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 in
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>
911 <!-- TYPE SYSTEM EXTENSIONS -->
912 <sect1 id="type-extensions">
913 <title>Type system extensions</title>
917 <title>Data types and type synonyms</title>
919 <sect3 id="nullary-types">
920 <title>Data types with no constructors</title>
922 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
923 a data type with no constructors. For example:</para>
927 data T a -- T :: * -> *
930 <para>Syntactically, the declaration lacks the "= constrs" part. The
931 type can be parameterised over types of any kind, but if the kind is
932 not <literal>*</literal> then an explicit kind annotation must be used
933 (see <xref linkend="sec-kinding"/>).</para>
935 <para>Such data types have only one value, namely bottom.
936 Nevertheless, they can be useful when defining "phantom types".</para>
939 <sect3 id="infix-tycons">
940 <title>Infix type constructors, classes, and type variables</title>
943 GHC allows type constructors, classes, and type variables to be operators, and
944 to be written infix, very much like expressions. More specifically:
947 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
948 The lexical syntax is the same as that for data constructors.
951 Data type and type-synonym declarations can be written infix, parenthesised
952 if you want further arguments. E.g.
954 data a :*: b = Foo a b
955 type a :+: b = Either a b
956 class a :=: b where ...
958 data (a :**: b) x = Baz a b x
959 type (a :++: b) y = Either (a,b) y
963 Types, and class constraints, can be written infix. For example
966 f :: (a :=: b) => a -> b
970 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
971 The lexical syntax is the same as that for variable operators, excluding "(.)",
972 "(!)", and "(*)". In a binding position, the operator must be
973 parenthesised. For example:
975 type T (+) = Int + Int
980 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
986 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
987 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
990 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
991 one cannot distinguish between the two in a fixity declaration; a fixity declaration
992 sets the fixity for a data constructor and the corresponding type constructor. For example:
996 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
997 and similarly for <literal>:*:</literal>.
998 <literal>Int `a` Bool</literal>.
1001 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1008 <sect3 id="type-synonyms">
1009 <title>Liberalised type synonyms</title>
1012 Type synonyms are like macros at the type level, and
1013 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1014 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1016 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1017 in a type synonym, thus:
1019 type Discard a = forall b. Show b => a -> b -> (a, String)
1024 g :: Discard Int -> (Int,String) -- A rank-2 type
1031 You can write an unboxed tuple in a type synonym:
1033 type Pr = (# Int, Int #)
1041 You can apply a type synonym to a forall type:
1043 type Foo a = a -> a -> Bool
1045 f :: Foo (forall b. b->b)
1047 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1049 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1054 You can apply a type synonym to a partially applied type synonym:
1056 type Generic i o = forall x. i x -> o x
1059 foo :: Generic Id []
1061 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1063 foo :: forall x. x -> [x]
1071 GHC currently does kind checking before expanding synonyms (though even that
1075 After expanding type synonyms, GHC does validity checking on types, looking for
1076 the following mal-formedness which isn't detected simply by kind checking:
1079 Type constructor applied to a type involving for-alls.
1082 Unboxed tuple on left of an arrow.
1085 Partially-applied type synonym.
1089 this will be rejected:
1091 type Pr = (# Int, Int #)
1096 because GHC does not allow unboxed tuples on the left of a function arrow.
1101 <sect3 id="existential-quantification">
1102 <title>Existentially quantified data constructors
1106 The idea of using existential quantification in data type declarations
1107 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1108 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1109 London, 1991). It was later formalised by Laufer and Odersky
1110 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1111 TOPLAS, 16(5), pp1411-1430, 1994).
1112 It's been in Lennart
1113 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1114 proved very useful. Here's the idea. Consider the declaration:
1120 data Foo = forall a. MkFoo a (a -> Bool)
1127 The data type <literal>Foo</literal> has two constructors with types:
1133 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1140 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1141 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1142 For example, the following expression is fine:
1148 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1154 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1155 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1156 isUpper</function> packages a character with a compatible function. These
1157 two things are each of type <literal>Foo</literal> and can be put in a list.
1161 What can we do with a value of type <literal>Foo</literal>?. In particular,
1162 what happens when we pattern-match on <function>MkFoo</function>?
1168 f (MkFoo val fn) = ???
1174 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1175 are compatible, the only (useful) thing we can do with them is to
1176 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1183 f (MkFoo val fn) = fn val
1189 What this allows us to do is to package heterogenous values
1190 together with a bunch of functions that manipulate them, and then treat
1191 that collection of packages in a uniform manner. You can express
1192 quite a bit of object-oriented-like programming this way.
1195 <sect4 id="existential">
1196 <title>Why existential?
1200 What has this to do with <emphasis>existential</emphasis> quantification?
1201 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1207 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1213 But Haskell programmers can safely think of the ordinary
1214 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1215 adding a new existential quantification construct.
1221 <title>Type classes</title>
1224 An easy extension is to allow
1225 arbitrary contexts before the constructor. For example:
1231 data Baz = forall a. Eq a => Baz1 a a
1232 | forall b. Show b => Baz2 b (b -> b)
1238 The two constructors have the types you'd expect:
1244 Baz1 :: forall a. Eq a => a -> a -> Baz
1245 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1251 But when pattern matching on <function>Baz1</function> the matched values can be compared
1252 for equality, and when pattern matching on <function>Baz2</function> the first matched
1253 value can be converted to a string (as well as applying the function to it).
1254 So this program is legal:
1261 f (Baz1 p q) | p == q = "Yes"
1263 f (Baz2 v fn) = show (fn v)
1269 Operationally, in a dictionary-passing implementation, the
1270 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1271 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1272 extract it on pattern matching.
1276 Notice the way that the syntax fits smoothly with that used for
1277 universal quantification earlier.
1283 <title>Record Constructors</title>
1286 GHC allows existentials to be used with records syntax as well. For example:
1289 data Counter a = forall self. NewCounter
1291 , _inc :: self -> self
1292 , _display :: self -> IO ()
1296 Here <literal>tag</literal> is a public field, with a well-typed selector
1297 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1298 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1299 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1300 compile-time error. In other words, <emphasis>GHC defines a record selector function
1301 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1302 (This example used an underscore in the fields for which record selectors
1303 will not be defined, but that is only programming style; GHC ignores them.)
1307 To make use of these hidden fields, we need to create some helper functions:
1310 inc :: Counter a -> Counter a
1311 inc (NewCounter x i d t) = NewCounter
1312 { _this = i x, _inc = i, _display = d, tag = t }
1314 display :: Counter a -> IO ()
1315 display NewCounter{ _this = x, _display = d } = d x
1318 Now we can define counters with different underlying implementations:
1321 counterA :: Counter String
1322 counterA = NewCounter
1323 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1325 counterB :: Counter String
1326 counterB = NewCounter
1327 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1330 display (inc counterA) -- prints "1"
1331 display (inc (inc counterB)) -- prints "##"
1334 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1335 <literal>forall</literal> may be omitted. For example, we can express
1336 the same <literal>Counter a</literal> using GADT:
1339 data Counter a where
1340 NewCounter { _this :: self
1341 , _inc :: self -> self
1342 , _display :: self -> IO ()
1348 At the moment, record update syntax is only supported for Haskell 98 data types,
1349 so the following function does <emphasis>not</emphasis> work:
1352 -- This is invalid; use explicit NewCounter instead for now
1353 setTag :: Counter a -> a -> Counter a
1354 setTag obj t = obj{ tag = t }
1363 <title>Restrictions</title>
1366 There are several restrictions on the ways in which existentially-quantified
1367 constructors can be use.
1376 When pattern matching, each pattern match introduces a new,
1377 distinct, type for each existential type variable. These types cannot
1378 be unified with any other type, nor can they escape from the scope of
1379 the pattern match. For example, these fragments are incorrect:
1387 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1388 is the result of <function>f1</function>. One way to see why this is wrong is to
1389 ask what type <function>f1</function> has:
1393 f1 :: Foo -> a -- Weird!
1397 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1402 f1 :: forall a. Foo -> a -- Wrong!
1406 The original program is just plain wrong. Here's another sort of error
1410 f2 (Baz1 a b) (Baz1 p q) = a==q
1414 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1415 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1416 from the two <function>Baz1</function> constructors.
1424 You can't pattern-match on an existentially quantified
1425 constructor in a <literal>let</literal> or <literal>where</literal> group of
1426 bindings. So this is illegal:
1430 f3 x = a==b where { Baz1 a b = x }
1433 Instead, use a <literal>case</literal> expression:
1436 f3 x = case x of Baz1 a b -> a==b
1439 In general, you can only pattern-match
1440 on an existentially-quantified constructor in a <literal>case</literal> expression or
1441 in the patterns of a function definition.
1443 The reason for this restriction is really an implementation one.
1444 Type-checking binding groups is already a nightmare without
1445 existentials complicating the picture. Also an existential pattern
1446 binding at the top level of a module doesn't make sense, because it's
1447 not clear how to prevent the existentially-quantified type "escaping".
1448 So for now, there's a simple-to-state restriction. We'll see how
1456 You can't use existential quantification for <literal>newtype</literal>
1457 declarations. So this is illegal:
1461 newtype T = forall a. Ord a => MkT a
1465 Reason: a value of type <literal>T</literal> must be represented as a
1466 pair of a dictionary for <literal>Ord t</literal> and a value of type
1467 <literal>t</literal>. That contradicts the idea that
1468 <literal>newtype</literal> should have no concrete representation.
1469 You can get just the same efficiency and effect by using
1470 <literal>data</literal> instead of <literal>newtype</literal>. If
1471 there is no overloading involved, then there is more of a case for
1472 allowing an existentially-quantified <literal>newtype</literal>,
1473 because the <literal>data</literal> version does carry an
1474 implementation cost, but single-field existentially quantified
1475 constructors aren't much use. So the simple restriction (no
1476 existential stuff on <literal>newtype</literal>) stands, unless there
1477 are convincing reasons to change it.
1485 You can't use <literal>deriving</literal> to define instances of a
1486 data type with existentially quantified data constructors.
1488 Reason: in most cases it would not make sense. For example:#
1491 data T = forall a. MkT [a] deriving( Eq )
1494 To derive <literal>Eq</literal> in the standard way we would need to have equality
1495 between the single component of two <function>MkT</function> constructors:
1499 (MkT a) == (MkT b) = ???
1502 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1503 It's just about possible to imagine examples in which the derived instance
1504 would make sense, but it seems altogether simpler simply to prohibit such
1505 declarations. Define your own instances!
1520 <sect2 id="multi-param-type-classes">
1521 <title>Class declarations</title>
1524 This section, and the next one, documents GHC's type-class extensions.
1525 There's lots of background in the paper <ulink
1526 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1527 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1528 Jones, Erik Meijer).
1531 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1535 <title>Multi-parameter type classes</title>
1537 Multi-parameter type classes are permitted. For example:
1541 class Collection c a where
1542 union :: c a -> c a -> c a
1550 <title>The superclasses of a class declaration</title>
1553 There are no restrictions on the context in a class declaration
1554 (which introduces superclasses), except that the class hierarchy must
1555 be acyclic. So these class declarations are OK:
1559 class Functor (m k) => FiniteMap m k where
1562 class (Monad m, Monad (t m)) => Transform t m where
1563 lift :: m a -> (t m) a
1569 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1570 of "acyclic" involves only the superclass relationships. For example,
1576 op :: D b => a -> b -> b
1579 class C a => D a where { ... }
1583 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1584 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1585 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1592 <sect3 id="class-method-types">
1593 <title>Class method types</title>
1596 Haskell 98 prohibits class method types to mention constraints on the
1597 class type variable, thus:
1600 fromList :: [a] -> s a
1601 elem :: Eq a => a -> s a -> Bool
1603 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1604 contains the constraint <literal>Eq a</literal>, constrains only the
1605 class type variable (in this case <literal>a</literal>).
1606 GHC lifts this restriction.
1613 <sect2 id="functional-dependencies">
1614 <title>Functional dependencies
1617 <para> Functional dependencies are implemented as described by Mark Jones
1618 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1619 In Proceedings of the 9th European Symposium on Programming,
1620 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1624 Functional dependencies are introduced by a vertical bar in the syntax of a
1625 class declaration; e.g.
1627 class (Monad m) => MonadState s m | m -> s where ...
1629 class Foo a b c | a b -> c where ...
1631 There should be more documentation, but there isn't (yet). Yell if you need it.
1634 <sect3><title>Rules for functional dependencies </title>
1636 In a class declaration, all of the class type variables must be reachable (in the sense
1637 mentioned in <xref linkend="type-restrictions"/>)
1638 from the free variables of each method type.
1642 class Coll s a where
1644 insert :: s -> a -> s
1647 is not OK, because the type of <literal>empty</literal> doesn't mention
1648 <literal>a</literal>. Functional dependencies can make the type variable
1651 class Coll s a | s -> a where
1653 insert :: s -> a -> s
1656 Alternatively <literal>Coll</literal> might be rewritten
1659 class Coll s a where
1661 insert :: s a -> a -> s a
1665 which makes the connection between the type of a collection of
1666 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1667 Occasionally this really doesn't work, in which case you can split the
1675 class CollE s => Coll s a where
1676 insert :: s -> a -> s
1683 <title>Background on functional dependencies</title>
1685 <para>The following description of the motivation and use of functional dependencies is taken
1686 from the Hugs user manual, reproduced here (with minor changes) by kind
1687 permission of Mark Jones.
1690 Consider the following class, intended as part of a
1691 library for collection types:
1693 class Collects e ce where
1695 insert :: e -> ce -> ce
1696 member :: e -> ce -> Bool
1698 The type variable e used here represents the element type, while ce is the type
1699 of the container itself. Within this framework, we might want to define
1700 instances of this class for lists or characteristic functions (both of which
1701 can be used to represent collections of any equality type), bit sets (which can
1702 be used to represent collections of characters), or hash tables (which can be
1703 used to represent any collection whose elements have a hash function). Omitting
1704 standard implementation details, this would lead to the following declarations:
1706 instance Eq e => Collects e [e] where ...
1707 instance Eq e => Collects e (e -> Bool) where ...
1708 instance Collects Char BitSet where ...
1709 instance (Hashable e, Collects a ce)
1710 => Collects e (Array Int ce) where ...
1712 All this looks quite promising; we have a class and a range of interesting
1713 implementations. Unfortunately, there are some serious problems with the class
1714 declaration. First, the empty function has an ambiguous type:
1716 empty :: Collects e ce => ce
1718 By "ambiguous" we mean that there is a type variable e that appears on the left
1719 of the <literal>=></literal> symbol, but not on the right. The problem with
1720 this is that, according to the theoretical foundations of Haskell overloading,
1721 we cannot guarantee a well-defined semantics for any term with an ambiguous
1725 We can sidestep this specific problem by removing the empty member from the
1726 class declaration. However, although the remaining members, insert and member,
1727 do not have ambiguous types, we still run into problems when we try to use
1728 them. For example, consider the following two functions:
1730 f x y = insert x . insert y
1733 for which GHC infers the following types:
1735 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1736 g :: (Collects Bool c, Collects Char c) => c -> c
1738 Notice that the type for f allows the two parameters x and y to be assigned
1739 different types, even though it attempts to insert each of the two values, one
1740 after the other, into the same collection. If we're trying to model collections
1741 that contain only one type of value, then this is clearly an inaccurate
1742 type. Worse still, the definition for g is accepted, without causing a type
1743 error. As a result, the error in this code will not be flagged at the point
1744 where it appears. Instead, it will show up only when we try to use g, which
1745 might even be in a different module.
1748 <sect4><title>An attempt to use constructor classes</title>
1751 Faced with the problems described above, some Haskell programmers might be
1752 tempted to use something like the following version of the class declaration:
1754 class Collects e c where
1756 insert :: e -> c e -> c e
1757 member :: e -> c e -> Bool
1759 The key difference here is that we abstract over the type constructor c that is
1760 used to form the collection type c e, and not over that collection type itself,
1761 represented by ce in the original class declaration. This avoids the immediate
1762 problems that we mentioned above: empty has type <literal>Collects e c => c
1763 e</literal>, which is not ambiguous.
1766 The function f from the previous section has a more accurate type:
1768 f :: (Collects e c) => e -> e -> c e -> c e
1770 The function g from the previous section is now rejected with a type error as
1771 we would hope because the type of f does not allow the two arguments to have
1773 This, then, is an example of a multiple parameter class that does actually work
1774 quite well in practice, without ambiguity problems.
1775 There is, however, a catch. This version of the Collects class is nowhere near
1776 as general as the original class seemed to be: only one of the four instances
1777 for <literal>Collects</literal>
1778 given above can be used with this version of Collects because only one of
1779 them---the instance for lists---has a collection type that can be written in
1780 the form c e, for some type constructor c, and element type e.
1784 <sect4><title>Adding functional dependencies</title>
1787 To get a more useful version of the Collects class, Hugs provides a mechanism
1788 that allows programmers to specify dependencies between the parameters of a
1789 multiple parameter class (For readers with an interest in theoretical
1790 foundations and previous work: The use of dependency information can be seen
1791 both as a generalization of the proposal for `parametric type classes' that was
1792 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1793 later framework for "improvement" of qualified types. The
1794 underlying ideas are also discussed in a more theoretical and abstract setting
1795 in a manuscript [implparam], where they are identified as one point in a
1796 general design space for systems of implicit parameterization.).
1798 To start with an abstract example, consider a declaration such as:
1800 class C a b where ...
1802 which tells us simply that C can be thought of as a binary relation on types
1803 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1804 included in the definition of classes to add information about dependencies
1805 between parameters, as in the following examples:
1807 class D a b | a -> b where ...
1808 class E a b | a -> b, b -> a where ...
1810 The notation <literal>a -> b</literal> used here between the | and where
1811 symbols --- not to be
1812 confused with a function type --- indicates that the a parameter uniquely
1813 determines the b parameter, and might be read as "a determines b." Thus D is
1814 not just a relation, but actually a (partial) function. Similarly, from the two
1815 dependencies that are included in the definition of E, we can see that E
1816 represents a (partial) one-one mapping between types.
1819 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
1820 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
1821 m>=0, meaning that the y parameters are uniquely determined by the x
1822 parameters. Spaces can be used as separators if more than one variable appears
1823 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
1824 annotated with multiple dependencies using commas as separators, as in the
1825 definition of E above. Some dependencies that we can write in this notation are
1826 redundant, and will be rejected because they don't serve any useful
1827 purpose, and may instead indicate an error in the program. Examples of
1828 dependencies like this include <literal>a -> a </literal>,
1829 <literal>a -> a a </literal>,
1830 <literal>a -> </literal>, etc. There can also be
1831 some redundancy if multiple dependencies are given, as in
1832 <literal>a->b</literal>,
1833 <literal>b->c </literal>, <literal>a->c </literal>, and
1834 in which some subset implies the remaining dependencies. Examples like this are
1835 not treated as errors. Note that dependencies appear only in class
1836 declarations, and not in any other part of the language. In particular, the
1837 syntax for instance declarations, class constraints, and types is completely
1841 By including dependencies in a class declaration, we provide a mechanism for
1842 the programmer to specify each multiple parameter class more precisely. The
1843 compiler, on the other hand, is responsible for ensuring that the set of
1844 instances that are in scope at any given point in the program is consistent
1845 with any declared dependencies. For example, the following pair of instance
1846 declarations cannot appear together in the same scope because they violate the
1847 dependency for D, even though either one on its own would be acceptable:
1849 instance D Bool Int where ...
1850 instance D Bool Char where ...
1852 Note also that the following declaration is not allowed, even by itself:
1854 instance D [a] b where ...
1856 The problem here is that this instance would allow one particular choice of [a]
1857 to be associated with more than one choice for b, which contradicts the
1858 dependency specified in the definition of D. More generally, this means that,
1859 in any instance of the form:
1861 instance D t s where ...
1863 for some particular types t and s, the only variables that can appear in s are
1864 the ones that appear in t, and hence, if the type t is known, then s will be
1865 uniquely determined.
1868 The benefit of including dependency information is that it allows us to define
1869 more general multiple parameter classes, without ambiguity problems, and with
1870 the benefit of more accurate types. To illustrate this, we return to the
1871 collection class example, and annotate the original definition of <literal>Collects</literal>
1872 with a simple dependency:
1874 class Collects e ce | ce -> e where
1876 insert :: e -> ce -> ce
1877 member :: e -> ce -> Bool
1879 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
1880 determined by the type of the collection ce. Note that both parameters of
1881 Collects are of kind *; there are no constructor classes here. Note too that
1882 all of the instances of Collects that we gave earlier can be used
1883 together with this new definition.
1886 What about the ambiguity problems that we encountered with the original
1887 definition? The empty function still has type Collects e ce => ce, but it is no
1888 longer necessary to regard that as an ambiguous type: Although the variable e
1889 does not appear on the right of the => symbol, the dependency for class
1890 Collects tells us that it is uniquely determined by ce, which does appear on
1891 the right of the => symbol. Hence the context in which empty is used can still
1892 give enough information to determine types for both ce and e, without
1893 ambiguity. More generally, we need only regard a type as ambiguous if it
1894 contains a variable on the left of the => that is not uniquely determined
1895 (either directly or indirectly) by the variables on the right.
1898 Dependencies also help to produce more accurate types for user defined
1899 functions, and hence to provide earlier detection of errors, and less cluttered
1900 types for programmers to work with. Recall the previous definition for a
1903 f x y = insert x y = insert x . insert y
1905 for which we originally obtained a type:
1907 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1909 Given the dependency information that we have for Collects, however, we can
1910 deduce that a and b must be equal because they both appear as the second
1911 parameter in a Collects constraint with the same first parameter c. Hence we
1912 can infer a shorter and more accurate type for f:
1914 f :: (Collects a c) => a -> a -> c -> c
1916 In a similar way, the earlier definition of g will now be flagged as a type error.
1919 Although we have given only a few examples here, it should be clear that the
1920 addition of dependency information can help to make multiple parameter classes
1921 more useful in practice, avoiding ambiguity problems, and allowing more general
1922 sets of instance declarations.
1928 <sect2 id="instance-decls">
1929 <title>Instance declarations</title>
1931 <sect3 id="instance-rules">
1932 <title>Relaxed rules for instance declarations</title>
1934 <para>An instance declaration has the form
1936 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 ...
1938 The part before the "<literal>=></literal>" is the
1939 <emphasis>context</emphasis>, while the part after the
1940 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
1944 In Haskell 98 the head of an instance declaration
1945 must be of the form <literal>C (T a1 ... an)</literal>, where
1946 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1947 and the <literal>a1 ... an</literal> are distinct type variables.
1948 Furthermore, the assertions in the context of the instance declaration
1949 must be of the form <literal>C a</literal> where <literal>a</literal>
1950 is a type variable that occurs in the head.
1953 The <option>-fglasgow-exts</option> flag loosens these restrictions
1954 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1955 the context and head of the instance declaration can each consist of arbitrary
1956 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1960 For each assertion in the context:
1962 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1963 <listitem><para>The assertion has fewer constructors and variables (taken together
1964 and counting repetitions) than the head</para></listitem>
1968 <listitem><para>The coverage condition. For each functional dependency,
1969 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
1970 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
1971 every type variable in
1972 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
1973 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
1974 substitution mapping each type variable in the class declaration to the
1975 corresponding type in the instance declaration.
1978 These restrictions ensure that context reduction terminates: each reduction
1979 step makes the problem smaller by at least one
1980 constructor. For example, the following would make the type checker
1981 loop if it wasn't excluded:
1983 instance C a => C a where ...
1985 For example, these are OK:
1987 instance C Int [a] -- Multiple parameters
1988 instance Eq (S [a]) -- Structured type in head
1990 -- Repeated type variable in head
1991 instance C4 a a => C4 [a] [a]
1992 instance Stateful (ST s) (MutVar s)
1994 -- Head can consist of type variables only
1996 instance (Eq a, Show b) => C2 a b
1998 -- Non-type variables in context
1999 instance Show (s a) => Show (Sized s a)
2000 instance C2 Int a => C3 Bool [a]
2001 instance C2 Int a => C3 [a] b
2005 -- Context assertion no smaller than head
2006 instance C a => C a where ...
2007 -- (C b b) has more more occurrences of b than the head
2008 instance C b b => Foo [b] where ...
2013 The same restrictions apply to instances generated by
2014 <literal>deriving</literal> clauses. Thus the following is accepted:
2016 data MinHeap h a = H a (h a)
2019 because the derived instance
2021 instance (Show a, Show (h a)) => Show (MinHeap h a)
2023 conforms to the above rules.
2027 A useful idiom permitted by the above rules is as follows.
2028 If one allows overlapping instance declarations then it's quite
2029 convenient to have a "default instance" declaration that applies if
2030 something more specific does not:
2036 <para>You can find lots of background material about the reason for these
2037 restrictions in the paper <ulink
2038 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2039 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2043 <sect3 id="undecidable-instances">
2044 <title>Undecidable instances</title>
2047 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2048 For example, sometimes you might want to use the following to get the
2049 effect of a "class synonym":
2051 class (C1 a, C2 a, C3 a) => C a where { }
2053 instance (C1 a, C2 a, C3 a) => C a where { }
2055 This allows you to write shorter signatures:
2061 f :: (C1 a, C2 a, C3 a) => ...
2063 The restrictions on functional dependencies (<xref
2064 linkend="functional-dependencies"/>) are particularly troublesome.
2065 It is tempting to introduce type variables in the context that do not appear in
2066 the head, something that is excluded by the normal rules. For example:
2068 class HasConverter a b | a -> b where
2071 data Foo a = MkFoo a
2073 instance (HasConverter a b,Show b) => Show (Foo a) where
2074 show (MkFoo value) = show (convert value)
2076 This is dangerous territory, however. Here, for example, is a program that would make the
2081 instance F [a] [[a]]
2082 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2084 Similarly, it can be tempting to lift the coverage condition:
2086 class Mul a b c | a b -> c where
2087 (.*.) :: a -> b -> c
2089 instance Mul Int Int Int where (.*.) = (*)
2090 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2091 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2093 The third instance declaration does not obey the coverage condition;
2094 and indeed the (somewhat strange) definition:
2096 f = \ b x y -> if b then x .*. [y] else y
2098 makes instance inference go into a loop, because it requires the constraint
2099 <literal>(Mul a [b] b)</literal>.
2102 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2103 the experimental flag <option>-fallow-undecidable-instances</option>
2104 <indexterm><primary>-fallow-undecidable-instances
2105 option</primary></indexterm>, you can use arbitrary
2106 types in both an instance context and instance head. Termination is ensured by having a
2107 fixed-depth recursion stack. If you exceed the stack depth you get a
2108 sort of backtrace, and the opportunity to increase the stack depth
2109 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2115 <sect3 id="instance-overlap">
2116 <title>Overlapping instances</title>
2118 In general, <emphasis>GHC requires that that it be unambiguous which instance
2120 should be used to resolve a type-class constraint</emphasis>. This behaviour
2121 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2122 <indexterm><primary>-fallow-overlapping-instances
2123 </primary></indexterm>
2124 and <option>-fallow-incoherent-instances</option>
2125 <indexterm><primary>-fallow-incoherent-instances
2126 </primary></indexterm>, as this section discusses. Both these
2127 flags are dynamic flags, and can be set on a per-module basis, using
2128 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2130 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2131 it tries to match every instance declaration against the
2133 by instantiating the head of the instance declaration. For example, consider
2136 instance context1 => C Int a where ... -- (A)
2137 instance context2 => C a Bool where ... -- (B)
2138 instance context3 => C Int [a] where ... -- (C)
2139 instance context4 => C Int [Int] where ... -- (D)
2141 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2142 but (C) and (D) do not. When matching, GHC takes
2143 no account of the context of the instance declaration
2144 (<literal>context1</literal> etc).
2145 GHC's default behaviour is that <emphasis>exactly one instance must match the
2146 constraint it is trying to resolve</emphasis>.
2147 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2148 including both declarations (A) and (B), say); an error is only reported if a
2149 particular constraint matches more than one.
2153 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2154 more than one instance to match, provided there is a most specific one. For
2155 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2156 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2157 most-specific match, the program is rejected.
2160 However, GHC is conservative about committing to an overlapping instance. For example:
2165 Suppose that from the RHS of <literal>f</literal> we get the constraint
2166 <literal>C Int [b]</literal>. But
2167 GHC does not commit to instance (C), because in a particular
2168 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2169 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2170 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2171 GHC will instead pick (C), without complaining about
2172 the problem of subsequent instantiations.
2175 The willingness to be overlapped or incoherent is a property of
2176 the <emphasis>instance declaration</emphasis> itself, controlled by the
2177 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2178 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2179 being defined. Neither flag is required in a module that imports and uses the
2180 instance declaration. Specifically, during the lookup process:
2183 An instance declaration is ignored during the lookup process if (a) a more specific
2184 match is found, and (b) the instance declaration was compiled with
2185 <option>-fallow-overlapping-instances</option>. The flag setting for the
2186 more-specific instance does not matter.
2189 Suppose an instance declaration does not matche the constraint being looked up, but
2190 does unify with it, so that it might match when the constraint is further
2191 instantiated. Usually GHC will regard this as a reason for not committing to
2192 some other constraint. But if the instance declaration was compiled with
2193 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2194 check for that declaration.
2197 All this makes it possible for a library author to design a library that relies on
2198 overlapping instances without the library client having to know.
2200 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2201 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2206 <title>Type synonyms in the instance head</title>
2209 <emphasis>Unlike Haskell 98, instance heads may use type
2210 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2211 As always, using a type synonym is just shorthand for
2212 writing the RHS of the type synonym definition. For example:
2216 type Point = (Int,Int)
2217 instance C Point where ...
2218 instance C [Point] where ...
2222 is legal. However, if you added
2226 instance C (Int,Int) where ...
2230 as well, then the compiler will complain about the overlapping
2231 (actually, identical) instance declarations. As always, type synonyms
2232 must be fully applied. You cannot, for example, write:
2237 instance Monad P where ...
2241 This design decision is independent of all the others, and easily
2242 reversed, but it makes sense to me.
2250 <sect2 id="type-restrictions">
2251 <title>Type signatures</title>
2253 <sect3><title>The context of a type signature</title>
2255 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2256 the form <emphasis>(class type-variable)</emphasis> or
2257 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2258 these type signatures are perfectly OK
2261 g :: Ord (T a ()) => ...
2265 GHC imposes the following restrictions on the constraints in a type signature.
2269 forall tv1..tvn (c1, ...,cn) => type
2272 (Here, we write the "foralls" explicitly, although the Haskell source
2273 language omits them; in Haskell 98, all the free type variables of an
2274 explicit source-language type signature are universally quantified,
2275 except for the class type variables in a class declaration. However,
2276 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2285 <emphasis>Each universally quantified type variable
2286 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2288 A type variable <literal>a</literal> is "reachable" if it it appears
2289 in the same constraint as either a type variable free in in
2290 <literal>type</literal>, or another reachable type variable.
2291 A value with a type that does not obey
2292 this reachability restriction cannot be used without introducing
2293 ambiguity; that is why the type is rejected.
2294 Here, for example, is an illegal type:
2298 forall a. Eq a => Int
2302 When a value with this type was used, the constraint <literal>Eq tv</literal>
2303 would be introduced where <literal>tv</literal> is a fresh type variable, and
2304 (in the dictionary-translation implementation) the value would be
2305 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2306 can never know which instance of <literal>Eq</literal> to use because we never
2307 get any more information about <literal>tv</literal>.
2311 that the reachability condition is weaker than saying that <literal>a</literal> is
2312 functionally dependent on a type variable free in
2313 <literal>type</literal> (see <xref
2314 linkend="functional-dependencies"/>). The reason for this is there
2315 might be a "hidden" dependency, in a superclass perhaps. So
2316 "reachable" is a conservative approximation to "functionally dependent".
2317 For example, consider:
2319 class C a b | a -> b where ...
2320 class C a b => D a b where ...
2321 f :: forall a b. D a b => a -> a
2323 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2324 but that is not immediately apparent from <literal>f</literal>'s type.
2330 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2331 universally quantified type variables <literal>tvi</literal></emphasis>.
2333 For example, this type is OK because <literal>C a b</literal> mentions the
2334 universally quantified type variable <literal>b</literal>:
2338 forall a. C a b => burble
2342 The next type is illegal because the constraint <literal>Eq b</literal> does not
2343 mention <literal>a</literal>:
2347 forall a. Eq b => burble
2351 The reason for this restriction is milder than the other one. The
2352 excluded types are never useful or necessary (because the offending
2353 context doesn't need to be witnessed at this point; it can be floated
2354 out). Furthermore, floating them out increases sharing. Lastly,
2355 excluding them is a conservative choice; it leaves a patch of
2356 territory free in case we need it later.
2367 <title>For-all hoisting</title>
2369 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2370 end of an arrow, thus:
2372 type Discard a = forall b. a -> b -> a
2374 g :: Int -> Discard Int
2377 Simply expanding the type synonym would give
2379 g :: Int -> (forall b. Int -> b -> Int)
2381 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2383 g :: forall b. Int -> Int -> b -> Int
2385 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2386 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2387 performs the transformation:</emphasis>
2389 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2391 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2393 (In fact, GHC tries to retain as much synonym information as possible for use in
2394 error messages, but that is a usability issue.) This rule applies, of course, whether
2395 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2396 valid way to write <literal>g</literal>'s type signature:
2398 g :: Int -> Int -> forall b. b -> Int
2402 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2405 type Foo a = (?x::Int) => Bool -> a
2410 g :: (?x::Int) => Bool -> Bool -> Int
2418 <sect2 id="implicit-parameters">
2419 <title>Implicit parameters</title>
2421 <para> Implicit parameters are implemented as described in
2422 "Implicit parameters: dynamic scoping with static types",
2423 J Lewis, MB Shields, E Meijer, J Launchbury,
2424 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2428 <para>(Most of the following, stil rather incomplete, documentation is
2429 due to Jeff Lewis.)</para>
2431 <para>Implicit parameter support is enabled with the option
2432 <option>-fimplicit-params</option>.</para>
2435 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2436 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2437 context. In Haskell, all variables are statically bound. Dynamic
2438 binding of variables is a notion that goes back to Lisp, but was later
2439 discarded in more modern incarnations, such as Scheme. Dynamic binding
2440 can be very confusing in an untyped language, and unfortunately, typed
2441 languages, in particular Hindley-Milner typed languages like Haskell,
2442 only support static scoping of variables.
2445 However, by a simple extension to the type class system of Haskell, we
2446 can support dynamic binding. Basically, we express the use of a
2447 dynamically bound variable as a constraint on the type. These
2448 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2449 function uses a dynamically-bound variable <literal>?x</literal>
2450 of type <literal>t'</literal>". For
2451 example, the following expresses the type of a sort function,
2452 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2454 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2456 The dynamic binding constraints are just a new form of predicate in the type class system.
2459 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2460 where <literal>x</literal> is
2461 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2462 Use of this construct also introduces a new
2463 dynamic-binding constraint in the type of the expression.
2464 For example, the following definition
2465 shows how we can define an implicitly parameterized sort function in
2466 terms of an explicitly parameterized <literal>sortBy</literal> function:
2468 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2470 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2476 <title>Implicit-parameter type constraints</title>
2478 Dynamic binding constraints behave just like other type class
2479 constraints in that they are automatically propagated. Thus, when a
2480 function is used, its implicit parameters are inherited by the
2481 function that called it. For example, our <literal>sort</literal> function might be used
2482 to pick out the least value in a list:
2484 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2485 least xs = head (sort xs)
2487 Without lifting a finger, the <literal>?cmp</literal> parameter is
2488 propagated to become a parameter of <literal>least</literal> as well. With explicit
2489 parameters, the default is that parameters must always be explicit
2490 propagated. With implicit parameters, the default is to always
2494 An implicit-parameter type constraint differs from other type class constraints in the
2495 following way: All uses of a particular implicit parameter must have
2496 the same type. This means that the type of <literal>(?x, ?x)</literal>
2497 is <literal>(?x::a) => (a,a)</literal>, and not
2498 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2502 <para> You can't have an implicit parameter in the context of a class or instance
2503 declaration. For example, both these declarations are illegal:
2505 class (?x::Int) => C a where ...
2506 instance (?x::a) => Foo [a] where ...
2508 Reason: exactly which implicit parameter you pick up depends on exactly where
2509 you invoke a function. But the ``invocation'' of instance declarations is done
2510 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2511 Easiest thing is to outlaw the offending types.</para>
2513 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2515 f :: (?x :: [a]) => Int -> Int
2518 g :: (Read a, Show a) => String -> String
2521 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2522 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2523 quite unambiguous, and fixes the type <literal>a</literal>.
2528 <title>Implicit-parameter bindings</title>
2531 An implicit parameter is <emphasis>bound</emphasis> using the standard
2532 <literal>let</literal> or <literal>where</literal> binding forms.
2533 For example, we define the <literal>min</literal> function by binding
2534 <literal>cmp</literal>.
2537 min = let ?cmp = (<=) in least
2541 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2542 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2543 (including in a list comprehension, or do-notation, or pattern guards),
2544 or a <literal>where</literal> clause.
2545 Note the following points:
2548 An implicit-parameter binding group must be a
2549 collection of simple bindings to implicit-style variables (no
2550 function-style bindings, and no type signatures); these bindings are
2551 neither polymorphic or recursive.
2554 You may not mix implicit-parameter bindings with ordinary bindings in a
2555 single <literal>let</literal>
2556 expression; use two nested <literal>let</literal>s instead.
2557 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2561 You may put multiple implicit-parameter bindings in a
2562 single binding group; but they are <emphasis>not</emphasis> treated
2563 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2564 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2565 parameter. The bindings are not nested, and may be re-ordered without changing
2566 the meaning of the program.
2567 For example, consider:
2569 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2571 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2572 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2574 f :: (?x::Int) => Int -> Int
2582 <sect3><title>Implicit parameters and polymorphic recursion</title>
2585 Consider these two definitions:
2588 len1 xs = let ?acc = 0 in len_acc1 xs
2591 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2596 len2 xs = let ?acc = 0 in len_acc2 xs
2598 len_acc2 :: (?acc :: Int) => [a] -> Int
2600 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2602 The only difference between the two groups is that in the second group
2603 <literal>len_acc</literal> is given a type signature.
2604 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2605 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2606 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2607 has a type signature, the recursive call is made to the
2608 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2609 as an implicit parameter. So we get the following results in GHCi:
2616 Adding a type signature dramatically changes the result! This is a rather
2617 counter-intuitive phenomenon, worth watching out for.
2621 <sect3><title>Implicit parameters and monomorphism</title>
2623 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2624 Haskell Report) to implicit parameters. For example, consider:
2632 Since the binding for <literal>y</literal> falls under the Monomorphism
2633 Restriction it is not generalised, so the type of <literal>y</literal> is
2634 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2635 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2636 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2637 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2638 <literal>y</literal> in the body of the <literal>let</literal> will see the
2639 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2640 <literal>14</literal>.
2645 <sect2 id="linear-implicit-parameters">
2646 <title>Linear implicit parameters</title>
2648 Linear implicit parameters are an idea developed by Koen Claessen,
2649 Mark Shields, and Simon PJ. They address the long-standing
2650 problem that monads seem over-kill for certain sorts of problem, notably:
2653 <listitem> <para> distributing a supply of unique names </para> </listitem>
2654 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2655 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2659 Linear implicit parameters are just like ordinary implicit parameters,
2660 except that they are "linear" -- that is, they cannot be copied, and
2661 must be explicitly "split" instead. Linear implicit parameters are
2662 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2663 (The '/' in the '%' suggests the split!)
2668 import GHC.Exts( Splittable )
2670 data NameSupply = ...
2672 splitNS :: NameSupply -> (NameSupply, NameSupply)
2673 newName :: NameSupply -> Name
2675 instance Splittable NameSupply where
2679 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2680 f env (Lam x e) = Lam x' (f env e)
2683 env' = extend env x x'
2684 ...more equations for f...
2686 Notice that the implicit parameter %ns is consumed
2688 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2689 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2693 So the translation done by the type checker makes
2694 the parameter explicit:
2696 f :: NameSupply -> Env -> Expr -> Expr
2697 f ns env (Lam x e) = Lam x' (f ns1 env e)
2699 (ns1,ns2) = splitNS ns
2701 env = extend env x x'
2703 Notice the call to 'split' introduced by the type checker.
2704 How did it know to use 'splitNS'? Because what it really did
2705 was to introduce a call to the overloaded function 'split',
2706 defined by the class <literal>Splittable</literal>:
2708 class Splittable a where
2711 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2712 split for name supplies. But we can simply write
2718 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2720 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2721 <literal>GHC.Exts</literal>.
2726 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2727 are entirely distinct implicit parameters: you
2728 can use them together and they won't intefere with each other. </para>
2731 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2733 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2734 in the context of a class or instance declaration. </para></listitem>
2738 <sect3><title>Warnings</title>
2741 The monomorphism restriction is even more important than usual.
2742 Consider the example above:
2744 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2745 f env (Lam x e) = Lam x' (f env e)
2748 env' = extend env x x'
2750 If we replaced the two occurrences of x' by (newName %ns), which is
2751 usually a harmless thing to do, we get:
2753 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2754 f env (Lam x e) = Lam (newName %ns) (f env e)
2756 env' = extend env x (newName %ns)
2758 But now the name supply is consumed in <emphasis>three</emphasis> places
2759 (the two calls to newName,and the recursive call to f), so
2760 the result is utterly different. Urk! We don't even have
2764 Well, this is an experimental change. With implicit
2765 parameters we have already lost beta reduction anyway, and
2766 (as John Launchbury puts it) we can't sensibly reason about
2767 Haskell programs without knowing their typing.
2772 <sect3><title>Recursive functions</title>
2773 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2776 foo :: %x::T => Int -> [Int]
2778 foo n = %x : foo (n-1)
2780 where T is some type in class Splittable.</para>
2782 Do you get a list of all the same T's or all different T's
2783 (assuming that split gives two distinct T's back)?
2785 If you supply the type signature, taking advantage of polymorphic
2786 recursion, you get what you'd probably expect. Here's the
2787 translated term, where the implicit param is made explicit:
2790 foo x n = let (x1,x2) = split x
2791 in x1 : foo x2 (n-1)
2793 But if you don't supply a type signature, GHC uses the Hindley
2794 Milner trick of using a single monomorphic instance of the function
2795 for the recursive calls. That is what makes Hindley Milner type inference
2796 work. So the translation becomes
2800 foom n = x : foom (n-1)
2804 Result: 'x' is not split, and you get a list of identical T's. So the
2805 semantics of the program depends on whether or not foo has a type signature.
2808 You may say that this is a good reason to dislike linear implicit parameters
2809 and you'd be right. That is why they are an experimental feature.
2815 <sect2 id="sec-kinding">
2816 <title>Explicitly-kinded quantification</title>
2819 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2820 to give the kind explicitly as (machine-checked) documentation,
2821 just as it is nice to give a type signature for a function. On some occasions,
2822 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2823 John Hughes had to define the data type:
2825 data Set cxt a = Set [a]
2826 | Unused (cxt a -> ())
2828 The only use for the <literal>Unused</literal> constructor was to force the correct
2829 kind for the type variable <literal>cxt</literal>.
2832 GHC now instead allows you to specify the kind of a type variable directly, wherever
2833 a type variable is explicitly bound. Namely:
2835 <listitem><para><literal>data</literal> declarations:
2837 data Set (cxt :: * -> *) a = Set [a]
2838 </screen></para></listitem>
2839 <listitem><para><literal>type</literal> declarations:
2841 type T (f :: * -> *) = f Int
2842 </screen></para></listitem>
2843 <listitem><para><literal>class</literal> declarations:
2845 class (Eq a) => C (f :: * -> *) a where ...
2846 </screen></para></listitem>
2847 <listitem><para><literal>forall</literal>'s in type signatures:
2849 f :: forall (cxt :: * -> *). Set cxt Int
2850 </screen></para></listitem>
2855 The parentheses are required. Some of the spaces are required too, to
2856 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2857 will get a parse error, because "<literal>::*->*</literal>" is a
2858 single lexeme in Haskell.
2862 As part of the same extension, you can put kind annotations in types
2865 f :: (Int :: *) -> Int
2866 g :: forall a. a -> (a :: *)
2870 atype ::= '(' ctype '::' kind ')
2872 The parentheses are required.
2877 <sect2 id="universal-quantification">
2878 <title>Arbitrary-rank polymorphism
2882 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2883 allows us to say exactly what this means. For example:
2891 g :: forall b. (b -> b)
2893 The two are treated identically.
2897 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2898 explicit universal quantification in
2900 For example, all the following types are legal:
2902 f1 :: forall a b. a -> b -> a
2903 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2905 f2 :: (forall a. a->a) -> Int -> Int
2906 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2908 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2910 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2911 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2912 The <literal>forall</literal> makes explicit the universal quantification that
2913 is implicitly added by Haskell.
2916 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2917 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2918 shows, the polymorphic type on the left of the function arrow can be overloaded.
2921 The function <literal>f3</literal> has a rank-3 type;
2922 it has rank-2 types on the left of a function arrow.
2925 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2926 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2927 that restriction has now been lifted.)
2928 In particular, a forall-type (also called a "type scheme"),
2929 including an operational type class context, is legal:
2931 <listitem> <para> On the left of a function arrow </para> </listitem>
2932 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2933 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2934 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2935 field type signatures.</para> </listitem>
2936 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2937 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2939 There is one place you cannot put a <literal>forall</literal>:
2940 you cannot instantiate a type variable with a forall-type. So you cannot
2941 make a forall-type the argument of a type constructor. So these types are illegal:
2943 x1 :: [forall a. a->a]
2944 x2 :: (forall a. a->a, Int)
2945 x3 :: Maybe (forall a. a->a)
2947 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2948 a type variable any more!
2957 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2958 the types of the constructor arguments. Here are several examples:
2964 data T a = T1 (forall b. b -> b -> b) a
2966 data MonadT m = MkMonad { return :: forall a. a -> m a,
2967 bind :: forall a b. m a -> (a -> m b) -> m b
2970 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2976 The constructors have rank-2 types:
2982 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2983 MkMonad :: forall m. (forall a. a -> m a)
2984 -> (forall a b. m a -> (a -> m b) -> m b)
2986 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2992 Notice that you don't need to use a <literal>forall</literal> if there's an
2993 explicit context. For example in the first argument of the
2994 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2995 prefixed to the argument type. The implicit <literal>forall</literal>
2996 quantifies all type variables that are not already in scope, and are
2997 mentioned in the type quantified over.
3001 As for type signatures, implicit quantification happens for non-overloaded
3002 types too. So if you write this:
3005 data T a = MkT (Either a b) (b -> b)
3008 it's just as if you had written this:
3011 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3014 That is, since the type variable <literal>b</literal> isn't in scope, it's
3015 implicitly universally quantified. (Arguably, it would be better
3016 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3017 where that is what is wanted. Feedback welcomed.)
3021 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3022 the constructor to suitable values, just as usual. For example,
3033 a3 = MkSwizzle reverse
3036 a4 = let r x = Just x
3043 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3044 mkTs f x y = [T1 f x, T1 f y]
3050 The type of the argument can, as usual, be more general than the type
3051 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3052 does not need the <literal>Ord</literal> constraint.)
3056 When you use pattern matching, the bound variables may now have
3057 polymorphic types. For example:
3063 f :: T a -> a -> (a, Char)
3064 f (T1 w k) x = (w k x, w 'c' 'd')
3066 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3067 g (MkSwizzle s) xs f = s (map f (s xs))
3069 h :: MonadT m -> [m a] -> m [a]
3070 h m [] = return m []
3071 h m (x:xs) = bind m x $ \y ->
3072 bind m (h m xs) $ \ys ->
3079 In the function <function>h</function> we use the record selectors <literal>return</literal>
3080 and <literal>bind</literal> to extract the polymorphic bind and return functions
3081 from the <literal>MonadT</literal> data structure, rather than using pattern
3087 <title>Type inference</title>
3090 In general, type inference for arbitrary-rank types is undecidable.
3091 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3092 to get a decidable algorithm by requiring some help from the programmer.
3093 We do not yet have a formal specification of "some help" but the rule is this:
3096 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3097 provides an explicit polymorphic type for x, or GHC's type inference will assume
3098 that x's type has no foralls in it</emphasis>.
3101 What does it mean to "provide" an explicit type for x? You can do that by
3102 giving a type signature for x directly, using a pattern type signature
3103 (<xref linkend="scoped-type-variables"/>), thus:
3105 \ f :: (forall a. a->a) -> (f True, f 'c')
3107 Alternatively, you can give a type signature to the enclosing
3108 context, which GHC can "push down" to find the type for the variable:
3110 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3112 Here the type signature on the expression can be pushed inwards
3113 to give a type signature for f. Similarly, and more commonly,
3114 one can give a type signature for the function itself:
3116 h :: (forall a. a->a) -> (Bool,Char)
3117 h f = (f True, f 'c')
3119 You don't need to give a type signature if the lambda bound variable
3120 is a constructor argument. Here is an example we saw earlier:
3122 f :: T a -> a -> (a, Char)
3123 f (T1 w k) x = (w k x, w 'c' 'd')
3125 Here we do not need to give a type signature to <literal>w</literal>, because
3126 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3133 <sect3 id="implicit-quant">
3134 <title>Implicit quantification</title>
3137 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3138 user-written types, if and only if there is no explicit <literal>forall</literal>,
3139 GHC finds all the type variables mentioned in the type that are not already
3140 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3144 f :: forall a. a -> a
3151 h :: forall b. a -> b -> b
3157 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3160 f :: (a -> a) -> Int
3162 f :: forall a. (a -> a) -> Int
3164 f :: (forall a. a -> a) -> Int
3167 g :: (Ord a => a -> a) -> Int
3168 -- MEANS the illegal type
3169 g :: forall a. (Ord a => a -> a) -> Int
3171 g :: (forall a. Ord a => a -> a) -> Int
3173 The latter produces an illegal type, which you might think is silly,
3174 but at least the rule is simple. If you want the latter type, you
3175 can write your for-alls explicitly. Indeed, doing so is strongly advised
3184 <sect2 id="scoped-type-variables">
3185 <title>Scoped type variables
3189 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3191 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3192 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3193 <listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
3197 f (xs::[a]) = ys ++ ys
3202 The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
3203 This brings the type variable <literal>a</literal> into scope; it scopes over
3204 all the patterns and right hand sides for this equation for <function>f</function>.
3205 In particular, it is in scope at the type signature for <varname>y</varname>.
3209 At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
3210 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
3211 implicitly universally quantified. (If there are no type variables in
3212 scope, all type variables mentioned in the signature are universally
3213 quantified, which is just as in Haskell 98.) In this case, since <varname>a</varname>
3214 is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
3215 the same as that of <varname>xs</varname>. In Haskell 98 it is not possible to declare
3216 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3217 it becomes possible to do so.
3221 Scoped type variables are implemented in both GHC and Hugs. Where the
3222 implementations differ from the specification below, those differences
3227 So much for the basic idea. Here are the details.
3231 <title>What a scoped type variable means</title>
3233 A lexically-scoped type variable is simply
3234 the name for a type. The restriction it expresses is that all occurrences
3235 of the same name mean the same type. For example:
3237 f :: [Int] -> Int -> Int
3238 f (xs::[a]) (y::a) = (head xs + y) :: a
3240 The pattern type signatures on the left hand side of
3241 <literal>f</literal> express the fact that <literal>xs</literal>
3242 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
3243 must have this same type. The type signature on the expression <literal>(head xs)</literal>
3244 specifies that this expression must have the same type <literal>a</literal>.
3245 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
3246 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
3247 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
3248 rules, which specified that a pattern-bound type variable should be universally quantified.)
3249 For example, all of these are legal:</para>
3252 t (x::a) (y::a) = x+y*2
3254 f (x::a) (y::b) = [x,y] -- a unifies with b
3256 g (x::a) = x + 1::Int -- a unifies with Int
3258 h x = let k (y::a) = [x,y] -- a is free in the
3259 in k x -- environment
3261 k (x::a) True = ... -- a unifies with Int
3262 k (x::Int) False = ...
3265 w (x::a) = x -- a unifies with [b]
3271 <title>Scope and implicit quantification</title>
3279 All the type variables mentioned in a pattern,
3280 that are not already in scope,
3281 are brought into scope by the pattern. We describe this set as
3282 the <emphasis>type variables bound by the pattern</emphasis>.
3285 f (x::a) = let g (y::(a,b)) = fst y
3289 The pattern <literal>(x::a)</literal> brings the type variable
3290 <literal>a</literal> into scope, as well as the term
3291 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
3292 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
3293 and brings into scope the type variable <literal>b</literal>.
3299 The type variable(s) bound by the pattern have the same scope
3300 as the term variable(s) bound by the pattern. For example:
3303 f (x::a) = <...rhs of f...>
3304 (p::b, q::b) = (1,2)
3305 in <...body of let...>
3307 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
3308 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
3309 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
3310 just like <literal>p</literal> and <literal>q</literal> do.
3311 Indeed, the newly bound type variables also scope over any ordinary, separate
3312 type signatures in the <literal>let</literal> group.
3319 The type variables bound by the pattern may be
3320 mentioned in ordinary type signatures or pattern
3321 type signatures anywhere within their scope.
3328 In ordinary type signatures, any type variable mentioned in the
3329 signature that is in scope is <emphasis>not</emphasis> universally quantified.
3337 Ordinary type signatures do not bring any new type variables
3338 into scope (except in the type signature itself!). So this is illegal:
3345 It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
3346 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
3347 and that is an incorrect typing.
3354 The pattern type signature is a monotype:
3359 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
3363 The type variables bound by a pattern type signature can only be instantiated to monotypes,
3364 not to type schemes.
3368 There is no implicit universal quantification on pattern type signatures (in contrast to
3369 ordinary type signatures).
3379 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3380 scope over the methods defined in the <literal>where</literal> part. For example:
3394 (Not implemented in Hugs yet, Dec 98).
3404 <sect3 id="decl-type-sigs">
3405 <title>Declaration type signatures</title>
3406 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3407 quantification (using <literal>forall</literal>) brings into scope the
3408 explicitly-quantified
3409 type variables, in the definition of the named function(s). For example:
3411 f :: forall a. [a] -> [a]
3412 f (x:xs) = xs ++ [ x :: a ]
3414 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3415 the definition of "<literal>f</literal>".
3417 <para>This only happens if the quantification in <literal>f</literal>'s type
3418 signature is explicit. For example:
3421 g (x:xs) = xs ++ [ x :: a ]
3423 This program will be rejected, because "<literal>a</literal>" does not scope
3424 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3425 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3426 quantification rules.
3430 <sect3 id="pattern-type-sigs">
3431 <title>Where a pattern type signature can occur</title>
3434 A pattern type signature can occur in any pattern. For example:
3439 A pattern type signature can be on an arbitrary sub-pattern, not
3444 f ((x,y)::(a,b)) = (y,x) :: (b,a)
3453 Pattern type signatures, including the result part, can be used
3454 in lambda abstractions:
3457 (\ (x::a, y) :: a -> x)
3464 Pattern type signatures, including the result part, can be used
3465 in <literal>case</literal> expressions:
3468 case e of { ((x::a, y) :: (a,b)) -> x }
3471 Note that the <literal>-></literal> symbol in a case alternative
3472 leads to difficulties when parsing a type signature in the pattern: in
3473 the absence of the extra parentheses in the example above, the parser
3474 would try to interpret the <literal>-></literal> as a function
3475 arrow and give a parse error later.
3483 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
3484 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3485 token or a parenthesised type of some sort). To see why,
3486 consider how one would parse this:
3500 Pattern type signatures can bind existential type variables.
3505 data T = forall a. MkT [a]
3508 f (MkT [t::a]) = MkT t3
3521 Pattern type signatures
3522 can be used in pattern bindings:
3525 f x = let (y, z::a) = x in ...
3526 f1 x = let (y, z::Int) = x in ...
3527 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3528 f3 :: (b->b) = \x -> x
3531 In all such cases, the binding is not generalised over the pattern-bound
3532 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3533 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3534 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3535 In contrast, the binding
3540 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3541 in <literal>f4</literal>'s scope.
3547 <para>Pattern type signatures are completely orthogonal to ordinary, separate
3548 type signatures. The two can be used independently or together.</para>
3552 <sect3 id="result-type-sigs">
3553 <title>Result type signatures</title>
3556 The result type of a function can be given a signature, thus:
3560 f (x::a) :: [a] = [x,x,x]
3564 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
3565 result type. Sometimes this is the only way of naming the type variable
3570 f :: Int -> [a] -> [a]
3571 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
3572 in \xs -> map g (reverse xs `zip` xs)
3577 The type variables bound in a result type signature scope over the right hand side
3578 of the definition. However, consider this corner-case:
3580 rev1 :: [a] -> [a] = \xs -> reverse xs
3582 foo ys = rev (ys::[a])
3584 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
3585 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
3586 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
3587 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
3588 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
3591 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
3592 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
3596 rev1 :: [a] -> [a] = \xs -> reverse xs
3601 Result type signatures are not yet implemented in Hugs.
3608 <sect2 id="deriving-typeable">
3609 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3612 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3613 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3614 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3615 classes <literal>Eq</literal>, <literal>Ord</literal>,
3616 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3619 GHC extends this list with two more classes that may be automatically derived
3620 (provided the <option>-fglasgow-exts</option> flag is specified):
3621 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3622 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3623 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3625 <para>An instance of <literal>Typeable</literal> can only be derived if the
3626 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3627 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3629 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3630 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3632 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3633 are used, and only <literal>Typeable1</literal> up to
3634 <literal>Typeable7</literal> are provided in the library.)
3635 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3636 class, whose kind suits that of the data type constructor, and
3637 then writing the data type instance by hand.
3641 <sect2 id="newtype-deriving">
3642 <title>Generalised derived instances for newtypes</title>
3645 When you define an abstract type using <literal>newtype</literal>, you may want
3646 the new type to inherit some instances from its representation. In
3647 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3648 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3649 other classes you have to write an explicit instance declaration. For
3650 example, if you define
3653 newtype Dollars = Dollars Int
3656 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3657 explicitly define an instance of <literal>Num</literal>:
3660 instance Num Dollars where
3661 Dollars a + Dollars b = Dollars (a+b)
3664 All the instance does is apply and remove the <literal>newtype</literal>
3665 constructor. It is particularly galling that, since the constructor
3666 doesn't appear at run-time, this instance declaration defines a
3667 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3668 dictionary, only slower!
3672 <sect3> <title> Generalising the deriving clause </title>
3674 GHC now permits such instances to be derived instead, so one can write
3676 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3679 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3680 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3681 derives an instance declaration of the form
3684 instance Num Int => Num Dollars
3687 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3691 We can also derive instances of constructor classes in a similar
3692 way. For example, suppose we have implemented state and failure monad
3693 transformers, such that
3696 instance Monad m => Monad (State s m)
3697 instance Monad m => Monad (Failure m)
3699 In Haskell 98, we can define a parsing monad by
3701 type Parser tok m a = State [tok] (Failure m) a
3704 which is automatically a monad thanks to the instance declarations
3705 above. With the extension, we can make the parser type abstract,
3706 without needing to write an instance of class <literal>Monad</literal>, via
3709 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3712 In this case the derived instance declaration is of the form
3714 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3717 Notice that, since <literal>Monad</literal> is a constructor class, the
3718 instance is a <emphasis>partial application</emphasis> of the new type, not the
3719 entire left hand side. We can imagine that the type declaration is
3720 ``eta-converted'' to generate the context of the instance
3725 We can even derive instances of multi-parameter classes, provided the
3726 newtype is the last class parameter. In this case, a ``partial
3727 application'' of the class appears in the <literal>deriving</literal>
3728 clause. For example, given the class
3731 class StateMonad s m | m -> s where ...
3732 instance Monad m => StateMonad s (State s m) where ...
3734 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3736 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3737 deriving (Monad, StateMonad [tok])
3740 The derived instance is obtained by completing the application of the
3741 class to the new type:
3744 instance StateMonad [tok] (State [tok] (Failure m)) =>
3745 StateMonad [tok] (Parser tok m)
3750 As a result of this extension, all derived instances in newtype
3751 declarations are treated uniformly (and implemented just by reusing
3752 the dictionary for the representation type), <emphasis>except</emphasis>
3753 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3754 the newtype and its representation.
3758 <sect3> <title> A more precise specification </title>
3760 Derived instance declarations are constructed as follows. Consider the
3761 declaration (after expansion of any type synonyms)
3764 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3770 The type <literal>t</literal> is an arbitrary type
3773 The <literal>vk+1...vn</literal> are type variables which do not occur in
3774 <literal>t</literal>, and
3777 The <literal>ci</literal> are partial applications of
3778 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3779 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3782 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3783 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3784 should not "look through" the type or its constructor. You can still
3785 derive these classes for a newtype, but it happens in the usual way, not
3786 via this new mechanism.
3789 Then, for each <literal>ci</literal>, the derived instance
3792 instance ci (t vk+1...v) => ci (T v1...vp)
3794 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3795 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3799 As an example which does <emphasis>not</emphasis> work, consider
3801 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3803 Here we cannot derive the instance
3805 instance Monad (State s m) => Monad (NonMonad m)
3808 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3809 and so cannot be "eta-converted" away. It is a good thing that this
3810 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3811 not, in fact, a monad --- for the same reason. Try defining
3812 <literal>>>=</literal> with the correct type: you won't be able to.
3816 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3817 important, since we can only derive instances for the last one. If the
3818 <literal>StateMonad</literal> class above were instead defined as
3821 class StateMonad m s | m -> s where ...
3824 then we would not have been able to derive an instance for the
3825 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3826 classes usually have one "main" parameter for which deriving new
3827 instances is most interesting.
3829 <para>Lastly, all of this applies only for classes other than
3830 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3831 and <literal>Data</literal>, for which the built-in derivation applies (section
3832 4.3.3. of the Haskell Report).
3833 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3834 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3835 the standard method is used or the one described here.)
3841 <sect2 id="typing-binds">
3842 <title>Generalised typing of mutually recursive bindings</title>
3845 The Haskell Report specifies that a group of bindings (at top level, or in a
3846 <literal>let</literal> or <literal>where</literal>) should be sorted into
3847 strongly-connected components, and then type-checked in dependency order
3848 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3849 Report, Section 4.5.1</ulink>).
3850 As each group is type-checked, any binders of the group that
3852 an explicit type signature are put in the type environment with the specified
3854 and all others are monomorphic until the group is generalised
3855 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3858 <para>Following a suggestion of Mark Jones, in his paper
3859 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3861 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3863 <emphasis>the dependency analysis ignores references to variables that have an explicit
3864 type signature</emphasis>.
3865 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3866 typecheck. For example, consider:
3868 f :: Eq a => a -> Bool
3869 f x = (x == x) || g True || g "Yes"
3871 g y = (y <= y) || f True
3873 This is rejected by Haskell 98, but under Jones's scheme the definition for
3874 <literal>g</literal> is typechecked first, separately from that for
3875 <literal>f</literal>,
3876 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3877 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3878 type is generalised, to get
3880 g :: Ord a => a -> Bool
3882 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3883 <literal>g</literal> in the type environment.
3887 The same refined dependency analysis also allows the type signatures of
3888 mutually-recursive functions to have different contexts, something that is illegal in
3889 Haskell 98 (Section 4.5.2, last sentence). With
3890 <option>-fglasgow-exts</option>
3891 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3892 type signatures; in practice this means that only variables bound by the same
3893 pattern binding must have the same context. For example, this is fine:
3895 f :: Eq a => a -> Bool
3896 f x = (x == x) || g True
3898 g :: Ord a => a -> Bool
3899 g y = (y <= y) || f True
3905 <!-- ==================== End of type system extensions ================= -->
3907 <!-- ====================== Generalised algebraic data types ======================= -->
3910 <title>Generalised Algebraic Data Types</title>
3912 <para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
3913 to give the type signatures of constructors explicitly. For example:
3916 Lit :: Int -> Term Int
3917 Succ :: Term Int -> Term Int
3918 IsZero :: Term Int -> Term Bool
3919 If :: Term Bool -> Term a -> Term a -> Term a
3920 Pair :: Term a -> Term b -> Term (a,b)
3922 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3923 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3924 for these <literal>Terms</literal>:
3928 eval (Succ t) = 1 + eval t
3929 eval (IsZero t) = eval t == 0
3930 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3931 eval (Pair e1 e2) = (eval e1, eval e2)
3933 These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
3935 <para> The extensions to GHC are these:
3938 Data type declarations have a 'where' form, as exemplified above. The type signature of
3939 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3940 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3941 have no scope. Indeed, one can write a kind signature instead:
3943 data Term :: * -> * where ...
3945 or even a mixture of the two:
3947 data Foo a :: (* -> *) -> * where ...
3949 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3952 data Foo a (b :: * -> *) where ...
3957 There are no restrictions on the type of the data constructor, except that the result
3958 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3959 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3963 You can use record syntax on a GADT-style data type declaration:
3967 Lit { val :: Int } :: Term Int
3968 Succ { num :: Term Int } :: Term Int
3969 Pred { num :: Term Int } :: Term Int
3970 IsZero { arg :: Term Int } :: Term Bool
3971 Pair { arg1 :: Term a
3974 If { cnd :: Term Bool
3979 For every constructor that has a field <literal>f</literal>, (a) the type of
3980 field <literal>f</literal> must be the same; and (b) the
3981 result type of the constructor must be the same; both modulo alpha conversion.
3982 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3984 single name. Although their field types are both <literal>Term Int</literal>,
3985 their selector functions actually have different types:
3988 num :: Term Int -> Term Int
3989 arg :: Term Bool -> Term Int
3992 At the moment, record updates are not yet possible with GADT, so support is
3993 limited to record construction, selection and pattern matching:
3996 someTerm :: Term Bool
3997 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
4000 eval Lit { val = i } = i
4001 eval Succ { num = t } = eval t + 1
4002 eval Pred { num = t } = eval t - 1
4003 eval IsZero { arg = t } = eval t == 0
4004 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
4005 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
4011 You can use strictness annotations, in the obvious places
4012 in the constructor type:
4015 Lit :: !Int -> Term Int
4016 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
4017 Pair :: Term a -> Term b -> Term (a,b)
4022 You can use a <literal>deriving</literal> clause on a GADT-style data type
4023 declaration, but only if the data type could also have been declared in
4024 Haskell-98 syntax. For example, these two declarations are equivalent
4026 data Maybe1 a where {
4027 Nothing1 :: Maybe a ;
4028 Just1 :: a -> Maybe a
4029 } deriving( Eq, Ord )
4031 data Maybe2 a = Nothing2 | Just2 a
4034 This simply allows you to declare a vanilla Haskell-98 data type using the
4035 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
4039 Pattern matching causes type refinement. For example, in the right hand side of the equation
4044 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
4045 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
4046 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
4048 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
4049 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
4050 occur. However, the refinement is quite general. For example, if we had:
4052 eval :: Term a -> a -> a
4053 eval (Lit i) j = i+j
4055 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
4056 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
4057 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
4063 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
4065 data T a = forall b. MkT b (b->a)
4066 data T' a where { MKT :: b -> (b->a) -> T' a }
4071 <!-- ====================== End of Generalised algebraic data types ======================= -->
4073 <!-- ====================== TEMPLATE HASKELL ======================= -->
4075 <sect1 id="template-haskell">
4076 <title>Template Haskell</title>
4078 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
4079 Template Haskell at <ulink url="http://www.haskell.org/th/">
4080 http://www.haskell.org/th/</ulink>, while
4082 the main technical innovations is discussed in "<ulink
4083 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4084 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4085 The details of the Template Haskell design are still in flux. Make sure you
4086 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
4087 (search for the type ExpQ).
4088 [Temporary: many changes to the original design are described in
4089 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4090 Not all of these changes are in GHC 6.2.]
4093 <para> The first example from that paper is set out below as a worked example to help get you started.
4097 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4098 Tim Sheard is going to expand it.)
4102 <title>Syntax</title>
4104 <para> Template Haskell has the following new syntactic
4105 constructions. You need to use the flag
4106 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4107 </indexterm>to switch these syntactic extensions on
4108 (<option>-fth</option> is no longer implied by
4109 <option>-fglasgow-exts</option>).</para>
4113 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4114 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4115 There must be no space between the "$" and the identifier or parenthesis. This use
4116 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4117 of "." as an infix operator. If you want the infix operator, put spaces around it.
4119 <para> A splice can occur in place of
4121 <listitem><para> an expression; the spliced expression must
4122 have type <literal>Q Exp</literal></para></listitem>
4123 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4124 <listitem><para> [Planned, but not implemented yet.] a
4125 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4127 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4128 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4134 A expression quotation is written in Oxford brackets, thus:
4136 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4137 the quotation has type <literal>Expr</literal>.</para></listitem>
4138 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4139 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4140 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4141 the quotation has type <literal>Type</literal>.</para></listitem>
4142 </itemizedlist></para></listitem>
4145 Reification is written thus:
4147 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4148 has type <literal>Dec</literal>. </para></listitem>
4149 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4150 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4151 <listitem><para> Still to come: fixities </para></listitem>
4153 </itemizedlist></para>
4160 <sect2> <title> Using Template Haskell </title>
4164 The data types and monadic constructor functions for Template Haskell are in the library
4165 <literal>Language.Haskell.THSyntax</literal>.
4169 You can only run a function at compile time if it is imported from another module. That is,
4170 you can't define a function in a module, and call it from within a splice in the same module.
4171 (It would make sense to do so, but it's hard to implement.)
4175 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4178 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4179 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4180 compiles and runs a program, and then looks at the result. So it's important that
4181 the program it compiles produces results whose representations are identical to
4182 those of the compiler itself.
4186 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4187 or file-at-a-time). There used to be a restriction to the former two, but that restriction
4192 <sect2> <title> A Template Haskell Worked Example </title>
4193 <para>To help you get over the confidence barrier, try out this skeletal worked example.
4194 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
4201 -- Import our template "pr"
4202 import Printf ( pr )
4204 -- The splice operator $ takes the Haskell source code
4205 -- generated at compile time by "pr" and splices it into
4206 -- the argument of "putStrLn".
4207 main = putStrLn ( $(pr "Hello") )
4213 -- Skeletal printf from the paper.
4214 -- It needs to be in a separate module to the one where
4215 -- you intend to use it.
4217 -- Import some Template Haskell syntax
4218 import Language.Haskell.TH
4220 -- Describe a format string
4221 data Format = D | S | L String
4223 -- Parse a format string. This is left largely to you
4224 -- as we are here interested in building our first ever
4225 -- Template Haskell program and not in building printf.
4226 parse :: String -> [Format]
4229 -- Generate Haskell source code from a parsed representation
4230 -- of the format string. This code will be spliced into
4231 -- the module which calls "pr", at compile time.
4232 gen :: [Format] -> ExpQ
4233 gen [D] = [| \n -> show n |]
4234 gen [S] = [| \s -> s |]
4235 gen [L s] = stringE s
4237 -- Here we generate the Haskell code for the splice
4238 -- from an input format string.
4239 pr :: String -> ExpQ
4240 pr s = gen (parse s)
4243 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
4246 $ ghc --make -fth main.hs -o main.exe
4249 <para>Run "main.exe" and here is your output:</para>
4259 <title>Using Template Haskell with Profiling</title>
4260 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
4262 <para>Template Haskell relies on GHC's built-in bytecode compiler and
4263 interpreter to run the splice expressions. The bytecode interpreter
4264 runs the compiled expression on top of the same runtime on which GHC
4265 itself is running; this means that the compiled code referred to by
4266 the interpreted expression must be compatible with this runtime, and
4267 in particular this means that object code that is compiled for
4268 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
4269 expression, because profiled object code is only compatible with the
4270 profiling version of the runtime.</para>
4272 <para>This causes difficulties if you have a multi-module program
4273 containing Template Haskell code and you need to compile it for
4274 profiling, because GHC cannot load the profiled object code and use it
4275 when executing the splices. Fortunately GHC provides a workaround.
4276 The basic idea is to compile the program twice:</para>
4280 <para>Compile the program or library first the normal way, without
4281 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
4284 <para>Then compile it again with <option>-prof</option>, and
4285 additionally use <option>-osuf
4286 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
4287 to name the object files differentliy (you can choose any suffix
4288 that isn't the normal object suffix here). GHC will automatically
4289 load the object files built in the first step when executing splice
4290 expressions. If you omit the <option>-osuf</option> flag when
4291 building with <option>-prof</option> and Template Haskell is used,
4292 GHC will emit an error message. </para>
4299 <!-- ===================== Arrow notation =================== -->
4301 <sect1 id="arrow-notation">
4302 <title>Arrow notation
4305 <para>Arrows are a generalization of monads introduced by John Hughes.
4306 For more details, see
4311 “Generalising Monads to Arrows”,
4312 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
4313 pp67–111, May 2000.
4319 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
4320 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
4326 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
4327 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
4333 and the arrows web page at
4334 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
4335 With the <option>-farrows</option> flag, GHC supports the arrow
4336 notation described in the second of these papers.
4337 What follows is a brief introduction to the notation;
4338 it won't make much sense unless you've read Hughes's paper.
4339 This notation is translated to ordinary Haskell,
4340 using combinators from the
4341 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4345 <para>The extension adds a new kind of expression for defining arrows:
4347 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
4348 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4350 where <literal>proc</literal> is a new keyword.
4351 The variables of the pattern are bound in the body of the
4352 <literal>proc</literal>-expression,
4353 which is a new sort of thing called a <firstterm>command</firstterm>.
4354 The syntax of commands is as follows:
4356 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
4357 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
4358 | <replaceable>cmd</replaceable><superscript>0</superscript>
4360 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
4361 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
4362 infix operators as for expressions, and
4364 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
4365 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
4366 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
4367 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
4368 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
4369 | <replaceable>fcmd</replaceable>
4371 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
4372 | ( <replaceable>cmd</replaceable> )
4373 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
4375 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
4376 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
4377 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
4378 | <replaceable>cmd</replaceable>
4380 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
4381 except that the bodies are commands instead of expressions.
4385 Commands produce values, but (like monadic computations)
4386 may yield more than one value,
4387 or none, and may do other things as well.
4388 For the most part, familiarity with monadic notation is a good guide to
4390 However the values of expressions, even monadic ones,
4391 are determined by the values of the variables they contain;
4392 this is not necessarily the case for commands.
4396 A simple example of the new notation is the expression
4398 proc x -> f -< x+1
4400 We call this a <firstterm>procedure</firstterm> or
4401 <firstterm>arrow abstraction</firstterm>.
4402 As with a lambda expression, the variable <literal>x</literal>
4403 is a new variable bound within the <literal>proc</literal>-expression.
4404 It refers to the input to the arrow.
4405 In the above example, <literal>-<</literal> is not an identifier but an
4406 new reserved symbol used for building commands from an expression of arrow
4407 type and an expression to be fed as input to that arrow.
4408 (The weird look will make more sense later.)
4409 It may be read as analogue of application for arrows.
4410 The above example is equivalent to the Haskell expression
4412 arr (\ x -> x+1) >>> f
4414 That would make no sense if the expression to the left of
4415 <literal>-<</literal> involves the bound variable <literal>x</literal>.
4416 More generally, the expression to the left of <literal>-<</literal>
4417 may not involve any <firstterm>local variable</firstterm>,
4418 i.e. a variable bound in the current arrow abstraction.
4419 For such a situation there is a variant <literal>-<<</literal>, as in
4421 proc x -> f x -<< x+1
4423 which is equivalent to
4425 arr (\ x -> (f x, x+1)) >>> app
4427 so in this case the arrow must belong to the <literal>ArrowApply</literal>
4429 Such an arrow is equivalent to a monad, so if you're using this form
4430 you may find a monadic formulation more convenient.
4434 <title>do-notation for commands</title>
4437 Another form of command is a form of <literal>do</literal>-notation.
4438 For example, you can write
4447 You can read this much like ordinary <literal>do</literal>-notation,
4448 but with commands in place of monadic expressions.
4449 The first line sends the value of <literal>x+1</literal> as an input to
4450 the arrow <literal>f</literal>, and matches its output against
4451 <literal>y</literal>.
4452 In the next line, the output is discarded.
4453 The arrow <function>returnA</function> is defined in the
4454 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4455 module as <literal>arr id</literal>.
4456 The above example is treated as an abbreviation for
4458 arr (\ x -> (x, x)) >>>
4459 first (arr (\ x -> x+1) >>> f) >>>
4460 arr (\ (y, x) -> (y, (x, y))) >>>
4461 first (arr (\ y -> 2*y) >>> g) >>>
4463 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
4464 first (arr (\ (x, z) -> x*z) >>> h) >>>
4465 arr (\ (t, z) -> t+z) >>>
4468 Note that variables not used later in the composition are projected out.
4469 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
4471 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
4472 module, this reduces to
4474 arr (\ x -> (x+1, x)) >>>
4476 arr (\ (y, x) -> (2*y, (x, y))) >>>
4478 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
4480 arr (\ (t, z) -> t+z)
4482 which is what you might have written by hand.
4483 With arrow notation, GHC keeps track of all those tuples of variables for you.
4487 Note that although the above translation suggests that
4488 <literal>let</literal>-bound variables like <literal>z</literal> must be
4489 monomorphic, the actual translation produces Core,
4490 so polymorphic variables are allowed.
4494 It's also possible to have mutually recursive bindings,
4495 using the new <literal>rec</literal> keyword, as in the following example:
4497 counter :: ArrowCircuit a => a Bool Int
4498 counter = proc reset -> do
4499 rec output <- returnA -< if reset then 0 else next
4500 next <- delay 0 -< output+1
4501 returnA -< output
4503 The translation of such forms uses the <function>loop</function> combinator,
4504 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
4510 <title>Conditional commands</title>
4513 In the previous example, we used a conditional expression to construct the
4515 Sometimes we want to conditionally execute different commands, as in
4522 which is translated to
4524 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
4525 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
4527 Since the translation uses <function>|||</function>,
4528 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
4532 There are also <literal>case</literal> commands, like
4538 y <- h -< (x1, x2)
4542 The syntax is the same as for <literal>case</literal> expressions,
4543 except that the bodies of the alternatives are commands rather than expressions.
4544 The translation is similar to that of <literal>if</literal> commands.
4550 <title>Defining your own control structures</title>
4553 As we're seen, arrow notation provides constructs,
4554 modelled on those for expressions,
4555 for sequencing, value recursion and conditionals.
4556 But suitable combinators,
4557 which you can define in ordinary Haskell,
4558 may also be used to build new commands out of existing ones.
4559 The basic idea is that a command defines an arrow from environments to values.
4560 These environments assign values to the free local variables of the command.
4561 Thus combinators that produce arrows from arrows
4562 may also be used to build commands from commands.
4563 For example, the <literal>ArrowChoice</literal> class includes a combinator
4565 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
4567 so we can use it to build commands:
4569 expr' = proc x -> do
4572 symbol Plus -< ()
4573 y <- term -< ()
4576 symbol Minus -< ()
4577 y <- term -< ()
4580 (The <literal>do</literal> on the first line is needed to prevent the first
4581 <literal><+> ...</literal> from being interpreted as part of the
4582 expression on the previous line.)
4583 This is equivalent to
4585 expr' = (proc x -> returnA -< x)
4586 <+> (proc x -> do
4587 symbol Plus -< ()
4588 y <- term -< ()
4590 <+> (proc x -> do
4591 symbol Minus -< ()
4592 y <- term -< ()
4595 It is essential that this operator be polymorphic in <literal>e</literal>
4596 (representing the environment input to the command
4597 and thence to its subcommands)
4598 and satisfy the corresponding naturality property
4600 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
4602 at least for strict <literal>k</literal>.
4603 (This should be automatic if you're not using <function>seq</function>.)
4604 This ensures that environments seen by the subcommands are environments
4605 of the whole command,
4606 and also allows the translation to safely trim these environments.
4607 The operator must also not use any variable defined within the current
4612 We could define our own operator
4614 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
4615 untilA body cond = proc x ->
4616 if cond x then returnA -< ()
4619 untilA body cond -< x
4621 and use it in the same way.
4622 Of course this infix syntax only makes sense for binary operators;
4623 there is also a more general syntax involving special brackets:
4627 (|untilA (increment -< x+y) (within 0.5 -< x)|)
4634 <title>Primitive constructs</title>
4637 Some operators will need to pass additional inputs to their subcommands.
4638 For example, in an arrow type supporting exceptions,
4639 the operator that attaches an exception handler will wish to pass the
4640 exception that occurred to the handler.
4641 Such an operator might have a type
4643 handleA :: ... => a e c -> a (e,Ex) c -> a e c
4645 where <literal>Ex</literal> is the type of exceptions handled.
4646 You could then use this with arrow notation by writing a command
4648 body `handleA` \ ex -> handler
4650 so that if an exception is raised in the command <literal>body</literal>,
4651 the variable <literal>ex</literal> is bound to the value of the exception
4652 and the command <literal>handler</literal>,
4653 which typically refers to <literal>ex</literal>, is entered.
4654 Though the syntax here looks like a functional lambda,
4655 we are talking about commands, and something different is going on.
4656 The input to the arrow represented by a command consists of values for
4657 the free local variables in the command, plus a stack of anonymous values.
4658 In all the prior examples, this stack was empty.
4659 In the second argument to <function>handleA</function>,
4660 this stack consists of one value, the value of the exception.
4661 The command form of lambda merely gives this value a name.
4666 the values on the stack are paired to the right of the environment.
4667 So operators like <function>handleA</function> that pass
4668 extra inputs to their subcommands can be designed for use with the notation
4669 by pairing the values with the environment in this way.
4670 More precisely, the type of each argument of the operator (and its result)
4671 should have the form
4673 a (...(e,t1), ... tn) t
4675 where <replaceable>e</replaceable> is a polymorphic variable
4676 (representing the environment)
4677 and <replaceable>ti</replaceable> are the types of the values on the stack,
4678 with <replaceable>t1</replaceable> being the <quote>top</quote>.
4679 The polymorphic variable <replaceable>e</replaceable> must not occur in
4680 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
4681 <replaceable>t</replaceable>.
4682 However the arrows involved need not be the same.
4683 Here are some more examples of suitable operators:
4685 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
4686 runReader :: ... => a e c -> a' (e,State) c
4687 runState :: ... => a e c -> a' (e,State) (c,State)
4689 We can supply the extra input required by commands built with the last two
4690 by applying them to ordinary expressions, as in
4694 (|runReader (do { ... })|) s
4696 which adds <literal>s</literal> to the stack of inputs to the command
4697 built using <function>runReader</function>.
4701 The command versions of lambda abstraction and application are analogous to
4702 the expression versions.
4703 In particular, the beta and eta rules describe equivalences of commands.
4704 These three features (operators, lambda abstraction and application)
4705 are the core of the notation; everything else can be built using them,
4706 though the results would be somewhat clumsy.
4707 For example, we could simulate <literal>do</literal>-notation by defining
4709 bind :: Arrow a => a e b -> a (e,b) c -> a e c
4710 u `bind` f = returnA &&& u >>> f
4712 bind_ :: Arrow a => a e b -> a e c -> a e c
4713 u `bind_` f = u `bind` (arr fst >>> f)
4715 We could simulate <literal>if</literal> by defining
4717 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
4718 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
4725 <title>Differences with the paper</title>
4730 <para>Instead of a single form of arrow application (arrow tail) with two
4731 translations, the implementation provides two forms
4732 <quote><literal>-<</literal></quote> (first-order)
4733 and <quote><literal>-<<</literal></quote> (higher-order).
4738 <para>User-defined operators are flagged with banana brackets instead of
4739 a new <literal>form</literal> keyword.
4748 <title>Portability</title>
4751 Although only GHC implements arrow notation directly,
4752 there is also a preprocessor
4754 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
4755 that translates arrow notation into Haskell 98
4756 for use with other Haskell systems.
4757 You would still want to check arrow programs with GHC;
4758 tracing type errors in the preprocessor output is not easy.
4759 Modules intended for both GHC and the preprocessor must observe some
4760 additional restrictions:
4765 The module must import
4766 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
4772 The preprocessor cannot cope with other Haskell extensions.
4773 These would have to go in separate modules.
4779 Because the preprocessor targets Haskell (rather than Core),
4780 <literal>let</literal>-bound variables are monomorphic.
4791 <!-- ==================== BANG PATTERNS ================= -->
4793 <sect1 id="sec-bang-patterns">
4794 <title>Bang patterns
4795 <indexterm><primary>Bang patterns</primary></indexterm>
4797 <para>GHC supports an extension of pattern matching called <emphasis>bang
4798 patterns</emphasis>. Bang patterns are under consideration for Haskell Prime.
4800 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">the
4801 Haskell prime feature description</ulink> contains more discussion and examples
4802 than the material below.
4805 Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
4808 <sect2 id="sec-bang-patterns-informal">
4809 <title>Informal description of bang patterns
4812 The main idea is to add a single new production to the syntax of patterns:
4816 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
4817 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
4822 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
4823 whereas without the bang it would be lazy.
4824 Bang patterns can be nested of course:
4828 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
4829 <literal>y</literal>.
4830 A bang only really has an effect if it precedes a variable or wild-card pattern:
4835 Here, <literal>f3</literal> and <literal>f4</literal> are identical; putting a bang before a pattern that
4836 forces evaluation anyway does nothing.
4838 Bang patterns work in <literal>case</literal> expressions too, of course:
4840 g5 x = let y = f x in body
4841 g6 x = case f x of { y -> body }
4842 g7 x = case f x of { !y -> body }
4844 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
4845 But <literal>g7</literal> evalutes <literal>(f x)</literal>, binds <literal>y</literal> to the
4846 result, and then evaluates <literal>body</literal>.
4848 Bang patterns work in <literal>let</literal> and <literal>where</literal>
4849 definitions too. For example:
4853 is a strict pattern: operationally, it evaluates <literal>e</literal>, matches
4854 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>
4855 The "<literal>!</literal>" should not be regarded as part of the pattern; after all,
4856 in a function argument <literal>![x,y]</literal> means the
4857 same as <literal>[x,y]</literal>. Rather, the "<literal>!</literal>"
4858 is part of the syntax of <literal>let</literal> bindings.
4863 <sect2 id="sec-bang-patterns-sem">
4864 <title>Syntax and semantics
4868 We add a single new production to the syntax of patterns:
4872 There is one problem with syntactic ambiguity. Consider:
4876 Is this a definition of the infix function "<literal>(!)</literal>",
4877 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
4878 ambiguity inf favour of the latter. If you want to define
4879 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
4884 The semantics of Haskell pattern matching is described in <ulink
4885 url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
4886 Section 3.17.2</ulink> of the Haskell Report. To this description add
4887 one extra item 10, saying:
4888 <itemizedlist><listitem><para>Matching
4889 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
4890 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
4891 <listitem><para>otherwise, <literal>pat</literal> is matched against
4892 <literal>v</literal></para></listitem>
4894 </para></listitem></itemizedlist>
4895 Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
4896 Section 3.17.3</ulink>, add a new case (t):
4898 case v of { !pat -> e; _ -> e' }
4899 = v `seq` case v of { pat -> e; _ -> e' }
4902 That leaves let expressions, whose translation is given in
4903 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
4905 of the Haskell Report.
4906 In the translation box, first apply
4907 the following transformation: for each pattern <literal>pi</literal> that is of
4908 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
4909 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
4910 have a bang at the top, apply the rules in the existing box.
4912 <para>The effect of the let rule is to force complete matching of the pattern
4913 <literal>qi</literal> before evaluation of the body is begun. The bang is
4914 retained in the translated form in case <literal>qi</literal> is a variable,
4922 The let-binding can be recursive. However, it is much more common for
4923 the let-binding to be non-recursive, in which case the following law holds:
4924 <literal>(let !p = rhs in body)</literal>
4926 <literal>(case rhs of !p -> body)</literal>
4929 A pattern with a bang at the outermost level is not allowed at the top level of
4935 <!-- ==================== ASSERTIONS ================= -->
4937 <sect1 id="sec-assertions">
4939 <indexterm><primary>Assertions</primary></indexterm>
4943 If you want to make use of assertions in your standard Haskell code, you
4944 could define a function like the following:
4950 assert :: Bool -> a -> a
4951 assert False x = error "assertion failed!"
4958 which works, but gives you back a less than useful error message --
4959 an assertion failed, but which and where?
4963 One way out is to define an extended <function>assert</function> function which also
4964 takes a descriptive string to include in the error message and
4965 perhaps combine this with the use of a pre-processor which inserts
4966 the source location where <function>assert</function> was used.
4970 Ghc offers a helping hand here, doing all of this for you. For every
4971 use of <function>assert</function> in the user's source:
4977 kelvinToC :: Double -> Double
4978 kelvinToC k = assert (k >= 0.0) (k+273.15)
4984 Ghc will rewrite this to also include the source location where the
4991 assert pred val ==> assertError "Main.hs|15" pred val
4997 The rewrite is only performed by the compiler when it spots
4998 applications of <function>Control.Exception.assert</function>, so you
4999 can still define and use your own versions of
5000 <function>assert</function>, should you so wish. If not, import
5001 <literal>Control.Exception</literal> to make use
5002 <function>assert</function> in your code.
5006 GHC ignores assertions when optimisation is turned on with the
5007 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
5008 <literal>assert pred e</literal> will be rewritten to
5009 <literal>e</literal>. You can also disable assertions using the
5010 <option>-fignore-asserts</option>
5011 option<indexterm><primary><option>-fignore-asserts</option></primary>
5012 </indexterm>.</para>
5015 Assertion failures can be caught, see the documentation for the
5016 <literal>Control.Exception</literal> library for the details.
5022 <!-- =============================== PRAGMAS =========================== -->
5024 <sect1 id="pragmas">
5025 <title>Pragmas</title>
5027 <indexterm><primary>pragma</primary></indexterm>
5029 <para>GHC supports several pragmas, or instructions to the
5030 compiler placed in the source code. Pragmas don't normally affect
5031 the meaning of the program, but they might affect the efficiency
5032 of the generated code.</para>
5034 <para>Pragmas all take the form
5036 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
5038 where <replaceable>word</replaceable> indicates the type of
5039 pragma, and is followed optionally by information specific to that
5040 type of pragma. Case is ignored in
5041 <replaceable>word</replaceable>. The various values for
5042 <replaceable>word</replaceable> that GHC understands are described
5043 in the following sections; any pragma encountered with an
5044 unrecognised <replaceable>word</replaceable> is (silently)
5047 <sect2 id="deprecated-pragma">
5048 <title>DEPRECATED pragma</title>
5049 <indexterm><primary>DEPRECATED</primary>
5052 <para>The DEPRECATED pragma lets you specify that a particular
5053 function, class, or type, is deprecated. There are two
5058 <para>You can deprecate an entire module thus:</para>
5060 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
5063 <para>When you compile any module that import
5064 <literal>Wibble</literal>, GHC will print the specified
5069 <para>You can deprecate a function, class, type, or data constructor, with the
5070 following top-level declaration:</para>
5072 {-# DEPRECATED f, C, T "Don't use these" #-}
5074 <para>When you compile any module that imports and uses any
5075 of the specified entities, GHC will print the specified
5077 <para> You can only depecate entities declared at top level in the module
5078 being compiled, and you can only use unqualified names in the list of
5079 entities being deprecated. A capitalised name, such as <literal>T</literal>
5080 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
5081 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
5082 both are in scope. If both are in scope, there is currently no way to deprecate
5083 one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
5086 Any use of the deprecated item, or of anything from a deprecated
5087 module, will be flagged with an appropriate message. However,
5088 deprecations are not reported for
5089 (a) uses of a deprecated function within its defining module, and
5090 (b) uses of a deprecated function in an export list.
5091 The latter reduces spurious complaints within a library
5092 in which one module gathers together and re-exports
5093 the exports of several others.
5095 <para>You can suppress the warnings with the flag
5096 <option>-fno-warn-deprecations</option>.</para>
5099 <sect2 id="include-pragma">
5100 <title>INCLUDE pragma</title>
5102 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
5103 of C header files that should be <literal>#include</literal>'d into
5104 the C source code generated by the compiler for the current module (if
5105 compiling via C). For example:</para>
5108 {-# INCLUDE "foo.h" #-}
5109 {-# INCLUDE <stdio.h> #-}</programlisting>
5111 <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
5112 your source file with any <literal>OPTIONS_GHC</literal>
5115 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
5116 to the <option>-#include</option> option (<xref
5117 linkend="options-C-compiler" />), because the
5118 <literal>INCLUDE</literal> pragma is understood by other
5119 compilers. Yet another alternative is to add the include file to each
5120 <literal>foreign import</literal> declaration in your code, but we
5121 don't recommend using this approach with GHC.</para>
5124 <sect2 id="inline-noinline-pragma">
5125 <title>INLINE and NOINLINE pragmas</title>
5127 <para>These pragmas control the inlining of function
5130 <sect3 id="inline-pragma">
5131 <title>INLINE pragma</title>
5132 <indexterm><primary>INLINE</primary></indexterm>
5134 <para>GHC (with <option>-O</option>, as always) tries to
5135 inline (or “unfold”) functions/values that are
5136 “small enough,” thus avoiding the call overhead
5137 and possibly exposing other more-wonderful optimisations.
5138 Normally, if GHC decides a function is “too
5139 expensive” to inline, it will not do so, nor will it
5140 export that unfolding for other modules to use.</para>
5142 <para>The sledgehammer you can bring to bear is the
5143 <literal>INLINE</literal><indexterm><primary>INLINE
5144 pragma</primary></indexterm> pragma, used thusly:</para>
5147 key_function :: Int -> String -> (Bool, Double)
5149 #ifdef __GLASGOW_HASKELL__
5150 {-# INLINE key_function #-}
5154 <para>(You don't need to do the C pre-processor carry-on
5155 unless you're going to stick the code through HBC—it
5156 doesn't like <literal>INLINE</literal> pragmas.)</para>
5158 <para>The major effect of an <literal>INLINE</literal> pragma
5159 is to declare a function's “cost” to be very low.
5160 The normal unfolding machinery will then be very keen to
5163 <para>Syntactically, an <literal>INLINE</literal> pragma for a
5164 function can be put anywhere its type signature could be
5167 <para><literal>INLINE</literal> pragmas are a particularly
5169 <literal>then</literal>/<literal>return</literal> (or
5170 <literal>bind</literal>/<literal>unit</literal>) functions in
5171 a monad. For example, in GHC's own
5172 <literal>UniqueSupply</literal> monad code, we have:</para>
5175 #ifdef __GLASGOW_HASKELL__
5176 {-# INLINE thenUs #-}
5177 {-# INLINE returnUs #-}
5181 <para>See also the <literal>NOINLINE</literal> pragma (<xref
5182 linkend="noinline-pragma"/>).</para>
5185 <sect3 id="noinline-pragma">
5186 <title>NOINLINE pragma</title>
5188 <indexterm><primary>NOINLINE</primary></indexterm>
5189 <indexterm><primary>NOTINLINE</primary></indexterm>
5191 <para>The <literal>NOINLINE</literal> pragma does exactly what
5192 you'd expect: it stops the named function from being inlined
5193 by the compiler. You shouldn't ever need to do this, unless
5194 you're very cautious about code size.</para>
5196 <para><literal>NOTINLINE</literal> is a synonym for
5197 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
5198 specified by Haskell 98 as the standard way to disable
5199 inlining, so it should be used if you want your code to be
5203 <sect3 id="phase-control">
5204 <title>Phase control</title>
5206 <para> Sometimes you want to control exactly when in GHC's
5207 pipeline the INLINE pragma is switched on. Inlining happens
5208 only during runs of the <emphasis>simplifier</emphasis>. Each
5209 run of the simplifier has a different <emphasis>phase
5210 number</emphasis>; the phase number decreases towards zero.
5211 If you use <option>-dverbose-core2core</option> you'll see the
5212 sequence of phase numbers for successive runs of the
5213 simplifier. In an INLINE pragma you can optionally specify a
5217 <para>"<literal>INLINE[k] f</literal>" means: do not inline
5218 <literal>f</literal>
5219 until phase <literal>k</literal>, but from phase
5220 <literal>k</literal> onwards be very keen to inline it.
5223 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
5224 <literal>f</literal>
5225 until phase <literal>k</literal>, but from phase
5226 <literal>k</literal> onwards do not inline it.
5229 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
5230 <literal>f</literal>
5231 until phase <literal>k</literal>, but from phase
5232 <literal>k</literal> onwards be willing to inline it (as if
5233 there was no pragma).
5236 <para>"<literal>INLINE[~k] f</literal>" means: be willing to inline
5237 <literal>f</literal>
5238 until phase <literal>k</literal>, but from phase
5239 <literal>k</literal> onwards do not inline it.
5242 The same information is summarised here:
5244 -- Before phase 2 Phase 2 and later
5245 {-# INLINE [2] f #-} -- No Yes
5246 {-# INLINE [~2] f #-} -- Yes No
5247 {-# NOINLINE [2] f #-} -- No Maybe
5248 {-# NOINLINE [~2] f #-} -- Maybe No
5250 {-# INLINE f #-} -- Yes Yes
5251 {-# NOINLINE f #-} -- No No
5253 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
5254 function body is small, or it is applied to interesting-looking arguments etc).
5255 Another way to understand the semantics is this:
5257 <listitem><para>For both INLINE and NOINLINE, the phase number says
5258 when inlining is allowed at all.</para></listitem>
5259 <listitem><para>The INLINE pragma has the additional effect of making the
5260 function body look small, so that when inlining is allowed it is very likely to
5265 <para>The same phase-numbering control is available for RULES
5266 (<xref linkend="rewrite-rules"/>).</para>
5270 <sect2 id="language-pragma">
5271 <title>LANGUAGE pragma</title>
5273 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
5274 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
5276 <para>This allows language extensions to be enabled in a portable way.
5277 It is the intention that all Haskell compilers support the
5278 <literal>LANGUAGE</literal> pragma with the same syntax, although not
5279 all extensions are supported by all compilers, of
5280 course. The <literal>LANGUAGE</literal> pragma should be used instead
5281 of <literal>OPTIONS_GHC</literal>, if possible.</para>
5283 <para>For example, to enable the FFI and preprocessing with CPP:</para>
5285 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
5287 <para>Any extension from the <literal>Extension</literal> type defined in
5289 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>
5293 <sect2 id="line-pragma">
5294 <title>LINE pragma</title>
5296 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
5297 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
5298 <para>This pragma is similar to C's <literal>#line</literal>
5299 pragma, and is mainly for use in automatically generated Haskell
5300 code. It lets you specify the line number and filename of the
5301 original code; for example</para>
5303 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
5305 <para>if you'd generated the current file from something called
5306 <filename>Foo.vhs</filename> and this line corresponds to line
5307 42 in the original. GHC will adjust its error messages to refer
5308 to the line/file named in the <literal>LINE</literal>
5312 <sect2 id="options-pragma">
5313 <title>OPTIONS_GHC pragma</title>
5314 <indexterm><primary>OPTIONS_GHC</primary>
5316 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
5319 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
5320 additional options that are given to the compiler when compiling
5321 this source file. See <xref linkend="source-file-options"/> for
5324 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
5325 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
5329 <title>RULES pragma</title>
5331 <para>The RULES pragma lets you specify rewrite rules. It is
5332 described in <xref linkend="rewrite-rules"/>.</para>
5335 <sect2 id="specialize-pragma">
5336 <title>SPECIALIZE pragma</title>
5338 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5339 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
5340 <indexterm><primary>overloading, death to</primary></indexterm>
5342 <para>(UK spelling also accepted.) For key overloaded
5343 functions, you can create extra versions (NB: more code space)
5344 specialised to particular types. Thus, if you have an
5345 overloaded function:</para>
5348 hammeredLookup :: Ord key => [(key, value)] -> key -> value
5351 <para>If it is heavily used on lists with
5352 <literal>Widget</literal> keys, you could specialise it as
5356 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
5359 <para>A <literal>SPECIALIZE</literal> pragma for a function can
5360 be put anywhere its type signature could be put.</para>
5362 <para>A <literal>SPECIALIZE</literal> has the effect of generating
5363 (a) a specialised version of the function and (b) a rewrite rule
5364 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
5365 un-specialised function into a call to the specialised one.</para>
5367 <para>The type in a SPECIALIZE pragma can be any type that is less
5368 polymorphic than the type of the original function. In concrete terms,
5369 if the original function is <literal>f</literal> then the pragma
5371 {-# SPECIALIZE f :: <type> #-}
5373 is valid if and only if the defintion
5375 f_spec :: <type>
5378 is valid. Here are some examples (where we only give the type signature
5379 for the original function, not its code):
5381 f :: Eq a => a -> b -> b
5382 {-# SPECIALISE f :: Int -> b -> b #-}
5384 g :: (Eq a, Ix b) => a -> b -> b
5385 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
5387 h :: Eq a => a -> a -> a
5388 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
5390 The last of these examples will generate a
5391 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
5392 well. If you use this kind of specialisation, let us know how well it works.
5395 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
5396 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
5397 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
5398 The <literal>INLINE</literal> pragma affects the specialised verison of the
5399 function (only), and applies even if the function is recursive. The motivating
5402 -- A GADT for arrays with type-indexed representation
5404 ArrInt :: !Int -> ByteArray# -> Arr Int
5405 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
5407 (!:) :: Arr e -> Int -> e
5408 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
5409 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
5410 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
5411 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
5413 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
5414 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
5415 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
5416 the specialised function will be inlined. It has two calls to
5417 <literal>(!:)</literal>,
5418 both at type <literal>Int</literal>. Both these calls fire the first
5419 specialisation, whose body is also inlined. The result is a type-based
5420 unrolling of the indexing function.</para>
5421 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
5422 on an ordinarily-recursive function.</para>
5424 <para>Note: In earlier versions of GHC, it was possible to provide your own
5425 specialised function for a given type:
5428 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
5431 This feature has been removed, as it is now subsumed by the
5432 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
5436 <sect2 id="specialize-instance-pragma">
5437 <title>SPECIALIZE instance pragma
5441 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
5442 <indexterm><primary>overloading, death to</primary></indexterm>
5443 Same idea, except for instance declarations. For example:
5446 instance (Eq a) => Eq (Foo a) where {
5447 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
5451 The pragma must occur inside the <literal>where</literal> part
5452 of the instance declaration.
5455 Compatible with HBC, by the way, except perhaps in the placement
5461 <sect2 id="unpack-pragma">
5462 <title>UNPACK pragma</title>
5464 <indexterm><primary>UNPACK</primary></indexterm>
5466 <para>The <literal>UNPACK</literal> indicates to the compiler
5467 that it should unpack the contents of a constructor field into
5468 the constructor itself, removing a level of indirection. For
5472 data T = T {-# UNPACK #-} !Float
5473 {-# UNPACK #-} !Float
5476 <para>will create a constructor <literal>T</literal> containing
5477 two unboxed floats. This may not always be an optimisation: if
5478 the <function>T</function> constructor is scrutinised and the
5479 floats passed to a non-strict function for example, they will
5480 have to be reboxed (this is done automatically by the
5483 <para>Unpacking constructor fields should only be used in
5484 conjunction with <option>-O</option>, in order to expose
5485 unfoldings to the compiler so the reboxing can be removed as
5486 often as possible. For example:</para>
5490 f (T f1 f2) = f1 + f2
5493 <para>The compiler will avoid reboxing <function>f1</function>
5494 and <function>f2</function> by inlining <function>+</function>
5495 on floats, but only when <option>-O</option> is on.</para>
5497 <para>Any single-constructor data is eligible for unpacking; for
5501 data T = T {-# UNPACK #-} !(Int,Int)
5504 <para>will store the two <literal>Int</literal>s directly in the
5505 <function>T</function> constructor, by flattening the pair.
5506 Multi-level unpacking is also supported:</para>
5509 data T = T {-# UNPACK #-} !S
5510 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
5513 <para>will store two unboxed <literal>Int#</literal>s
5514 directly in the <function>T</function> constructor. The
5515 unpacker can see through newtypes, too.</para>
5517 <para>If a field cannot be unpacked, you will not get a warning,
5518 so it might be an idea to check the generated code with
5519 <option>-ddump-simpl</option>.</para>
5521 <para>See also the <option>-funbox-strict-fields</option> flag,
5522 which essentially has the effect of adding
5523 <literal>{-# UNPACK #-}</literal> to every strict
5524 constructor field.</para>
5529 <!-- ======================= REWRITE RULES ======================== -->
5531 <sect1 id="rewrite-rules">
5532 <title>Rewrite rules
5534 <indexterm><primary>RULES pragma</primary></indexterm>
5535 <indexterm><primary>pragma, RULES</primary></indexterm>
5536 <indexterm><primary>rewrite rules</primary></indexterm></title>
5539 The programmer can specify rewrite rules as part of the source program
5540 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
5541 the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on,
5542 and (b) the <option>-frules-off</option> flag
5543 (<xref linkend="options-f"/>) is not specified, and (c) the
5544 <option>-fglasgow-exts</option> (<xref linkend="options-language"/>)
5553 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
5560 <title>Syntax</title>
5563 From a syntactic point of view:
5569 There may be zero or more rules in a <literal>RULES</literal> pragma.
5576 Each rule has a name, enclosed in double quotes. The name itself has
5577 no significance at all. It is only used when reporting how many times the rule fired.
5583 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
5584 immediately after the name of the rule. Thus:
5587 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
5590 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
5591 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
5600 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
5601 is set, so you must lay out your rules starting in the same column as the
5602 enclosing definitions.
5609 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
5610 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
5611 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
5612 by spaces, just like in a type <literal>forall</literal>.
5618 A pattern variable may optionally have a type signature.
5619 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
5620 For example, here is the <literal>foldr/build</literal> rule:
5623 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
5624 foldr k z (build g) = g k z
5627 Since <function>g</function> has a polymorphic type, it must have a type signature.
5634 The left hand side of a rule must consist of a top-level variable applied
5635 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
5638 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
5639 "wrong2" forall f. f True = True
5642 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
5649 A rule does not need to be in the same module as (any of) the
5650 variables it mentions, though of course they need to be in scope.
5656 Rules are automatically exported from a module, just as instance declarations are.
5667 <title>Semantics</title>
5670 From a semantic point of view:
5676 Rules are only applied if you use the <option>-O</option> flag.
5682 Rules are regarded as left-to-right rewrite rules.
5683 When GHC finds an expression that is a substitution instance of the LHS
5684 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
5685 By "a substitution instance" we mean that the LHS can be made equal to the
5686 expression by substituting for the pattern variables.
5693 The LHS and RHS of a rule are typechecked, and must have the
5701 GHC makes absolutely no attempt to verify that the LHS and RHS
5702 of a rule have the same meaning. That is undecidable in general, and
5703 infeasible in most interesting cases. The responsibility is entirely the programmer's!
5710 GHC makes no attempt to make sure that the rules are confluent or
5711 terminating. For example:
5714 "loop" forall x,y. f x y = f y x
5717 This rule will cause the compiler to go into an infinite loop.
5724 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
5730 GHC currently uses a very simple, syntactic, matching algorithm
5731 for matching a rule LHS with an expression. It seeks a substitution
5732 which makes the LHS and expression syntactically equal modulo alpha
5733 conversion. The pattern (rule), but not the expression, is eta-expanded if
5734 necessary. (Eta-expanding the expression can lead to laziness bugs.)
5735 But not beta conversion (that's called higher-order matching).
5739 Matching is carried out on GHC's intermediate language, which includes
5740 type abstractions and applications. So a rule only matches if the
5741 types match too. See <xref linkend="rule-spec"/> below.
5747 GHC keeps trying to apply the rules as it optimises the program.
5748 For example, consider:
5757 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
5758 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
5759 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
5760 not be substituted, and the rule would not fire.
5767 In the earlier phases of compilation, GHC inlines <emphasis>nothing
5768 that appears on the LHS of a rule</emphasis>, because once you have substituted
5769 for something you can't match against it (given the simple minded
5770 matching). So if you write the rule
5773 "map/map" forall f,g. map f . map g = map (f.g)
5776 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
5777 It will only match something written with explicit use of ".".
5778 Well, not quite. It <emphasis>will</emphasis> match the expression
5784 where <function>wibble</function> is defined:
5787 wibble f g = map f . map g
5790 because <function>wibble</function> will be inlined (it's small).
5792 Later on in compilation, GHC starts inlining even things on the
5793 LHS of rules, but still leaves the rules enabled. This inlining
5794 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
5801 All rules are implicitly exported from the module, and are therefore
5802 in force in any module that imports the module that defined the rule, directly
5803 or indirectly. (That is, if A imports B, which imports C, then C's rules are
5804 in force when compiling A.) The situation is very similar to that for instance
5816 <title>List fusion</title>
5819 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
5820 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
5821 intermediate list should be eliminated entirely.
5825 The following are good producers:
5837 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
5843 Explicit lists (e.g. <literal>[True, False]</literal>)
5849 The cons constructor (e.g <literal>3:4:[]</literal>)
5855 <function>++</function>
5861 <function>map</function>
5867 <function>take</function>, <function>filter</function>
5873 <function>iterate</function>, <function>repeat</function>
5879 <function>zip</function>, <function>zipWith</function>
5888 The following are good consumers:
5900 <function>array</function> (on its second argument)
5906 <function>length</function>
5912 <function>++</function> (on its first argument)
5918 <function>foldr</function>
5924 <function>map</function>
5930 <function>take</function>, <function>filter</function>
5936 <function>concat</function>
5942 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
5948 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
5949 will fuse with one but not the other)
5955 <function>partition</function>
5961 <function>head</function>
5967 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
5973 <function>sequence_</function>
5979 <function>msum</function>
5985 <function>sortBy</function>
5994 So, for example, the following should generate no intermediate lists:
5997 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
6003 This list could readily be extended; if there are Prelude functions that you use
6004 a lot which are not included, please tell us.
6008 If you want to write your own good consumers or producers, look at the
6009 Prelude definitions of the above functions to see how to do so.
6014 <sect2 id="rule-spec">
6015 <title>Specialisation
6019 Rewrite rules can be used to get the same effect as a feature
6020 present in earlier versions of GHC.
6021 For example, suppose that:
6024 genericLookup :: Ord a => Table a b -> a -> b
6025 intLookup :: Table Int b -> Int -> b
6028 where <function>intLookup</function> is an implementation of
6029 <function>genericLookup</function> that works very fast for
6030 keys of type <literal>Int</literal>. You might wish
6031 to tell GHC to use <function>intLookup</function> instead of
6032 <function>genericLookup</function> whenever the latter was called with
6033 type <literal>Table Int b -> Int -> b</literal>.
6034 It used to be possible to write
6037 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
6040 This feature is no longer in GHC, but rewrite rules let you do the same thing:
6043 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
6046 This slightly odd-looking rule instructs GHC to replace
6047 <function>genericLookup</function> by <function>intLookup</function>
6048 <emphasis>whenever the types match</emphasis>.
6049 What is more, this rule does not need to be in the same
6050 file as <function>genericLookup</function>, unlike the
6051 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
6052 have an original definition available to specialise).
6055 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
6056 <function>intLookup</function> really behaves as a specialised version
6057 of <function>genericLookup</function>!!!</para>
6059 <para>An example in which using <literal>RULES</literal> for
6060 specialisation will Win Big:
6063 toDouble :: Real a => a -> Double
6064 toDouble = fromRational . toRational
6066 {-# RULES "toDouble/Int" toDouble = i2d #-}
6067 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
6070 The <function>i2d</function> function is virtually one machine
6071 instruction; the default conversion—via an intermediate
6072 <literal>Rational</literal>—is obscenely expensive by
6079 <title>Controlling what's going on</title>
6087 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
6093 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
6094 If you add <option>-dppr-debug</option> you get a more detailed listing.
6100 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
6103 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
6104 {-# INLINE build #-}
6108 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
6109 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
6110 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
6111 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
6118 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
6119 see how to write rules that will do fusion and yet give an efficient
6120 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
6130 <sect2 id="core-pragma">
6131 <title>CORE pragma</title>
6133 <indexterm><primary>CORE pragma</primary></indexterm>
6134 <indexterm><primary>pragma, CORE</primary></indexterm>
6135 <indexterm><primary>core, annotation</primary></indexterm>
6138 The external core format supports <quote>Note</quote> annotations;
6139 the <literal>CORE</literal> pragma gives a way to specify what these
6140 should be in your Haskell source code. Syntactically, core
6141 annotations are attached to expressions and take a Haskell string
6142 literal as an argument. The following function definition shows an
6146 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
6149 Semantically, this is equivalent to:
6157 However, when external for is generated (via
6158 <option>-fext-core</option>), there will be Notes attached to the
6159 expressions <function>show</function> and <varname>x</varname>.
6160 The core function declaration for <function>f</function> is:
6164 f :: %forall a . GHCziShow.ZCTShow a ->
6165 a -> GHCziBase.ZMZN GHCziBase.Char =
6166 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
6168 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
6170 (tpl1::GHCziBase.Int ->
6172 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6174 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
6175 (tpl3::GHCziBase.ZMZN a ->
6176 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
6184 Here, we can see that the function <function>show</function> (which
6185 has been expanded out to a case expression over the Show dictionary)
6186 has a <literal>%note</literal> attached to it, as does the
6187 expression <varname>eta</varname> (which used to be called
6188 <varname>x</varname>).
6195 <sect1 id="special-ids">
6196 <title>Special built-in functions</title>
6197 <para>GHC has a few built-in funcions with special behaviour,
6198 described in this section. All are exported by
6199 <literal>GHC.Exts</literal>.</para>
6201 <sect2> <title>The <literal>inline</literal> function </title>
6203 The <literal>inline</literal> function is somewhat experimental.
6207 The call <literal>(inline f)</literal> arranges that <literal>f</literal>
6208 is inlined, regardless of its size. More precisely, the call
6209 <literal>(inline f)</literal> rewrites to the right-hand side of <literal>f</literal>'s
6211 This allows the programmer to control inlining from
6212 a particular <emphasis>call site</emphasis>
6213 rather than the <emphasis>definition site</emphasis> of the function
6214 (c.f. <literal>INLINE</literal> pragmas <xref linkend="inline-noinline-pragma"/>).
6217 This inlining occurs regardless of the argument to the call
6218 or the size of <literal>f</literal>'s definition; it is unconditional.
6219 The main caveat is that <literal>f</literal>'s definition must be
6220 visible to the compiler. That is, <literal>f</literal> must be
6221 let-bound in the current scope.
6222 If no inlining takes place, the <literal>inline</literal> function
6223 expands to the identity function in Phase zero; so its use imposes
6226 <para> If the function is defined in another
6227 module, GHC only exposes its inlining in the interface file if the
6228 function is sufficiently small that it <emphasis>might</emphasis> be
6229 inlined by the automatic mechanism. There is currently no way to tell
6230 GHC to expose arbitrarily-large functions in the interface file. (This
6231 shortcoming is something that could be fixed, with some kind of pragma.)
6235 <sect2> <title>The <literal>lazy</literal> function </title>
6237 The <literal>lazy</literal> function restrains strictness analysis a little:
6241 The call <literal>(lazy e)</literal> means the same as <literal>e</literal>,
6242 but <literal>lazy</literal> has a magical property so far as strictness
6243 analysis is concerned: it is lazy in its first argument,
6244 even though its semantics is strict. After strictness analysis has run,
6245 calls to <literal>lazy</literal> are inlined to be the identity function.
6248 This behaviour is occasionally useful when controlling evaluation order.
6249 Notably, <literal>lazy</literal> is used in the library definition of
6250 <literal>Control.Parallel.par</literal>:
6253 par x y = case (par# x) of { _ -> lazy y }
6255 If <literal>lazy</literal> were not lazy, <literal>par</literal> would
6256 look strict in <literal>y</literal> which would defeat the whole
6257 purpose of <literal>par</literal>.
6261 <sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
6263 The function <literal>unsafeCoerce#</literal> allows you to side-step the
6264 typechecker entirely. It has type
6266 unsafeCoerce# :: a -> b
6268 That is, it allows you to coerce any type into any other type. If you use this
6269 function, you had better get it right, otherwise segmentation faults await.
6270 It is generally used when you want to write a program that you know is
6271 well-typed, but where Haskell's type system is not expressive enough to prove
6272 that it is well typed.
6278 <sect1 id="generic-classes">
6279 <title>Generic classes</title>
6281 <para>(Note: support for generic classes is currently broken in
6285 The ideas behind this extension are described in detail in "Derivable type classes",
6286 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
6287 An example will give the idea:
6295 fromBin :: [Int] -> (a, [Int])
6297 toBin {| Unit |} Unit = []
6298 toBin {| a :+: b |} (Inl x) = 0 : toBin x
6299 toBin {| a :+: b |} (Inr y) = 1 : toBin y
6300 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
6302 fromBin {| Unit |} bs = (Unit, bs)
6303 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
6304 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
6305 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
6306 (y,bs'') = fromBin bs'
6309 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
6310 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
6311 which are defined thus in the library module <literal>Generics</literal>:
6315 data a :+: b = Inl a | Inr b
6316 data a :*: b = a :*: b
6319 Now you can make a data type into an instance of Bin like this:
6321 instance (Bin a, Bin b) => Bin (a,b)
6322 instance Bin a => Bin [a]
6324 That is, just leave off the "where" clause. Of course, you can put in the
6325 where clause and over-ride whichever methods you please.
6329 <title> Using generics </title>
6330 <para>To use generics you need to</para>
6333 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
6334 <option>-fgenerics</option> (to generate extra per-data-type code),
6335 and <option>-package lang</option> (to make the <literal>Generics</literal> library
6339 <para>Import the module <literal>Generics</literal> from the
6340 <literal>lang</literal> package. This import brings into
6341 scope the data types <literal>Unit</literal>,
6342 <literal>:*:</literal>, and <literal>:+:</literal>. (You
6343 don't need this import if you don't mention these types
6344 explicitly; for example, if you are simply giving instance
6345 declarations.)</para>
6350 <sect2> <title> Changes wrt the paper </title>
6352 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
6353 can be written infix (indeed, you can now use
6354 any operator starting in a colon as an infix type constructor). Also note that
6355 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
6356 Finally, note that the syntax of the type patterns in the class declaration
6357 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
6358 alone would ambiguous when they appear on right hand sides (an extension we
6359 anticipate wanting).
6363 <sect2> <title>Terminology and restrictions</title>
6365 Terminology. A "generic default method" in a class declaration
6366 is one that is defined using type patterns as above.
6367 A "polymorphic default method" is a default method defined as in Haskell 98.
6368 A "generic class declaration" is a class declaration with at least one
6369 generic default method.
6377 Alas, we do not yet implement the stuff about constructor names and
6384 A generic class can have only one parameter; you can't have a generic
6385 multi-parameter class.
6391 A default method must be defined entirely using type patterns, or entirely
6392 without. So this is illegal:
6395 op :: a -> (a, Bool)
6396 op {| Unit |} Unit = (Unit, True)
6399 However it is perfectly OK for some methods of a generic class to have
6400 generic default methods and others to have polymorphic default methods.
6406 The type variable(s) in the type pattern for a generic method declaration
6407 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:
6411 op {| p :*: q |} (x :*: y) = op (x :: p)
6419 The type patterns in a generic default method must take one of the forms:
6425 where "a" and "b" are type variables. Furthermore, all the type patterns for
6426 a single type constructor (<literal>:*:</literal>, say) must be identical; they
6427 must use the same type variables. So this is illegal:
6431 op {| a :+: b |} (Inl x) = True
6432 op {| p :+: q |} (Inr y) = False
6434 The type patterns must be identical, even in equations for different methods of the class.
6435 So this too is illegal:
6439 op1 {| a :*: b |} (x :*: y) = True
6442 op2 {| p :*: q |} (x :*: y) = False
6444 (The reason for this restriction is that we gather all the equations for a particular type consructor
6445 into a single generic instance declaration.)
6451 A generic method declaration must give a case for each of the three type constructors.
6457 The type for a generic method can be built only from:
6459 <listitem> <para> Function arrows </para> </listitem>
6460 <listitem> <para> Type variables </para> </listitem>
6461 <listitem> <para> Tuples </para> </listitem>
6462 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
6464 Here are some example type signatures for generic methods:
6467 op2 :: Bool -> (a,Bool)
6468 op3 :: [Int] -> a -> a
6471 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
6475 This restriction is an implementation restriction: we just havn't got around to
6476 implementing the necessary bidirectional maps over arbitrary type constructors.
6477 It would be relatively easy to add specific type constructors, such as Maybe and list,
6478 to the ones that are allowed.</para>
6483 In an instance declaration for a generic class, the idea is that the compiler
6484 will fill in the methods for you, based on the generic templates. However it can only
6489 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
6494 No constructor of the instance type has unboxed fields.
6498 (Of course, these things can only arise if you are already using GHC extensions.)
6499 However, you can still give an instance declarations for types which break these rules,
6500 provided you give explicit code to override any generic default methods.
6508 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
6509 what the compiler does with generic declarations.
6514 <sect2> <title> Another example </title>
6516 Just to finish with, here's another example I rather like:
6520 nCons {| Unit |} _ = 1
6521 nCons {| a :*: b |} _ = 1
6522 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
6525 tag {| Unit |} _ = 1
6526 tag {| a :*: b |} _ = 1
6527 tag {| a :+: b |} (Inl x) = tag x
6528 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
6534 <sect1 id="monomorphism">
6535 <title>Control over monomorphism</title>
6537 <para>GHC supports two flags that control the way in which generalisation is
6538 carried out at let and where bindings.
6542 <title>Switching off the dreaded Monomorphism Restriction</title>
6543 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
6545 <para>Haskell's monomorphism restriction (see
6546 <ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
6548 of the Haskell Report)
6549 can be completely switched off by
6550 <option>-fno-monomorphism-restriction</option>.
6555 <title>Monomorphic patteern bindings</title>
6556 <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
6557 <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
6559 <para> As an experimental change, we are exploring the possibility of
6560 making pattern bindings monomorphic; that is, not generalised at all.
6561 A pattern binding is a binding whose LHS has no function arguments,
6562 and is not a simple variable. For example:
6564 f x = x -- Not a pattern binding
6565 f = \x -> x -- Not a pattern binding
6566 f :: Int -> Int = \x -> x -- Not a pattern binding
6568 (g,h) = e -- A pattern binding
6569 (f) = e -- A pattern binding
6570 [x] = e -- A pattern binding
6572 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
6573 default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
6582 ;;; Local Variables: ***
6584 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
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