation done by the type checker makes
2743 the parameter explicit:
2745 f :: NameSupply -> Env -> Expr -> Expr
2746 f ns env (Lam x e) = Lam x' (f ns1 env e)
2748 (ns1,ns2) = splitNS ns
2750 env = extend env x x'
2752 Notice the call to 'split' introduced by the type checker.
2753 How did it know to use 'splitNS'? Because what it really did
2754 was to introduce a call to the overloaded function 'split',
2755 defined by the class <literal>Splittable</literal>:
2757 class Splittable a where
2760 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2761 split for name supplies. But we can simply write
2767 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2769 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2770 <literal>GHC.Exts</literal>.
2775 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2776 are entirely distinct implicit parameters: you
2777 can use them together and they won't intefere with each other. </para>
2780 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2782 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2783 in the context of a class or instance declaration. </para></listitem>
2787 <sect3><title>Warnings</title>
2790 The monomorphism restriction is even more important than usual.
2791 Consider the example above:
2793 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2794 f env (Lam x e) = Lam x' (f env e)
2797 env' = extend env x x'
2799 If we replaced the two occurrences of x' by (newName %ns), which is
2800 usually a harmless thing to do, we get:
2802 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2803 f env (Lam x e) = Lam (newName %ns) (f env e)
2805 env' = extend env x (newName %ns)
2807 But now the name supply is consumed in <emphasis>three</emphasis> places
2808 (the two calls to newName,and the recursive call to f), so
2809 the result is utterly different. Urk! We don't even have
2813 Well, this is an experimental change. With implicit
2814 parameters we have already lost beta reduction anyway, and
2815 (as John Launchbury puts it) we can't sensibly reason about
2816 Haskell programs without knowing their typing.
2821 <sect3><title>Recursive functions</title>
2822 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2825 foo :: %x::T => Int -> [Int]
2827 foo n = %x : foo (n-1)
2829 where T is some type in class Splittable.</para>
2831 Do you get a list of all the same T's or all different T's
2832 (assuming that split gives two distinct T's back)?
2834 If you supply the type signature, taking advantage of polymorphic
2835 recursion, you get what you'd probably expect. Here's the
2836 translated term, where the implicit param is made explicit:
2839 foo x n = let (x1,x2) = split x
2840 in x1 : foo x2 (n-1)
2842 But if you don't supply a type signature, GHC uses the Hindley
2843 Milner trick of using a single monomorphic instance of the function
2844 for the recursive calls. That is what makes Hindley Milner type inference
2845 work. So the translation becomes
2849 foom n = x : foom (n-1)
2853 Result: 'x' is not split, and you get a list of identical T's. So the
2854 semantics of the program depends on whether or not foo has a type signature.
2857 You may say that this is a good reason to dislike linear implicit parameters
2858 and you'd be right. That is why they are an experimental feature.
2864 ================ END OF Linear Implicit Parameters commented out -->
2866 <sect2 id="sec-kinding">
2867 <title>Explicitly-kinded quantification</title>
2870 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2871 to give the kind explicitly as (machine-checked) documentation,
2872 just as it is nice to give a type signature for a function. On some occasions,
2873 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2874 John Hughes had to define the data type:
2876 data Set cxt a = Set [a]
2877 | Unused (cxt a -> ())
2879 The only use for the <literal>Unused</literal> constructor was to force the correct
2880 kind for the type variable <literal>cxt</literal>.
2883 GHC now instead allows you to specify the kind of a type variable directly, wherever
2884 a type variable is explicitly bound. Namely:
2886 <listitem><para><literal>data</literal> declarations:
2888 data Set (cxt :: * -> *) a = Set [a]
2889 </screen></para></listitem>
2890 <listitem><para><literal>type</literal> declarations:
2892 type T (f :: * -> *) = f Int
2893 </screen></para></listitem>
2894 <listitem><para><literal>class</literal> declarations:
2896 class (Eq a) => C (f :: * -> *) a where ...
2897 </screen></para></listitem>
2898 <listitem><para><literal>forall</literal>'s in type signatures:
2900 f :: forall (cxt :: * -> *). Set cxt Int
2901 </screen></para></listitem>
2906 The parentheses are required. Some of the spaces are required too, to
2907 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2908 will get a parse error, because "<literal>::*->*</literal>" is a
2909 single lexeme in Haskell.
2913 As part of the same extension, you can put kind annotations in types
2916 f :: (Int :: *) -> Int
2917 g :: forall a. a -> (a :: *)
2921 atype ::= '(' ctype '::' kind ')
2923 The parentheses are required.
2928 <sect2 id="universal-quantification">
2929 <title>Arbitrary-rank polymorphism
2933 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2934 allows us to say exactly what this means. For example:
2942 g :: forall b. (b -> b)
2944 The two are treated identically.
2948 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2949 explicit universal quantification in
2951 For example, all the following types are legal:
2953 f1 :: forall a b. a -> b -> a
2954 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2956 f2 :: (forall a. a->a) -> Int -> Int
2957 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2959 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2961 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2962 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2963 The <literal>forall</literal> makes explicit the universal quantification that
2964 is implicitly added by Haskell.
2967 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2968 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2969 shows, the polymorphic type on the left of the function arrow can be overloaded.
2972 The function <literal>f3</literal> has a rank-3 type;
2973 it has rank-2 types on the left of a function arrow.
2976 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2977 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2978 that restriction has now been lifted.)
2979 In particular, a forall-type (also called a "type scheme"),
2980 including an operational type class context, is legal:
2982 <listitem> <para> On the left of a function arrow </para> </listitem>
2983 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2984 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2985 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2986 field type signatures.</para> </listitem>
2987 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2988 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2990 There is one place you cannot put a <literal>forall</literal>:
2991 you cannot instantiate a type variable with a forall-type. So you cannot
2992 make a forall-type the argument of a type constructor. So these types are illegal:
2994 x1 :: [forall a. a->a]
2995 x2 :: (forall a. a->a, Int)
2996 x3 :: Maybe (forall a. a->a)
2998 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2999 a type variable any more!
3008 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3009 the types of the constructor arguments. Here are several examples:
3015 data T a = T1 (forall b. b -> b -> b) a
3017 data MonadT m = MkMonad { return :: forall a. a -> m a,
3018 bind :: forall a b. m a -> (a -> m b) -> m b
3021 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3027 The constructors have rank-2 types:
3033 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3034 MkMonad :: forall m. (forall a. a -> m a)
3035 -> (forall a b. m a -> (a -> m b) -> m b)
3037 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3043 Notice that you don't need to use a <literal>forall</literal> if there's an
3044 explicit context. For example in the first argument of the
3045 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3046 prefixed to the argument type. The implicit <literal>forall</literal>
3047 quantifies all type variables that are not already in scope, and are
3048 mentioned in the type quantified over.
3052 As for type signatures, implicit quantification happens for non-overloaded
3053 types too. So if you write this:
3056 data T a = MkT (Either a b) (b -> b)
3059 it's just as if you had written this:
3062 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3065 That is, since the type variable <literal>b</literal> isn't in scope, it's
3066 implicitly universally quantified. (Arguably, it would be better
3067 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3068 where that is what is wanted. Feedback welcomed.)
3072 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3073 the constructor to suitable values, just as usual. For example,
3084 a3 = MkSwizzle reverse
3087 a4 = let r x = Just x
3094 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3095 mkTs f x y = [T1 f x, T1 f y]
3101 The type of the argument can, as usual, be more general than the type
3102 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3103 does not need the <literal>Ord</literal> constraint.)
3107 When you use pattern matching, the bound variables may now have
3108 polymorphic types. For example:
3114 f :: T a -> a -> (a, Char)
3115 f (T1 w k) x = (w k x, w 'c' 'd')
3117 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3118 g (MkSwizzle s) xs f = s (map f (s xs))
3120 h :: MonadT m -> [m a] -> m [a]
3121 h m [] = return m []
3122 h m (x:xs) = bind m x $ \y ->
3123 bind m (h m xs) $ \ys ->
3130 In the function <function>h</function> we use the record selectors <literal>return</literal>
3131 and <literal>bind</literal> to extract the polymorphic bind and return functions
3132 from the <literal>MonadT</literal> data structure, rather than using pattern
3138 <title>Type inference</title>
3141 In general, type inference for arbitrary-rank types is undecidable.
3142 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3143 to get a decidable algorithm by requiring some help from the programmer.
3144 We do not yet have a formal specification of "some help" but the rule is this:
3147 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3148 provides an explicit polymorphic type for x, or GHC's type inference will assume
3149 that x's type has no foralls in it</emphasis>.
3152 What does it mean to "provide" an explicit type for x? You can do that by
3153 giving a type signature for x directly, using a pattern type signature
3154 (<xref linkend="scoped-type-variables"/>), thus:
3156 \ f :: (forall a. a->a) -> (f True, f 'c')
3158 Alternatively, you can give a type signature to the enclosing
3159 context, which GHC can "push down" to find the type for the variable:
3161 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3163 Here the type signature on the expression can be pushed inwards
3164 to give a type signature for f. Similarly, and more commonly,
3165 one can give a type signature for the function itself:
3167 h :: (forall a. a->a) -> (Bool,Char)
3168 h f = (f True, f 'c')
3170 You don't need to give a type signature if the lambda bound variable
3171 is a constructor argument. Here is an example we saw earlier:
3173 f :: T a -> a -> (a, Char)
3174 f (T1 w k) x = (w k x, w 'c' 'd')
3176 Here we do not need to give a type signature to <literal>w</literal>, because
3177 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3184 <sect3 id="implicit-quant">
3185 <title>Implicit quantification</title>
3188 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3189 user-written types, if and only if there is no explicit <literal>forall</literal>,
3190 GHC finds all the type variables mentioned in the type that are not already
3191 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3195 f :: forall a. a -> a
3202 h :: forall b. a -> b -> b
3208 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3211 f :: (a -> a) -> Int
3213 f :: forall a. (a -> a) -> Int
3215 f :: (forall a. a -> a) -> Int
3218 g :: (Ord a => a -> a) -> Int
3219 -- MEANS the illegal type
3220 g :: forall a. (Ord a => a -> a) -> Int
3222 g :: (forall a. Ord a => a -> a) -> Int
3224 The latter produces an illegal type, which you might think is silly,
3225 but at least the rule is simple. If you want the latter type, you
3226 can write your for-alls explicitly. Indeed, doing so is strongly advised
3233 <sect2 id="impredicative-polymorphism">
3234 <title>Impredicative polymorphism
3236 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3237 that you can call a polymorphic function at a polymorphic type, and
3238 parameterise data structures over polymorphic types. For example:
3240 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3241 f (Just g) = Just (g [3], g "hello")
3244 Notice here that the <literal>Maybe</literal> type is parameterised by the
3245 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3248 <para>The technical details of this extension are described in the paper
3249 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3250 type inference for higher-rank types and impredicativity</ulink>,
3251 which appeared at ICFP 2006.
3255 <sect2 id="scoped-type-variables">
3256 <title>Lexically scoped type variables
3260 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3261 which some type signatures are simply impossible to write. For example:
3263 f :: forall a. [a] -> [a]
3269 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3270 the entire definition of <literal>f</literal>.
3271 In particular, it is in scope at the type signature for <varname>ys</varname>.
3272 In Haskell 98 it is not possible to declare
3273 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3274 it becomes possible to do so.
3276 <para>Lexically-scoped type variables are enabled by
3277 <option>-fglasgow-exts</option>.
3279 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3280 variables work, compared to earlier releases. Read this section
3284 <title>Overview</title>
3286 <para>The design follows the following principles
3288 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3289 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3290 design.)</para></listitem>
3291 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3292 type variables. This means that every programmer-written type signature
3293 (includin one that contains free scoped type variables) denotes a
3294 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3295 checker, and no inference is involved.</para></listitem>
3296 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3297 changing the program.</para></listitem>
3301 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3303 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3304 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3305 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3306 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3310 In Haskell, a programmer-written type signature is implicitly quantifed over
3311 its free type variables (<ulink
3312 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3314 of the Haskel Report).
3315 Lexically scoped type variables affect this implicit quantification rules
3316 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3317 quantified. For example, if type variable <literal>a</literal> is in scope,
3320 (e :: a -> a) means (e :: a -> a)
3321 (e :: b -> b) means (e :: forall b. b->b)
3322 (e :: a -> b) means (e :: forall b. a->b)
3330 <sect3 id="decl-type-sigs">
3331 <title>Declaration type signatures</title>
3332 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3333 quantification (using <literal>forall</literal>) brings into scope the
3334 explicitly-quantified
3335 type variables, in the definition of the named function(s). For example:
3337 f :: forall a. [a] -> [a]
3338 f (x:xs) = xs ++ [ x :: a ]
3340 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3341 the definition of "<literal>f</literal>".
3343 <para>This only happens if the quantification in <literal>f</literal>'s type
3344 signature is explicit. For example:
3347 g (x:xs) = xs ++ [ x :: a ]
3349 This program will be rejected, because "<literal>a</literal>" does not scope
3350 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3351 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3352 quantification rules.
3356 <sect3 id="exp-type-sigs">
3357 <title>Expression type signatures</title>
3359 <para>An expression type signature that has <emphasis>explicit</emphasis>
3360 quantification (using <literal>forall</literal>) brings into scope the
3361 explicitly-quantified
3362 type variables, in the annotated expression. For example:
3364 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3366 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3367 type variable <literal>s</literal> into scope, in the annotated expression
3368 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3373 <sect3 id="pattern-type-sigs">
3374 <title>Pattern type signatures</title>
3376 A type signature may occur in any pattern; this is a <emphasis>pattern type
3377 signature</emphasis>.
3380 -- f and g assume that 'a' is already in scope
3381 f = \(x::Int, y::a) -> x
3383 h ((x,y) :: (Int,Bool)) = (y,x)
3385 In the case where all the type variables in the pattern type sigature are
3386 already in scope (i.e. bound by the enclosing context), matters are simple: the
3387 signature simply constrains the type of the pattern in the obvious way.
3390 There is only one situation in which you can write a pattern type signature that
3391 mentions a type variable that is not already in scope, namely in pattern match
3392 of an existential data constructor. For example:
3394 data T = forall a. MkT [a]
3397 k (MkT [t::a]) = MkT t3
3401 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3402 variable that is not already in scope. Indeed, it cannot already be in scope,
3403 because it is bound by the pattern match. GHC's rule is that in this situation
3404 (and only then), a pattern type signature can mention a type variable that is
3405 not already in scope; the effect is to bring it into scope, standing for the
3406 existentially-bound type variable.
3409 If this seems a little odd, we think so too. But we must have
3410 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3411 could not name existentially-bound type variables in subequent type signatures.
3414 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3415 signature is allowed to mention a lexical variable that is not already in
3417 For example, both <literal>f</literal> and <literal>g</literal> would be
3418 illegal if <literal>a</literal> was not already in scope.
3424 <!-- ==================== Commented out part about result type signatures
3426 <sect3 id="result-type-sigs">
3427 <title>Result type signatures</title>
3430 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3433 {- f assumes that 'a' is already in scope -}
3434 f x y :: [a] = [x,y,x]
3436 g = \ x :: [Int] -> [3,4]
3438 h :: forall a. [a] -> a
3442 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3443 the result of the function. Similarly, the body of the lambda in the RHS of
3444 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3445 alternative in <literal>h</literal> is <literal>a</literal>.
3447 <para> A result type signature never brings new type variables into scope.</para>
3449 There are a couple of syntactic wrinkles. First, notice that all three
3450 examples would parse quite differently with parentheses:
3452 {- f assumes that 'a' is already in scope -}
3453 f x (y :: [a]) = [x,y,x]
3455 g = \ (x :: [Int]) -> [3,4]
3457 h :: forall a. [a] -> a
3461 Now the signature is on the <emphasis>pattern</emphasis>; and
3462 <literal>h</literal> would certainly be ill-typed (since the pattern
3463 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3465 Second, 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:
3477 <sect3 id="cls-inst-scoped-tyvars">
3478 <title>Class and instance declarations</title>
3481 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3482 scope over the methods defined in the <literal>where</literal> part. For example:
3499 <sect2 id="deriving-typeable">
3500 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3503 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3504 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3505 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3506 classes <literal>Eq</literal>, <literal>Ord</literal>,
3507 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3510 GHC extends this list with two more classes that may be automatically derived
3511 (provided the <option>-fglasgow-exts</option> flag is specified):
3512 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3513 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3514 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3516 <para>An instance of <literal>Typeable</literal> can only be derived if the
3517 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3518 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3520 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3521 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3523 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3524 are used, and only <literal>Typeable1</literal> up to
3525 <literal>Typeable7</literal> are provided in the library.)
3526 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3527 class, whose kind suits that of the data type constructor, and
3528 then writing the data type instance by hand.
3532 <sect2 id="newtype-deriving">
3533 <title>Generalised derived instances for newtypes</title>
3536 When you define an abstract type using <literal>newtype</literal>, you may want
3537 the new type to inherit some instances from its representation. In
3538 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3539 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3540 other classes you have to write an explicit instance declaration. For
3541 example, if you define
3544 newtype Dollars = Dollars Int
3547 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3548 explicitly define an instance of <literal>Num</literal>:
3551 instance Num Dollars where
3552 Dollars a + Dollars b = Dollars (a+b)
3555 All the instance does is apply and remove the <literal>newtype</literal>
3556 constructor. It is particularly galling that, since the constructor
3557 doesn't appear at run-time, this instance declaration defines a
3558 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3559 dictionary, only slower!
3563 <sect3> <title> Generalising the deriving clause </title>
3565 GHC now permits such instances to be derived instead, so one can write
3567 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3570 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3571 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3572 derives an instance declaration of the form
3575 instance Num Int => Num Dollars
3578 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3582 We can also derive instances of constructor classes in a similar
3583 way. For example, suppose we have implemented state and failure monad
3584 transformers, such that
3587 instance Monad m => Monad (State s m)
3588 instance Monad m => Monad (Failure m)
3590 In Haskell 98, we can define a parsing monad by
3592 type Parser tok m a = State [tok] (Failure m) a
3595 which is automatically a monad thanks to the instance declarations
3596 above. With the extension, we can make the parser type abstract,
3597 without needing to write an instance of class <literal>Monad</literal>, via
3600 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3603 In this case the derived instance declaration is of the form
3605 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3608 Notice that, since <literal>Monad</literal> is a constructor class, the
3609 instance is a <emphasis>partial application</emphasis> of the new type, not the
3610 entire left hand side. We can imagine that the type declaration is
3611 ``eta-converted'' to generate the context of the instance
3616 We can even derive instances of multi-parameter classes, provided the
3617 newtype is the last class parameter. In this case, a ``partial
3618 application'' of the class appears in the <literal>deriving</literal>
3619 clause. For example, given the class
3622 class StateMonad s m | m -> s where ...
3623 instance Monad m => StateMonad s (State s m) where ...
3625 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3627 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3628 deriving (Monad, StateMonad [tok])
3631 The derived instance is obtained by completing the application of the
3632 class to the new type:
3635 instance StateMonad [tok] (State [tok] (Failure m)) =>
3636 StateMonad [tok] (Parser tok m)
3641 As a result of this extension, all derived instances in newtype
3642 declarations are treated uniformly (and implemented just by reusing
3643 the dictionary for the representation type), <emphasis>except</emphasis>
3644 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3645 the newtype and its representation.
3649 <sect3> <title> A more precise specification </title>
3651 Derived instance declarations are constructed as follows. Consider the
3652 declaration (after expansion of any type synonyms)
3655 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3661 The <literal>ci</literal> are partial applications of
3662 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3663 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3666 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3669 The type <literal>t</literal> is an arbitrary type.
3672 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3673 nor in the <literal>ci</literal>, and
3676 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3677 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3678 should not "look through" the type or its constructor. You can still
3679 derive these classes for a newtype, but it happens in the usual way, not
3680 via this new mechanism.
3683 Then, for each <literal>ci</literal>, the derived instance
3686 instance ci t => ci (T v1...vk)
3688 As an example which does <emphasis>not</emphasis> work, consider
3690 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3692 Here we cannot derive the instance
3694 instance Monad (State s m) => Monad (NonMonad m)
3697 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3698 and so cannot be "eta-converted" away. It is a good thing that this
3699 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3700 not, in fact, a monad --- for the same reason. Try defining
3701 <literal>>>=</literal> with the correct type: you won't be able to.
3705 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3706 important, since we can only derive instances for the last one. If the
3707 <literal>StateMonad</literal> class above were instead defined as
3710 class StateMonad m s | m -> s where ...
3713 then we would not have been able to derive an instance for the
3714 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3715 classes usually have one "main" parameter for which deriving new
3716 instances is most interesting.
3718 <para>Lastly, all of this applies only for classes other than
3719 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3720 and <literal>Data</literal>, for which the built-in derivation applies (section
3721 4.3.3. of the Haskell Report).
3722 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3723 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3724 the standard method is used or the one described here.)
3730 <sect2 id="typing-binds">
3731 <title>Generalised typing of mutually recursive bindings</title>
3734 The Haskell Report specifies that a group of bindings (at top level, or in a
3735 <literal>let</literal> or <literal>where</literal>) should be sorted into
3736 strongly-connected components, and then type-checked in dependency order
3737 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3738 Report, Section 4.5.1</ulink>).
3739 As each group is type-checked, any binders of the group that
3741 an explicit type signature are put in the type environment with the specified
3743 and all others are monomorphic until the group is generalised
3744 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3747 <para>Following a suggestion of Mark Jones, in his paper
3748 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3750 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3752 <emphasis>the dependency analysis ignores references to variables that have an explicit
3753 type signature</emphasis>.
3754 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3755 typecheck. For example, consider:
3757 f :: Eq a => a -> Bool
3758 f x = (x == x) || g True || g "Yes"
3760 g y = (y <= y) || f True
3762 This is rejected by Haskell 98, but under Jones's scheme the definition for
3763 <literal>g</literal> is typechecked first, separately from that for
3764 <literal>f</literal>,
3765 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3766 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3767 type is generalised, to get
3769 g :: Ord a => a -> Bool
3771 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3772 <literal>g</literal> in the type environment.
3776 The same refined dependency analysis also allows the type signatures of
3777 mutually-recursive functions to have different contexts, something that is illegal in
3778 Haskell 98 (Section 4.5.2, last sentence). With
3779 <option>-fglasgow-exts</option>
3780 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3781 type signatures; in practice this means that only variables bound by the same
3782 pattern binding must have the same context. For example, this is fine:
3784 f :: Eq a => a -> Bool
3785 f x = (x == x) || g True
3787 g :: Ord a => a -> Bool
3788 g y = (y <= y) || f True
3794 <!-- ==================== End of type system extensions ================= -->
3796 <!-- ====================== Generalised algebraic data types ======================= -->
3799 <title>Generalised Algebraic Data Types (GADTs)</title>
3801 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types by allowing you
3802 to give the type signatures of constructors explicitly. For example:
3805 Lit :: Int -> Term Int
3806 Succ :: Term Int -> Term Int
3807 IsZero :: Term Int -> Term Bool
3808 If :: Term Bool -> Term a -> Term a -> Term a
3809 Pair :: Term a -> Term b -> Term (a,b)
3811 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3812 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3813 for these <literal>Terms</literal>:
3817 eval (Succ t) = 1 + eval t
3818 eval (IsZero t) = eval t == 0
3819 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3820 eval (Pair e1 e2) = (eval e1, eval e2)
3822 These and many other examples are given in papers by Hongwei Xi, and
3823 Tim Sheard. There is a longer introduction
3824 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3826 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
3827 may use different notation to that implemented in GHC.
3830 The rest of this section outlines the extensions to GHC that support GADTs.
3831 It is far from comprehensive, but the design closely follows that described in
3833 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
3834 unification-based type inference for GADTs</ulink>,
3835 which appeared in ICFP 2006.
3838 Data type declarations have a 'where' form, as exemplified above. The type signature of
3839 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3840 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3841 have no scope. Indeed, one can write a kind signature instead:
3843 data Term :: * -> * where ...
3845 or even a mixture of the two:
3847 data Foo a :: (* -> *) -> * where ...
3849 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3852 data Foo a (b :: * -> *) where ...
3857 There are no restrictions on the type of the data constructor, except that the result
3858 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3859 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3863 You can use record syntax on a GADT-style data type declaration:
3867 Lit { val :: Int } :: Term Int
3868 Succ { num :: Term Int } :: Term Int
3869 Pred { num :: Term Int } :: Term Int
3870 IsZero { arg :: Term Int } :: Term Bool
3871 Pair { arg1 :: Term a
3874 If { cnd :: Term Bool
3879 For every constructor that has a field <literal>f</literal>, (a) the type of
3880 field <literal>f</literal> must be the same; and (b) the
3881 result type of the constructor must be the same; both modulo alpha conversion.
3882 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3884 single name. Although their field types are both <literal>Term Int</literal>,
3885 their selector functions actually have different types:
3888 num :: Term Int -> Term Int
3889 arg :: Term Bool -> Term Int
3892 At the moment, record updates are not yet possible with GADT, so support is
3893 limited to record construction, selection and pattern matching:
3896 someTerm :: Term Bool
3897 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3900 eval Lit { val = i } = i
3901 eval Succ { num = t } = eval t + 1
3902 eval Pred { num = t } = eval t - 1
3903 eval IsZero { arg = t } = eval t == 0
3904 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3905 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3911 You can use strictness annotations, in the obvious places
3912 in the constructor type:
3915 Lit :: !Int -> Term Int
3916 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3917 Pair :: Term a -> Term b -> Term (a,b)
3922 You can use a <literal>deriving</literal> clause on a GADT-style data type
3923 declaration, but only if the data type could also have been declared in
3924 Haskell-98 syntax. For example, these two declarations are equivalent
3926 data Maybe1 a where {
3927 Nothing1 :: Maybe1 a ;
3928 Just1 :: a -> Maybe1 a
3929 } deriving( Eq, Ord )
3931 data Maybe2 a = Nothing2 | Just2 a
3934 This simply allows you to declare a vanilla Haskell-98 data type using the
3935 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3939 Pattern matching causes type refinement. For example, in the right hand side of the equation
3944 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3945 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3946 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3948 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3949 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3950 occur. However, the refinement is quite general. For example, if we had:
3952 eval :: Term a -> a -> a
3953 eval (Lit i) j = i+j
3955 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3956 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3957 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3963 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3965 data T a = forall b. MkT b (b->a)
3966 data T' a where { MKT :: b -> (b->a) -> T' a }
3971 <!-- ====================== End of Generalised algebraic data types ======================= -->
3973 <!-- ====================== TEMPLATE HASKELL ======================= -->
3975 <sect1 id="template-haskell">
3976 <title>Template Haskell</title>
3978 <para>Template Haskell allows you to do compile-time meta-programming in
3981 the main technical innovations is discussed in "<ulink
3982 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3983 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3986 There is a Wiki page about
3987 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
3988 http://www.haskell.org/th/</ulink>, and that is the best place to look for
3992 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
3993 Haskell library reference material</ulink>
3994 (search for the type ExpQ).
3995 [Temporary: many changes to the original design are described in
3996 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3997 Not all of these changes are in GHC 6.6.]
4000 <para> The first example from that paper is set out below as a worked example to help get you started.
4004 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4005 Tim Sheard is going to expand it.)
4009 <title>Syntax</title>
4011 <para> Template Haskell has the following new syntactic
4012 constructions. You need to use the flag
4013 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4014 </indexterm>to switch these syntactic extensions on
4015 (<option>-fth</option> is no longer implied by
4016 <option>-fglasgow-exts</option>).</para>
4020 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4021 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4022 There must be no space between the "$" and the identifier or parenthesis. This use
4023 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4024 of "." as an infix operator. If you want the infix operator, put spaces around it.
4026 <para> A splice can occur in place of
4028 <listitem><para> an expression; the spliced expression must
4029 have type <literal>Q Exp</literal></para></listitem>
4030 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4031 <listitem><para> [Planned, but not implemented yet.] a
4032 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4034 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4035 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4041 A expression quotation is written in Oxford brackets, thus:
4043 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4044 the quotation has type <literal>Expr</literal>.</para></listitem>
4045 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4046 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4047 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4048 the quotation has type <literal>Type</literal>.</para></listitem>
4049 </itemizedlist></para></listitem>
4052 Reification is written thus:
4054 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4055 has type <literal>Dec</literal>. </para></listitem>
4056 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4057 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4058 <listitem><para> Still to come: fixities </para></listitem>
4060 </itemizedlist></para>
4067 <sect2> <title> Using Template Haskell </title>
4071 The data types and monadic constructor functions for Template Haskell are in the library
4072 <literal>Language.Haskell.THSyntax</literal>.
4076 You can only run a function at compile time if it is imported from another module. That is,
4077 you can't define a function in a module, and call it from within a splice in the same module.
4078 (It would make sense to do so, but it's hard to implement.)
4082 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4085 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4086 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4087 compiles and runs a program, and then looks at the result. So it's important that
4088 the program it compiles produces results whose representations are identical to
4089 those of the compiler itself.
4093 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4094 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4099 <sect2> <title> A Template Haskell Worked Example </title>
4100 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4101 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4108 -- Import our template "pr"
4109 import Printf ( pr )
4111 -- The splice operator $ takes the Haskell source code
4112 -- generated at compile time by "pr" and splices it into
4113 -- the argument of "putStrLn".
4114 main = putStrLn ( $(pr "Hello") )
4120 -- Skeletal printf from the paper.
4121 -- It needs to be in a separate module to the one where
4122 -- you intend to use it.
4124 -- Import some Template Haskell syntax
4125 import Language.Haskell.TH
4127 -- Describe a format string
4128 data Format = D | S | L String
4130 -- Parse a format string. This is left largely to you
4131 -- as we are here interested in building our first ever
4132 -- Template Haskell program and not in building printf.
4133 parse :: String -> [Format]
4136 -- Generate Haskell source code from a parsed representation
4137 -- of the format string. This code will be spliced into
4138 -- the module which calls "pr", at compile time.
4139 gen :: [Format] -> ExpQ
4140 gen [D] = [| \n -> show n |]
4141 gen [S] = [| \s -> s |]
4142 gen [L s] = stringE s
4144 -- Here we generate the Haskell code for the splice
4145 -- from an input format string.
4146 pr :: String -> ExpQ
4147 pr s = gen (parse s)
4150 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4153 $ ghc --make -fth main.hs -o main.exe
4156 <para>Run "main.exe" and here is your output:</para>
4166 <title>Using Template Haskell with Profiling</title>
4167 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4169 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4170 interpreter to run the splice expressions. The bytecode interpreter
4171 runs the compiled expression on top of the same runtime on which GHC
4172 itself is running; this means that the compiled code referred to by
4173 the interpreted expression must be compatible with this runtime, and
4174 in particular this means that object code that is compiled for
4175 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4176 expression, because profiled object code is only compatible with the
4177 profiling version of the runtime.</para>
4179 <para>This causes difficulties if you have a multi-module program
4180 containing Template Haskell code and you need to compile it for
4181 profiling, because GHC cannot load the profiled object code and use it
4182 when executing the splices. Fortunately GHC provides a workaround.
4183 The basic idea is to compile the program twice:</para>
4187 <para>Compile the program or library first the normal way, without
4188 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4191 <para>Then compile it again with <option>-prof</option>, and
4192 additionally use <option>-osuf
4193 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4194 to name the object files differentliy (you can choose any suffix
4195 that isn't the normal object suffix here). GHC will automatically
4196 load the object files built in the first step when executing splice
4197 expressions. If you omit the <option>-osuf</option> flag when
4198 building with <option>-prof</option> and Template Haskell is used,
4199 GHC will emit an error message. </para>
4206 <!-- ===================== Arrow notation =================== -->
4208 <sect1 id="arrow-notation">
4209 <title>Arrow notation
4212 <para>Arrows are a generalization of monads introduced by John Hughes.
4213 For more details, see
4218 “Generalising Monads to Arrows”,
4219 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4220 pp67–111, May 2000.
4226 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4227 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4233 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4234 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4240 and the arrows web page at
4241 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4242 With the <option>-farrows</option> flag, GHC supports the arrow
4243 notation described in the second of these papers.
4244 What follows is a brief introduction to the notation;
4245 it won't make much sense unless you've read Hughes's paper.
4246 This notation is translated to ordinary Haskell,
4247 using combinators from the
4248 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4252 <para>The extension adds a new kind of expression for defining arrows:
4254 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4255 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4257 where <literal>proc</literal> is a new keyword.
4258 The variables of the pattern are bound in the body of the
4259 <literal>proc</literal>-expression,
4260 which is a new sort of thing called a <firstterm>command</firstterm>.
4261 The syntax of commands is as follows:
4263 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4264 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4265 | <replaceable>cmd</replaceable><superscript>0</superscript>
4267 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4268 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4269 infix operators as for expressions, and
4271 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4272 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4273 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4274 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4275 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4276 | <replaceable>fcmd</replaceable>
4278 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4279 | ( <replaceable>cmd</replaceable> )
4280 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4282 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4283 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4284 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4285 | <replaceable>cmd</replaceable>
4287 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4288 except that the bodies are commands instead of expressions.
4292 Commands produce values, but (like monadic computations)
4293 may yield more than one value,
4294 or none, and may do other things as well.
4295 For the most part, familiarity with monadic notation is a good guide to
4297 However the values of expressions, even monadic ones,
4298 are determined by the values of the variables they contain;
4299 this is not necessarily the case for commands.
4303 A simple example of the new notation is the expression
4305 proc x -> f -< x+1
4307 We call this a <firstterm>procedure</firstterm> or
4308 <firstterm>arrow abstraction</firstterm>.
4309 As with a lambda expression, the variable <literal>x</literal>
4310 is a new variable bound within the <literal>proc</literal>-expression.
4311 It refers to the input to the arrow.
4312 In the above example, <literal>-<</literal> is not an identifier but an
4313 new reserved symbol used for building commands from an expression of arrow
4314 type and an expression to be fed as input to that arrow.
4315 (The weird look will make more sense later.)
4316 It may be read as analogue of application for arrows.
4317 The above example is equivalent to the Haskell expression
4319 arr (\ x -> x+1) >>> f
4321 That would make no sense if the expression to the left of
4322 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4323 More generally, the expression to the left of <literal>-<</literal>
4324 may not involve any <firstterm>local variable</firstterm>,
4325 i.e. a variable bound in the current arrow abstraction.
4326 For such a situation there is a variant <literal>-<<</literal>, as in
4328 proc x -> f x -<< x+1
4330 which is equivalent to
4332 arr (\ x -> (f x, x+1)) >>> app
4334 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4336 Such an arrow is equivalent to a monad, so if you're using this form
4337 you may find a monadic formulation more convenient.
4341 <title>do-notation for commands</title>
4344 Another form of command is a form of <literal>do</literal>-notation.
4345 For example, you can write
4354 You can read this much like ordinary <literal>do</literal>-notation,
4355 but with commands in place of monadic expressions.
4356 The first line sends the value of <literal>x+1</literal> as an input to
4357 the arrow <literal>f</literal>, and matches its output against
4358 <literal>y</literal>.
4359 In the next line, the output is discarded.
4360 The arrow <function>returnA</function> is defined in the
4361 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4362 module as <literal>arr id</literal>.
4363 The above example is treated as an abbreviation for
4365 arr (\ x -> (x, x)) >>>
4366 first (arr (\ x -> x+1) >>> f) >>>
4367 arr (\ (y, x) -> (y, (x, y))) >>>
4368 first (arr (\ y -> 2*y) >>> g) >>>
4370 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4371 first (arr (\ (x, z) -> x*z) >>> h) >>>
4372 arr (\ (t, z) -> t+z) >>>
4375 Note that variables not used later in the composition are projected out.
4376 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4378 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4379 module, this reduces to
4381 arr (\ x -> (x+1, x)) >>>
4383 arr (\ (y, x) -> (2*y, (x, y))) >>>
4385 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4387 arr (\ (t, z) -> t+z)
4389 which is what you might have written by hand.
4390 With arrow notation, GHC keeps track of all those tuples of variables for you.
4394 Note that although the above translation suggests that
4395 <literal>let</literal>-bound variables like <literal>z</literal> must be
4396 monomorphic, the actual translation produces Core,
4397 so polymorphic variables are allowed.
4401 It's also possible to have mutually recursive bindings,
4402 using the new <literal>rec</literal> keyword, as in the following example:
4404 counter :: ArrowCircuit a => a Bool Int
4405 counter = proc reset -> do
4406 rec output <- returnA -< if reset then 0 else next
4407 next <- delay 0 -< output+1
4408 returnA -< output
4410 The translation of such forms uses the <function>loop</function> combinator,
4411 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4417 <title>Conditional commands</title>
4420 In the previous example, we used a conditional expression to construct the
4422 Sometimes we want to conditionally execute different commands, as in
4429 which is translated to
4431 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4432 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4434 Since the translation uses <function>|||</function>,
4435 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4439 There are also <literal>case</literal> commands, like
4445 y <- h -< (x1, x2)
4449 The syntax is the same as for <literal>case</literal> expressions,
4450 except that the bodies of the alternatives are commands rather than expressions.
4451 The translation is similar to that of <literal>if</literal> commands.
4457 <title>Defining your own control structures</title>
4460 As we're seen, arrow notation provides constructs,
4461 modelled on those for expressions,
4462 for sequencing, value recursion and conditionals.
4463 But suitable combinators,
4464 which you can define in ordinary Haskell,
4465 may also be used to build new commands out of existing ones.
4466 The basic idea is that a command defines an arrow from environments to values.
4467 These environments assign values to the free local variables of the command.
4468 Thus combinators that produce arrows from arrows
4469 may also be used to build commands from commands.
4470 For example, the <literal>ArrowChoice</literal> class includes a combinator
4472 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4474 so we can use it to build commands:
4476 expr' = proc x -> do
4479 symbol Plus -< ()
4480 y <- term -< ()
4483 symbol Minus -< ()
4484 y <- term -< ()
4487 (The <literal>do</literal> on the first line is needed to prevent the first
4488 <literal><+> ...</literal> from being interpreted as part of the
4489 expression on the previous line.)
4490 This is equivalent to
4492 expr' = (proc x -> returnA -< x)
4493 <+> (proc x -> do
4494 symbol Plus -< ()
4495 y <- term -< ()
4497 <+> (proc x -> do
4498 symbol Minus -< ()
4499 y <- term -< ()
4502 It is essential that this operator be polymorphic in <literal>e</literal>
4503 (representing the environment input to the command
4504 and thence to its subcommands)
4505 and satisfy the corresponding naturality property
4507 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4509 at least for strict <literal>k</literal>.
4510 (This should be automatic if you're not using <function>seq</function>.)
4511 This ensures that environments seen by the subcommands are environments
4512 of the whole command,
4513 and also allows the translation to safely trim these environments.
4514 The operator must also not use any variable defined within the current
4519 We could define our own operator
4521 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4522 untilA body cond = proc x ->
4523 if cond x then returnA -< ()
4526 untilA body cond -< x
4528 and use it in the same way.
4529 Of course this infix syntax only makes sense for binary operators;
4530 there is also a more general syntax involving special brackets:
4534 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4541 <title>Primitive constructs</title>
4544 Some operators will need to pass additional inputs to their subcommands.
4545 For example, in an arrow type supporting exceptions,
4546 the operator that attaches an exception handler will wish to pass the
4547 exception that occurred to the handler.
4548 Such an operator might have a type
4550 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4552 where <literal>Ex</literal> is the type of exceptions handled.
4553 You could then use this with arrow notation by writing a command
4555 body `handleA` \ ex -> handler
4557 so that if an exception is raised in the command <literal>body</literal>,
4558 the variable <literal>ex</literal> is bound to the value of the exception
4559 and the command <literal>handler</literal>,
4560 which typically refers to <literal>ex</literal>, is entered.
4561 Though the syntax here looks like a functional lambda,
4562 we are talking about commands, and something different is going on.
4563 The input to the arrow represented by a command consists of values for
4564 the free local variables in the command, plus a stack of anonymous values.
4565 In all the prior examples, this stack was empty.
4566 In the second argument to <function>handleA</function>,
4567 this stack consists of one value, the value of the exception.
4568 The command form of lambda merely gives this value a name.
4573 the values on the stack are paired to the right of the environment.
4574 So operators like <function>handleA</function> that pass
4575 extra inputs to their subcommands can be designed for use with the notation
4576 by pairing the values with the environment in this way.
4577 More precisely, the type of each argument of the operator (and its result)
4578 should have the form
4580 a (...(e,t1), ... tn) t
4582 where <replaceable>e</replaceable> is a polymorphic variable
4583 (representing the environment)
4584 and <replaceable>ti</replaceable> are the types of the values on the stack,
4585 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4586 The polymorphic variable <replaceable>e</replaceable> must not occur in
4587 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4588 <replaceable>t</replaceable>.
4589 However the arrows involved need not be the same.
4590 Here are some more examples of suitable operators:
4592 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4593 runReader :: ... => a e c -> a' (e,State) c
4594 runState :: ... => a e c -> a' (e,State) (c,State)
4596 We can supply the extra input required by commands built with the last two
4597 by applying them to ordinary expressions, as in
4601 (|runReader (do { ... })|) s
4603 which adds <literal>s</literal> to the stack of inputs to the command
4604 built using <function>runReader</function>.
4608 The command versions of lambda abstraction and application are analogous to
4609 the expression versions.
4610 In particular, the beta and eta rules describe equivalences of commands.
4611 These three features (operators, lambda abstraction and application)
4612 are the core of the notation; everything else can be built using them,
4613 though the results would be somewhat clumsy.
4614 For example, we could simulate <literal>do</literal>-notation by defining
4616 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4617 u `bind` f = returnA &&& u >>> f
4619 bind_ :: Arrow a => a e b -> a e c -> a e c
4620 u `bind_` f = u `bind` (arr fst >>> f)
4622 We could simulate <literal>if</literal> by defining
4624 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4625 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4632 <title>Differences with the paper</title>
4637 <para>Instead of a single form of arrow application (arrow tail) with two
4638 translations, the implementation provides two forms
4639 <quote><literal>-<</literal></quote> (first-order)
4640 and <quote><literal>-<<</literal></quote> (higher-order).
4645 <para>User-defined operators are flagged with banana brackets instead of
4646 a new <literal>form</literal> keyword.
4655 <title>Portability</title>
4658 Although only GHC implements arrow notation directly,
4659 there is also a preprocessor
4661 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4662 that translates arrow notation into Haskell 98
4663 for use with other Haskell systems.
4664 You would still want to check arrow programs with GHC;
4665 tracing type errors in the preprocessor output is not easy.
4666 Modules intended for both GHC and the preprocessor must observe some
4667 additional restrictions:
4672 The module must import
4673 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4679 The preprocessor cannot cope with other Haskell extensions.
4680 These would have to go in separate modules.
4686 Because the preprocessor targets Haskell (rather than Core),
4687 <literal>let</literal>-bound variables are monomorphic.
4698 <!-- ==================== BANG PATTERNS ================= -->
4700 <sect1 id="sec-bang-patterns">
4701 <title>Bang patterns
4702 <indexterm><primary>Bang patterns</primary></indexterm>
4704 <para>GHC supports an extension of pattern matching called <emphasis>bang
4705 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4707 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
4708 prime feature description</ulink> contains more discussion and examples
4709 than the material below.
4712 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4715 <sect2 id="sec-bang-patterns-informal">
4716 <title>Informal description of bang patterns
4719 The main idea is to add a single new production to the syntax of patterns:
4723 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4724 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4729 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4730 whereas without the bang it would be lazy.
4731 Bang patterns can be nested of course:
4735 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4736 <literal>y</literal>.
4737 A bang only really has an effect if it precedes a variable or wild-card pattern:
4742 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4743 forces evaluation anyway does nothing.
4745 Bang patterns work in <literal>case</literal> expressions too, of course:
4747 g5 x = let y = f x in body
4748 g6 x = case f x of { y -> body }
4749 g7 x = case f x of { !y -> body }
4751 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4752 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4753 result, and then evaluates <literal>body</literal>.
4755 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4756 definitions too. For example:
4760 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4761 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4762 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4763 in a function argument <literal>![x,y]</literal> means the
4764 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4765 is part of the syntax of <literal>let</literal> bindings.
4770 <sect2 id="sec-bang-patterns-sem">
4771 <title>Syntax and semantics
4775 We add a single new production to the syntax of patterns:
4779 There is one problem with syntactic ambiguity. Consider:
4783 Is this a definition of the infix function "<literal>(!)</literal>",
4784 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4785 ambiguity inf favour of the latter. If you want to define
4786 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4791 The semantics of Haskell pattern matching is described in <ulink
4792 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4793 Section 3.17.2</ulink> of the Haskell Report. To this description add
4794 one extra item 10, saying:
4795 <itemizedlist><listitem><para>Matching
4796 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4797 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4798 <listitem><para>otherwise, <literal>pat</literal> is matched against
4799 <literal>v</literal></para></listitem>
4801 </para></listitem></itemizedlist>
4802 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4803 Section 3.17.3</ulink>, add a new case (t):
4805 case v of { !pat -> e; _ -> e' }
4806 = v `seq` case v of { pat -> e; _ -> e' }
4809 That leaves let expressions, whose translation is given in
4810 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4812 of the Haskell Report.
4813 In the translation box, first apply
4814 the following transformation: for each pattern <literal>pi</literal> that is of
4815 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4816 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4817 have a bang at the top, apply the rules in the existing box.
4819 <para>The effect of the let rule is to force complete matching of the pattern
4820 <literal>qi</literal> before evaluation of the body is begun. The bang is
4821 retained in the translated form in case <literal>qi</literal> is a variable,
4829 The let-binding can be recursive. However, it is much more common for
4830 the let-binding to be non-recursive, in which case the following law holds:
4831 <literal>(let !p = rhs in body)</literal>
4833 <literal>(case rhs of !p -> body)</literal>
4836 A pattern with a bang at the outermost level is not allowed at the top level of
4842 <!-- ==================== ASSERTIONS ================= -->
4844 <sect1 id="sec-assertions">
4846 <indexterm><primary>Assertions</primary></indexterm>
4850 If you want to make use of assertions in your standard Haskell code, you
4851 could define a function like the following:
4857 assert :: Bool -> a -> a
4858 assert False x = error "assertion failed!"
4865 which works, but gives you back a less than useful error message --
4866 an assertion failed, but which and where?
4870 One way out is to define an extended <function>assert</function> function which also
4871 takes a descriptive string to include in the error message and
4872 perhaps combine this with the use of a pre-processor which inserts
4873 the source location where <function>assert</function> was used.
4877 Ghc offers a helping hand here, doing all of this for you. For every
4878 use of <function>assert</function> in the user's source:
4884 kelvinToC :: Double -> Double
4885 kelvinToC k = assert (k >= 0.0) (k+273.15)
4891 Ghc will rewrite this to also include the source location where the
4898 assert pred val ==> assertError "Main.hs|15" pred val
4904 The rewrite is only performed by the compiler when it spots
4905 applications of <function>Control.Exception.assert</function>, so you
4906 can still define and use your own versions of
4907 <function>assert</function>, should you so wish. If not, import
4908 <literal>Control.Exception</literal> to make use
4909 <function>assert</function> in your code.
4913 GHC ignores assertions when optimisation is turned on with the
4914 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
4915 <literal>assert pred e</literal> will be rewritten to
4916 <literal>e</literal>. You can also disable assertions using the
4917 <option>-fignore-asserts</option>
4918 option<indexterm><primary><option>-fignore-asserts</option></primary>
4919 </indexterm>.</para>
4922 Assertion failures can be caught, see the documentation for the
4923 <literal>Control.Exception</literal> library for the details.
4929 <!-- =============================== PRAGMAS =========================== -->
4931 <sect1 id="pragmas">
4932 <title>Pragmas</title>
4934 <indexterm><primary>pragma</primary></indexterm>
4936 <para>GHC supports several pragmas, or instructions to the
4937 compiler placed in the source code. Pragmas don't normally affect
4938 the meaning of the program, but they might affect the efficiency
4939 of the generated code.</para>
4941 <para>Pragmas all take the form
4943 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
4945 where <replaceable>word</replaceable> indicates the type of
4946 pragma, and is followed optionally by information specific to that
4947 type of pragma. Case is ignored in
4948 <replaceable>word</replaceable>. The various values for
4949 <replaceable>word</replaceable> that GHC understands are described
4950 in the following sections; any pragma encountered with an
4951 unrecognised <replaceable>word</replaceable> is (silently)
4954 <sect2 id="deprecated-pragma">
4955 <title>DEPRECATED pragma</title>
4956 <indexterm><primary>DEPRECATED</primary>
4959 <para>The DEPRECATED pragma lets you specify that a particular
4960 function, class, or type, is deprecated. There are two
4965 <para>You can deprecate an entire module thus:</para>
4967 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
4970 <para>When you compile any module that import
4971 <literal>Wibble</literal>, GHC will print the specified
4976 <para>You can deprecate a function, class, type, or data constructor, with the
4977 following top-level declaration:</para>
4979 {-# DEPRECATED f, C, T "Don't use these" #-}
4981 <para>When you compile any module that imports and uses any
4982 of the specified entities, GHC will print the specified
4984 <para> You can only depecate entities declared at top level in the module
4985 being compiled, and you can only use unqualified names in the list of
4986 entities being deprecated. A capitalised name, such as <literal>T</literal>
4987 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
4988 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
4989 both are in scope. If both are in scope, there is currently no way to deprecate
4990 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
4993 Any use of the deprecated item, or of anything from a deprecated
4994 module, will be flagged with an appropriate message. However,
4995 deprecations are not reported for
4996 (a) uses of a deprecated function within its defining module, and
4997 (b) uses of a deprecated function in an export list.
4998 The latter reduces spurious complaints within a library
4999 in which one module gathers together and re-exports
5000 the exports of several others.
5002 <para>You can suppress the warnings with the flag
5003 <option>-fno-warn-deprecations</option>.</para>
5006 <sect2 id="include-pragma">
5007 <title>INCLUDE pragma</title>
5009 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5010 of C header files that should be <literal>#include</literal>'d into
5011 the C source code generated by the compiler for the current module (if
5012 compiling via C). For example:</para>
5015 {-# INCLUDE "foo.h" #-}
5016 {-# INCLUDE <stdio.h> #-}</programlisting>
5018 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5019 your source file with any <literal>OPTIONS_GHC</literal>
5022 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5023 to the <option>-#include</option> option (<xref
5024 linkend="options-C-compiler" />), because the
5025 <literal>INCLUDE</literal> pragma is understood by other
5026 compilers. Yet another alternative is to add the include file to each
5027 <literal>foreign import</literal> declaration in your code, but we
5028 don't recommend using this approach with GHC.</para>
5031 <sect2 id="inline-noinline-pragma">
5032 <title>INLINE and NOINLINE pragmas</title>
5034 <para>These pragmas control the inlining of function
5037 <sect3 id="inline-pragma">
5038 <title>INLINE pragma</title>
5039 <indexterm><primary>INLINE</primary></indexterm>
5041 <para>GHC (with <option>-O</option>, as always) tries to
5042 inline (or “unfold”) functions/values that are
5043 “small enough,” thus avoiding the call overhead
5044 and possibly exposing other more-wonderful optimisations.
5045 Normally, if GHC decides a function is “too
5046 expensive” to inline, it will not do so, nor will it
5047 export that unfolding for other modules to use.</para>
5049 <para>The sledgehammer you can bring to bear is the
5050 <literal>INLINE</literal><indexterm><primary>INLINE
5051 pragma</primary></indexterm> pragma, used thusly:</para>
5054 key_function :: Int -> String -> (Bool, Double)
5056 #ifdef __GLASGOW_HASKELL__
5057 {-# INLINE key_function #-}
5061 <para>(You don't need to do the C pre-processor carry-on
5062 unless you're going to stick the code through HBC—it
5063 doesn't like <literal>INLINE</literal> pragmas.)</para>
5065 <para>The major effect of an <literal>INLINE</literal> pragma
5066 is to declare a function's “cost” to be very low.
5067 The normal unfolding machinery will then be very keen to
5070 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5071 function can be put anywhere its type signature could be
5074 <para><literal>INLINE</literal> pragmas are a particularly
5076 <literal>then</literal>/<literal>return</literal> (or
5077 <literal>bind</literal>/<literal>unit</literal>) functions in
5078 a monad. For example, in GHC's own
5079 <literal>UniqueSupply</literal> monad code, we have:</para>
5082 #ifdef __GLASGOW_HASKELL__
5083 {-# INLINE thenUs #-}
5084 {-# INLINE returnUs #-}
5088 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5089 linkend="noinline-pragma"/>).</para>
5092 <sect3 id="noinline-pragma">
5093 <title>NOINLINE pragma</title>
5095 <indexterm><primary>NOINLINE</primary></indexterm>
5096 <indexterm><primary>NOTINLINE</primary></indexterm>
5098 <para>The <literal>NOINLINE</literal> pragma does exactly what
5099 you'd expect: it stops the named function from being inlined
5100 by the compiler. You shouldn't ever need to do this, unless
5101 you're very cautious about code size.</para>
5103 <para><literal>NOTINLINE</literal> is a synonym for
5104 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5105 specified by Haskell 98 as the standard way to disable
5106 inlining, so it should be used if you want your code to be
5110 <sect3 id="phase-control">
5111 <title>Phase control</title>
5113 <para> Sometimes you want to control exactly when in GHC's
5114 pipeline the INLINE pragma is switched on. Inlining happens
5115 only during runs of the <emphasis>simplifier</emphasis>. Each
5116 run of the simplifier has a different <emphasis>phase
5117 number</emphasis>; the phase number decreases towards zero.
5118 If you use <option>-dverbose-core2core</option> you'll see the
5119 sequence of phase numbers for successive runs of the
5120 simplifier. In an INLINE pragma you can optionally specify a
5124 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5125 <literal>f</literal>
5126 until phase <literal>k</literal>, but from phase
5127 <literal>k</literal> onwards be very keen to inline it.
5130 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5131 <literal>f</literal>
5132 until phase <literal>k</literal>, but from phase
5133 <literal>k</literal> onwards do not inline it.
5136 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5137 <literal>f</literal>
5138 until phase <literal>k</literal>, but from phase
5139 <literal>k</literal> onwards be willing to inline it (as if
5140 there was no pragma).
5143 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5144 <literal>f</literal>
5145 until phase <literal>k</literal>, but from phase
5146 <literal>k</literal> onwards do not inline it.
5149 The same information is summarised here:
5151 -- Before phase 2 Phase 2 and later
5152 {-# INLINE [2] f #-} -- No Yes
5153 {-# INLINE [~2] f #-} -- Yes No
5154 {-# NOINLINE [2] f #-} -- No Maybe
5155 {-# NOINLINE [~2] f #-} -- Maybe No
5157 {-# INLINE f #-} -- Yes Yes
5158 {-# NOINLINE f #-} -- No No
5160 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5161 function body is small, or it is applied to interesting-looking arguments etc).
5162 Another way to understand the semantics is this:
5164 <listitem><para>For both INLINE and NOINLINE, the phase number says
5165 when inlining is allowed at all.</para></listitem>
5166 <listitem><para>The INLINE pragma has the additional effect of making the
5167 function body look small, so that when inlining is allowed it is very likely to
5172 <para>The same phase-numbering control is available for RULES
5173 (<xref linkend="rewrite-rules"/>).</para>
5177 <sect2 id="language-pragma">
5178 <title>LANGUAGE pragma</title>
5180 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5181 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5183 <para>This allows language extensions to be enabled in a portable way.
5184 It is the intention that all Haskell compilers support the
5185 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5186 all extensions are supported by all compilers, of
5187 course. The <literal>LANGUAGE</literal> pragma should be used instead
5188 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5190 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5192 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5194 <para>Any extension from the <literal>Extension</literal> type defined in
5196 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>
5200 <sect2 id="line-pragma">
5201 <title>LINE pragma</title>
5203 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5204 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5205 <para>This pragma is similar to C's <literal>#line</literal>
5206 pragma, and is mainly for use in automatically generated Haskell
5207 code. It lets you specify the line number and filename of the
5208 original code; for example</para>
5210 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5212 <para>if you'd generated the current file from something called
5213 <filename>Foo.vhs</filename> and this line corresponds to line
5214 42 in the original. GHC will adjust its error messages to refer
5215 to the line/file named in the <literal>LINE</literal>
5219 <sect2 id="options-pragma">
5220 <title>OPTIONS_GHC pragma</title>
5221 <indexterm><primary>OPTIONS_GHC</primary>
5223 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5226 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5227 additional options that are given to the compiler when compiling
5228 this source file. See <xref linkend="source-file-options"/> for
5231 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5232 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5236 <title>RULES pragma</title>
5238 <para>The RULES pragma lets you specify rewrite rules. It is
5239 described in <xref linkend="rewrite-rules"/>.</para>
5242 <sect2 id="specialize-pragma">
5243 <title>SPECIALIZE pragma</title>
5245 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5246 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5247 <indexterm><primary>overloading, death to</primary></indexterm>
5249 <para>(UK spelling also accepted.) For key overloaded
5250 functions, you can create extra versions (NB: more code space)
5251 specialised to particular types. Thus, if you have an
5252 overloaded function:</para>
5255 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5258 <para>If it is heavily used on lists with
5259 <literal>Widget</literal> keys, you could specialise it as
5263 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5266 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5267 be put anywhere its type signature could be put.</para>
5269 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5270 (a) a specialised version of the function and (b) a rewrite rule
5271 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5272 un-specialised function into a call to the specialised one.</para>
5274 <para>The type in a SPECIALIZE pragma can be any type that is less
5275 polymorphic than the type of the original function. In concrete terms,
5276 if the original function is <literal>f</literal> then the pragma
5278 {-# SPECIALIZE f :: <type> #-}
5280 is valid if and only if the defintion
5282 f_spec :: <type>
5285 is valid. Here are some examples (where we only give the type signature
5286 for the original function, not its code):
5288 f :: Eq a => a -> b -> b
5289 {-# SPECIALISE f :: Int -> b -> b #-}
5291 g :: (Eq a, Ix b) => a -> b -> b
5292 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5294 h :: Eq a => a -> a -> a
5295 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5297 The last of these examples will generate a
5298 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5299 well. If you use this kind of specialisation, let us know how well it works.
5302 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5303 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5304 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5305 The <literal>INLINE</literal> pragma affects the specialised verison of the
5306 function (only), and applies even if the function is recursive. The motivating
5309 -- A GADT for arrays with type-indexed representation
5311 ArrInt :: !Int -> ByteArray# -> Arr Int
5312 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5314 (!:) :: Arr e -> Int -> e
5315 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5316 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5317 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5318 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5320 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5321 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5322 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5323 the specialised function will be inlined. It has two calls to
5324 <literal>(!:)</literal>,
5325 both at type <literal>Int</literal>. Both these calls fire the first
5326 specialisation, whose body is also inlined. The result is a type-based
5327 unrolling of the indexing function.</para>
5328 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5329 on an ordinarily-recursive function.</para>
5331 <para>Note: In earlier versions of GHC, it was possible to provide your own
5332 specialised function for a given type:
5335 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5338 This feature has been removed, as it is now subsumed by the
5339 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5343 <sect2 id="specialize-instance-pragma">
5344 <title>SPECIALIZE instance pragma
5348 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5349 <indexterm><primary>overloading, death to</primary></indexterm>
5350 Same idea, except for instance declarations. For example:
5353 instance (Eq a) => Eq (Foo a) where {
5354 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5358 The pragma must occur inside the <literal>where</literal> part
5359 of the instance declaration.
5362 Compatible with HBC, by the way, except perhaps in the placement
5368 <sect2 id="unpack-pragma">
5369 <title>UNPACK pragma</title>
5371 <indexterm><primary>UNPACK</primary></indexterm>
5373 <para>The <literal>UNPACK</literal> indicates to the compiler
5374 that it should unpack the contents of a constructor field into
5375 the constructor itself, removing a level of indirection. For
5379 data T = T {-# UNPACK #-} !Float
5380 {-# UNPACK #-} !Float
5383 <para>will create a constructor <literal>T</literal> containing
5384 two unboxed floats. This may not always be an optimisation: if
5385 the <function>T</function> constructor is scrutinised and the
5386 floats passed to a non-strict function for example, they will
5387 have to be reboxed (this is done automatically by the
5390 <para>Unpacking constructor fields should only be used in
5391 conjunction with <option>-O</option>, in order to expose
5392 unfoldings to the compiler so the reboxing can be removed as
5393 often as possible. For example:</para>
5397 f (T f1 f2) = f1 + f2
5400 <para>The compiler will avoid reboxing <function>f1</function>
5401 and <function>f2</function> by inlining <function>+</function>
5402 on floats, but only when <option>-O</option> is on.</para>
5404 <para>Any single-constructor data is eligible for unpacking; for
5408 data T = T {-# UNPACK #-} !(Int,Int)
5411 <para>will store the two <literal>Int</literal>s directly in the
5412 <function>T</function> constructor, by flattening the pair.
5413 Multi-level unpacking is also supported:</para>
5416 data T = T {-# UNPACK #-} !S
5417 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5420 <para>will store two unboxed <literal>Int#</literal>s
5421 directly in the <function>T</function> constructor. The
5422 unpacker can see through newtypes, too.</para>
5424 <para>If a field cannot be unpacked, you will not get a warning,
5425 so it might be an idea to check the generated code with
5426 <option>-ddump-simpl</option>.</para>
5428 <para>See also the <option>-funbox-strict-fields</option> flag,
5429 which essentially has the effect of adding
5430 <literal>{-# UNPACK #-}</literal> to every strict
5431 constructor field.</para>
5436 <!-- ======================= REWRITE RULES ======================== -->
5438 <sect1 id="rewrite-rules">
5439 <title>Rewrite rules
5441 <indexterm><primary>RULES pragma</primary></indexterm>
5442 <indexterm><primary>pragma, RULES</primary></indexterm>
5443 <indexterm><primary>rewrite rules</primary></indexterm></title>
5446 The programmer can specify rewrite rules as part of the source program
5447 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5448 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5449 and (b) the <option>-frules-off</option> flag
5450 (<xref linkend="options-f"/>) is not specified, and (c) the
5451 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5460 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5467 <title>Syntax</title>
5470 From a syntactic point of view:
5476 There may be zero or more rules in a <literal>RULES</literal> pragma.
5483 Each rule has a name, enclosed in double quotes. The name itself has
5484 no significance at all. It is only used when reporting how many times the rule fired.
5490 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5491 immediately after the name of the rule. Thus:
5494 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5497 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5498 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5507 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5508 is set, so you must lay out your rules starting in the same column as the
5509 enclosing definitions.
5516 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5517 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5518 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5519 by spaces, just like in a type <literal>forall</literal>.
5525 A pattern variable may optionally have a type signature.
5526 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5527 For example, here is the <literal>foldr/build</literal> rule:
5530 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5531 foldr k z (build g) = g k z
5534 Since <function>g</function> has a polymorphic type, it must have a type signature.
5541 The left hand side of a rule must consist of a top-level variable applied
5542 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5545 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5546 "wrong2" forall f. f True = True
5549 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5556 A rule does not need to be in the same module as (any of) the
5557 variables it mentions, though of course they need to be in scope.
5563 Rules are automatically exported from a module, just as instance declarations are.
5574 <title>Semantics</title>
5577 From a semantic point of view:
5583 Rules are only applied if you use the <option>-O</option> flag.
5589 Rules are regarded as left-to-right rewrite rules.
5590 When GHC finds an expression that is a substitution instance of the LHS
5591 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5592 By "a substitution instance" we mean that the LHS can be made equal to the
5593 expression by substituting for the pattern variables.
5600 The LHS and RHS of a rule are typechecked, and must have the
5608 GHC makes absolutely no attempt to verify that the LHS and RHS
5609 of a rule have the same meaning. That is undecidable in general, and
5610 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5617 GHC makes no attempt to make sure that the rules are confluent or
5618 terminating. For example:
5621 "loop" forall x,y. f x y = f y x
5624 This rule will cause the compiler to go into an infinite loop.
5631 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5637 GHC currently uses a very simple, syntactic, matching algorithm
5638 for matching a rule LHS with an expression. It seeks a substitution
5639 which makes the LHS and expression syntactically equal modulo alpha
5640 conversion. The pattern (rule), but not the expression, is eta-expanded if
5641 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5642 But not beta conversion (that's called higher-order matching).
5646 Matching is carried out on GHC's intermediate language, which includes
5647 type abstractions and applications. So a rule only matches if the
5648 types match too. See <xref linkend="rule-spec"/> below.
5654 GHC keeps trying to apply the rules as it optimises the program.
5655 For example, consider:
5664 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5665 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5666 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5667 not be substituted, and the rule would not fire.
5674 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5675 that appears on the LHS of a rule</emphasis>, because once you have substituted
5676 for something you can't match against it (given the simple minded
5677 matching). So if you write the rule
5680 "map/map" forall f,g. map f . map g = map (f.g)
5683 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5684 It will only match something written with explicit use of ".".
5685 Well, not quite. It <emphasis>will</emphasis> match the expression
5691 where <function>wibble</function> is defined:
5694 wibble f g = map f . map g
5697 because <function>wibble</function> will be inlined (it's small).
5699 Later on in compilation, GHC starts inlining even things on the
5700 LHS of rules, but still leaves the rules enabled. This inlining
5701 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5708 All rules are implicitly exported from the module, and are therefore
5709 in force in any module that imports the module that defined the rule, directly
5710 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5711 in force when compiling A.) The situation is very similar to that for instance
5723 <title>List fusion</title>
5726 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5727 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5728 intermediate list should be eliminated entirely.
5732 The following are good producers:
5744 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5750 Explicit lists (e.g. <literal>[True, False]</literal>)
5756 The cons constructor (e.g <literal>3:4:[]</literal>)
5762 <function>++</function>
5768 <function>map</function>
5774 <function>take</function>, <function>filter</function>
5780 <function>iterate</function>, <function>repeat</function>
5786 <function>zip</function>, <function>zipWith</function>
5795 The following are good consumers:
5807 <function>array</function> (on its second argument)
5813 <function>length</function>
5819 <function>++</function> (on its first argument)
5825 <function>foldr</function>
5831 <function>map</function>
5837 <function>take</function>, <function>filter</function>
5843 <function>concat</function>
5849 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5855 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5856 will fuse with one but not the other)
5862 <function>partition</function>
5868 <function>head</function>
5874 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5880 <function>sequence_</function>
5886 <function>msum</function>
5892 <function>sortBy</function>
5901 So, for example, the following should generate no intermediate lists:
5904 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
5910 This list could readily be extended; if there are Prelude functions that you use
5911 a lot which are not included, please tell us.
5915 If you want to write your own good consumers or producers, look at the
5916 Prelude definitions of the above functions to see how to do so.
5921 <sect2 id="rule-spec">
5922 <title>Specialisation
5926 Rewrite rules can be used to get the same effect as a feature
5927 present in earlier versions of GHC.
5928 For example, suppose that:
5931 genericLookup :: Ord a => Table a b -> a -> b
5932 intLookup :: Table Int b -> Int -> b
5935 where <function>intLookup</function> is an implementation of
5936 <function>genericLookup</function> that works very fast for
5937 keys of type <literal>Int</literal>. You might wish
5938 to tell GHC to use <function>intLookup</function> instead of
5939 <function>genericLookup</function> whenever the latter was called with
5940 type <literal>Table Int b -> Int -> b</literal>.
5941 It used to be possible to write
5944 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
5947 This feature is no longer in GHC, but rewrite rules let you do the same thing:
5950 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
5953 This slightly odd-looking rule instructs GHC to replace
5954 <function>genericLookup</function> by <function>intLookup</function>
5955 <emphasis>whenever the types match</emphasis>.
5956 What is more, this rule does not need to be in the same
5957 file as <function>genericLookup</function>, unlike the
5958 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
5959 have an original definition available to specialise).
5962 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
5963 <function>intLookup</function> really behaves as a specialised version
5964 of <function>genericLookup</function>!!!</para>
5966 <para>An example in which using <literal>RULES</literal> for
5967 specialisation will Win Big:
5970 toDouble :: Real a => a -> Double
5971 toDouble = fromRational . toRational
5973 {-# RULES "toDouble/Int" toDouble = i2d #-}
5974 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
5977 The <function>i2d</function> function is virtually one machine
5978 instruction; the default conversion—via an intermediate
5979 <literal>Rational</literal>—is obscenely expensive by
5986 <title>Controlling what's going on</title>
5994 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6000 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6001 If you add <option>-dppr-debug</option> you get a more detailed listing.
6007 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6010 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6011 {-# INLINE build #-}
6015 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6016 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6017 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6018 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6025 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6026 see how to write rules that will do fusion and yet give an efficient
6027 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6037 <sect2 id="core-pragma">
6038 <title>CORE pragma</title>
6040 <indexterm><primary>CORE pragma</primary></indexterm>
6041 <indexterm><primary>pragma, CORE</primary></indexterm>
6042 <indexterm><primary>core, annotation</primary></indexterm>
6045 The external core format supports <quote>Note</quote> annotations;
6046 the <literal>CORE</literal> pragma gives a way to specify what these
6047 should be in your Haskell source code. Syntactically, core
6048 annotations are attached to expressions and take a Haskell string
6049 literal as an argument. The following function definition shows an
6053 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6056 Semantically, this is equivalent to:
6064 However, when external for is generated (via
6065 <option>-fext-core</option>), there will be Notes attached to the
6066 expressions <function>show</function> and <varname>x</varname>.
6067 The core function declaration for <function>f</function> is:
6071 f :: %forall a . GHCziShow.ZCTShow a ->
6072 a -> GHCziBase.ZMZN GHCziBase.Char =
6073 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6075 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6077 (tpl1::GHCziBase.Int ->
6079 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6081 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6082 (tpl3::GHCziBase.ZMZN a ->
6083 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6091 Here, we can see that the function <function>show</function> (which
6092 has been expanded out to a case expression over the Show dictionary)
6093 has a <literal>%note</literal> attached to it, as does the
6094 expression <varname>eta</varname> (which used to be called
6095 <varname>x</varname>).
6102 <sect1 id="special-ids">
6103 <title>Special built-in functions</title>
6104 <para>GHC has a few built-in funcions with special behaviour,
6105 described in this section. All are exported by
6106 <literal>GHC.Exts</literal>.</para>
6108 <sect2> <title>The <literal>inline</literal> function </title>
6110 The <literal>inline</literal> function is somewhat experimental.
6114 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6115 is inlined, regardless of its size. More precisely, the call
6116 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6118 This allows the programmer to control inlining from
6119 a particular <emphasis>call site</emphasis>
6120 rather than the <emphasis>definition site</emphasis> of the function
6121 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6124 This inlining occurs regardless of the argument to the call
6125 or the size of <literal>f</literal>'s definition; it is unconditional.
6126 The main caveat is that <literal>f</literal>'s definition must be
6127 visible to the compiler. That is, <literal>f</literal> must be
6128 let-bound in the current scope.
6129 If no inlining takes place, the <literal>inline</literal> function
6130 expands to the identity function in Phase zero; so its use imposes
6133 <para> If the function is defined in another
6134 module, GHC only exposes its inlining in the interface file if the
6135 function is sufficiently small that it <emphasis>might</emphasis> be
6136 inlined by the automatic mechanism. There is currently no way to tell
6137 GHC to expose arbitrarily-large functions in the interface file. (This
6138 shortcoming is something that could be fixed, with some kind of pragma.)
6142 <sect2> <title>The <literal>lazy</literal> function </title>
6144 The <literal>lazy</literal> function restrains strictness analysis a little:
6148 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6149 but <literal>lazy</literal> has a magical property so far as strictness
6150 analysis is concerned: it is lazy in its first argument,
6151 even though its semantics is strict. After strictness analysis has run,
6152 calls to <literal>lazy</literal> are inlined to be the identity function.
6155 This behaviour is occasionally useful when controlling evaluation order.
6156 Notably, <literal>lazy</literal> is used in the library definition of
6157 <literal>Control.Parallel.par</literal>:
6160 par x y = case (par# x) of { _ -> lazy y }
6162 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6163 look strict in <literal>y</literal> which would defeat the whole
6164 purpose of <literal>par</literal>.
6168 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6170 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6171 typechecker entirely. It has type
6173 unsafeCoerce# :: a -> b
6175 That is, it allows you to coerce any type into any other type. If you use this
6176 function, you had better get it right, otherwise segmentation faults await.
6177 It is generally used when you want to write a program that you know is
6178 well-typed, but where Haskell's type system is not expressive enough to prove
6179 that it is well typed.
6185 <sect1 id="generic-classes">
6186 <title>Generic classes</title>
6189 The ideas behind this extension are described in detail in "Derivable type classes",
6190 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6191 An example will give the idea:
6199 fromBin :: [Int] -> (a, [Int])
6201 toBin {| Unit |} Unit = []
6202 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6203 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6204 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6206 fromBin {| Unit |} bs = (Unit, bs)
6207 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6208 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6209 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6210 (y,bs'') = fromBin bs'
6213 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6214 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6215 which are defined thus in the library module <literal>Generics</literal>:
6219 data a :+: b = Inl a | Inr b
6220 data a :*: b = a :*: b
6223 Now you can make a data type into an instance of Bin like this:
6225 instance (Bin a, Bin b) => Bin (a,b)
6226 instance Bin a => Bin [a]
6228 That is, just leave off the "where" clause. Of course, you can put in the
6229 where clause and over-ride whichever methods you please.
6233 <title> Using generics </title>
6234 <para>To use generics you need to</para>
6237 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6238 <option>-fgenerics</option> (to generate extra per-data-type code),
6239 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6243 <para>Import the module <literal>Generics</literal> from the
6244 <literal>lang</literal> package. This import brings into
6245 scope the data types <literal>Unit</literal>,
6246 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6247 don't need this import if you don't mention these types
6248 explicitly; for example, if you are simply giving instance
6249 declarations.)</para>
6254 <sect2> <title> Changes wrt the paper </title>
6256 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6257 can be written infix (indeed, you can now use
6258 any operator starting in a colon as an infix type constructor). Also note that
6259 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6260 Finally, note that the syntax of the type patterns in the class declaration
6261 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6262 alone would ambiguous when they appear on right hand sides (an extension we
6263 anticipate wanting).
6267 <sect2> <title>Terminology and restrictions</title>
6269 Terminology. A "generic default method" in a class declaration
6270 is one that is defined using type patterns as above.
6271 A "polymorphic default method" is a default method defined as in Haskell 98.
6272 A "generic class declaration" is a class declaration with at least one
6273 generic default method.
6281 Alas, we do not yet implement the stuff about constructor names and
6288 A generic class can have only one parameter; you can't have a generic
6289 multi-parameter class.
6295 A default method must be defined entirely using type patterns, or entirely
6296 without. So this is illegal:
6299 op :: a -> (a, Bool)
6300 op {| Unit |} Unit = (Unit, True)
6303 However it is perfectly OK for some methods of a generic class to have
6304 generic default methods and others to have polymorphic default methods.
6310 The type variable(s) in the type pattern for a generic method declaration
6311 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:
6315 op {| p :*: q |} (x :*: y) = op (x :: p)
6323 The type patterns in a generic default method must take one of the forms:
6329 where "a" and "b" are type variables. Furthermore, all the type patterns for
6330 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6331 must use the same type variables. So this is illegal:
6335 op {| a :+: b |} (Inl x) = True
6336 op {| p :+: q |} (Inr y) = False
6338 The type patterns must be identical, even in equations for different methods of the class.
6339 So this too is illegal:
6343 op1 {| a :*: b |} (x :*: y) = True
6346 op2 {| p :*: q |} (x :*: y) = False
6348 (The reason for this restriction is that we gather all the equations for a particular type consructor
6349 into a single generic instance declaration.)
6355 A generic method declaration must give a case for each of the three type constructors.
6361 The type for a generic method can be built only from:
6363 <listitem> <para> Function arrows </para> </listitem>
6364 <listitem> <para> Type variables </para> </listitem>
6365 <listitem> <para> Tuples </para> </listitem>
6366 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6368 Here are some example type signatures for generic methods:
6371 op2 :: Bool -> (a,Bool)
6372 op3 :: [Int] -> a -> a
6375 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6379 This restriction is an implementation restriction: we just havn't got around to
6380 implementing the necessary bidirectional maps over arbitrary type constructors.
6381 It would be relatively easy to add specific type constructors, such as Maybe and list,
6382 to the ones that are allowed.</para>
6387 In an instance declaration for a generic class, the idea is that the compiler
6388 will fill in the methods for you, based on the generic templates. However it can only
6393 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6398 No constructor of the instance type has unboxed fields.
6402 (Of course, these things can only arise if you are already using GHC extensions.)
6403 However, you can still give an instance declarations for types which break these rules,
6404 provided you give explicit code to override any generic default methods.
6412 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6413 what the compiler does with generic declarations.
6418 <sect2> <title> Another example </title>
6420 Just to finish with, here's another example I rather like:
6424 nCons {| Unit |} _ = 1
6425 nCons {| a :*: b |} _ = 1
6426 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6429 tag {| Unit |} _ = 1
6430 tag {| a :*: b |} _ = 1
6431 tag {| a :+: b |} (Inl x) = tag x
6432 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6438 <sect1 id="monomorphism">
6439 <title>Control over monomorphism</title>
6441 <para>GHC supports two flags that control the way in which generalisation is
6442 carried out at let and where bindings.
6446 <title>Switching off the dreaded Monomorphism Restriction</title>
6447 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6449 <para>Haskell's monomorphism restriction (see
6450 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6452 of the Haskell Report)
6453 can be completely switched off by
6454 <option>-fno-monomorphism-restriction</option>.
6459 <title>Monomorphic pattern bindings</title>
6460 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6461 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6463 <para> As an experimental change, we are exploring the possibility of
6464 making pattern bindings monomorphic; that is, not generalised at all.
6465 A pattern binding is a binding whose LHS has no function arguments,
6466 and is not a simple variable. For example:
6468 f x = x -- Not a pattern binding
6469 f = \x -> x -- Not a pattern binding
6470 f :: Int -> Int = \x -> x -- Not a pattern binding
6472 (g,h) = e -- A pattern binding
6473 (f) = e -- A pattern binding
6474 [x] = e -- A pattern binding
6476 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6477 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6486 ;;; Local Variables: ***
6488 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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